From 09959fef4453937d0062e88929bcb9ded6447f04 Mon Sep 17 00:00:00 2001 From: Quleaf Date: Mon, 24 Apr 2023 21:28:09 +0800 Subject: [PATCH] update to v2.4.0 --- README.md | 4 +- README_CN.md | 4 +- applications/credit_risk_analysis/config.toml | 13 + .../credit_risk_analysis/credit_risk.py | 52 + .../introduction_cn.ipynb | 214 ++++ .../introduction_en.ipynb | 214 ++++ .../deuteron_binding_energy/config.toml | 24 + .../deuteron_binding_energy.py | 90 ++ .../introduction_cn.ipynb | 276 +++++ .../introduction_en.ipynb | 281 +++++ applications/deuteron_binding_energy/utils.py | 78 ++ .../introduction_cn.ipynb | 16 +- .../qcaan_generated_vs_original_20230313.png | Bin 0 -> 87241 bytes .../inference.toml | 15 + .../introduction_cn.ipynb | 226 ++++ .../introduction_en.ipynb | 217 ++++ .../params/params_G_epoch20.pdparams | Bin 0 -> 6780221 bytes .../params/params_qnn_epoch20.pdparams | Bin 0 -> 897 bytes .../qcaan_generation.py | 41 + .../qcaan_model.png | Bin 0 -> 143843 bytes 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paddle_quantum/ansatz/layer.py create mode 100644 paddle_quantum/data_analysis/power_flow.py create mode 100644 paddle_quantum/data_analysis/rand_num.py delete mode 100644 paddle_quantum/gate/functional/multi_qubit_gate.py delete mode 100644 paddle_quantum/gate/functional/single_qubit_gate.py delete mode 100644 paddle_quantum/gate/layer.py create mode 100644 paddle_quantum/gate/matrix.py create mode 100644 paddle_quantum/qml/bert_qtc.py create mode 100644 paddle_quantum/qml/qcaan.py delete mode 100644 tutorials/quantum_simulation/output/summary_data.npz diff --git a/README.md b/README.md index 1943641..0204242 100644 --- a/README.md +++ b/README.md @@ -33,7 +33,7 @@ English | [简体中文](README_CN.md) - + @@ -83,7 +83,7 @@ pip install paddle-quantum or download all the files and finish the installation locally, ```bash -git clone http://github.com/PaddlePaddle/quantum +git clone https://github.com/PaddlePaddle/quantum cd quantum pip install -e . ``` diff --git a/README_CN.md b/README_CN.md index 69c1ff0..ffc51e8 100644 --- a/README_CN.md +++ b/README_CN.md @@ -34,7 +34,7 @@ - + @@ -84,7 +84,7 @@ pip install paddle-quantum 用户也可以选择下载全部文件后进行本地安装, ```bash -git clone http://github.com/PaddlePaddle/quantum +git clone https://github.com/PaddlePaddle/quantum cd quantum pip install -e . ``` diff --git a/applications/credit_risk_analysis/config.toml b/applications/credit_risk_analysis/config.toml new file mode 100644 index 0000000..302387c --- /dev/null +++ b/applications/credit_risk_analysis/config.toml @@ -0,0 +1,13 @@ +# The config for credit risk analysis model +# number of assets. +num_assets = 4 +# basic default probabilities. +base_default_prob = [0.15, 0.25, 0.39, 0.58] +# sensitivity. +sensitivity = [0.37, 0.21, 0.32, 0.02] +# loss given default. +lgd = [5, 1, 3, 4] +# confidence level. +confidence_level = 0.99 +# degree of simulation. Higher the degree, preciser the simulation. +degree_of_simulation = 4 diff --git a/applications/credit_risk_analysis/credit_risk.py b/applications/credit_risk_analysis/credit_risk.py new file mode 100644 index 0000000..31af630 --- /dev/null +++ b/applications/credit_risk_analysis/credit_risk.py @@ -0,0 +1,52 @@ +# !/usr/bin/env python3 +# Copyright (c) 2020 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +import argparse +import os +import warnings +import logging +import time +from typing import Dict + +warnings.filterwarnings('ignore') +os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python' + +import toml +from paddle_quantum.finance import CreditRiskAnalyzer + + +def main(args): + time_start = time.strftime("%Y%m%d-%H:%M:%S", time.localtime()) + logging.info(f"Job start at {time_start:s}") + + parsed_configs: Dict = toml.load(args.config) + + # input credit portfolio settings + num_assets = parsed_configs["num_assets"] + base_default_prob = parsed_configs["base_default_prob"] + sensitivity = parsed_configs["sensitivity"] + lgd = parsed_configs["lgd"] + confidence_level = parsed_configs["confidence_level"] + degree_of_simulation = parsed_configs["degree_of_simulation"] + + estimator = CreditRiskAnalyzer(num_assets, base_default_prob, sensitivity, lgd, + confidence_level, degree_of_simulation) + print("The Value at Risk of these assets are", estimator.estimate_var()) + + +if __name__ == '__main__': + parser = argparse.ArgumentParser(description="Credit risk analysis with paddle quantum.") + parser.add_argument("--config", type=str, help="Input the config file with toml format.") + main(parser.parse_args()) diff --git a/applications/credit_risk_analysis/introduction_cn.ipynb b/applications/credit_risk_analysis/introduction_cn.ipynb new file mode 100644 index 0000000..6992c7c --- /dev/null +++ b/applications/credit_risk_analysis/introduction_cn.ipynb @@ -0,0 +1,214 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 信贷风险分析\n", + "\n", + "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "风险分析的任务是评估给定资产在面临金融系统波动时的风险,即在险价值 Value at Risk(VaR)。该价值可以衡量在金融系统下给定资产的潜在损失。决定资产在险价值的因素有很多,包括金融机构对于风险的不同偏好、金融系统的波动特征和资产本身的含风险性质。2014 年 Rutkowski 与 Tarca [1] 给出了一个计算风险资本的数学模型。该模型认为整体金融系统的波动应该遵循高斯布朗运动,从而能够计算出较高可信度下处于该系统中资产损失上界的最小值。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "当应用于信贷风险分析问题时,该模型可以用于评估银行的信贷风险监管资本,即银行所持有信贷资产组合在当前金融系统下的在险价值。在该模型中,我们记给定的信贷资产组合为 $\\{ 0, ..., K-1 \\}$, 且决定资产组合总损失的随机变量为\n", + "$$\n", + "\\mathcal{L} = \\sum_{k=0}^{K - 1} \\lambda_k X_k(Z)\n", + "。$$\n", + "这里,$\\lambda_k$ 为第 $k$ 个信贷资产的违约损失(loss given default);$Z$ 为描述金融系统波动过程的潜在随机变量(latent random variable),且其概率分布默认为标准正态分布;$X_k(Z)$ 为描述金融系统下资产违约过程的伯努利随机变量。具体地,当 $Z = z$ 时,随机变量 $X_k(Z)$ 的参数 $p_k(z)$,即第 $k$ 个资产的违约概率,取决于该资产对于系统风险的敏感度(sensitivity)$\\rho_k \\in [0, 1]$ 以及无系统风险下该资产的基础违约概率(base default probability)$p_k^{(0)} \\in [0, 1]$。在标定置信度(confidence level)之后,信贷资产组合的在险价值应定义为『于置信度 $\\alpha$ 下,信贷资产损失上界的最小值』,即\n", + "$$\n", + "\\textrm{VaR}_\\alpha(\\mathcal{L}) := \\inf \\{ x \\,|\\, \\textrm{Pr}(\\mathcal{L} \\leq x) \\geq \\alpha \\}\n", + "。$$\n", + "例如,若银行持有的一组信贷资产在置信度 $99\\%$ 下的在险价值正好为 $100$ 万,那么当该资产组合出现违约情况时,由于违约而造成的资产损失超过 $100$ 万的概率不高于 $1\\%$。在经典计算中,信贷风险分析问题中的在险价值可以通过经典蒙特卡罗(classical Monte Carlo)方法和二分搜索(bisection search)方法估算:\n", + "1. 根据资产组合性质,选定初始 VaR 猜测值 $\\check{x}$。\n", + "2. 使用经典蒙特卡罗算法估算概率值 $p_{\\check{x}} = \\textrm{Pr}(\\mathcal{L} \\leq \\check{x})$。\n", + "3. 将概率值 $p_{\\check{x}}$ 与 $\\alpha$ 比较,并根据比较结果和二分搜索方法更新猜测值 $\\check{x}$。\n", + "4. 若更新值达到收敛标准,输出 $\\check{x} = \\textrm{VaR}_\\alpha(\\mathcal{L})$;否则返回第 $2$ 步。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 量子解决方案\n", + "\n", + "不同于经典算法,量子计算可以使用量子振幅估计(quantum amplitude estimation)算法替换上述第 2 步中使用的经典蒙特卡罗算法,来提高概率值 $p_{\\check{x}}$ 的估算效率。通过量子叠加和纠缠的特性,量子方案与经典方案相比有望在采样次数上获取平方加速的优势 [2]。接下来我们展示如何使用量桨来模拟该量子方案,从而完成信贷风险分析的在险价值计算问题。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 在线演示" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们已经给出了一个设置好的参数,可以直接用于风险资产组合的在险价值计算。只需要在 `config.toml` 这个配置文件中进行对应的配置,然后输入命令 \n", + "`python credit_risk.py --config config.toml`\n", + "即可对配置好的资产组合进行在险价值计算。\n", + "\n", + "这里,我们给出一个在线演示的版本,可以在线进行测试。首先定义配置文件的内容:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "cra_toml = r\"\"\"\n", + "# 用于信贷风险分析模型的整体配置文件。\n", + "# 资产数量。\n", + "num_assets = 4\n", + "# 基础违约概率。\n", + "base_default_prob = [0.15, 0.25, 0.39, 0.58]\n", + "# 敏感度。\n", + "sensitivity = [0.37, 0.21, 0.32, 0.02]\n", + "# 违约损失。\n", + "lgd = [5, 1, 3, 4]\n", + "# 置信度。\n", + "confidence_level = 0.99\n", + "# 估计精度系数。系数越高,则估计的结果越精确。\n", + "degree_of_simulation = 4\n", + "\"\"\"" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "量桨的金融模块实现了量子解决方案的数值模拟。我们可以从 ``paddle_quantum.finance`` 模块里导入 ``CreditRiskAnalyzer`` 来解决配置好的在险价值计算问题。" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-----------------------------------------------------------------------------------\n", + "Begin bisection search for VaR with confidence level >= 99.0%.\n", + "-----------------------------------------------------------------------------------\n", + "Lower guess: level Middle guess: level Upper guess: level \n", + " -1 : 0.000 6 : 0.691 13 : 1.000 \n", + " 6 : 0.691 9 : 0.941 13 : 1.000 \n", + " 9 : 0.941 11 : 0.962 13 : 1.000 \n", + " 11 : 0.962 12 : 0.990 13 : 1.000 \n", + "-----------------------------------------------------------------------------------\n", + "Estimated VaR is 12 with confidence level 99.0%.\n", + "-----------------------------------------------------------------------------------\n", + "该资产组合的在险价值大约为 12\n" + ] + } + ], + "source": [ + "import os\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")\n", + "os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python'\n", + "\n", + "import toml\n", + "from paddle_quantum.finance import CreditRiskAnalyzer\n", + "\n", + "config = toml.loads(cra_toml)\n", + "num_assets = config[\"num_assets\"]\n", + "base_default_prob = config[\"base_default_prob\"]\n", + "sensitivity = config[\"sensitivity\"]\n", + "lgd = config[\"lgd\"]\n", + "confidence_level = config[\"confidence_level\"]\n", + "degree_of_simulation = config[\"degree_of_simulation\"]\n", + "\n", + "estimator = CreditRiskAnalyzer(num_assets, base_default_prob, sensitivity, lgd, confidence_level, degree_of_simulation)\n", + "print(\"该资产组合的在险价值大约为\", estimator.estimate_var())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "___\n", + "\n", + "# 注意事项\n", + "\n", + "这里提供的模型只用于特定模型的信贷风险分析问题。\n", + "\n", + "# 引用信息\n", + "\n", + "```\n", + "@article{rutkowski2015regulatory,\n", + " title={Regulatory capital modeling for credit risk},\n", + " author={Rutkowski, Marek and Tarca, Silvio},\n", + " journal={International Journal of Theoretical and Applied Finance},\n", + " volume={18},\n", + " number={05},\n", + " pages={1550034},\n", + " year={2015},\n", + " publisher={World Scientific}\n", + "}\n", + "\n", + "@article{egger2020credit,\n", + " title={Credit risk analysis using quantum computers},\n", + " author={Egger, Daniel J and Guti{\\'e}rrez, Ricardo Garc{\\'\\i}a and Mestre, Jordi Cahu{\\'e} and Woerner, Stefan},\n", + " journal={IEEE Transactions on Computers},\n", + " volume={70},\n", + " number={12},\n", + " pages={2136--2145},\n", + " year={2020},\n", + " publisher={IEEE}\n", + "}\n", + "```\n", + "\n", + "# 参考文献\n", + "\n", + "[1] Rutkowski, Marek, and Silvio Tarca. \"Regulatory capital modeling for credit risk.\" International Journal of Theoretical and Applied Finance 18.05 (2015): 1550034.\n", + "\n", + "[2] Egger, Daniel J., et al. \"Credit risk analysis using quantum computers.\" IEEE Transactions on Computers 70.12 (2020): 2136-2145." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pq", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/applications/credit_risk_analysis/introduction_en.ipynb b/applications/credit_risk_analysis/introduction_en.ipynb new file mode 100644 index 0000000..d9a63b0 --- /dev/null +++ b/applications/credit_risk_analysis/introduction_en.ipynb @@ -0,0 +1,214 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Credit Risk Analysis\n", + "\n", + "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The task of risk analysis is to access the risk of given assets facing the fluctuations of financial systems, i.e. the Value at Risk (VaR). Such quantity can measure the potent loss of given assets in a financial system. There are many factors determining the Value of Risk of assets, including the favor of risk for different financial organizations, the characteristics of system fluctuations and the risk-related properties of assets. In 2014 Rutkowski and Tarca [1] provided a mathematical model that estimates the risk measure. This model suggests that the whole financial system can be modelled by a Brownian motion process, so that the minimum upper bound of assets' loss can be computed under an appropriate confidence level." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Credit risk analysis is a direct application of such model, which can evaluate the regulatory capital for credit risk in banking industry i.e. the VaR of credit asset combination held under the current financial . In this model, we denote the given asset combination as $\\{ 0, ..., K-1 \\}$, and the risk measures of the total loss as\n", + "$$\n", + "\\mathcal{L} = \\sum_{k=0}^{K - 1} \\lambda_k X_k(Z)\n", + ".$$\n", + "Here, $\\lambda_k$ is the loss given default of the $k$-th asset; $Z$ is the standard Gaussian variable that implicitly models the process of financial system; $X_k(Z)$ is the Bernoulli variable that models the default process of the $k$-th asset. In particular, when $Z = z$, the parameter $p_k(z)$ of random variable $X_k(Z)$ i.e. the default probability of the $k$-th asset, is dependent on the basic default probability without the effect of financial system $p_k^{(0)} \\in [0, 1]$, and the asset sensitivity to the system risk $\\rho_k \\in [0, 1]$. After settling the confidence level, the Value at Risk in the problem of credit risk analysis shall be defined as \"the minimum upper bound of credit asset combination under confidence level $\\alpha$\". That is,\n", + "$$\n", + "\\textrm{VaR}_\\alpha(\\mathcal{L}) := \\inf \\{ x \\,|\\, \\textrm{Pr}(\\mathcal{L} \\leq x) \\geq \\alpha \\}\n", + ".$$\n", + "For example, if the VaR of a combination of credit assets held by a bank happens to be one million under confidence level $99\\%$, then the probability that the total loss given default of such combination is greater than one million is less than $1\\%$. In classical calculations, the VaR in the problem of credit risk analysis can be estimated by classical Monte Carlo and bisection search methods:\n", + "1. Choose an appropriate VaR guess $\\check{x}$ according to the properties of assets.\n", + "2. Use classical Monte Carlo method to estimate the probability $p_{\\check{x}} = \\textrm{Pr}(\\mathcal{L} \\leq \\check{x})$.\n", + "3. Compare the probability with $\\alpha$, and update the VaR guess $\\check{x}$ according to the comparison result and bisection search method.\n", + "4. If the convergence criteria is met, output $\\check{x} = \\textrm{VaR}_\\alpha(\\mathcal{L})$; otherwise return to step $2$." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum solution\n", + "\n", + "Unlike classical algorithms, quantum computation can use the algorithm of quantum amplitude estimation (QAE) to replace the classical Monte Carlo method in the second step mentioned above, to enhance the efficiency of probability estimation. Through the characteristics of quantum superposition and entanglement, such quantum scheme is expected to obtain the advantage of quadratic acceleration compared with classical schemes [2]. Next, we will show how to use Paddle Quantum to simulate this quantum scheme to complete the VaR computational problem of credit risk analysis." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Online demonstration" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have set a parameter that can be used directly for the VaR computation of asset combinations. Just configure it in the configuration file `config.toml` and enter the command \n", + "`python credit_risk.py --config config.toml`.\n", + "The VaR of configured assets is then be computed.\n", + "\n", + "Here, we give a version of the online demo that can be tested online. First define the contents of the configuration file:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "cra_toml = r\"\"\"\n", + "# The config for credit risk analysis model\n", + "# number of assets.\n", + "num_assets = 4\n", + "# basic default probabilities.\n", + "base_default_prob = [0.15, 0.25, 0.39, 0.58]\n", + "# sensitivity.\n", + "sensitivity = [0.37, 0.21, 0.32, 0.02]\n", + "# loss given default.\n", + "lgd = [5, 1, 3, 4]\n", + "# confidence level.\n", + "confidence_level = 0.99\n", + "# degree of simulation. Higher the degree, preciser the simulation.\n", + "degree_of_simulation = 4\n", + "\"\"\"" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The financial module of the Paddle Quantum enables numerical simulation of quantum amplitude estimation scheme. We can import ``CreditRiskAnalyzer`` from the ``paddle_quantum.finance`` module to solve the configured VaR computational problem." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-----------------------------------------------------------------------------------\n", + "Begin bisection search for VaR with confidence level >= 99.0%.\n", + "-----------------------------------------------------------------------------------\n", + "Lower guess: level Middle guess: level Upper guess: level \n", + " -1 : 0.000 6 : 0.691 13 : 1.000 \n", + " 6 : 0.691 9 : 0.941 13 : 1.000 \n", + " 9 : 0.941 11 : 0.962 13 : 1.000 \n", + " 11 : 0.962 12 : 0.990 13 : 1.000 \n", + "-----------------------------------------------------------------------------------\n", + "Estimated VaR is 12 with confidence level 99.0%.\n", + "-----------------------------------------------------------------------------------\n", + "The Value at Risk of these assets are 12\n" + ] + } + ], + "source": [ + "import os\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")\n", + "os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python'\n", + "\n", + "import toml\n", + "from paddle_quantum.finance import CreditRiskAnalyzer\n", + "\n", + "config = toml.loads(cra_toml)\n", + "num_assets = config[\"num_assets\"]\n", + "base_default_prob = config[\"base_default_prob\"]\n", + "sensitivity = config[\"sensitivity\"]\n", + "lgd = config[\"lgd\"]\n", + "confidence_level = config[\"confidence_level\"]\n", + "degree_of_simulation = config[\"degree_of_simulation\"]\n", + "\n", + "estimator = CreditRiskAnalyzer(num_assets, base_default_prob, sensitivity, lgd, confidence_level, degree_of_simulation)\n", + "print(\"The Value at Risk of these assets are\", estimator.estimate_var())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "___\n", + "\n", + "# Note\n", + "\n", + "The model presented here is only intended to solve the credit risk analysis problem of a particular model.\n", + "\n", + "# Citation\n", + "\n", + "```\n", + "@article{rutkowski2015regulatory,\n", + " title={Regulatory capital modeling for credit risk},\n", + " author={Rutkowski, Marek and Tarca, Silvio},\n", + " journal={International Journal of Theoretical and Applied Finance},\n", + " volume={18},\n", + " number={05},\n", + " pages={1550034},\n", + " year={2015},\n", + " publisher={World Scientific}\n", + "}\n", + "\n", + "@article{egger2020credit,\n", + " title={Credit risk analysis using quantum computers},\n", + " author={Egger, Daniel J and Guti{\\'e}rrez, Ricardo Garc{\\'\\i}a and Mestre, Jordi Cahu{\\'e} and Woerner, Stefan},\n", + " journal={IEEE Transactions on Computers},\n", + " volume={70},\n", + " number={12},\n", + " pages={2136--2145},\n", + " year={2020},\n", + " publisher={IEEE}\n", + "}\n", + "```\n", + "\n", + "# References\n", + "\n", + "[1] Rutkowski, Marek, and Silvio Tarca. \"Regulatory capital modeling for credit risk.\" International Journal of Theoretical and Applied Finance 18.05 (2015): 1550034.\n", + "\n", + "[2] Egger, Daniel J., et al. \"Credit risk analysis using quantum computers.\" IEEE Transactions on Computers 70.12 (2020): 2136-2145." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pq", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/applications/deuteron_binding_energy/config.toml b/applications/deuteron_binding_energy/config.toml new file mode 100644 index 0000000..6137e87 --- /dev/null +++ b/applications/deuteron_binding_energy/config.toml @@ -0,0 +1,24 @@ +# A description of the task of this configuration file, this is optional. "Binding energy" stands for calculating deuteron binding energy. +task = "Binding energy" + +# Set the dimension of the fermionic Hamiltonian +N = 3 +# Set the parameters used in VQE +hbar_omega = 7 +V0 = -5.6865811 +# Whether return the exact ground state energy of the Hamiltonian, **NOTE: should use `true` or `false` instead of `True` or `False`** +calc_exact = true + +# This field stores configurations of the variational quantum eigensolver (VQE) method. +[VQE] +# Number of optimization cycles, default is 100. +num_iterations = 100 +# The convergence criteria for the VQE optimization, default is 1e-5. +tol = 1e-5 +# The number of optimization steps after which we record the loss value. +save_every = 10 + +# This field specifies the optimizer used in the VQE method, default is `Adam`, see here for available optimizers https://www.paddlepaddle.org.cn/documentation/docs/zh/api/paddle/optimizer/Overview_cn.html +[optimizer.Adam] +# The learning rate of the optimizer, see here for more details https://www.paddlepaddle.org.cn/documentation/docs/zh/api/paddle/optimizer/Adam_cn.html, default is 0.4. +learning_rate = 0.5 \ No newline at end of file diff --git a/applications/deuteron_binding_energy/deuteron_binding_energy.py b/applications/deuteron_binding_energy/deuteron_binding_energy.py new file mode 100644 index 0000000..8bd4d5f --- /dev/null +++ b/applications/deuteron_binding_energy/deuteron_binding_energy.py @@ -0,0 +1,90 @@ +# !/usr/bin/env python3 +# Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the 'License'); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an 'AS IS' BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +from typing import Dict +import warnings +import time +import logging +import argparse +import toml +import numpy as np +import paddle.optimizer as optim +from paddle_quantum.gate import RY, X +from paddle_quantum.qchem import GroundStateSolver, HartreeFock +from utils import DeuteronHamiltonian +logging.basicConfig(filename="log", filemode="w", format="%(message)s", level=logging.INFO) + + +def main(args): + time_start = time.strftime("%Y%m%d-%H:%M:%S", time.localtime()) + logging.info(f"Job start at {time_start:s}") + + parsed_configs: Dict = toml.load(args.config) + + # build deuteron Hamiltonian + num_qubits = parsed_configs["N"] + omega = parsed_configs["hbar_omega"] + V0 = parsed_configs["V0"] + deuham = DeuteronHamiltonian(omega, V0) + deuhN = deuham.get_hamiltonian(num_qubits) + + # build HartreeFock circuit + cir = HartreeFock(num_qubits) + cir.insert(0, X(0)) + cir.insert(1, RY(range(1, num_qubits))) + + # load optimizer + if parsed_configs.get("optimizer") is None: + optimizer_name = "Adam" + optimizer_settings = { + "Adam": { + "learning_rate": 0.4 + } + } + optimizer = optim.Adam + else: + optimizer_settings = parsed_configs["optimizer"] + optimizer_name = list(optimizer_settings.keys())[0] + optimizer = getattr(optim, optimizer_name) + + # calculate properties + if parsed_configs.get("VQE") is None: + vqe_settings = { + "num_iterations": 100, + "tol": 1e-5, + "save_every": 10 + } + else: + vqe_settings = parsed_configs["VQE"] + solver = GroundStateSolver(optimizer, **vqe_settings) + e, _ = solver.solve(cir, ham=deuhN, **optimizer_settings[optimizer_name]) + + logging.info("\n#######################################\nSummary\n#######################################") + logging.info(f"Binding energy={e:.5f}") + + if parsed_configs.get("calc_exact") is True: + warnings.warn(f"Calculate exact binding energy will diagonalize {2**num_qubits:d}*{2**num_qubits} matrix, shouldn't be used if `N` is large.") + exact_e = np.linalg.eigvalsh(deuhN.construct_h_matrix())[0] + logging.info(f"Exact binding energy={exact_e:.5f}") + logging.info(f"Relative error={abs(e-exact_e)/abs(exact_e):.5f}") + + time_stop = time.strftime("%Y%m%d-%H:%M:%S", time.localtime()) + logging.info(f"\nJob end at {time_stop:s}\n") + + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description="Calculate deuteron binding energy.") + parser.add_argument("--config", type=str, help="Input the config file with toml format.") + main(parser.parse_args()) \ No newline at end of file diff --git a/applications/deuteron_binding_energy/introduction_cn.ipynb b/applications/deuteron_binding_energy/introduction_cn.ipynb new file mode 100644 index 0000000..e8c059d --- /dev/null +++ b/applications/deuteron_binding_energy/introduction_cn.ipynb @@ -0,0 +1,276 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 氘核结合能计算\n", + "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*\n", + "\n", + "结合能是将系统分离成其组成部分所需的能量。它是系统稳定性的衡量标准,是必须添加到系统中以将其分解的能量。结合能的概念在物理学和化学的许多领域都有重要应用,如核物理学、原子物理学和材料科学。在核物理学中,每个核子的结合能用于确定原子核的稳定性,并解释核聚变和裂变现象。在原子物理学中,结合能用于确定原子和分子之间键的强度,并解释它们的物理和化学性质。在材料科学中,结合能用于确定固体中键的强度,并设计具有特定属性的材料以供各种应用。\n", + "\n", + "氘核是一种稳定的氢同位素,其核内含有一个质子和一个中子。它的质量大约相当于氢原子质量的两倍,是整个同位素家族中构成最简单的一位。氘核在核聚变反应中起着至关重要的作用,并常用作核物理实验中的靶标。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 氘核哈密顿量的定义\n", + "用来计算氘核结合能的哈密顿量一般被定义为如下形式\n", + "$$\n", + "\\begin{equation}\n", + "\\hat{H}_N = \\sum_{n,n^{\\prime}=0}^{N-1}\\langle n^{\\prime}|\\hat{T}+\\hat{V}|n\\rangle\\hat{a}^{\\dagger}_{n^{\\prime}}\\hat{a}_n\n", + "\\end{equation}\n", + "$$\n", + "其中 $\\hat{T}$ 代表动能算符,$\\hat{V}$ 代表势能算符,$N$ 表示哈密顿量的维度。它们分别被表示如下:\n", + "$$\n", + "\\begin{align}\n", + "& \\langle n^{\\prime}|\\hat{T}|n\\rangle = \\frac{\\hbar\\omega}{2}\\left[\n", + " (2n+3/2)\\delta_{n^{\\prime},n}-\\sqrt{n(n+1/2)}\\delta_{n^{\\prime}+1,n}-\\sqrt{(n+1)(n+3/2)}\\delta_{n^{\\prime}-1,n}\n", + "\\right],\\nonumber\\\\\n", + "& \\langle n^{\\prime}|\\hat{V}|n\\rangle = V_0\\delta_{0,n}\\delta_{n^{\\prime},n}.\\nonumber\n", + "\\end{align}\n", + "$$\n", + "这里面 $\\hat{a}^{\\dagger}_n$ 是产生算符,$\\hat{a}_n$ 是湮灭算符。结合能就是这个哈密顿量在 $N\\to\\infty$ 对应的基态能量(这可以通过计算 $N=1,2,3$ 的能量做外插得到)。\n", + "\n", + "在量桨中,构造这样一个哈密顿量只需要我们传入参数 $\\omega$ 和 $V_0$。同时,根据文献 \\[1\\],我们将上述公式中的 $\\hbar\\omega$ 设置为 $7\\text{MeV}$,并将 $V_0$ 设置为 $−5.68658111\\text{MeV}$。" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "H2= 5.906709445000001 I\n", + "0.21829055499999983 Z0\n", + "-2.1433035249352805 X0, X1\n", + "-2.1433035249352805 Y0, Y1\n", + "-6.125 Z1 \n", + "\n", + "H3= 15.531709445 I\n", + "0.21829055499999983 Z0\n", + "-2.1433035249352805 X0, X1\n", + "-2.1433035249352805 Y0, Y1\n", + "-6.125 Z1\n", + "-3.913118960624632 X1, X2\n", + "-3.913118960624632 Y1, Y2\n", + "-9.625 Z2\n" + ] + } + ], + "source": [ + "from utils import DeuteronHamiltonian\n", + "\n", + "omega = 7\n", + "V0 = -5.68658111\n", + "hamiltonian = DeuteronHamiltonian(omega, V0)\n", + "\n", + "# N=2\n", + "deut_h_2 = hamiltonian.get_hamiltonian(2)\n", + "print(\"H2=\", deut_h_2, \"\\n\") # H_2 = 5.906709I + 0.218291Z0 − 6.125Z1 - 2.143304 (X0X1 + Y0Y1)\n", + "\n", + "# N=3\n", + "deut_h_3 = hamiltonian.get_hamiltonian(3)\n", + "print(\"H3=\", deut_h_3) # H_3 = H_2 + 9.625(I − Z2) − 3.913119 (X1X2 + Y1Y2)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "> 注:在本教程中,产生和湮灭算符通过约当-魏格纳 \\[2\\] 变换转化为泡利矩阵 $I$, $X$, $Y$, $Z$ 的张量积表示。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 搭建变分量子线路\n", + "我们利用变分量子算法来计算哈密顿量 $\\hat{H}_2$ 和 $\\hat{H}_3$ 的基态能量,为了使计算更加准确,我们选择了幺正耦合簇量子线路作为变分量子线路。由于量子噪声的原因,浅层线路在近期中等规模含噪量子(NISQ)硬件上表现会更好,因此,我们依据问题的情况对量子线路进行了化简,得到如下简化线路。" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum circuit for deuteron N=2.\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum circuit for deuteron N=3.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from utils import DeuteronUCC2, DeuteronUCC3\n", + "\n", + "# Simplified UCC circuit for H_2\n", + "cir2 = DeuteronUCC2()\n", + "print(\"Quantum circuit for deuteron N=2.\")\n", + "cir2.plot()\n", + "\n", + "# Simplified UCC circuit for H_3\n", + "cir3 = DeuteronUCC3()\n", + "print(\"Quantum circuit for deuteron N=3.\")\n", + "cir3.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 利用变分量子算法(VQE)计算哈密顿量基态能量\n", + "量桨为基态能量计算问题提供了一个简单易用的`GroundStateSolver`接口,我们只需要把哈密顿量和对应的量子线路输入就可以方便地得到基态能量。接下来我们就用它来计算氘核的结合能。 " + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Binding energy (N=2): exact=-1.749, numerical=-1.74849, relative_error=0.00029.\n", + "Binding energy (N=3): exact=-2.046, numerical=-2.04567, relative_error=0.00016.\n" + ] + } + ], + "source": [ + "import paddle\n", + "from paddle.optimizer import Adam\n", + "from paddle_quantum.qchem import GroundStateSolver\n", + "\n", + "paddle.seed(126)\n", + "\n", + "binding_e = []\n", + "for ham, cir in [(deut_h_2, cir2), (deut_h_3, cir3)]:\n", + " solver = GroundStateSolver(Adam, num_iterations=100, tol=1e-5)\n", + " e, _ = solver.solve(cir, ham=ham, learning_rate=0.5)\n", + " binding_e.append(e)\n", + "\n", + "print(f\"Binding energy (N=2): exact=-1.749, numerical={binding_e[0]:.5f}, relative_error={abs(binding_e[0]-(-1.749))/1.749:.5f}.\")\n", + "print(f\"Binding energy (N=3): exact=-2.046, numerical={binding_e[1]:.5f}, relative_error={abs(binding_e[1]-(-2.046))/2.046:.5f}.\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 哈密顿量 $\\hat{H}_2$ 的结合能随参数 $\\theta$ 的变化\n", + "由于哈密顿量 $\\hat{H}_2$ 只有一个变分参数 $\\theta$,我们可以画出它的期望值 $\\lang\\hat{H}_2\\rangle$ 随 $\\theta$ 变化的曲线,然后检查一下我们前面的VQE算法是否找到了真正的基态能量。" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "angles = np.arange(-np.pi, 1.1*np.pi, 0.1*np.pi)\n", + "qm_expectvals = []\n", + "for theta in angles:\n", + " cir = DeuteronUCC2(theta)\n", + " psi = cir()\n", + " qm_expectvals.append(psi.expec_val(deut_h_2))\n", + "print(f\"The minimum value is {min(qm_expectvals):.5f}.\")\n", + "\n", + "fig = plt.figure(figsize=(4, 3))\n", + "ax = fig.gca()\n", + "ax.plot(angles, qm_expectvals)\n", + "ax.set_xlabel(r\"$\\theta$\")\n", + "ax.set_ylabel(r\"$\\langle\\hat{H}_2\\rangle$ (MeV)\")\n", + "ax.set_xticks([-np.pi, -np.pi/2, 0.0, np.pi/2, np.pi], [r\"$-\\pi$\", r\"$-\\pi/2$\", r\"$0$\", r\"$\\pi/2$\", r\"$\\pi$\"])\n", + "ax.set_yticks([0, 5, 10], [\"0\", \"5\", \"10\"])\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 参考文献\n", + "\\[1\\] Dumitrescu E F, McCaskey A J, Hagen G, et al. Cloud quantum computing of an atomic nucleus[J]. Physical review letters, 2018, 120(21): 210501.\n", + "\n", + "\\[2\\] [什么是约当-魏格纳(Jordan-Wigner)变换?](https://www.zhihu.com/question/457552295?utm_id=0)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "modellib", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.15" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/applications/deuteron_binding_energy/introduction_en.ipynb b/applications/deuteron_binding_energy/introduction_en.ipynb new file mode 100644 index 0000000..8524b77 --- /dev/null +++ b/applications/deuteron_binding_energy/introduction_en.ipynb @@ -0,0 +1,281 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Calculation of deuteron binding energy\n", + "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*\n", + "\n", + "Binding energy is the energy required to separate a system into its constituent parts. It is a measure of the stability of a system, and is the amount of energy that must be added to a system to break it apart. The concept of the binding energy has important applications in many areas of physics and chemistry, such as nuclear physics, atomic physics, and materials science. In nuclear physics, the binding energy per nucleon is used to determine the stability of atomic nuclei and to explain the phenomena of nuclear fusion and fission. In atomic physics, the binding energy is used to determine the strength of the bonds between atoms and molecules, and to explain their physical and chemical properties. In materials science, the binding energy is used to determine the strength of bonds in solids, and to design materials with specific properties for various applications.\n", + "\n", + "A deuteron is a stable isotope of hydrogen with one proton and one neutron in its nucleus. It has a mass approximately equal to twice that of a hydrogen atom and is the simplest isotope of elements in the periodic table. Deuterons play a crucial role in nuclear fusion reactions and are commonly used as a target in nuclear physics experiments." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Define deuteron Hamiltonian\n", + "The Hamiltonian used for calculation of deuteron binding energy is\n", + "$$\n", + "\\begin{equation}\n", + "\\hat{H}_N = \\sum_{n,n^{\\prime}=0}^{N-1}\\langle n^{\\prime}|\\hat{T}+\\hat{V}|n\\rangle\\hat{a}^{\\dagger}_{n^{\\prime}}\\hat{a}_n\n", + "\\end{equation}\n", + "$$\n", + "where $\\hat{T}$ is the kinetic energy operator, $\\hat{V}$ is the potential energy operator, $N$ is the dimension of the Hamiltonian. $\\hat{T}$ and $\\hat{V}$ can be explicitly written as\n", + "$$\n", + "\\begin{align}\n", + "& \\langle n^{\\prime}|\\hat{T}|n\\rangle = \\frac{\\hbar\\omega}{2}\\left[\n", + " (2n+3/2)\\delta_{n^{\\prime},n}-\\sqrt{n(n+1/2)}\\delta_{n^{\\prime}+1,n}-\\sqrt{(n+1)(n+3/2)}\\delta_{n^{\\prime}-1,n}\n", + "\\right],\\nonumber\\\\\n", + "& \\langle n^{\\prime}|\\hat{V}|n\\rangle = V_0\\delta_{0,n}\\delta_{n^{\\prime},n},\\nonumber\n", + "\\end{align}\n", + "$$\n", + "where $\\hat{a}^{\\dagger}_n$ is the creation operator and $\\hat{a}_n$ is the annihilation operator. Binding energy is the ground state energy of this Hamiltonian when $N\\to\\infty$ (We can obtain the binding energy by first calculating ground state energies when $N=1,2,3$, and then extrapolating to $N=\\infty$).\n", + "\n", + "To build this Hamiltonian in Paddle Quantum, we set $\\hbar\\omega=7\\text{Mev}$ and $V_0=−5.68658111\\text{Mev}$ \\[1\\].\n" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "H2= 5.906709445000001 I\n", + "0.21829055499999983 Z0\n", + "-2.1433035249352805 X0, X1\n", + "-2.1433035249352805 Y0, Y1\n", + "-6.125 Z1 \n", + "\n", + "H3= 15.531709445 I\n", + "0.21829055499999983 Z0\n", + "-2.1433035249352805 X0, X1\n", + "-2.1433035249352805 Y0, Y1\n", + "-6.125 Z1\n", + "-3.913118960624632 X1, X2\n", + "-3.913118960624632 Y1, Y2\n", + "-9.625 Z2\n" + ] + } + ], + "source": [ + "from utils import DeuteronHamiltonian\n", + "\n", + "omega = 7\n", + "V0 = -5.68658111\n", + "hamiltonian = DeuteronHamiltonian(omega, V0)\n", + "\n", + "# N=2\n", + "deut_h_2 = hamiltonian.get_hamiltonian(2)\n", + "print(\"H2=\", deut_h_2, \"\\n\") # H_2 = 5.906709I + 0.218291Z0 − 6.125Z1 - 2.143304 (X0X1 + Y0Y1)\n", + "\n", + "# N=3\n", + "deut_h_3 = hamiltonian.get_hamiltonian(3)\n", + "print(\"H3=\", deut_h_3) # H_3 = H_2 + 9.625(I − Z2) − 3.913119 (X1X2 + Y1Y2)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "> **NOTE**: In this tutorial, in order to encode the Hamiltonian on a quantum computer, we use Jordan-Wigner transformation \\[2\\] to transform creation and annihilation operators into Pauli basis." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Build the variational quantum circuit\n", + "We use variational quantum algorithm to calculate the ground state energy of $\\hat{H}_2$ and $\\hat{H}_3$, and we choose unitary coupled cluster (UCC) ansatz as our variational quantum circuit. Since NISQ quantum hardware is better at handling shallow circuit, we use problem specific constraints to simplify the original UCC circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum circuit for deuteron N=2.\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Quantum circuit for deuteron N=3.\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from utils import DeuteronUCC2, DeuteronUCC3\n", + "\n", + "# Simplified UCC circuit for H_2\n", + "cir2 = DeuteronUCC2()\n", + "print(\"Quantum circuit for deuteron N=2.\")\n", + "cir2.plot()\n", + "\n", + "# Simplified UCC circuit for H_3\n", + "cir3 = DeuteronUCC3()\n", + "print(\"Quantum circuit for deuteron N=3.\")\n", + "cir3.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Calculate ground state energy using variational quantum eigensolver (VQE)\n", + "Paddle Quantum has provided us easy-to-use `GroundStateSolver` to calculate ground state energy for a given hamiltonian, and we will use this function to calculate deuteron binding energy." + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Binding energy (N=2): exact=-1.749, numerical=-1.74888, relative_error=0.00007.\n", + "Binding energy (N=3): exact=-2.046, numerical=-2.04526, relative_error=0.00036.\n" + ] + } + ], + "source": [ + "import paddle\n", + "from paddle.optimizer import Adam\n", + "from paddle_quantum.qchem import GroundStateSolver\n", + "\n", + "paddle.seed(126)\n", + "\n", + "binding_e = []\n", + "for ham, cir in [(deut_h_2, cir2), (deut_h_3, cir3)]:\n", + " solver = GroundStateSolver(Adam, num_iterations=100, tol=1e-5)\n", + " e, _ = solver.solve(cir, ham=ham, learning_rate=0.5)\n", + " binding_e.append(e)\n", + "\n", + "print(f\"Binding energy (N=2): exact=-1.749, numerical={binding_e[0]:.5f}, relative_error={abs(binding_e[0]-(-1.749))/1.749:.5f}.\")\n", + "print(f\"Binding energy (N=3): exact=-2.046, numerical={binding_e[1]:.5f}, relative_error={abs(binding_e[1]-(-2.046))/2.046:.5f}.\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Variation of $\\hat{H}_2$ binding energy with $\\theta$\n", + "Since the energy of $\\hat{H}_2$ only has variational parameter $\\theta$, we can plot the variation of $\\langle\\hat{H}_2\\rangle$ with respect to $\\theta$, and check that our VQE method has approached the true minimum." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "angles = np.arange(-np.pi, 1.1*np.pi, 0.1*np.pi)\n", + "qm_expectvals = []\n", + "for theta in angles:\n", + " cir = DeuteronUCC2(theta)\n", + " psi = cir()\n", + " qm_expectvals.append(psi.expec_val(deut_h_2))\n", + "print(f\"The minimum value is {min(qm_expectvals):.5f}.\")\n", + "\n", + "fig = plt.figure(figsize=(4, 3))\n", + "ax = fig.gca()\n", + "ax.plot(angles, qm_expectvals)\n", + "ax.set_xlabel(r\"$\\theta$\")\n", + "ax.set_ylabel(r\"$\\langle\\hat{H}_2\\rangle$ (MeV)\")\n", + "ax.set_xticks([-np.pi, -np.pi/2, 0.0, np.pi/2, np.pi], [r\"$-\\pi$\", r\"$-\\pi/2$\", r\"$0$\", r\"$\\pi/2$\", r\"$\\pi$\"])\n", + "ax.set_yticks([0, 5, 10], [\"0\", \"5\", \"10\"])\n", + "plt.show()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Reference\n", + "\\[1\\] Dumitrescu E F, McCaskey A J, Hagen G, et al. Cloud quantum computing of an atomic nucleus[J]. Physical review letters, 2018, 120(21): 210501\n", + "\n", + "\\[2\\] [Jordan-Wigner transform](https://en.wikipedia.org/wiki/Jordan%E2%80%93Wigner_transformation)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "modellib", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.15" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "8f24120f890011f53feb4ed62c47961d8565ec1de8b7cb23548c15bd6da8f2d2" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/applications/deuteron_binding_energy/utils.py b/applications/deuteron_binding_energy/utils.py new file mode 100644 index 0000000..501aa5e --- /dev/null +++ b/applications/deuteron_binding_energy/utils.py @@ -0,0 +1,78 @@ +# !/usr/bin/env python3 +# Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the 'License'); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an 'AS IS' BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +from typing import Optional +import logging +from paddle_quantum import Hamiltonian +from paddle_quantum.ansatz import Circuit +from openfermion import FermionOperator, jordan_wigner +import numpy as np + +__all__ = ["DeuteronHamiltonian", "DeuteronUCC2", "DeuteronUCC3"] + + +class DeuteronHamiltonian(object): + def __init__(self, omega: float, V0: float) -> None: + self.omega = omega + self.V0 = V0 + logging.info("\n#######################################\nDeuteron Hamiltonian\n#######################################") + logging.info(f"hbar_omega: {omega:.5f}") + logging.info(f"V0: {V0:.5f}") + + def get_hamiltonian(self, N: int) -> Hamiltonian: + h = FermionOperator("0^ 0", self.V0) + for i in range(N): + h += 0.5*self.omega*(2*i+1.5)*FermionOperator(f"{i:d}^ {i:d}") + if i < N-1: + h += -0.5*self.omega*np.sqrt((i+1)*(i+1.5))*FermionOperator(f"{i+1:d}^ {i:d}") + if i > 0: + h += -0.5*self.omega*np.sqrt(i*(i+0.5))*FermionOperator(f"{i-1:d}^ {i:d}") + h_qubit = jordan_wigner(h) + return Hamiltonian.from_qubit_operator(h_qubit) + + +class DeuteronUCC2(Circuit): + def __init__(self, theta: Optional[float] = None): + num_qubits = 2 + super().__init__(num_qubits) + + self.x(0) + self.ry(1) + self.cx([1, 0]) + if isinstance(theta, float): + self.update_param(theta) + + +class DeuteronUCC3(Circuit): + def __init__(self, theta: Optional[np.array] = None): + num_qubits = 3 + super().__init__(num_qubits) + + self.x(0) + self.ry(1) + self.ry(2) + self.cx([2, 0]) + self.cx([0, 1]) + self.ry(1) + self.cx([0, 1]) + self.cx([1, 0]) + if isinstance(theta, np.ndarray): + self.update_param(theta) + +if __name__ == "__main__": + deuteron_h = DeuteronHamiltonian(7, -5.6865811) + h1 = deuteron_h.get_hamiltonian(1) + h2 = deuteron_h.get_hamiltonian(2) + h3 = deuteron_h.get_hamiltonian(3) diff --git a/applications/handwritten_digits_classification/introduction_cn.ipynb b/applications/handwritten_digits_classification/introduction_cn.ipynb index 70b8e4e..f19f8e9 100644 --- a/applications/handwritten_digits_classification/introduction_cn.ipynb +++ b/applications/handwritten_digits_classification/introduction_cn.ipynb @@ -1,7 +1,6 @@ { "cells": [ { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -17,7 +16,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -46,7 +44,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -89,7 +86,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -142,15 +138,13 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "在这里,我们只需要修改要配置文件中的图片路径,再运行整个代码,就可以快速对其它图片进行测试。" + "在这里,我们只需要修改配置文件中的图片路径,再运行整个代码,就可以快速对其它图片进行测试。" ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -168,7 +162,6 @@ ] }, { - "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -190,7 +183,7 @@ ], "metadata": { "kernelspec": { - "display_name": "py37", + "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, @@ -204,12 +197,11 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.15 (default, Nov 10 2022, 12:46:26) \n[Clang 14.0.6 ]" + "version": "3.7.16" }, - "orig_nbformat": 4, "vscode": { "interpreter": { - "hash": "49b49097121cb1ab3a8a640b71467d7eda4aacc01fc9ff84d52fcb3bd4007bf1" + "hash": "d3caffbb123012c2d0622db402df9f37d80adc57c1cef1fdb856f61446d88d0a" } } }, diff --git a/applications/handwritten_digits_generation/gen_pics/qcaan_generated_vs_original_20230313.png b/applications/handwritten_digits_generation/gen_pics/qcaan_generated_vs_original_20230313.png new file mode 100644 index 0000000000000000000000000000000000000000..2dad893cf6641e5a9d2a849d8d94fd28db359759 GIT binary patch literal 87241 zcmeGEWmuNq);5k}i-CcSfI%rGNJ(0#q#^<$Dc#*|BA}q8fJmu`2na}*3W$`bfJjSs zckgrhTmSd{w&VMLj%OXqWpLluyyhI^tTDZ=$zI;R<l#tuA;oQ#k z`2Y5dqq#y9|NHeKe2dZ|NSGrs8&-fXM$2vzI_ z0mli3**15vUAuNYmuC7>RFu8CvRGDGnK#h(Lc}?^l-~V?Y=q!#zVPvx8NDA-=kgW? z5_oud)iUyn+K&heAC~aHnQ7KytNku1>8lCfaf#h=vJp8QeE8nt{tUlrYUK8Gr}i>R zba;v_wcDMl+x8@7= zR!7>~KW__5H?E)fvXwJS=rPSic-vBsH)YB6qxEB7*;FzfzZ7v!)vee^=hSyp-F?}X z&arD(hFObb^-B@u6s;0n_cXn#L%)9gnp>Kz4i$Ffp6speE!nTZASf87AL$w#7wNW; 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zh#H-cRa!VWEX`Dx?a`+17GtW6ZG!^biPs7VHf9leP09wi2gVH##Lx7_hEd)fR`e9L z^9+2WR?Q6!Jy)k!w6S$;WOPo|kY*BeR{*aWW}CDr(Bprn8Cla65531mXQ@A_Rsz|Y z`G(%|lB5j^rrfc(3sN2(EgDqn_DD9hY~9Gdqh2#_FzHv*a)beyxCT5)MEDHA`7|;z z58S{p49hepY{|p&P;HyKuCaA&3H($N4#xTPd&hj1FSo9&s?z#%Xa39|Et!?2r90a7 zI98p`C8nTwqhls)vo}h$ICBpnmW^BDJL57H^Au6vEdKT|{nht4VXW-!mrxEmeo7oR z%gK_Lm@LE{MPn|^UiF3Gd(5+eoYYO}@iQI6Nk%8rgk(XNW^p>nsK<(~nWBsWiv zyub<&%85GCI_i4AgP5qeR|DH+6}C<>OMy?~>ip)S@aG6VSW$jaSEY5~a*3786WCvt@~8F>{;fCI=y#I- y_Yb+7|B+VzZ_UR4|AwwZcf01](#qcaan_ref) 是一种量子生成模型,能够从现有的数据中学习,从而生成更加逼真的新数据。其可应用于数据生成、数据扩充和无监督学习。\n", + "\n", + "该模型主要是基于生成对抗网络(Generative Adversarial Network, GAN)来设计的。GAN 是一种深度学习模型,主要包含生成器(Generator)和判别器(Discriminator)两个神经网络。生成器通过将从高斯分布中采样的噪音样本作为输入,生成假样本。判别器则负责对真假样本进行分类。两个网络相互博弈、不断优化,使得生成器生成的样本逐渐更加逼真。\n", + "\n", + "该模型主要将 GAN 中的输入由高斯噪音分布替换为由参数化量子电路刻画的量子态分布。具体模型参考下图。除了 GAN 的两个网络外,我们还需要训练第三个量子神经网络 QNN 用来刻画生成器的输入,即先验分布 Prior,并使其接近判别器的倒数第二层隐空间(Latent space)的分布。在本教程中,我们使用的 QNN 主要包含若干层 U3 门和强纠缠门。一个包含 n qubits, D 层的量子电路可以简单地使用如下两行代码实现:\n", + "\n", + "```code\n", + "cir = paddle_quantum.ansatz.Circuit(n)\n", + "cir.complex_entangled_layer(D)\n", + "```\n", + "\n", + "#### QCAAN 优势\n", + "\n", + "- 相较于经典的(伪)高斯分布,量子态分布是真随机,可以解决生成器(Generator)的快启动(kick-start)问题;\n", + "- 原文作者[1](#qcaan_ref) 声称使用量子态分布可以缓解 GAN 的训练不稳定问题,以致能够生成更高清、更多样的图片。\n", + "\n", + "\n", + "\n", + "

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量子电路关联对抗网络1 模型示意图。右边是GAN的两个网络:生成器和判别器。左边是用来刻画先验分布的量子神经网络。训练阶段,三个网络交替训练;推断阶段:先从量子神经网络中采样,然后将采样结果输入到生成器中生成逼真的图片。
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\n" + ] + }, + { + "cell_type": "markdown", + "id": "067dca1c", + "metadata": {}, + "source": [ + "### 如何使用\n", + "\n", + "#### 使用 QCAAN 模型进行推断\n", + "\n", + "这里我们给出了一个训练好的模型,可以直接用于手写数字图片的生成。只需输入命令 \n", + "```code\n", + "python qcaan_generation.py --config inference.toml \n", + "```\n", + "即可。\n", + "\n", + "#### 在线演示\n", + "首先定义配置文件 inference.toml 的内容:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "70ae9579", + "metadata": {}, + "outputs": [], + "source": [ + "inference_toml = r\"\"\"\n", + "# QC-AAN 模型的整体配置文件。\n", + "# 当前配置的 mode 选择。 可以是: 'train' 或者 'inference'。这里我们选择 'inference'。\n", + "# mode = 'inference'\n", + "# 用以存储模型的模型名字\n", + "# model_name = 'qcaan-model'\n", + "# 加载训练好的模型的参数的路径。绝对路径和相对路径都可以。\n", + "params_path = \"params\"\n", + "# 量子电路包含的量子比特数目。\n", + "num_qubits = 8\n", + "# 量子电路包含的 complex entangled layers 的层数。\n", + "num_depths = 4\n", + "# 隐藏特征数目,表示生成器的输入的维度。\n", + "latent_dim = 16\n", + "# 人工设置种子参数用以展示模型的可复现性。\n", + "manual_seed = 20230313\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "357622e0", + "metadata": {}, + "source": [ + "接下来是生成图片的代码。\n", + "\n", + "每次先从训练好的 QNN 量子态中采样60个样本(注意0,1 串被放缩成1,-1串),然后输入到生成器中生成60张新图,以及随机选取40张 MNIST 中的原图作为对比。如果想换一批新图,则修改一下上面 inference.toml 文件中最后一行的 manual_seed 参数即可。" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "28b5e038", + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/liguangxi02/opt/anaconda3/envs/PaddleQ/lib/python3.7/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "This program is running on your cpu!\n", + "\n", + "Model loaded, generating new images...\n", + "The first 10 QNN samples are listed below:\n", + " [[ 1. 1. 1. -1. 1. 1. -1. 1. -1. 1. 1. -1. -1. 1. 1. -1.]\n", + " [ 1. 1. -1. -1. 1. -1. -1. 1. 1. -1. -1. -1. -1. 1. 1. -1.]\n", + " [ 1. 1. -1. -1. -1. -1. -1. -1. -1. 1. -1. -1. 1. -1. 1. 1.]\n", + " [ 1. 1. 1. -1. 1. -1. -1. -1. 1. 1. 1. 1. 1. -1. -1. -1.]\n", + " [-1. 1. 1. 1. -1. 1. -1. -1. 1. -1. -1. -1. -1. -1. -1. -1.]\n", + " [-1. -1. 1. 1. -1. -1. -1. -1. -1. 1. -1. -1. -1. 1. -1. 1.]\n", + " [ 1. 1. 1. -1. 1. -1. -1. 1. 1. -1. 1. -1. -1. -1. 1. 1.]\n", + " [-1. -1. 1. -1. -1. 1. -1. -1. 1. 1. -1. -1. -1. -1. 1. -1.]\n", + " [ 1. -1. 1. -1. 1. 1. 1. 1. -1. 1. 1. -1. 1. 1. 1. 1.]\n", + " [-1. -1. -1. 1. 1. -1. -1. -1. 1. 1. -1. -1. 1. -1. 1. -1.]]\n", + "\n", + "The generated pictures are saved to the file named 'gen_pics/qcaan_generated_vs_original_20230313.png'.\n", + "\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import os\n", + "import warnings\n", + "import toml\n", + "from paddle_quantum.qml.qcaan import model_test\n", + "\n", + "warnings.filterwarnings('ignore')\n", + "os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python'\n", + "\n", + "config = toml.loads(inference_toml)\n", + "model_test(**config)\n" + ] + }, + { + "cell_type": "markdown", + "id": "fc02c8eb", + "metadata": {}, + "source": [ + "### 注意事项\n", + "- 这里我们给出的是已经训练好的模型。如果想自己重新训练,则只需输入命令 \n", + "```code\n", + "python qcaan_generation.py --config train.toml \n", + "```\n", + "即可。其中,也可以对文件 train.toml 进行修改,以设置不同的训练参数。\n", + "- 如果想换个数据集测试模型,则需要查看源码文件 ./paddle_quantum/qml/qcaan.py,并对其中加载数据集部分重新设置一下,可能还需要对模型网络架构,超参数等进行微调。" + ] + }, + { + "cell_type": "markdown", + "id": "4ee4ee2d", + "metadata": {}, + "source": [ + "### 参考文献\n", + "\n", + "
\n", + "\n", + "- [1] Rudolph, Manuel S., et al. \"Generation of high-resolution handwritten digits with an ion-trap quantum computer.\" Physical Review X 12.3 (2022): 031010." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.16" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/applications/handwritten_digits_generation/introduction_en.ipynb b/applications/handwritten_digits_generation/introduction_en.ipynb new file mode 100644 index 0000000..598af86 --- /dev/null +++ b/applications/handwritten_digits_generation/introduction_en.ipynb @@ -0,0 +1,217 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "bad0a9d9", + "metadata": {}, + "source": [ + "## Handwritten Digits Generation\n", + "\n", + "Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.\n", + "\n", + "### Generation Model\n", + "\n", + "The generation model is a vital model type in machine learning, which is used to generate data that conforms to some distribution. Generally speaking, the generation model can learn the distribution characteristics of data from some training data and generate new data according to these characteristics.\n", + "\n", + "Generation models can be divided into probabilistic generation models and non-probabilistic generation models. The probabilistic generation model refers to the generation model that can build the probability distribution model of data, such as the common Gaussian mixed model, naive Bayesian model, etc. These models can usually be trained by maximum likelihood estimation, and then generate new data according to these models that conforms to the data distribution. The non-probabilistic generation model refers to that it does not rely on the probability distribution model, but directly generates new data by learning the characteristics and laws of the data. For example, the generative adversarial network (GAN) is a non-probabilistic generation model. It learns to generate data through the confrontation of two neural networks.\n", + "\n", + "Generation models have been widely used in natural language processing, image processing, audio processing and other fields. For example, you can use the generation model to generate natural language text, images, audio and other content. You can also use the generation model to perform tasks such as image and audio noise reduction, style conversion, etc.\n", + "\n", + "### Generation of MNIST Handwritten Digital Images Using QCAAN Model\n", + "\n", + "#### Brief Introduction of QCAAN\n", + "\n", + "Quantum-Circuit Associative Adversarial Network (QCAAN) [1](#qcaan_ref) is a quantum generation model,\n", + "which is able to learn from existing data to generate more realistic new data. It can be applied to data generation, data expansion and unsupervised learning.\n", + "\n", + "The model is mainly designed based on Generative Adversarial Network (GAN). GAN is a type of deep learning model that consists of two neural networks: the Generator and the Discriminator. The Generator generates fake samples by taking noise samples from Gaussian distribution as input, while the discriminator classifies real and fake samples. The two networks compete with each other and are continuously optimized to make the generated samples more realistic.\n", + "\n", + "In this model, the Gaussian noise input in the classical generative adversarial network (GAN) is replaced by the quantum state distribution described by the parameterized quantum circuit. Refer to the figure below for the model details. Except for the two networks in a GAN, we need to train a third network (QNN) to depict the input prior of the Generator, and make it close to the latent space distribution of the second-last layer of the Discriminator. In this model, our employed QNN mainly contains several layers of U3 gates and strongly entangled gates. A quantum circuit with n qubits and D layers can be simply implemented by using the following Paddle-Quantum codes:\n", + "\n", + "```code\n", + "cir = paddle_quantum.ansatz.Circuit(n)\n", + "cir.complex_entangled_layer(D)\n", + "```\n", + "\n", + "#### Advantages of QCAAN \n", + "\n", + "- Compared to classical (pseudo) Gaussian distribution, quantum state distrition is truly random, which can solve the kick-start problem of the Generator.\n", + "- The authors [1](#qcaan_ref) claimed that the quantum state distribution helps to stabilize the GAN, which would cause the GAN to generate both higher quality and more diverse images.\n", + "\n", + "\n", + "\n", + "
\n", + " \n", + "
\n", + "
Figure of Quantum Circuit Associative Adversarial Network1. On the right are two networks of GAN: Generator and Discriminator. On the left is a quantum neural network used to characterize prior distribution. During training, the three networks are alternatively trained; during inference, samples are first taken from the quantum neural network and then fed into the generator to generate realistic images.
\n", + "
\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "6c77ae63", + "metadata": {}, + "source": [ + "### How to Use\n", + "\n", + "#### Use QCAAN to Infer\n", + "\n", + "Here, we provide an trained model, which can directly generate handwritten digits. Just enter the following command\n", + "```code\n", + "python qcaan_generation.py --config inference.toml \n", + "```\n", + "\n", + "\n", + "#### Online Demo\n", + "First define the contents of the configuration file inference.toml:" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "5b486563", + "metadata": {}, + "outputs": [], + "source": [ + "inference_toml = r\"\"\"\n", + "# The full config of the QC-AAN model.\n", + "# The mode of this config. Available values: 'train' | 'inference'. Here we choose 'inference'.\n", + "# mode = 'inference'\n", + "# The name of the model, which is used to save the model.\n", + "# model_name = 'qcaan-model'\n", + "# The path to load the parameters of the trained model. Both relative and absolute paths are allowed.\n", + "params_path = \"params\"\n", + "# The number of qubits which the quantum circuit contains.\n", + "num_qubits = 8\n", + "# The number of depths of complex entangled layers which the quantum circuit contains.\n", + "num_depths = 4\n", + "# latent feature numbers which represents the input dimension of the generator.\n", + "latent_dim = 16\n", + "# The manual seed for reproducibility.\n", + "manual_seed = 20230313\n", + "\"\"\"" + ] + }, + { + "cell_type": "markdown", + "id": "9e2e491d", + "metadata": {}, + "source": [ + "Next is the code for genenration.\n", + "\n", + "Each time we first randomly sample 60 samples (note that 0,1 strings are scaled to 1,-1 strings) from the trained quantum state distribution, then feed them to the Generator to generate 60 new images. We also randomly select 40 original MNIST images as comparison. If you want to change a batch of new images, you could modify the manual_seed in the last line of the above file inference.toml.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "cbc0de59", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n", + "This program is running on your cpu!\n", + "\n", + "Model loaded, generating new images...\n", + "The first 10 QNN samples are listed below:\n", + " [[ 1. 1. 1. -1. 1. 1. -1. 1. -1. 1. 1. -1. -1. 1. 1. -1.]\n", + " [ 1. 1. -1. -1. 1. -1. -1. 1. 1. -1. -1. -1. -1. 1. 1. -1.]\n", + " [ 1. 1. -1. -1. -1. -1. -1. -1. -1. 1. -1. -1. 1. -1. 1. 1.]\n", + " [ 1. 1. 1. -1. 1. -1. -1. -1. 1. 1. 1. 1. 1. -1. -1. -1.]\n", + " [-1. 1. 1. 1. -1. 1. -1. -1. 1. -1. -1. -1. -1. -1. -1. -1.]\n", + " [-1. -1. 1. 1. -1. -1. -1. -1. -1. 1. -1. -1. -1. 1. -1. 1.]\n", + " [ 1. 1. 1. -1. 1. -1. -1. 1. 1. -1. 1. -1. -1. -1. 1. 1.]\n", + " [-1. -1. 1. -1. -1. 1. -1. -1. 1. 1. -1. -1. -1. -1. 1. -1.]\n", + " [ 1. -1. 1. -1. 1. 1. 1. 1. -1. 1. 1. -1. 1. 1. 1. 1.]\n", + " [-1. -1. -1. 1. 1. -1. -1. -1. 1. 1. -1. -1. 1. -1. 1. -1.]]\n", + "\n", + "The generated pictures are saved to the file named 'gen_pics/qcaan_generated_vs_original_20230313.png'.\n", + "\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import os\n", + "import warnings\n", + "\n", + "warnings.filterwarnings('ignore')\n", + "os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python'\n", + "\n", + "import toml\n", + "from paddle_quantum.qml.qcaan import model_test\n", + "\n", + "config = toml.loads(inference_toml)\n", + "model_test(**config)\n" + ] + }, + { + "cell_type": "markdown", + "id": "d8dff072", + "metadata": {}, + "source": [ + "### Note\n", + "- Here we only give the trained model. If you want to retrain this model, just enter the command\n", + "```code\n", + "python qcaan_generation.py --config train.toml \n", + "```\n", + "You can also modify the file train.toml to set different training parameters.\n", + "- If you want to change a dataset to test model, you need to view the source code file ./paddle_quantum/qml/qcaan.py, and modify the data loading part. You may also need to modify slightly the model network architectures and hyper-parameters, etc.\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "id": "6d6e1df0", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "
\n", + "\n", + "- [1] Rudolph, Manuel S., et al. \"Generation of high-resolution handwritten digits with an ion-trap quantum computer.\" Physical Review X 12.3 (2022): 031010." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.16" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/applications/handwritten_digits_generation/params/params_G_epoch20.pdparams b/applications/handwritten_digits_generation/params/params_G_epoch20.pdparams new file mode 100644 index 0000000000000000000000000000000000000000..b4a41cb3ea6eb53a981d3f168704ff0548cf0450 GIT binary patch literal 6780221 zcmX7vc~}o$*v3m6rA0+i*-2U`S^Ca%l#uL2WhYcZC`9<7ec!axUQ)JJQr~%=l2j5x 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{}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 量子随机数生成器\n", + "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*\n", + "\n", + "随机数生成器是通过算法、物理信号、环境噪音等来产生随机数列的方法或装置,其在如密码学、机器学习等诸多领域扮演重要角色,它直接影响了密码的可破解性、机器学习模型的泛化性能。经典计算机通过如线性同余法等伪随机算法生成伪随机数,存在一定的缺陷,比如存在周期性等。而量子计算机可以利用量子测量的不确定性生成真随机数,具有不可预测性。本模型库封装了能够调用百度量子云平台上线的百度自研量子计算机、模拟器、第三方硬件生成随机数的方法。\n", + "\n", + "## 生成原理\n", + "利用量子计算机可对零初始态 $|0\\rangle$ 作用 $H$ 门,得到量子态 $|\\psi\\rangle$, \n", + "$$\n", + "|\\psi\\rangle = \\frac{\\sqrt2}{2} |0\\rangle + \\frac{\\sqrt2}{2} |1\\rangle .\n", + "$$\n", + "该量子态 $|\\psi\\rangle$ 在 Pauli-$Z$ 量子测量(即计算基测量,以 $|0\\rangle\\langle 0|$,$|1\\rangle \\langle 1 |$ 为测量算子)下为 $0$ 或为 $1$ 的概率均为 $\\frac12$。量子态坍缩的不确定性可以保证得到的 $0$ 或 $1$ 的结果为真随机。重复上述流程即可得到随机比特串,流程示意图如下。\n", + "![random_number](./randnum_CN.png)\n", + "\n", + "若实际量子计算机为无噪声理想量子计算机,则测量结果为真随机。不过当前量子计算机均存在一定的噪声,因此我们同时封装了经典的隐私增强算法 [1],其可以通过利用两台独立的量子计算机(或一台量子计算机的两个独立比特)分别测量得到更长的比特串数据并对两者数据进行后处理提取较短的比特串数据,从而过滤噪声的影响。提取过程示意图如下。\n", + "![extractor](./extractor_CN.png)\n", + "\n", + "## 如何使用\n", + "### 快速使用\n", + "用户可以通过在命令行下输入 `python randnum.py --config config.toml` 即可运行,其中 `config.toml` 为模型配置文件,用户可修改该文件内的参数或输入其它文件实现自定义参数。\n", + "### 在线演示\n", + "同时,我们这里给出一个在线演示的版本,可以在线进行调试。首先定义配置文件的内容:" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "example_toml = r'''\n", + "# 所需比特串长度\n", + "bit_len = 10\n", + "\n", + "# 处理器硬件\n", + "backend = 'local_baidu_sim2' # 本地模拟器\n", + "# backend = 'cloud_baidu_qpu_qian' # 百度自研量子计算机 乾始 (Qian)\n", + "\n", + "# 用户 token,在使用云端服务时需要输入\n", + "token = ''\n", + "\n", + "# 是否使用隐私增强后处理,toml 文件中 true 和 false 都应为小写\n", + "extract = false\n", + "\n", + "# 信息安全参数,越小则越接近真随机(后处理所需参数,不启动后处理时无需修改)\n", + "security = 1e-8\n", + "\n", + "# 处理器硬件 1 和 2 的最小熵(后处理所需参数,不启动后处理时无需修改,取值范围 (0,1))\n", + "min_entr_1 = 0.9 \n", + "min_entr_2 = 0.9\n", + "\n", + "# 日志文件路径\n", + "log_path = './qrng.log'\n", + "'''" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "接下来执行模型运行过程。" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Applications/anaconda3/envs/pqtest/lib/python3.7/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + }, + { + "data": { + "text/plain": [ + "[0, 0, 0, 1, 1, 1, 1, 0, 1, 0]" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "import warnings\n", + "import toml\n", + "from paddle_quantum.data_analysis.rand_num import random_number_generation\n", + "warnings.filterwarnings('ignore')\n", + "random_number_generation(**toml.loads(example_toml))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在这里,我们只需要修改 `example_toml` 字典中的参数,再运行上文全部代码,就可以快速自定义调试。如需使用百度自研量子计算机“乾始”,可将 `backend` 参数的输入修改为 ` 'cloud_baidu_qpu_qian'` (需保留引号,python 字符串数据类型),并输入自己账户 `token`。(若无 `token` 可前往[百度量易伏平台](https://quantum-hub.baidu.com/)注册。)\n", + "## 注意事项\n", + "- 请保持环境中 `Qcompute` 版本更新,过低版本会导致新上线后端无法识别。后端 `'cloud_baidu_qpu_qian'` 要求 `>= 3.0.0`。\n", + "- 使用百度量子云平台的后端时需输入 `token`,请留意个人账户中对应云服务的剩余可用时长。\n", + "- 使用云服务时请留意[百度量子云平台](https://quantum-hub.baidu.com/)的各机器运行状态和服务时间。\n", + "\n", + "## 引用信息\n", + "```\n", + "@article{hayashi2016more,\n", + " title={More efficient privacy amplification with less random seeds via dual universal hash function},\n", + " author={Hayashi, Masahito and Tsurumaru, Toyohiro},\n", + " journal={IEEE Transactions on Information Theory},\n", + " volume={62},\n", + " number={4},\n", + " pages={2213--2232},\n", + " year={2016},\n", + " publisher={IEEE}\n", + "}\n", + "```\n", + "## 参考文献\n", + "[1] Hayashi, Masahito, and Toyohiro Tsurumaru. \"More efficient privacy amplification with less random seeds via dual universal hash function.\" IEEE Transactions on Information Theory 62.4 (2016): 2213-2232." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.15" + }, + "vscode": { + "interpreter": { + "hash": "d3caffbb123012c2d0622db402df9f37d80adc57c1cef1fdb856f61446d88d0a" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/applications/random_number/introduction_en.ipynb b/applications/random_number/introduction_en.ipynb new file mode 100644 index 0000000..2432d61 --- /dev/null +++ b/applications/random_number/introduction_en.ipynb @@ -0,0 +1,139 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Quantum Random Number Generator\n", + "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*\n", + "\n", + "Random number generators are methods or devices to generate random number series by algorithms, physical signals, environmental noise, etc. They play an important role in many fields such as cryptography, machine learning, etc. They directly affect the crackability of the key, and the generalization performance of the machine learning model. Classical computers generate pseudo-random numbers by pseudo-random algorithms such as the linear congruence method, which has certain drawbacks like periodicity. In contrast, quantum computers can generate truly random numbers by exploiting the uncertainty of quantum measurements, which is unpredictable. This model library encapsulates methods that can call Baidu's own quantum computers, simulators, and third-party hardware that are online on the Baidu Quantum Cloud Platform to generate random numbers.\n", + "\n", + "## Method\n", + "The quantum computer can be used to act $H$ gates on the zero initial state $|0\\rangle$ to obtain the quantum state $|\\psi\\rangle$,\n", + "$$\n", + "|\\psi\\rangle = \\frac{\\sqrt2}{2} |0\\rangle + \\frac{\\sqrt2}{2} |1\\rangle .\n", + "$$\n", + "The quantum state $|\\psi\\rangle$ has a probability of being $0$ or $1$ under Pauli-$Z$ quantum measurement (or named computational basis measurement, whose measurement operators are $|0\\rangle\\langle 0|$, $|1\\rangle \\langle 1 |$.) with $\\frac12$. The uncertainty of the collapse of the quantum state ensures that the result obtained for $0$ or $1$ is truly random. Repeat the above process to obtain a random bit string, and the flow diagram is as follows.\n", + "![random_number](./randnum_EN.png)\n", + "\n", + "If the actual quantum computer is a noise-free ideal quantum computer, the measurement result is truly random. However, current quantum computers are noisy, so we also encapsulate the classical privacy-enhancing algorithm, which can filter the effect of noise by using two independent quantum computers (or two independent qubits of one quantum computer) to measure separately to get a long string. Then extract a short string by post-process. The diagram of extractor is shown below.\n", + "![extractor](./extractor_EN.png)\n", + "## User's Guide\n", + "### Quick Start\n", + "The user can run it by typing `python randnum.py --config config.toml` at the command line, where `config.toml` is the model configuration file, and the user can modify the parameters in this file or enter other files to customize the parameters.\n", + "### Online Demonstration\n", + "In the meantime, we give here a version of the online demo that can be customized online. First define the contents of the configuration file." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "example_toml = r'''\n", + "# the target length of random bit string\n", + "bit_len = 10\n", + "\n", + "# backend processor\n", + "backend = 'local_baidu_sim2' # local simulator\n", + "# backend = 'cloud_baidu_qpu_qian' # Baidu's QPU Qian\n", + "\n", + "# user's token, needed when using cloud service\n", + "token = ''\n", + "\n", + "# whether to execute the privacy-enhancing post-process, please use lowercase here\n", + "extract = false\n", + "\n", + "# security parameter, the smaller it is, the closer it is to true random (only needed in post-process)\n", + "security = 1e-8\n", + "\n", + "# min-entropy of the hardware 1 and 2 (only needed in post-process, range from (0,1))\n", + "min_entr_1 = 0.9 \n", + "min_entr_2 = 0.9\n", + "\n", + "# log file path\n", + "log_path = './qrng.log'\n", + "'''" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we run the model." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import warnings\n", + "import toml\n", + "from paddle_quantum.data_analysis.rand_num import random_number_generation\n", + "warnings.filterwarnings('ignore')\n", + "random_number_generation(**toml.loads(example_toml))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here, we just need to modify the parameters in the `example_toml` dictionary and run the code above to quickly customize the model. If you want to use Baidu's own quantum computer \"Qian\", you can modify the `backend` parameter to ` 'cloud_baidu_qpu_qian'` (keep the quotes, python string data type), and enter your account `token`. (If you don't have `token`, you can go to [Baidu Quantum Cloud Platform](https://quantum-hub.baidu.com/) to register.)\n", + "## Note\n", + "- Please keep the `Qcompute` version in your environment up to date, too low a version will not recognize the backend. `'cloud_baidu_qpu_qian'` needs `Qcompute >= 3.0.0`.\n", + "\n", + "- When using the backend of Baidu Quantum Cloud Platform, you need to input `token`, please pay attention to the remaining available hours of the corresponding cloud service in your personal account.\n", + "- When using cloud services, please pay attention to the running status and service time of each machine on [Baidu Quantum Cloud Platform](https://quantum-hub.baidu.com/).\n", + "\n", + "## Citation\n", + "```\n", + "@article{hayashi2016more,\n", + " title={More efficient privacy amplification with less random seeds via dual universal hash function},\n", + " author={Hayashi, Masahito and Tsurumaru, Toyohiro},\n", + " journal={IEEE Transactions on Information Theory},\n", + " volume={62},\n", + " number={4},\n", + " pages={2213--2232},\n", + " year={2016},\n", + " publisher={IEEE}\n", + "}\n", + "```\n", + "\n", + "## Reference\n", + "[1] Hayashi, Masahito, and Toyohiro Tsurumaru. \"More efficient privacy amplification with less random seeds via dual universal hash function.\" IEEE Transactions on Information Theory 62.4 (2016): 2213-2232.\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.15" + }, + "vscode": { + "interpreter": { + "hash": "d3caffbb123012c2d0622db402df9f37d80adc57c1cef1fdb856f61446d88d0a" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/applications/random_number/randnum.py b/applications/random_number/randnum.py new file mode 100644 index 0000000..7d4d62a --- /dev/null +++ b/applications/random_number/randnum.py @@ -0,0 +1,34 @@ +# !/usr/bin/env python3 +# Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +r""" +Quantum random number generator. +""" +import os +import warnings +import toml +import argparse +from paddle_quantum.data_analysis.rand_num import random_number_generation + + +warnings.filterwarnings('ignore') +os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python' + +if __name__ == "__main__": + parser = argparse.ArgumentParser(description="Quantum random number generation.") + parser.add_argument( + 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zIwVng=tp^&Veg6lH&bno>}`=6LW0!%F6moX=Y#UC^Y2K7GE##CnXNv%Tuynz<$x%m zv#GZv300Q&Et8b3aV=P$S}a`N)Gn`iLMQ@aM4w=9M6qoj*leJzK}99}H&wTnT{5Y9 zM5l!t6L3L*zF2H#5hNfe{Bdtb5Wr>oi=)xnTYx1z3@xm+u00&mf8`_ 构建,即金融系统风险默认遵从标准正态分布。 + + .. py:method:: estimate_var() + + 使用量子振幅估计算法分析配置好的风险资产。 + + :return: 资产组合的在险价值。 + :rtype: float diff --git a/docs_zh_CN/source/paddle_quantum.gate.base.rst b/docs_zh_CN/source/paddle_quantum.gate.base.rst index eed713d..23432c7 100644 --- a/docs_zh_CN/source/paddle_quantum.gate.base.rst +++ b/docs_zh_CN/source/paddle_quantum.gate.base.rst @@ -3,23 +3,37 @@ paddle\_quantum.gate.base 量子门的基类的功能实现。 -.. py:class:: Gate(depth=1, backend=None, dtype=None, name_scope=None) +.. py:class:: Gate(matrix=None, qubits_idx=None, depth=1, gate_info=None, num_qubits=None, check_legality=True, num_acted_qubits=None, backend=None, dtype=None, name_scope=None) - 基类::py:class:`paddle_quantum.base.Operator` + 基类::py:class:`paddle_quantum.channel.base.Channel` 量子门的基类。 + :param matrix: 量子门的矩阵 + :type matrix: paddle.Tensor + :param qubits_idx: 作用在的量子比特的编号。 + :type qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] :param depth: 层数,默认为 ``1``。 :type depth: int, optional + :param gate_info: 量子门的信息,用于信息追溯或者画图。 + :type gate_info: dict, optional + :param check_legality: 表示的完整性校验,默认为 ``True``。 + :type check_legality: bool + :param num_acted_qubits: 量子门作用的量子比特的数量,默认为 ``None``。 + :type num_acted_qubits: int :param backend: 执行门的后端,默认为 ``None``。 :type backend: paddle_quantum.Backend, optional :param dtype: 数据的类型,默认为 ``None``。 :type dtype: str, optional - :param name_scope: 为 Layer 内部参数命名而采用的名称前缀。如果前缀为 "mylayer",在一个类名为MyLayer的Layer中, - 参数名为"mylayer_0.w_n",其中 "w" 是参数的名称,"n" 为自动生成的具有唯一性的后缀。如果为 ``None``, - 前缀名将为小写的类名。默认为 ``None``。 + :param name_scope: 为 Layer 内部参数命名而采用的名称前缀。如果前缀为 "mylayer",在一个类名为MyLayer的Layer中,参数名为"mylayer_0.w_n",其中 "w" 是参数的名称,"n" 为自动生成的具有唯一性的后缀。如果为 ``None``,前缀名将为小写的类名。默认为 ``None``。 :type name_scope: str, optional + .. py:property:: matrix() + + 此门的酉矩阵 + + :raises ValueError: 需要在门的实例给出矩阵。 + .. py:method:: gate_history_generation() 生成量子门的历史记录 @@ -47,12 +61,39 @@ paddle\_quantum.gate.base 使用者可以覆写此函数,从而自定义显示方式。 -.. py:class:: ParamGate +.. py:class:: ParamGate(generator, param=None, depth=1, num_acted_param=1, param_sharing=False, qubits_idx=None, gate_info=None, num_qubits=None, check_legality=True, num_acted_qubits=None, backend=None, dtype=None, name_scope=None) 基类::py:class:`paddle_quantum.gate.base.Gate` 可参数化量子门的基类。 + :param generator: 用于产生量子门酉矩阵的函数。 + :type generator: Callable[[Tensor],Tensor] + :param param: 输入参数,默认为 ``None`` i.e. 随机。 + :type param: Union[Tensor,float,List[float]] + :param qubits_idx: 作用在的量子比特的编号。默认为 ``None`` i.e. list(range(num_acted_qubits))。 + :type qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] + :param depth: 层数,默认为 ``1``。 + :type depth: int, optional + :param num_acted_param: 单次操作需要的参数数量。 + :type num_acted_param: int, optional + :param param_sharing: 所有操作是否共享相同的一组参数。 + :type param_sharing: bool + :param gate_info: 量子门的信息,用于信息追溯或者画图。 + :type gate_info: dict, optional + :param num_qubits: 量子比特总数,默认为 ``None`` + :type num_qubits: int + :param check_legality: 表示的完整性校验,默认为 ``True``。 + :type check_legality: bool + :param num_acted_qubits: 量子门作用的量子比特的数量,默认为 ``None``。 + :type num_acted_qubits: int + :param backend: 执行门的后端,默认为 ``None``。 + :type backend: paddle_quantum.Backend, optional + :param dtype: 数据的类型,默认为 ``None``。 + :type dtype: str, optional + :param name_scope: 为 Layer 内部参数命名而采用的名称前缀。如果前缀为 "mylayer",在一个类名为MyLayer的Layer中,参数名为"mylayer_0.w_n",其中 "w" 是参数的名称,"n" 为自动生成的具有唯一性的后缀。如果为 ``None``,前缀名将为小写的类名。默认为 ``None``。 + :type name_scope: str, optional + .. py:method:: theta_generation(param, param_shape) 规范可参数化量子门的输入,并根据输入决定是否要管理或者生成参数 @@ -74,6 +115,18 @@ paddle\_quantum.gate.base .. py:method:: gate_history_generation() - 生成可参数化量子门的历史记录 + 生成量子门的历史记录 + + .. py:method:: display_in_circuit(ax, x) + + 画出量子电路图,在 `Circuit` 类中被调用。 + + :param ax: ``matplotlib.axes.Axes`` 的实例. + :type ax: matplotlib.axes.Axes + :param x: 开始的水平位置。 + :type x: float + + :return: 占用的总宽度。 + :rtype: float diff --git a/docs_zh_CN/source/paddle_quantum.gate.custom.rst b/docs_zh_CN/source/paddle_quantum.gate.custom.rst index fd9d10f..98626f7 100644 --- a/docs_zh_CN/source/paddle_quantum.gate.custom.rst +++ b/docs_zh_CN/source/paddle_quantum.gate.custom.rst @@ -3,7 +3,7 @@ paddle\_quantum.gate.custom 自定义量子门和受控量子门的功能实现。 -.. py:class:: Oracle(oracle, qubits_idx, num_qubits=None, depth=1, gate_name='O') +.. py:class:: Oracle(oracle, qubits_idx, num_qubits=None, depth=1, gate_info=None) 基类::py:class:`paddle_quantum.gate.base.Gate` @@ -17,10 +17,10 @@ paddle\_quantum.gate.custom :type num_qubits: int, optional :param depth: 层数,默认为 ``1``。 :type depth: int, optional - :param gate_name: oracle 的名字,默认为 ``O``。 - :type gate_name: str, optional + :param gate_info: 量子门的信息,用于信息追溯或者画图。 + :type gate_info: dict, optional -.. py:class:: ControlOracle(oracle, qubits_idx, num_qubits=None, depth=1, gate_name='cO') +.. py:class:: ControlOracle(oracle, qubits_idx, num_qubits=None, depth=1, gate_info=None) 基类::py:class:`paddle_quantum.gate.base.Gate` @@ -34,5 +34,28 @@ paddle\_quantum.gate.custom :type num_qubits: int, optional :param depth: 层数,默认为 ``1``。 :type depth: int, optional - :param gate_name: oracle 的名字,默认为 ``cO``。 - :type gate_name: str, optional + :param gate_info: 量子门的信息,用于信息追溯或者画图。 + :type gate_info: dict, optional + +.. py:class:: ParamOracle(generator, param=None, depth=1, num_acted_param=1, param_sharing=False, qubits_idx=None, gate_info=None, num_qubits=None) + + 基类::py:class:`paddle_quantum.gate.base.Gate` + + 一个参数化的 oracle 门。 + + :param oracle: 用于产生 oracle 的函数。 + :type oracle: Callable[[Tensor],Tensor] + :param param: 输入参数,默认为 ``None`` i.e. 随机。 + :type param: Union[Tensor,float,List[float]] + :param qubits_idx: 作用在的量子比特的编号。 + :type qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] + :param depth: 层数,默认为 ``1``。 + :type depth: int, optional + :param num_acted_param: 单次操作需要的参数数量。 + :type num_acted_param: int, optional + :param param_sharing: 所有操作是否共享相同的一组参数。 + :type param_sharing: bool + :param gate_info: 量子门的信息,用于信息追溯或者画图。 + :type gate_info: dict, optional + :param num_qubits: 量子比特总数,默认为 ``None`` + :type num_qubits: int diff --git a/docs_zh_CN/source/paddle_quantum.gate.encoding.rst b/docs_zh_CN/source/paddle_quantum.gate.encoding.rst index b5710b4..73b0e6a 100644 --- a/docs_zh_CN/source/paddle_quantum.gate.encoding.rst +++ b/docs_zh_CN/source/paddle_quantum.gate.encoding.rst @@ -5,7 +5,7 @@ paddle\_quantum.gate.encoding .. py:class:: BasisEncoding(qubits_idx='full', num_qubits=None) - 基类::py:class:`paddle_quantum.gate.base.Gate` + 基类::py:class:`paddle_quantum.base.Operator` 将输入的经典数据编码成量子态的基态编码门。 @@ -19,7 +19,7 @@ paddle\_quantum.gate.encoding .. py:class:: AmplitudeEncoding(qubits_idx='full', num_qubits=None) - 基类::py:class:`paddle_quantum.gate.base.Gate` + 基类::py:class:`paddle_quantum.base.Operator` 将输入的经典数据编码成量子态的振幅编码门。 @@ -30,7 +30,7 @@ paddle\_quantum.gate.encoding .. py:class:: AngleEncoding(feature, qubits_idx='full', num_qubits=None, encoding_gate=None) - 基类::py:class:`paddle_quantum.gate.base.Gate` + 基类::py:class:`paddle_quantum.base.Operator` 将输入的经典数据编码成量子态的角度编码门。 @@ -45,7 +45,7 @@ paddle\_quantum.gate.encoding .. py:class:: IQPEncoding(feature, qubits_idx=None, num_qubits=None, num_repeat=1) - 基类::py:class:`paddle_quantum.gate.base.Gate` + 基类::py:class:`paddle_quantum.base.Operator` 将输入的经典数据编码成量子态的 IQP 编码门。 diff --git a/docs_zh_CN/source/paddle_quantum.gate.functional.base.rst b/docs_zh_CN/source/paddle_quantum.gate.functional.base.rst deleted file mode 100644 index 1ea2b95..0000000 --- a/docs_zh_CN/source/paddle_quantum.gate.functional.base.rst +++ /dev/null @@ -1,21 +0,0 @@ -paddle\_quantum.gate.functional.base -=========================================== - -量子门的基础函数的功能实现。 - -.. py:function:: simulation(state, gate, qubit_idx, num_qubits, backend) - - 在输入态上作用一个量子门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param gate: 要执行的门。 - :type gate: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: Union[int, List[int]] - :param num_qubits: 总的量子比特个数。 - :type num_qubits: int - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle.Tensor diff --git a/docs_zh_CN/source/paddle_quantum.gate.functional.multi_qubit_gate.rst b/docs_zh_CN/source/paddle_quantum.gate.functional.multi_qubit_gate.rst deleted file mode 100644 index 32a9c07..0000000 --- a/docs_zh_CN/source/paddle_quantum.gate.functional.multi_qubit_gate.rst +++ /dev/null @@ -1,309 +0,0 @@ -paddle\_quantum.gate.functional.multi\_qubit\_gate -========================================================= - -多量子比特量子门的函数的功能实现。 - -.. py:function:: cnot(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 CNOT 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: cx(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 CNOT 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: cy(state, qubit_idx, dtype, backend) - - 在输入态上作用一个受控 Y 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: cz(state, qubit_idx, dtype, backend) - - 在输入态上作用一个受控 Z 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: swap(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 SWAP 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: cp(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个受控 P 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: crx(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个关于 x 轴的受控单量子比特旋转门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: cry(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个关于 y 轴的受控单量子比特旋转门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: crz(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个关于 z 轴的受控单量子比特旋转门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: cu(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个受控单量子比特旋转门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: rxx(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个 RXX 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: ryy(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个 RYY 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: rzz(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个 RZZ 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: ms(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 Mølmer-Sørensen (MS) 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: cswap(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 CSWAP (Fredkin) 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: toffoli(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 Toffoli 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: universal_two_qubits(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个两量子比特通用门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: universal_three_qubits(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个三量子比特通用门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: oracle(state, oracle, qubit_idx, backend) - - 在输入态上作用一个 oracle 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param oracle: 要执行的 oracle。 - :type oracle: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: list - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State diff --git a/docs_zh_CN/source/paddle_quantum.gate.functional.rst b/docs_zh_CN/source/paddle_quantum.gate.functional.rst deleted file mode 100644 index 3f13425..0000000 --- a/docs_zh_CN/source/paddle_quantum.gate.functional.rst +++ /dev/null @@ -1,14 +0,0 @@ -paddle\_quantum.gate.functional -======================================= - -不同量子门的函数的功能实现。 - -.. rubric:: Submodules - -.. toctree:: - :maxdepth: 4 - - paddle_quantum.gate.functional.base - paddle_quantum.gate.functional.multi_qubit_gate - paddle_quantum.gate.functional.single_qubit_gate - paddle_quantum.gate.functional.visual diff --git a/docs_zh_CN/source/paddle_quantum.gate.functional.single_qubit_gate.rst b/docs_zh_CN/source/paddle_quantum.gate.functional.single_qubit_gate.rst deleted file mode 100644 index 5c3cfb9..0000000 --- a/docs_zh_CN/source/paddle_quantum.gate.functional.single_qubit_gate.rst +++ /dev/null @@ -1,209 +0,0 @@ -paddle\_quantum.gate.functional.single\_qubit\_gate -========================================================== - -单量子比特量子门的函数的功能实现。 - -.. py:function:: h(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 Hadamard 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: s(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 S 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: sdg(state, qubit_idx, dtype, backend) - - 在输入态上作用一个S dagger(逆S)门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: t(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 T 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: tdg(state, qubit_idx, dtype, backend) - - 在输入态上作用一个T dagger(逆T)门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: x(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 X 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: y(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 Y 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: z(state, qubit_idx, dtype, backend) - - 在输入态上作用一个 Z 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: p(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个 P 门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: rx(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个关于 x 轴的单量子比特旋转门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: ry(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个关于 y 轴的单量子比特旋转门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: rz(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个关于 z 轴的单量子比特旋转门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State - -.. py:function:: u3(state, theta, qubit_idx, dtype, backend) - - 在输入态上作用一个单量子比特旋转门。 - - :param state: 输入态。 - :type state: paddle_quantum.State - :param theta: 量子门参数。 - :type theta: paddle.Tensor - :param qubit_idx: 作用在的量子比特的编号。 - :type qubit_idx: int - :param dtype: 数据的类型。 - :type dtype: str - :param backend: 运行模拟的后端。 - :type backend: paddle_quantum.Backend - :return: 输出态。 - :rtype: paddle_quantum.State diff --git a/docs_zh_CN/source/paddle_quantum.gate.functional.visual.rst b/docs_zh_CN/source/paddle_quantum.gate.functional.visual.rst deleted file mode 100644 index ba5b5e5..0000000 --- a/docs_zh_CN/source/paddle_quantum.gate.functional.visual.rst +++ /dev/null @@ -1,30 +0,0 @@ -paddle\_quantum.gate.functional.visual -======================================= - -可视化 ``paddle_quantum.ansatz.Circuit`` 类中量子门的函数 - -.. py:function:: scale_circuit_plot_param(scale) - - 根据 ``scale`` 修改 ``__CIRCUIT_PLOT_PARAM`` 的字典参数。 - - :param scale: 画图参数的缩放标量。 - :type scale: float - -.. py:function:: set_circuit_plot_param(**kwargs) - - 自定义画图参数字典 ``__CIRCUIT_PLOT_PARAM``。 - - :param kwargs: 需要更新的字典 ``__CIRCUIT_PLOT_PARAM`` 参数。 - :type scale: Any - -.. py:function:: get_circuit_plot_param() - - 输出画图参数字典 ``__CIRCUIT_PLOT_PARAM``。 - - :return: ``__CIRCUIT_PLOT_PARAM`` 字典的拷贝。 - :rtype: dict - -.. py:function:: reset_circuit_plot_param() - - 重置画图参数字典 ``__CIRCUIT_PLOT_PARAM``。 - diff --git a/docs_zh_CN/source/paddle_quantum.gate.layer.rst b/docs_zh_CN/source/paddle_quantum.gate.layer.rst deleted file mode 100644 index 4c9177c..0000000 --- a/docs_zh_CN/source/paddle_quantum.gate.layer.rst +++ /dev/null @@ -1,154 +0,0 @@ -paddle\_quantum.gate.layer -================================= - -量子电路模板的功能实现。 - -.. py:function:: qubits_idx_filter(qubits_idx, num_qubits) - - 检查 ``qubits_idx`` 与 ``num_qubits`` 是否合法。 - - :param qubits_idx: 量子比特的编号。 - :type qubits_idx: Union[Iterable[int], str] - :param num_qubits: 总的量子比特个数。 - :type num_qubits: int - :raises RuntimeError: 须声明 ``qubits_idx`` 或 ``num_qubits`` 以实例化类。 - :raises ValueError: ``qubits_idx`` 须为 ``Iterable`` 或 ``'full'``。 - :return: 检查过的量子比特的编号。 - :rtype: List[Iterable[int]] - -.. py:class:: SuperpositionLayer(qubits_idx='full', num_qubits=None, depth=1) - - 基类::py:class:`paddle_quantum.gate.base.Gate` - - Hadamard 门组成的层。 - - :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 - :type qubits_idx: Union[Iterable[int], str], optional - :param num_qubits: 总的量子比特个数,默认为 ``None``。 - :type num_qubits: int, optional - :param depth: 层数,默认为 ``1``。 - :type depth: int, optional - -.. py:class:: WeakSuperpositionLayer(qubits_idx='full', num_qubits=None, depth=1) - - 基类::py:class:`paddle_quantum.gate.base.Gate` - - 转角度为 :math:`\pi/4` 的 Ry 门组成的层。 - - :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 - :type qubits_idx: Union[Iterable[int], str], optional - :param num_qubits: 总的量子比特个数,默认为 ``None``。 - :type num_qubits: int, optional - :param depth: 层数,默认为 ``1``。 - :type depth: int, optional - -.. py:class:: LinearEntangledLayer(qubits_idx='full', num_qubits=None, depth=1) - - 基类::py:class:`paddle_quantum.gate.base.Gate` - - 包含 Ry 门、Rz 门,和 CNOT 门的线性纠缠层。 - - :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 - :type qubits_idx: Union[Iterable[int], str], optional - :param num_qubits: 总的量子比特个数,默认为 ``None``。 - :type num_qubits: int, optional - :param depth: 层数,默认为 ``1``。 - :type depth: int, optional - -.. py:class:: RealEntangledLayer(qubits_idx='full', num_qubits=None, depth=1) - - 基类::py:class:`paddle_quantum.gate.base.Gate` - - 包含 Ry 门和 CNOT 门的强纠缠层。 - - .. note:: - - 这一层量子门的数学表示形式为实数酉矩阵。电路模板来自论文:https://arxiv.org/pdf/1905.10876.pdf。 - - :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 - :type qubits_idx: Union[Iterable[int], str], optional - :param num_qubits: 总的量子比特个数,默认为 ``None``。 - :type num_qubits: int, optional - :param depth: 层数,默认为 ``1``。 - :type depth: int, optional - -.. py:class:: ComplexEntangledLayer(qubits_idx='full', num_qubits=None, depth=1) - - 基类::py:class:`paddle_quantum.gate.base.Gate` - - 包含 U3 门和 CNOT 门的强纠缠层。 - - .. note:: - - 这一层量子门的数学表示形式为复数酉矩阵。电路模板来自论文:https://arxiv.org/abs/1804.00633。 - - :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 - :type qubits_idx: Union[Iterable[int], str], optional - :param num_qubits: 总的量子比特个数,默认为 ``None``。 - :type num_qubits: int, optional - :param depth: 层数,默认为 ``1``。 - :type depth: int, optional - -.. py:class:: RealBlockLayer(qubits_idx='full', num_qubits=None, depth=1) - - 基类::py:class:`paddle_quantum.gate.base.Gate` - - 包含 Ry 门和 CNOT 门的弱纠缠层。 - - .. note:: - - 这一层量子门的数学表示形式为实数酉矩阵。 - - :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 - :type qubits_idx: Union[Iterable[int], str], optional - :param num_qubits: 总的量子比特个数,默认为 ``None``。 - :type num_qubits: int, optional - :param depth: 层数,默认为 ``1``。 - :type depth: int, optional - -.. py:class:: ComplexBlockLayer(qubits_idx='full', num_qubits=None, depth=1) - - 基类::py:class:`paddle_quantum.gate.base.Gate` - - 包含 U3 门和 CNOT 门的弱纠缠层。 - - .. note:: - - 这一层量子门的数学表示形式为复数酉矩阵。 - - :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 - :type qubits_idx: Union[Iterable[int], str], optional - :param num_qubits: 总的量子比特个数,默认为 ``None``。 - :type num_qubits: int, optional - :param depth: 层数,默认为 ``1``。 - :type depth: int, optional - -.. py:class:: QAOALayer(Gate) - - 基类::py:class:`paddle_quantum.gate.base.Gate` - - QAOA 驱动层 - - .. note:: - - 仅支持 MaxCut 问题 - - :param edges: 图的边 - :type edges: Iterable - :param nodes: 图的节点 - :type nodes: Iterable - :param depth: 层数,默认为 ``1``。 - :type depth: int, optional - -.. py:class:: QAOALayerWeighted(Gate) - - 基类::py:class:`paddle_quantum.gate.base.Gate` - - 带权重的 QAOA 驱动层 - - :param edges: 带权重的图的边 - :type edges: Dict[Tuple[int, int], float] - :param nodes: 带权重的图的节点 - :type nodes: Dict[int, float] - :param depth: 层数,默认为 ``1``。 - :type depth: int, optional diff --git a/docs_zh_CN/source/paddle_quantum.gate.matrix.rst b/docs_zh_CN/source/paddle_quantum.gate.matrix.rst new file mode 100644 index 0000000..4731c44 --- /dev/null +++ b/docs_zh_CN/source/paddle_quantum.gate.matrix.rst @@ -0,0 +1,601 @@ +paddle\_quantum.gate.matrix +=============================================== + +门的矩阵实现。 + +以下是单比特量子门的矩阵。 + +.. py:function:: h_gate(dtype=None) + + 生成矩阵 + + .. math:: + + \begin{align} + H = \frac{1}{\sqrt{2}} + \begin{bmatrix} + 1&1\\ + 1&-1 + \end{bmatrix} + \end{align} + + + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: H 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: s_gate(dtype=None) + + 生成矩阵 + + .. math:: + + \begin{align} + S = + \begin{bmatrix} + 1&0\\ + 0&i + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: S 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: sdg_gate(dtype=None) + + 生成矩阵 + + .. math:: + + \begin{align} + S^\dagger = + \begin{bmatrix} + 1&0\\ + 0&-i + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: :math:`S^\dagger` 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: t_gate(dtype=None) + + 生成矩阵 + + .. math:: + + \begin{align} + T = + \begin{bmatrix} + 1&0\\ + 0&e^\frac{i\pi}{4} + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: T 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: tdg_gate(dtype=None) + + 生成矩阵 + + .. math:: + + \begin{align} + T^\dagger = + \begin{bmatrix} + 1&0\\ + 0&e^{-\frac{i\pi}{4}} + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: :math:`T^\dagger` 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: x_gate(dtype=None) + + 生成矩阵 + + .. math:: + + \begin{align} + X = + \begin{bmatrix} + 0&1\\ + 1&0 + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: X 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: y_gate(dtype=None) + + 生成矩阵 + + .. math:: + + \begin{align} + Y = + \begin{bmatrix} + 0&-i\\ + i&0 + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: Y 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: z_gate(dtype=None) + + 生成矩阵 + + .. math:: + + \begin{align} + Z = + \begin{bmatrix} + 1&0\\ + 0&-1 + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: Z 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: p_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + P = + \begin{bmatrix} + 1 & 0 \\ + 0 & e^{i\theta} + \end{bmatrix} + \end{align} + + :param theta: P 门的参数。 + :type theta: paddle.Tensor + :return: P 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: rx_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + R_X = + \begin{bmatrix} + \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ + -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + :param theta: :math:`R_X` 门的参数。 + :type theta: paddle.Tensor + :return: :math:`R_X` 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: ry_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + R_Y = + \begin{bmatrix} + \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ + \sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + :param theta: :math:`R_Y` 门的参数。 + :type theta: paddle.Tensor + :return: :math:`R_Y` 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: rz_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + R_Z = + \begin{bmatrix} + e^{-i\frac{\theta}{2}} & 0 \\ + 0 & e^{i\frac{\theta}{2}} + \end{bmatrix} + \end{align} + + :param theta: :math:`R_Z` 门的参数。 + :type theta: paddle.Tensor + :return: :math:`R_Z` 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: u3_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + U_3(\theta, \phi, \lambda) = + \begin{bmatrix} + \cos\frac\theta2&-e^{i\lambda}\sin\frac\theta2\\ + e^{i\phi}\sin\frac\theta2&e^{i(\phi+\lambda)}\cos\frac\theta2 + \end{bmatrix} + \end{align} + + :param theta: :math:`U_3` 门的参数。 + :type theta: paddle.Tensor + :return: :math:`U_3` 门的矩阵。 + :rtype: paddle.Tensor + +以下是多量子比特门的矩阵 + +.. py:function:: cnot_gate(dtype) + + 生成矩阵 + + .. math:: + + \begin{align} + CNOT &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes X\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 \\ + 0 & 0 & 1 & 0 + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: CNOT 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: cy_gate(dtype) + + 生成矩阵 + + .. math:: + + \begin{align} + CY &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Y\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & -i \\ + 0 & 0 & i & 0 + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: CY 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: cz_gate(dtype) + + 生成矩阵 + + .. math:: + + \begin{align} + CZ &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Z\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & -1 + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: CZ 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: swap_gate(dtype) + + 生成矩阵 + + .. math:: + + \begin{align} + SWAP = + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: SWAP 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: cp_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + CP = + \begin{bmatrix} + 1 & 0 & 0 & 0\\ + 0 & 1 & 0 & 0\\ + 0 & 0 & 1 & 0\\ + 0 & 0 & 0 & e^{i\theta} + \end{bmatrix} + \end{align} + + :param theta: CP 门的参数。 + :type theta: paddle.Tensor + :return: CP 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: crx_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + CR_X &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes R_X\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ + 0 & 0 & -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + :param theta: :math:`CR_X` 门的参数。 + :type theta: paddle.Tensor + :return: :math:`CR_X` 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: cry_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + CR_Y &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes R_Y\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ + 0 & 0 & \sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + :param theta: :math:`CR_Y` 门的参数。 + :type theta: paddle.Tensor + :return: :math:`CR_Y` 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: crz_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + CR_Z &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes R_Z\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ + 0 & 0 & \sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + :param theta: :math:`CR_Z` 门的参数。 + :type theta: paddle.Tensor + :return: :math:`CR_Z` 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: cu_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + CU + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & \cos\frac\theta2 &-e^{i\lambda}\sin\frac\theta2 \\ + 0 & 0 & e^{i\phi}\sin\frac\theta2&e^{i(\phi+\lambda)}\cos\frac\theta2 + \end{bmatrix} + \end{align} + + :param theta: CU 门的参数。 + :type theta: paddle.Tensor + :return: CU 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: rxx_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + RXX(\theta) = + \begin{bmatrix} + \cos\frac{\theta}{2} & 0 & 0 & -i\sin\frac{\theta}{2} \\ + 0 & \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} & 0 \\ + 0 & -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} & 0 \\ + -i\sin\frac{\theta}{2} & 0 & 0 & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + :param theta: RXX 门的参数。 + :type theta: paddle.Tensor + :return: RXX 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: ryy_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + RYY(\theta) = + \begin{bmatrix} + \cos\frac{\theta}{2} & 0 & 0 & i\sin\frac{\theta}{2} \\ + 0 & \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} & 0 \\ + 0 & -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} & 0 \\ + i\sin\frac{\theta}{2} & 0 & 0 & cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + :param theta: RYY 门的参数。 + :type theta: paddle.Tensor + :return: RYY 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: rzz_gate(theta) + + 生成矩阵 + + .. math:: + + \begin{align} + RZZ(\theta) = + \begin{bmatrix} + e^{-i\frac{\theta}{2}} & 0 & 0 & 0 \\ + 0 & e^{i\frac{\theta}{2}} & 0 & 0 \\ + 0 & 0 & e^{i\frac{\theta}{2}} & 0 \\ + 0 & 0 & 0 & e^{-i\frac{\theta}{2}} + \end{bmatrix} + \end{align} + + :param theta: RZZ 门的参数。 + :type theta: paddle.Tensor + :return: RZZ 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: ms_gate(dtype) + + 生成矩阵 + + .. math:: + + \begin{align} + \mathit{MS} = \mathit{R_{XX}}(-\frac{\pi}{2}) = \frac{1}{\sqrt{2}} + \begin{bmatrix} + 1 & 0 & 0 & i \\ + 0 & 1 & i & 0 \\ + 0 & i & 1 & 0 \\ + i & 0 & 0 & 1 + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: MS 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: cswap_gate(dtype) + + 生成矩阵 + + .. math:: + + \begin{align} + CSWAP = + \begin{bmatrix} + 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: CSWAP 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: toffoli_gate(dtype) + + 生成矩阵 + + .. math:: + + \begin{align} + Toffoli = + \begin{bmatrix} + 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 + \end{bmatrix} + \end{align} + + :param dtype: 此矩阵的类型,默认值为 ``'None'``。 + :type dtype: str, optional + :return: Toffoli 门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: universal2_gate(theta) + + :param theta: 两量子比特通用门参数。 + :type theta: paddle.Tensor + :return: 两量子比特通用门的矩阵。 + :rtype: paddle.Tensor + +.. py:function:: universal3_gate(theta) + + :param theta: 三量子比特通用门参数。 + :type theta: paddle.Tensor + :return: 三量子比特通用门的矩阵。 + :rtype: paddle.Tensor diff --git a/docs_zh_CN/source/paddle_quantum.gate.multi_qubit_gate.rst b/docs_zh_CN/source/paddle_quantum.gate.multi_qubit_gate.rst index 59e3512..a53b340 100644 --- a/docs_zh_CN/source/paddle_quantum.gate.multi_qubit_gate.rst +++ b/docs_zh_CN/source/paddle_quantum.gate.multi_qubit_gate.rst @@ -60,8 +60,8 @@ paddle\_quantum.gate.multi\_qubit\_gate \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ - 0 & 0 & 0 & -1j \\ - 0 & 0 & 1j & 0 + 0 & 0 & 0 & -i \\ + 0 & 0 & i & 0 \end{bmatrix} \end{align} @@ -137,12 +137,15 @@ paddle\_quantum.gate.multi\_qubit\_gate .. math:: - \begin{bmatrix} - 1 & 0 & 0 & 0\\ - 0 & 1 & 0 & 0\\ - 0 & 0 & 1 & 0\\ - 0 & 0 & 0 & e^{i\theta} - \end{bmatrix} + \begin{align} + CP = + \begin{bmatrix} + 1 & 0 & 0 & 0\\ + 0 & 1 & 0 & 0\\ + 0 & 0 & 1 & 0\\ + 0 & 0 & 0 & e^{i\theta} + \end{bmatrix} + \end{align} :param qubits_idx: 作用在的量子比特的编号,默认为 ``'cycle'``。 :type qubits_idx: Union[Iterable, str], optional @@ -167,7 +170,7 @@ paddle\_quantum.gate.multi\_qubit\_gate .. math:: \begin{align} - CRx &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Rx\\ + CR_X &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes R_X\\ &= \begin{bmatrix} 1 & 0 & 0 & 0 \\ @@ -200,7 +203,7 @@ paddle\_quantum.gate.multi\_qubit\_gate .. math:: \begin{align} - CRy &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Ry\\ + CR_Y &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes R_Y\\ &= \begin{bmatrix} 1 & 0 & 0 & 0 \\ @@ -233,7 +236,7 @@ paddle\_quantum.gate.multi\_qubit\_gate .. math:: \begin{align} - CRz &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Rz\\ + CR_Z &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes R_Z\\ &= \begin{bmatrix} 1 & 0 & 0 & 0 \\ @@ -453,6 +456,7 @@ paddle\_quantum.gate.multi\_qubit\_gate .. math:: \begin{align} + Toffoli = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ diff --git a/docs_zh_CN/source/paddle_quantum.gate.rst b/docs_zh_CN/source/paddle_quantum.gate.rst index a198249..4cdd8d3 100644 --- a/docs_zh_CN/source/paddle_quantum.gate.rst +++ b/docs_zh_CN/source/paddle_quantum.gate.rst @@ -3,13 +3,6 @@ paddle\_quantum.gate 量子门的功能实现。 -.. rubric:: Subpackages - -.. toctree:: - :maxdepth: 4 - - paddle_quantum.gate.functional - .. rubric:: Submodules .. toctree:: @@ -19,6 +12,6 @@ paddle\_quantum.gate paddle_quantum.gate.clifford paddle_quantum.gate.custom paddle_quantum.gate.encoding - paddle_quantum.gate.layer + paddle_quantum.gate.matrix paddle_quantum.gate.multi_qubit_gate paddle_quantum.gate.single_qubit_gate diff --git a/docs_zh_CN/source/paddle_quantum.gate.single_qubit_gate.rst b/docs_zh_CN/source/paddle_quantum.gate.single_qubit_gate.rst index 9866d32..a18dbae 100644 --- a/docs_zh_CN/source/paddle_quantum.gate.single_qubit_gate.rst +++ b/docs_zh_CN/source/paddle_quantum.gate.single_qubit_gate.rst @@ -12,12 +12,14 @@ paddle\_quantum.gate.single\_qubit\_gate 其矩阵形式为: .. math:: - - H = \frac{1}{\sqrt{2}} + + \begin{align} + H = \frac{1}{\sqrt{2}} \begin{bmatrix} 1&1\\ 1&-1 \end{bmatrix} + \end{align} :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional @@ -36,11 +38,13 @@ paddle\_quantum.gate.single\_qubit\_gate .. math:: - S = + \begin{align} + S = \begin{bmatrix} 1&0\\ 0&i \end{bmatrix} + \end{align} :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional @@ -53,23 +57,25 @@ paddle\_quantum.gate.single\_qubit\_gate 基类::py:class:`paddle_quantum.gate.base.Gate` - 单量子比特S dagger(逆S)门。 + 单量子比特:math: S^\dagger(逆S)门。 其矩阵形式为: .. math:: - S ^\dagger = - \begin{bmatrix} - 1 & 0\ \ - 0 & -i - \end{bmatrix} + \begin{align} + S ^\dagger = + \begin{bmatrix} + 1 & 0\\ + 0 & -i + \end{bmatrix} + \end{align} - :param qubits_idx:作用在的量子比特的编号,默认为``'full'``。 + :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional - :param num_qubits:总的量子比特个数,默认为``None``。 + :param num_qubits: 总的量子比特个数,默认为 ``None``。 :type num_qubits: int, optional - :param depth: 层数,默认为``1``。 + :param depth: 层数,默认为 ``1``。 :type depth: int, optional .. py:class:: T(qubits_idx='full', num_qubits=None, depth=1) @@ -82,12 +88,14 @@ paddle\_quantum.gate.single\_qubit\_gate .. math:: - T = + \begin{align} + T = \begin{bmatrix} 1&0\\ 0&e^\frac{i\pi}{4} \end{bmatrix} - + \end{align} + :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional :param num_qubits: 总的量子比特个数,默认为 ``None``。 @@ -99,23 +107,25 @@ paddle\_quantum.gate.single\_qubit\_gate 基类::py:class:`paddle_quantum.gate.base.Gate` - 单量子比特T dagger(逆T)门。 + 单量子比特:math: T^\dagger(逆T)门。 其矩阵形式为: .. math:: - T ^\dagger = - \begin{bmatrix} - 1 & 0\ \ - 0 & e^{-\frac{i\pi}{4}} - \end{bmatrix} + \begin{align} + T ^\dagger = + \begin{bmatrix} + 1 & 0\\ + 0 & e^{-\frac{i\pi}{4}} + \end{bmatrix} + \end{align} - :param qubits_idx:作用在的量子比特的编号,默认为``'full'``。 + :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional - :param num_qubits:总的量子比特个数,默认为``None``。 + :param num_qubits: 总的量子比特个数,默认为 ``None``。 :type num_qubits: int, optional - :param depth: 层数,默认为``1``。 + :param depth: 层数,默认为 ``1``。 :type depth: int, optional .. py:class:: X(qubits_idx='full', num_qubits=None, depth=1) @@ -128,10 +138,13 @@ paddle\_quantum.gate.single\_qubit\_gate .. math:: - \begin{bmatrix} - 0 & 1 \\ - 1 & 0 - \end{bmatrix} + \begin{align} + X = + \begin{bmatrix} + 0 & 1 \\ + 1 & 0 + \end{bmatrix} + \end{align} :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional @@ -150,10 +163,13 @@ paddle\_quantum.gate.single\_qubit\_gate .. math:: - \begin{bmatrix} - 0 & -i \\ - i & 0 - \end{bmatrix} + \begin{align} + Y = + \begin{bmatrix} + 0 & -i \\ + i & 0 + \end{bmatrix} + \end{align} :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional @@ -172,10 +188,13 @@ paddle\_quantum.gate.single\_qubit\_gate .. math:: - \begin{bmatrix} - 1 & 0 \\ - 0 & -1 - \end{bmatrix} + \begin{align} + Z = + \begin{bmatrix} + 1 & 0 \\ + 0 & -1 + \end{bmatrix} + \end{align} :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional @@ -194,10 +213,13 @@ paddle\_quantum.gate.single\_qubit\_gate .. math:: - \begin{bmatrix} - 1 & 0 \\ - 0 & e^{i\theta} - \end{bmatrix} + \begin{align} + P = + \begin{bmatrix} + 1 & 0 \\ + 0 & e^{i\theta} + \end{bmatrix} + \end{align} :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional @@ -221,10 +243,13 @@ paddle\_quantum.gate.single\_qubit\_gate .. math:: - \begin{bmatrix} - \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ - -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} - \end{bmatrix} + \begin{align} + R_X = + \begin{bmatrix} + \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ + -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional @@ -248,10 +273,13 @@ paddle\_quantum.gate.single\_qubit\_gate .. math:: - \begin{bmatrix} - \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ - \sin\frac{\theta}{2} & \cos\frac{\theta}{2} - \end{bmatrix} + \begin{align} + R_Y = + \begin{bmatrix} + \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ + \sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional @@ -275,10 +303,13 @@ paddle\_quantum.gate.single\_qubit\_gate .. math:: - \begin{bmatrix} - e^{-i\frac{\theta}{2}} & 0 \\ - 0 & e^{i\frac{\theta}{2}} - \end{bmatrix} + \begin{align} + R_Z = + \begin{bmatrix} + e^{-i\frac{\theta}{2}} & 0 \\ + 0 & e^{i\frac{\theta}{2}} + \end{bmatrix} + \end{align} :param qubits_idx: 作用在的量子比特的编号,默认为 ``'full'``。 :type qubits_idx: Union[Iterable, int, str], optional @@ -303,7 +334,7 @@ paddle\_quantum.gate.single\_qubit\_gate .. math:: \begin{align} - U3(\theta, \phi, \lambda) = + U_3(\theta, \phi, \lambda) = \begin{bmatrix} \cos\frac\theta2&-e^{i\lambda}\sin\frac\theta2\\ e^{i\phi}\sin\frac\theta2&e^{i(\phi+\lambda)}\cos\frac\theta2 diff --git a/docs_zh_CN/source/paddle_quantum.linalg.rst b/docs_zh_CN/source/paddle_quantum.linalg.rst index c961c2a..aa024eb 100644 --- a/docs_zh_CN/source/paddle_quantum.linalg.rst +++ b/docs_zh_CN/source/paddle_quantum.linalg.rst @@ -47,6 +47,39 @@ paddle\_quantum.linalg :return: 决定是否 :math:`P` 为厄密矩阵且本征值均为非负实数 :rtype: bool +.. py:function:: is_state_vector(vec, eps=1e-6) + + 验证 ``vec`` 是否为合法的态向量 + + :param vec: 候选态向量 + :type vec: Union[np.ndarray,paddle.Tensor] + :param eps: 容错率,默认为 ``None`` i.e. 不做判定 + :type eps: float, optional + + :return: 判断候选态向量是否归一,返回量子比特数量或错误信息 + :rtype: Tuple[bool,int] + + .. note:: + + 错误信息为 ``-1`` 时,候选量子态未归一;错误信息为 ``-2`` 时,候选量子态维度不是2的整数次方;错误信息为 ``-3`` 时, ``vec`` 不是向量。 + +.. py:function:: is_density_matrix(rho, eps=None) + + 验证 ``rho`` 是否为合法的密度矩阵 + + :param rho: 候选密度矩阵 + :type rho: Union[np.ndarray,paddle.Tensor] + :param eps: 容错率,默认为 ``None`` i.e. 不做判定 + :type eps: float, optional + + :return: 判断候选密度矩阵是否为迹数为1的半正定矩阵,返回量子比特数量或错误信息 + :rtype: Tuple[bool,int] + + .. note:: + + 错误信息为 ``-1`` 时,候选密度矩阵不是半正定矩阵;错误信息为 ``-2`` 时,候选密度矩阵迹数不为1;错误信息为 ``-3`` 时,候选密度矩阵维度不是2的整数次方;错误信息为 ``-4`` 时, ``rho`` 不是方阵。 + + .. py:function:: is_projector(mat, eps=1e-6) 验证矩阵 ``P`` 是否为映射算子 @@ -217,7 +250,8 @@ paddle\_quantum.linalg .. code-block:: python - from paddle_quantum.linalg import density_op_random, NKron + from paddle_quantum.state import density_op_random + from paddle_quantum.linalg import NKron A = density_op_random(2) B = density_op_random(2) C = density_op_random(2) diff --git a/docs_zh_CN/source/paddle_quantum.loss.measure.rst b/docs_zh_CN/source/paddle_quantum.loss.measure.rst index 416e719..49b9af8 100644 --- a/docs_zh_CN/source/paddle_quantum.loss.measure.rst +++ b/docs_zh_CN/source/paddle_quantum.loss.measure.rst @@ -3,7 +3,7 @@ paddle\_quantum.loss.measure 测量的损失函数的功能实现。 -.. py:class:: ExpecVal(hamiltonian, shots) +.. py:class:: ExpecVal(hamiltonian, shots=0) 基类::py:class:`paddle_quantum.Operator` @@ -16,7 +16,7 @@ paddle\_quantum.loss.measure :param shots: 测量的次数。默认是 ``0``,使用解析解。只有当后端为 QuLeaf 时,才需要指定该参数。 :type shots: int, optional - .. py:method:: forward(state) + .. py:method:: forward(state, decompose=False) 计算可观测量对于输入的量子态的期望值。 @@ -24,6 +24,8 @@ paddle\_quantum.loss.measure :param state: 输入量子态,它将被用来计算期望值。 :type state: paddle_quantum.State + :param decompose: 输出每项可观测量的期望值。默认为 ``False``,表示返回输入量子态的期望值之和。 + :type decompose: bool, optional :raises NotImplementedError: 所指定的后端必须为量桨已经实现的后端。 :return: 计算得到的期望值,如果后端是 QuLeaf,则返回根据采样计算的到的结果。 :rtype: paddle.Tensor diff --git a/docs_zh_CN/source/paddle_quantum.mbqc.mcalculus.rst b/docs_zh_CN/source/paddle_quantum.mbqc.mcalculus.rst new file mode 100644 index 0000000..55eb20b --- /dev/null +++ b/docs_zh_CN/source/paddle_quantum.mbqc.mcalculus.rst @@ -0,0 +1,56 @@ +paddle\_quantum.mbqc.mcalculus +=================================== + +此模块包含处理 MBQC 测量模式的相关操作。 + +.. py:class:: MCalculus() + + 基类:``object`` + + 定义测量模式类。 + + 跟据文献 [The measurement calculus, arXiv: 0704.1263] 的测量语言,该类提供处理测量模式的各种基本操作。 + + .. py:method:: track_progress(track) + + 显示测量模式处理过程的进度条开关。 + + :param track: ``True`` 为打开进度条显示,``False`` 为关闭进度条显示,默认为 ``True`` + :type track: Optional[bool] + + .. py:method:: set_circuit(circuit) + + 对 ``MCalculus`` 类设置量子电路。 + + :param circuit: 量子电路 + :type circuit: Circuit + + .. py:method:: standardize() + + 对测量模式进行标准化。 + + 该方法对测量模式进行标准化操作,转化成等价的 EMC 模型。即将所有的 ``CommandE`` 交换到最前面,其次是 ``CommandM``, ``CommandX`` 和 ``CommandZ``。为了简化测量模式,该方法在标准化各类命令之后还对 ``CommandM`` 进行 Pauli 简化。 + + .. py:method:: shift_signals() + + 信号转移操作。 + + .. note:: + + 这是用户选择性调用的方法之一。 + + .. py:method:: get_pattern() + + 返回测量模式。 + + :return: 处理后的测量模式 + :rtype: Pattern + + .. py:method:: optimize_by_row() + + 按照行序优先的原则对测量模式中的测量顺序进行优化。 + + .. warning:: + + 这是一种启发式的优化算法,对于特定的测量模式可以起到优化测量顺序的作用,不排除存在更优的测量顺序。例如,对于浅层量子电路, + 按照行序优先原则,测量完同一量子位上的量子门、测量对应的节点后,该量子位不再起作用,进而减少后续计算时可能涉及到的节点数目。 diff --git a/docs_zh_CN/source/paddle_quantum.mbqc.qobject.rst b/docs_zh_CN/source/paddle_quantum.mbqc.qobject.rst index bb69cd7..fa219e3 100644 --- a/docs_zh_CN/source/paddle_quantum.mbqc.qobject.rst +++ b/docs_zh_CN/source/paddle_quantum.mbqc.qobject.rst @@ -1,2 +1,696 @@ paddle\_quantum.mbqc.qobject ============================ + +此模块包含量子信息处理的常用对象,如量子态、量子电路、测量模式等。 + +.. py:class:: State(vector, system) + :noindex: + + 基类:``object`` + + 定义量子态。 + + :param vector: 量子态的列向量 + :type vector: Optional[paddle.Tensor] + :param system: 量子态的系统标签列表 + :type system: Optional[list] + +.. py:class:: Circuit(width) + :noindex: + + 基类:``object`` + + 定义量子电路。 + + :param width: 电路的宽度(比特数) + :type width: int + + .. warning:: + + 当前版本仅支持 ``H, X, Y, Z, S, T, Rx, Ry, Rz, Rz_5, U, CNOT, CNOT_15, CZ`` 中的量子门以及测量操作。 + + .. py:method:: h(which_qubit) + :noindex: + + 添加 ``Hadamard`` 门。 + + 其矩阵形式为: + + .. math:: + + \frac{1}{\sqrt{2}}\begin{bmatrix} 1&1\\1&-1 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + cir.h(which_qubit) + print(cir.get_circuit()) + + :: + + [['h', [0], None]] + + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: x(which_qubit) + :noindex: + + 添加 ``Pauli X`` 门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + cir.x(which_qubit) + print(cir.get_circuit()) + + :: + + [['x', [0], None]] + + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: y(which_qubit) + :noindex: + + 添加 ``Pauli Y`` 门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + cir.y(which_qubit) + print(cir.get_circuit()) + + :: + + [['y', [0], None]] + + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: z(which_qubit) + :noindex: + + 添加 ``Pauli Z`` 门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + cir.z(which_qubit) + print(cir.get_circuit()) + + :: + + [['z', [0], None]] + + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: s(which_qubit) + :noindex: + + 添加 ``S`` 门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1&0\\0& i \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + cir.s(which_qubit) + print(cir.get_circuit()) + + :: + + [['s', [0], None]] + + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: t(which_qubit) + :noindex: + + 添加 ``T`` 门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1&0\\0& e^{i\pi/ 4} \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + cir.t(which_qubit) + print(cir.get_circuit()) + + :: + + [['t', [0], None]] + + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: rx(theta, which_qubit) + :noindex: + + 添加关于 x 轴的旋转门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle import to_tensor + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + angle = to_tensor([1], dtype='float64') + cir.rx(angle, which_qubit) + print(cir.get_circuit()) + + :: + + [['rx', [0], Tensor(shape=[1], dtype=float64, place=CPUPlace, stop_gradient=True, [1.])]] + + :param theta: 旋转角度 + :type theta: paddle.Tensor + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: ry(theta, which_qubit) + :noindex: + + 添加关于 y 轴的旋转门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ \sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle import to_tensor + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + angle = to_tensor([1], dtype='float64') + cir.ry(angle, which_qubit) + print(cir.get_circuit()) + + :: + + [['ry', [0], Tensor(shape=[1], dtype=float64, place=CPUPlace, stop_gradient=True, [1.])]] + + :param theta: 旋转角度 + :type theta: paddle.Tensor + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: rz(theta, which_qubit) + :noindex: + + 添加关于 z 轴的旋转门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 \\ 0 & e^{i\theta} \end{bmatrix} + + + 代码示例: + + .. code-block:: python + + from paddle import to_tensor + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + angle = to_tensor([1], dtype='float64') + cir.rz(angle, which_qubit) + print(cir.get_circuit()) + + :: + + [['rz', [0], Tensor(shape=[1], dtype=float64, place=CPUPlace, stop_gradient=True, [1.])]] + + :param theta: 旋转角度 + :type theta: paddle.Tensor + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: rz_5(theta, which_qubit) + :noindex: + + 添加关于 z 轴的旋转门(该旋转门对应的测量模式由五个量子比特构成)。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 \\ 0 & e^{i\theta} \end{bmatrix} + + + 代码示例: + + .. code-block:: python + + from paddle import to_tensor + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + angle = to_tensor([1], dtype='float64') + cir.rz(angle, which_qubit) + print(cir.get_circuit()) + + :: + + [['rz_5', [0], Tensor(shape=[1], dtype=float64, place=CPUPlace, stop_gradient=True, [1.])]] + + :param theta: 旋转角度 + :type theta: paddle.Tensor + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: u(params, which_qubit) + + 添加单量子比特的任意酉门。 + + .. warning:: + + 这里的酉门采用 ``Rz Rx Rz`` 分解, + + 其分解形式为: + + .. math:: + + U(\alpha, \beta, \gamma) = Rz(\gamma) Rx(\beta) Rz(\alpha) + + 代码示例: + + .. code-block:: python + + from paddle import to_tensor + from numpy import pi + from paddle_quantum.mbqc.qobject import Circuit + width = 1 + cir = Circuit(width) + which_qubit = 0 + alpha = to_tensor([pi / 2], dtype='float64') + beta = to_tensor([pi], dtype='float64') + gamma = to_tensor([- pi / 2], dtype='float64') + cir.u([alpha, beta, gamma], which_qubit) + print(cir.get_circuit()) + + :: + + [['u', [0], [Tensor(shape=[1], dtype=float64, place=CPUPlace, stop_gradient=True, + [1.57079633]), Tensor(shape=[1], dtype=float64, place=CPUPlace, stop_gradient=True, + [3.14159265]), Tensor(shape=[1], dtype=float64, place=CPUPlace, stop_gradient=True, + [-1.57079633])]]] + + :param params: 单比特酉门的三个旋转角度 + :type params: List[paddle.Tensor] + :param which_qubit: 作用量子门的量子位编号 + :type which_qubit: int + + .. py:method:: cnot(which_qubits) + :noindex: + + 添加控制非门。 + + 当 ``which_qubits`` 为 ``[0, 1]`` 时,其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + width = 2 + cir = Circuit(width) + which_qubits = [0, 1] + cir.cnot(which_qubits) + print(cir.get_circuit()) + :: + + [['cnot', [0, 1], None]] + + :param which_qubits: 作用量子门的量子位,其中列表第一个元素为控制位,第二个元素为受控位 + :type which_qubits: List[int] + + .. py:method:: cnot_15(which_qubits) + + 添加控制非门(该门对应的测量模式由十五个量子比特构成)。 + + 当 ``which_qubits`` 为 ``[0, 1]`` 时,其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + width = 2 + cir = Circuit(width) + which_qubits = [0, 1] + cir.cnot_15(which_qubits) + print(cir.get_circuit()) + :: + + [['cnot_15', [0, 1], None]] + + :param which_qubits: 作用量子门的量子位,其中列表第一个元素为控制位,第二个元素为受控位 + :type which_qubits: List[int] + + .. py:method:: cz(which_qubits) + :noindex: + + 添加控制 Z 门。 + + 当 ``which_qubits`` 为 ``[0, 1]`` 时,其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + width = 2 + cir = Circuit(width) + which_qubits = [0, 1] + cir.cz(which_qubits) + print(cir.get_circuit()) + :: + + [['cz', [0, 1], None]] + + :param which_qubits: 作用量子门的量子位,其中列表第一个元素为控制位,第二个元素为受控位 + :type which_qubits: List[int] + + .. py:method:: measure(which_qubit, basis_list) + + 对量子电路输出的量子态进行测量。 + + .. note:: + + 除默认的 Z 测量外,此处的测量方式可以由用户自定义,但需要将测量方式与测量比特相对应。 + + .. warning:: + + 此方法只接受三种输入方式: + 1. 不输入任何参数,表示对所有的量子位进行 Z 测量; + 2. 输入量子位,但不输入测量基,表示对输入的量子位进行 Z 测量; + 3. 输入量子位和对应测量基,表示对输入量子位进行指定的测量。 + 如果用户希望自定义测量基参数,需要注意输入格式为 ``[angle, plane, domain_s, domain_t]``, + 且当前版本的测量平面 ``plane`` 只能支持 ``XY`` 或 ``YZ``。 + + :param which_qubit: 被测量的量子位 + :type which_qubit: Optional[int] + :param basis_list: 测量方式 + :type basis_list: Optional[list] + + .. py:method:: is_valid() + + 检查输入的量子电路是否符合规定。 + + 我们规定输入的量子电路中,每一个量子位上至少作用一个量子门。 + + :return: 量子电路是否符合规定的布尔值 + :rtype: bool + + .. py:method:: get_width() + + 返回量子电路的宽度。 + + :return: 量子电路的宽度 + :rtype: int + + .. py:method:: get_circuit() + + 返回量子电路列表。 + + :return: 量子电路列表 + :rtype: list + + .. py:method:: get_measured_qubits() + + 返回量子电路中测量的比特位。 + + :return: 量子电路中测量的比特位列表 + :rtype: list + + .. py:method:: print_circuit_list() + + 打印电路图的列表。 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + from paddle import to_tensor + from numpy import pi + + n = 2 + theta = to_tensor([pi], dtype="float64") + cir = Circuit(n) + cir.h(0) + cir.cnot([0, 1]) + cir.rx(theta, 1) + cir.measure() + cir.print_circuit_list() + + :: + + -------------------------------------------------- + Current circuit + -------------------------------------------------- + Gate Name Qubit Index Parameter + -------------------------------------------------- + h [0] None + cnot [0, 1] None + rx [1] 3.141592653589793 + m [0] [0.0, 'YZ', [], []] + m [1] [0.0, 'YZ', [], []] + -------------------------------------------------- + + :return: 用来打印的字符串 + :rtype: string + +.. py:class:: Pattern(name, space, input_, output_, commands) + + 基类:``object`` + + 定义测量模式。 + + 该测量模式的结构依据文献 [The measurement calculus, arXiv: 0704.1263]。 + + :param name: 测量模式的名称 + :type name: str + :param space: 测量模式所有节点列表 + :type space: list + :param input_: 测量模式的输入节点列表 + :type input_: list + :param output_: 测量模式的输出节点列表 + :type output_: list + :param commands: 测量模式的命令列表 + :type commands: list + + .. py:class:: CommandE + + 基类:``object`` + + 定义纠缠命令类。 + + .. note:: + + 此处纠缠命令对应作用控制 Z 门。 + + :param which_qubits: 作用纠缠命令的两个节点标签构成的列表 + :type which_qubits: list + + .. py:class:: CommandM + + 基类:``object`` + + 定义测量命令类。 + + 测量命令有五个属性,分别为测量比特的标签 ``which_qubit``,原始的测量角度 ``angle``,测量平面 ``plane``,域 s 对应的节点标签列表 ``domain_s``,域 t 对应的节点标签列表 ``domain_t``。设原始角度为 :math:`\alpha`,则考虑域中节点依赖关系后的测量角度 :math:`\theta` 为: + + .. math:: + + \theta = (-1)^s \times \alpha + t \times \pi + + .. note:: + + 域 s 和域 t 是 MBQC 模型中的概念,分别记录了 Pauli X 算符和 Pauli Z 算符对测量角度产生的影响,二者共同记录了该测量节点对其他节点的测量结果的依赖关系。 + + .. warning:: + + 该命令当前只支持 XY 和 YZ 平面的测量。 + + :param which_qubit: 作用测量命令的节点标签 + :type which_qubit: Any + :param angle: 原始的测量角度 + :type angle: paddle.Tensor + :param plane: 测量平面 + :type plane: str + :param domain_s: 域 s 对应的节点标签列表 + :type domain_s: list + :param domain_t: 域 t 对应的节点标签列表 + :type domain_t: list + + .. py:class:: CommandX + + 基类:``object`` + + 定义 Pauli X 副产品修正命令类。 + + :param which_qubit: 作用修正算符的节点标签 + :type which_qubit: Any + :param domain: 依赖关系列表 + :type domain: list + + .. py:class:: CommandZ + + 基类:``object`` + + 定义 Pauli Z 副产品修正命令。 + + .. note:: + + 此处纠缠命令对应作用控制 Z 门。 + + :param which_qubit: 作用修正算符的节点标签 + :type which_qubit: Any + :param domain: 依赖关系列表 + :type domain: list + + .. py:class:: CommandS + + 基类:``object`` + + 定义“信号转移”命令类。 + + .. note:: + + “信号转移”是一类特殊的操作,用于消除测量命令对域 t 中节点的依赖关系,在某些情况下对测量模式进行简化。 + + :param which_qubit: 消除依赖关系的测量命令作用的节点标签 + :type which_qubit: Any + :param domain: 依赖关系列表 + :type domain: list + + .. py:method:: print_command_list() + + 打印该 ``Pattern`` 类中的命令的信息,便于用户查看。 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.qobject import Circuit + from paddle_quantum.mbqc.mcalculus import MCalculus + + n = 1 + cir = Circuit(n) + cir.h(0) + pat = MCalculus() + pat.set_circuit(cir) + pattern = pat.get_pattern() + pattern.print_command_list() + + :: + + ----------------------------------------------------------- + Current Command List + ----------------------------------------------------------- + Command: E + which_qubits: [('0/1', '0/1'), ('0/1', '1/1')] + ----------------------------------------------------------- + Command: M + which_qubit: ('0/1', '0/1') + plane: XY + angle: 0.0 + domain_s: [] + domain_t: [] + ----------------------------------------------------------- + Command: X + which_qubit: ('0/1', '1/1') + domain: [('0/1', '0/1')] + ----------------------------------------------------------- diff --git a/docs_zh_CN/source/paddle_quantum.mbqc.rst b/docs_zh_CN/source/paddle_quantum.mbqc.rst index 813af53..32823b0 100644 --- a/docs_zh_CN/source/paddle_quantum.mbqc.rst +++ b/docs_zh_CN/source/paddle_quantum.mbqc.rst @@ -8,6 +8,7 @@ paddle\_quantum.mbqc .. toctree:: :maxdepth: 4 + paddle_quantum.mbqc.mcalculus paddle_quantum.mbqc.qobject paddle_quantum.mbqc.simulator paddle_quantum.mbqc.transpiler diff --git a/docs_zh_CN/source/paddle_quantum.mbqc.simulator.rst b/docs_zh_CN/source/paddle_quantum.mbqc.simulator.rst index 5ab2eb1..148ad4d 100644 --- a/docs_zh_CN/source/paddle_quantum.mbqc.simulator.rst +++ b/docs_zh_CN/source/paddle_quantum.mbqc.simulator.rst @@ -1,2 +1,283 @@ paddle\_quantum.mbqc.simulator ============================== + +此模块包含构造 MBQC 模型的常用类和配套的运算模拟工具。 + +.. py:class:: MBQC() + + 基类:``object`` + + 定义基于测量的量子计算模型 ``MBQC`` 类。 + + 用户可以通过实例化该类来定义自己的 MBQC 模型。 + + .. py:method:: set_graph(graph) + + 设置 MBQC 模型中的图。 + + 该函数用于将用户自己构造的图传递给 ``MBQC`` 实例。 + + :param graph: MBQC 模型中的图,由列表 ``[V, E]`` 给出, 其中 ``V`` 为节点列表,``E`` 为边列表 + :type graph: list + + .. py:method:: get_graph() + + 获取图的信息。 + + 该函数用于将用户自己构造的图传递给 ``MBQC`` 实例。 + + :return: 图 + :rtype: networkx.Graph + + .. py:method:: set_pattern(pattern) + + 设置 MBQC 模型的测量模式。 + + 该函数用于将用户由电路图翻译得到或自己构造的测量模式传递给 ``MBQC`` 实例。 + + :param pattern: MBQC 算法对应的测量模式 + :type pattern: Pattern + + .. py:method:: get_pattern() + + 获取测量模式的信息。 + + :return: 测量模式 + :rtype: Pattern + + .. py:method:: set_input_state(state) + + 设置需要替换的输入量子态。 + + .. warning:: + + 与电路模型不同,MBQC 模型通常默认初始态为加态。如果用户不调用此方法设置初始量子态,则默认为加态。 + 如果用户以测量模式运行 MBQC,则此处输入量子态的系统标签会被限制为从零开始的自然数,类型为整型。 + + :param state: 需要替换的量子态,默认为加态 + :type state: Optional[State] + + .. py:method:: draw_process(draw, pos, pause_time) + + 动态过程图绘制,用以实时展示 MBQC 模型的模拟计算过程。 + + .. warning:: + + 与电路模型不同,MBQC 模型通常默认初始态为加态。如果用户不调用此方法设置初始量子态,则默认为加态。 + 如果用户以测量模式运行 MBQC,则此处输入量子态的系统标签会被限制为从零开始的自然数,类型为整型。 + + :param draw: 是否绘制动态过程图的布尔开关 + :type draw: Optional[bool] + :param pos: 节点坐标的字典数据或者内置的坐标选择,内置的坐标选择有: ``True`` 为测量模式自带的坐标,``False`` 为 ``spring_layout`` 坐标 + :type pos: Optional[bool] + :param pause_time: 需要替换的量子态,默认为加态 + :type pause_time: Optional[float] + + .. py:method:: track_process(track) + + 显示 MBQC 模型运行进度的开关。 + + :param track: ``True`` 打开进度条显示功能, ``False`` 关闭进度条显示功能 + :type track: Optional[bool] + + .. py:method:: measure(which_qubit, basis_list) + + 显示 MBQC 模型运行进度的开关。 + + .. note:: + + 这是用户在实例化 MBQC 类之后最常调用的方法之一,此处我们对单比特测量模拟进行了最大程度的优化,随着用户对该函数的调用,MBQC 类将自动完成激活相关节点、生成所需的图态以及对特定比特进行测量的全过程,并记录测量结果和对应测量后的量子态。用户每调用一次该函数,就完成一次对单比特的测量操作。 + + .. warning:: + + 当且仅当用户调用 ``measure`` 类方法时,MBQC 模型才真正进行运算。 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.simulator import MBQC + from paddle_quantum.mbqc.qobject import State + from paddle_quantum.mbqc.utils import zero_state, basis + + G = [['1', '2', '3'], [('1', '2'), ('2', '3')]] + mbqc = MBQC() + mbqc.set_graph(G) + state = State(zero_state(), ['1']) + mbqc.set_input_state(state) + mbqc.measure('1', basis('X')) + mbqc.measure('2', basis('X')) + print("Measurement outcomes: ", mbqc.get_classical_output()) + + :: + + Measurement outcomes: {'1': 0, '2': 1} + + :param which_qubit: 待测量量子比特的系统标签,可以是 ``str``, ``tuple`` 等任意数据类型,但需要和 MBQC 模型的图上标签匹配 + :type which_qubit: Any + :param basis_list: 测量基向量构成的列表,列表元素为 ``Tensor`` 类型的列向量 + :type basis_list: list + + .. py:method:: sum_outcomes(which_qubits, start) + + 根据输入的量子系统标签,在存储测量结果的字典中找到对应的测量结果,并进行求和。 + + .. note:: + + 在进行副产品纠正操作和定义适应性测量角度时,用户可以调用该方法对特定比特的测量结果求和。 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.simulator import MBQC + from paddle_quantum.mbqc.qobject import State + from paddle_quantum.mbqc.utils import zero_state, basis + + G = [['1', '2', '3'], [('1', '2'), ('2', '3')]] + mbqc = MBQC() + mbqc.set_graph(G) + input_state = State(zero_state(), ['1']) + mbqc.set_input_state(input_state) + mbqc.measure('1', basis('X')) + mbqc.measure('2', basis('X')) + mbqc.measure('3', basis('X')) + print("All measurement outcomes: ", mbqc.get_classical_output()) + print("Sum of outcomes of qubits '1' and '2': ", mbqc.sum_outcomes(['1', '2'])) + print("Sum of outcomes of qubits '1', '2' and '3' with an extra 1: ", mbqc.sum_outcomes(['1', '2', '3'], 1)) + + :: + + All measurement outcomes: {'1': 0, '2': 0, '3': 1} + Sum of outcomes of qubits '1' and '2': 0 + Sum of outcomes of qubits '1', '2' and '3' with an extra 1: 2 + + :param which_qubits: 需要查找测量结果并求和的比特的系统标签列表 + :type which_qubits: list + :param start: 对结果进行求和后需要额外相加的整数 + :type start: int + :return: 指定比特的测量结果的和 + :rtype: int + + .. py:method:: correct_byproduct(gate, which_qubit, power) + + 对测量后的量子态进行副产品纠正。 + + .. note:: + + 这是用户在实例化 MBQC 类并完成测量后,经常需要调用的一个方法。 + + 代码示例: + + 此处展示的是 MBQC 模型下实现隐形传态的一个例子。 + + .. code-block:: python + + from paddle_quantum.mbqc.simulator import MBQC + from paddle_quantum.mbqc.qobject import State + from paddle_quantum.mbqc.utils import random_state_vector, basis, compare_by_vector + + G = [['1', '2', '3'], [('1', '2'), ('2', '3')]] + state = State(random_state_vector(1), ['1']) + mbqc = MBQC() + mbqc.set_graph(G) + mbqc.set_input_state(state) + mbqc.measure('1', basis('X')) + mbqc.measure('2', basis('X')) + outcome = mbqc.get_classical_output() + mbqc.correct_byproduct('Z', '3', outcome['1']) + mbqc.correct_byproduct('X', '3', outcome['2']) + state_out = mbqc.get_quantum_output() + state_std = State(state.vector, ['3']) + compare_by_vector(state_out, state_std) + + :: + + Norm difference of the given states is: 0.0 + They are exactly the same states. + + :param gate: ``'X'`` 或者 ``'Z'``,分别表示 Pauli X 或 Z 门修正 + :type gate: str + :param which_qubit: 待操作的量子比特的系统标签,可以是 ``str``, ``tuple`` 等任意数据类 + :type which_qubit: list + :param power: 副产品纠正算符的指数 + :type power: int + + .. py:method:: run_pattern() + + 按照设置的测量模式对 MBQC 模型进行模拟。 + + .. warning:: + + 该方法必须在 ``set_pattern`` 调用后调用。 + + .. py:method:: get_classical_output() + + 获取 MBQC 模型运行后的经典输出结果。 + + :return: 如果用户输入是测量模式,则返回测量输出节点得到的比特串,与原电路的测量结果相一致,没有被测量的比特位填充 "?",如果用户输入是图,则返回所有节点的测量结果 + :rtype: Union[str, dict] + + .. py:method:: get_history() + + 获取 MBQC 计算模拟时的中间步骤信息。 + + :return: 生成图态、进行测量、纠正副产品后运算结果构成的列表 + :rtype: list + + .. py:method:: get_quantum_output() + + 获取 MBQC 模型运行后的量子态输出结果。 + + :return: MBQC 模型运行后的量子态 + :rtype: State + +.. py:function:: simulate_by_mbqc(circuit, input_state) + + 使用等价的 MBQC 模型模拟量子电路。 + + 该函数通过将量子电路转化为等价的 MBQC 模型并运行,从而获得等价于原始量子电路的输出结果。 + + .. warning:: + + 此处输入的 ``circuit`` 参数包含了测量操作。 + 另,MBQC 模型默认初始态为加态,因此,如果用户不输入参数 ``input_state`` 设置初始量子态,则默认为加态。 + + :param circuit: 量子电路图 + :type circuit: Circuit + :param input_state: 量子电路的初始量子态,默认为 :math:`|+\rangle` 态 + :type input_state: Optional[State] + :return: + 包含如下两个元素: + + - str: 经典输出 + - State: 量子输出 + :rtype: Tuple[str, State] + +.. py:function:: sample_by_mbqc(circuit, input_state, plot, shots, print_or_not) + + 将 MBQC 模型重复运行多次,获得经典结果的统计分布。 + + 该函数通过将量子电路转化为等价的 MBQC 模型并运行,从而获得等价于原始量子电路的输出结果。 + + .. warning:: + + 此处输入的 circuit 参数包含了测量操作。 + 另,MBQC 模型默认初始态为加态,因此,如果用户不输入参数 `input_state` 设置初始量子态,则默认为加态。 + + :param circuit: 量子电路图 + :type circuit: Circuit + :param input_state: 量子电路的初始量子态,默认为加态 + :type input_state: Optional[State] + :param plot: 绘制经典采样结果的柱状图开关,默认为关闭状态 + :type plot: Optional[bool] + :param shots: 采样次数,默认为 1024 次 + :type shots: Optional[int] + :param print_or_not: 是否打印采样结果和绘制采样进度,默认为开启状态 + :type print_or_not: Optional[bool] + :return: + 包含如下两个元素: + + - 经典结果构成的频率字典 + - 经典测量结果和所有采样结果(包括经典输出和量子输出)的列表 + :rtype: Tuple[dict, list] diff --git a/docs_zh_CN/source/paddle_quantum.mbqc.transpiler.rst b/docs_zh_CN/source/paddle_quantum.mbqc.transpiler.rst index c51886a..2d26f70 100644 --- a/docs_zh_CN/source/paddle_quantum.mbqc.transpiler.rst +++ b/docs_zh_CN/source/paddle_quantum.mbqc.transpiler.rst @@ -1,2 +1,17 @@ paddle\_quantum.mbqc.transpiler =============================== + +此模块包含电路模型和 MBQC 测量模式的转义工具。 + +.. py:function:: transpile(circuit, track) + + 将输入的量子电路翻译为等价的测量模式。 + + 该函数通过将量子电路转化为等价的 MBQC 模型并运行,从而获得等价于原始量子电路的输出结果。 + + :param circuit: 量子电路,包含可能的测量部分 + :type circuit: Circuit + :param track: 是否显示翻译进度条的开关 + :type track: bool + :return: 等价的测量模式 + :rtype: Pattern diff --git a/docs_zh_CN/source/paddle_quantum.mbqc.utils.rst b/docs_zh_CN/source/paddle_quantum.mbqc.utils.rst index cfa3bc8..1856e45 100644 --- a/docs_zh_CN/source/paddle_quantum.mbqc.utils.rst +++ b/docs_zh_CN/source/paddle_quantum.mbqc.utils.rst @@ -1,2 +1,806 @@ paddle\_quantum.mbqc.utils ========================== + +此模块包含计算所需的各种常用类和函数。 + +.. py:function:: plus_state() + + 定义加态。 + + 其矩阵形式为: + + .. math:: + + \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ 1 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import plus_state + print("State vector of plus state: \n", plus_state().numpy()) + + :: + + State vector of plus state: + [[0.70710678] + [0.70710678]] + + :return: 加态对应的 ``Tensor`` 形式 + :rtype: paddle.Tensor + +.. py:function:: minus_state() + + 定义减态。 + + 其矩阵形式为: + + .. math:: + + \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ -1 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import minus_state + print("State vector of minus state: \n", minus_state().numpy()) + + :: + + State vector of minus state: + [[ 0.70710678] + [-0.70710678]] + + :return: 减态对应的 ``Tensor`` 形式 + :rtype: paddle.Tensor + +.. py:function:: zero_state() + :noindex: + + 定义零态。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 \\ 0 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import zero_state + print("State vector of zero state: \n", zero_state().numpy()) + + :: + + State vector of zero state: + [[1.] + [0.]] + + :return: 零态对应的 ``Tensor`` 形式 + :rtype: paddle.Tensor + +.. py:function:: one_state() + + 定义一态。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 0 \\ 1 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import one_state + print("State vector of one state: \n", one_state().numpy()) + + :: + + State vector of one state: + [[0.] + [1.]] + + :return: 一态对应的 ``Tensor`` 形式 + :rtype: paddle.Tensor + +.. py:function:: h_gate() + :noindex: + + 定义 ``Hadamard`` 门。 + + 其矩阵形式为: + + .. math:: + + \frac{1}{\sqrt{2}} \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import h_gate + print("Matrix of Hadamard gate: \n", h_gate().numpy()) + + :: + + Matrix of Hadamard gate: + [[ 0.70710678 0.70710678] + [ 0.70710678 -0.70710678]] + + :return: ``Hadamard`` 门对应矩阵的 ``Tensor`` 形式 + :rtype: paddle.Tensor + +.. py:function:: s_gate() + :noindex: + + 定义 ``S`` 门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 \\ 0 & i \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import s_gate + print("Matrix of S gate:\n", s_gate().numpy()) + + :: + + Matrix of S gate: + [[1.+0.j 0.+0.j] + [0.+0.j 0.+1.j]] + + :return: ``S`` 门矩阵对应的 ``Tensor`` 形式 + :rtype: paddle.Tensor + +.. py:function:: t_gate() + :noindex: + + 定义 ``T`` 门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 \\ 0 & e^{i \pi / 4} \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import t_gate + print("Matrix of T gate: \n", t_gate().numpy()) + + :: + + Matrix of T gate: + [[1. +0.j 0. +0.j ] + [0. +0.j 0.70710678+0.70710678j]] + + :return: ``T`` 门矩阵对应的 ``Tensor`` 形式 + :rtype: paddle.Tensor + +.. py:function:: cz_gate() + :noindex: + + 定义 ``Controlled-Z`` 门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import cz_gate + print("Matrix of CZ gate: \n", cz_gate().numpy()) + + :: + + Matrix of CZ gate: + [[ 1. 0. 0. 0.] + [ 0. 1. 0. 0.] + [ 0. 0. 1. 0.] + [ 0. 0. 0. -1.]] + + :return: ``Controlled-Z`` 门矩阵对应的 ``Tensor`` 形式 + :rtype: paddle.Tensor + +.. py:function:: cnot_gate() + :noindex: + + 定义 ``Controlled-NOT (CNOT)`` 门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import cnot_gate + print("Matrix of CNOT gate: \n", cnot_gate().numpy()) + + :: + + Matrix of CNOT gate: + [[1. 0. 0. 0.] + [0. 1. 0. 0.] + [0. 0. 0. 1.] + [0. 0. 1. 0.]] + + :return: ``Controlled-NOT (CNOT)`` 门矩阵对应的 ``Tensor`` 形式 + :rtype: paddle.Tensor + +.. py:function:: swap_gate() + :noindex: + + 定义 ``SWAP`` 门。 + + 其矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import swap_gate + print("Matrix of Swap gate: \n", swap_gate().numpy()) + + :: + + Matrix of Swap gate: + [[1. 0. 0. 0.] + [0. 0. 1. 0.] + [0. 1. 0. 0.] + [0. 0. 0. 1.]] + + :return: ``SWAP`` 门矩阵对应的 ``Tensor`` 形式 + :rtype: paddle.Tensor + +.. py:function:: pauli_gate(gate) + + 定义 ``Pauli`` 门。 + + 单位阵 ``I`` 的矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} + + ``Pauli X`` 门的矩阵形式为: + + .. math:: + + \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} + + ``Pauli Y`` 门的矩阵形式为: + + .. math:: + + \begin{bmatrix} 0 & - i \\ i & 0 \end{bmatrix} + + ``Pauli Z`` 门的矩阵形式为: + + .. math:: + + \begin{bmatrix} 1 & 0 \\ 0 & - 1 \end{bmatrix} + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import pauli_gate + I = pauli_gate('I') + X = pauli_gate('X') + Y = pauli_gate('Y') + Z = pauli_gate('Z') + print("Matrix of Identity gate: \n", I.numpy()) + print("Matrix of Pauli X gate: \n", X.numpy()) + print("Matrix of Pauli Y gate: \n", Y.numpy()) + print("Matrix of Pauli Z gate: \n", Z.numpy()) + + :: + + Matrix of Identity gate: + [[1. 0.] + [0. 1.]] + Matrix of Pauli X gate: + [[0. 1.] + [1. 0.]] + Matrix of Pauli Y gate: + [[ 0.+0.j -0.-1.j] + [ 0.+1.j 0.+0.j]] + Matrix of Pauli Z gate: + [[ 1. 0.] + [ 0. -1.]] + + :param gate: Pauli 门的索引字符,"I", "X", "Y", "Z" 分别表示对应的门 + :type gate: str + :return: Pauli 门对应的矩阵 + :rtype: paddle.Tensor + +.. py:function:: rotation_gate(gate) + + 定义旋转门矩阵。 + + .. math:: + + R_{x}(\theta) = \cos(\theta / 2) I - i\sin(\theta / 2) X + + R_{y}(\theta) = \cos(\theta / 2) I - i\sin(\theta / 2) Y + + R_{z}(\theta) = \cos(\theta / 2) I - i\sin(\theta / 2) Z + + 代码示例: + + .. code-block:: python + + from numpy import pi + from paddle import to_tensor + from paddle_quantum.mbqc.utils import rotation_gate + + theta = to_tensor([pi / 6], dtype='float64') + Rx = rotation_gate('x', theta) + Ry = rotation_gate('y', theta) + Rz = rotation_gate('z', theta) + print("Matrix of Rotation X gate with angle pi/6: \n", Rx.numpy()) + print("Matrix of Rotation Y gate with angle pi/6: \n", Ry.numpy()) + print("Matrix of Rotation Z gate with angle pi/6: \n", Rz.numpy()) + + :: + + Matrix of Rotation X gate with angle pi/6: + [[0.96592583+0.j 0. -0.25881905j] + [0. -0.25881905j 0.96592583+0.j ]] + Matrix of Rotation Y gate with angle pi/6: + [[ 0.96592583+0.j -0.25881905+0.j] + [ 0.25881905+0.j 0.96592583+0.j]] + Matrix of Rotation Z gate with angle pi/6: + [[0.96592583-0.25881905j 0. +0.j ] + [0. +0.j 0.96592583+0.25881905j]] + + :param axis: 旋转轴,绕 ``X`` 轴旋转输入 'x',绕 ``Y`` 轴旋转输入 'y',绕 ``Z`` 轴旋转输入 'z' + :type axis: str + :param theta: 旋转的角度 + :type theta: paddle.Tensor + :return: 旋转门对应的矩阵 + :rtype: paddle.Tensor + +.. py:function:: to_projector(vector) + + 把列向量转化为密度矩阵(或测量基对应的投影算符)。 + + .. math:: + + |\psi\rangle \to |\psi\rangle\langle\psi| + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import zero_state, plus_state + from paddle_quantum.mbqc.utils import to_projector + + zero_proj = to_projector(zero_state()) + plus_proj = to_projector(plus_state()) + print("The projector of zero state: \n", zero_proj.numpy()) + print("The projector of plus state: \n", plus_proj.numpy()) + + :: + + The projector of zero state: + [[1. 0.] + [0. 0.]] + The projector of plus state: + [[0.5 0.5] + [0.5 0.5]] + + :param vector: 量子态列向量(或投影测量中的测量基向量) + :type vector: paddle.Tensor + :return: 密度矩阵(或测量基对应的投影算符) + :rtype: paddle.Tensor + +.. py:function:: basis(label, theta) + + 测量基。 + + .. note:: + + 常用的测量方式有 XY-平面测量,YZ-平面测量,X 测量,Y 测量,Z 测量。 + + .. math:: + + \begin{align*} + & M^{XY}(\theta) = \{R_{z}(\theta)|+\rangle, R_{z}(\theta)|-\rangle\}\\ + & M^{YZ}(\theta) = \{R_{x}(\theta)|0\rangle, R_{x}(\theta)|1\rangle\}\\ + & X = M^{XY}(0)\\ + & Y = M^{YZ}(\pi / 2) = M^{XY}(-\pi / 2)\\ + & Z = M_{YZ}(0) + \end{align*} + + 代码示例: + + .. code-block:: python + + from numpy import pi + from paddle import to_tensor + from paddle_quantum.mbqc.utils import basis + theta = to_tensor(pi / 6, dtype='float64') + YZ_plane_basis = basis('YZ', theta) + XY_plane_basis = basis('XY', theta) + X_basis = basis('X') + Y_basis = basis('Y') + Z_basis = basis('Z') + print("Measurement basis in YZ plane: \n", YZ_plane_basis) + print("Measurement basis in XY plane: \n", XY_plane_basis) + print("Measurement basis of X: \n", X_basis) + print("Measurement basis of Y: \n", Y_basis) + print("Measurement basis of Z: \n", Z_basis) + + :: + + Measurement basis in YZ plane: + [Tensor(shape=[2, 1], dtype=complex128, place=CPUPlace, stop_gradient=True, + [[(0.9659258262890683+0j)], + [-0.25881904510252074j ]]), + Tensor(shape=[2, 1], dtype=complex128, place=CPUPlace, stop_gradient=True, + [[-0.25881904510252074j ], + [(0.9659258262890683+0j)]])] + Measurement basis in XY plane: + [Tensor(shape=[2, 1], dtype=complex128, place=CPUPlace, stop_gradient=True, + [[(0.6830127018922193-0.1830127018922193j)], + [(0.6830127018922193+0.1830127018922193j)]]), + Tensor(shape=[2, 1], dtype=complex128, place=CPUPlace, stop_gradient=True, + [[ (0.6830127018922193-0.1830127018922193j)], + [(-0.6830127018922193-0.1830127018922193j)]])] + Measurement basis of X: + [Tensor(shape=[2, 1], dtype=float64, place=CPUPlace, stop_gradient=True, + [[0.70710678], + [0.70710678]]), + Tensor(shape=[2, 1], dtype=float64, place=CPUPlace, stop_gradient=True, + [[ 0.70710678], + [-0.70710678]])] + Measurement basis of Y: + [Tensor(shape=[2, 1], dtype=complex128, place=CPUPlace, stop_gradient=True, + [[(0.5-0.5j)], + [(0.5+0.5j)]]), + Tensor(shape=[2, 1], dtype=complex128, place=CPUPlace, stop_gradient=True, + [[ (0.5-0.5j)], + [(-0.5-0.5j)]])] + Measurement basis of Z: + [Tensor(shape=[2, 1], dtype=float64, place=CPUPlace, stop_gradient=True, + [[1.], + [0.]]), + Tensor(shape=[2, 1], dtype=float64, place=CPUPlace, stop_gradient=True, + [[0.], + [1.]])] + + :param label: 测量基索引字符,"XY" 表示 XY-平面测量,"YZ" 表示 YZ-平面测量,"X" 表示 X 测量,"Y" 表示 Y 测量,"Z" 表示 Z 测量 + :type label: str + :param theta: 测量角度,这里只有 XY-平面测量和 YZ-平面测量时需要 + :type theta: Optional[paddle.Tensor] + :return: 测量基向量构成的列表,列表元素为 ``Tensor`` 类型 + :rtype: List[paddle.Tensor] + +.. py:function:: kron(tensor_list) + + 把列表中的所有元素做张量积。 + + .. math:: + + [A, B, C, \cdots] \to A \otimes B \otimes C \otimes \cdots + + 代码示例 1: + + .. code-block:: python + + from paddle import to_tensor + from paddle_quantum.mbqc.utils import pauli_gate, kron + tensor0 = pauli_gate('I') + tensor1 = to_tensor([[1, 1], [1, 1]], dtype='float64') + tensor2 = to_tensor([[1, 2], [3, 4]], dtype='float64') + tensor_list = [tensor0, tensor1, tensor2] + tensor_all = kron(tensor_list) + print("The tensor product result: \n", tensor_all.numpy()) + + :: + + The tensor product result: + [[1. 2. 1. 2. 0. 0. 0. 0.] + [3. 4. 3. 4. 0. 0. 0. 0.] + [1. 2. 1. 2. 0. 0. 0. 0.] + [3. 4. 3. 4. 0. 0. 0. 0.] + [0. 0. 0. 0. 1. 2. 1. 2.] + [0. 0. 0. 0. 3. 4. 3. 4.] + [0. 0. 0. 0. 1. 2. 1. 2.] + [0. 0. 0. 0. 3. 4. 3. 4.]] + + 代码示例 2: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import pauli_gate, kron + tensor0 = pauli_gate('I') + tensor_list = [tensor0] + tensor_all = kron(tensor_list) + print("The tensor product result: \n", tensor_all.numpy()) + + :: + + The tensor product result: + [[1. 0.] + [0. 1.]] + + :param tensor_list: 需要做张量积的元素组成的列表 + :type tensor_list: List[paddle.Tensor] + :return: 所有元素做张量积运算得到的 ``Tensor``,当列表中只有一个 ``Tensor`` 时,返回该 ``Tensor`` 本身 + :rtype: paddle.Tensor + +.. py:function:: permute_to_front(state, which_system) + + 将一个量子态中某个子系统的顺序变换到最前面。 + + 假设当前系统的量子态列向量 :math:`\psi\rangle` 可以分解成多个子系统列向量的 tensor product 形式: + + .. math:: + + |\psi\rangle = |\psi_1\rangle \otimes |\psi_2\rangle \otimes |\psi_3\rangle \otimes \cdots + + 每个 :math:`|\psi_i\rangle` 的系统标签为 :math:`i` ,则当前总系统的标签为: + + .. math:: + + \text{label} = \{1, 2, 3, \cdots \} + + 假设需要操作的子系统的标签为:i + + 输出新系统量子态的列向量为: + + .. math:: + + |\psi_i\rangle \otimes |\psi_1\rangle \otimes \cdots |\psi_{i-1}\rangle \otimes |\psi_{i+1}\rangle \otimes \cdots + + :param state: 需要操作的量子态 + :type state: State + :param which_system: 要变换到最前面的子系统标签 + :type which_system: str + :return: 系统顺序变换后的量子态 + :rtype: State + +.. py:function:: permute_systems(state, new_system) + :noindex: + + 变换量子态的系统到指定顺序。 + + 假设当前系统的量子态列向量 :math:`|\psi\rangle` 可以分解成多个子系统列向量的 tensor product 形式: + + .. math:: + + |\psi\rangle = |\psi_1\rangle \otimes |\psi_2\rangle \otimes |\psi_3\rangle \otimes \cdots + + 每个 :math:`\psi_i\rangle` 的系统标签为 :math:`i` ,则当前总系统的标签为: + + .. math:: + + \text{label} = \{1, 2, 3, \cdots \} + + 给定新系统的标签顺序为: + + .. math:: + + \{i_1, i_2, i_3, \cdots \} + + 输出新系统量子态的列向量为: + + .. math:: + + |\psi_{i_1}\rangle \otimes |\psi_{i_2}\rangle \otimes |\psi_{i_3}\rangle \otimes \cdots + + :param state: 需要操作的量子态 + :type state: State + :param new_system: 目标系统顺序 + :type new_system: list + :return: 系统顺序变换后的量子态 + :rtype: State + +.. py:function:: compare_by_density(state1, state2) + + 通过密度矩阵形式比较两个量子态是否相同。 + + :param state1: 第一个量子态 + :type state1: State + :param state2: 第二个量子态 + :type state2: State + +.. py:function:: compare_by_vector(state1, state2) + + 通过列向量形式比较两个量子态是否相同。 + + :param state1: 第一个量子态 + :type state1: State + :param state2: 第二个量子态 + :type state2: State + +.. py:function:: random_state_vector(n, is_real) + + 随机生成一个量子态列向量。 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import random_state_vector + random_vec = random_state_vector(2) + print(random_vec.numpy()) + random_vec = random_state_vector(1, is_real=True) + print(random_vec.numpy()) + + :: + + [[-0.06831946+0.04548425j] + [ 0.60460088-0.16733175j] + [ 0.39185213-0.24831266j] + [ 0.45911355-0.41680807j]] + [[0.77421121] + [0.63292732]] + + :param n: 随机生成的量子态的比特数 + :type n: int + :param is_real: ``True`` 表示实数量子态,``False`` 表示复数量子态,默认为 ``False`` + :type is_real: Optional[bool] + :return: 随机生成量子态的列向量 + :rtype: paddle.Tensor + +.. py:function:: div_str_to_float(div_str) + + 将除式字符串转化为对应的浮点数。 + + 例如将字符串 '3/2' 转化为 1.5。 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import div_str_to_float + division_str = "1/2" + division_float = div_str_to_float(division_str) + print("The corresponding float value is: ", division_float) + + :: + + The corresponding float value is: 0.5 + + :param div_str: 除式字符串 + :type div_str: str + :return: 除式对应的浮点数结果 + :rtype: float + +.. py:function:: int_to_div_str(idx1, idx2) + + 将两个整数转化为除式字符串。 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import int_to_div_str + one = 1 + two = 2 + division_string = int_to_div_str(one, two) + print("The corresponding division string is: ", division_string) + + :: + + The corresponding division string is: 1/2 + + :param idx1: 第一个整数 + :type idx1: int + :param idx2: 第二个整数 + :type idx2: int + :return: 对应的除式字符串 + :rtype: str + +.. py:function:: print_progress(current_progress, progress_name, track) + + 画出当前步骤的进度条。 + + 代码示例: + + .. code-block:: python + + from paddle_quantum.mbqc.utils import print_progress + print_progress(14/100, "Current Progress") + + :: + + Current Progress |■■■■■■■ | 14.00% + + :param current_progress: 当前的进度百分比 + :type current_progress: float + :param progress_name: 当前步骤的名称 + :type progress_name: str + :param track: 是否绘图的布尔开关 + :type track: bool + :return: 对应的除式字符串 + :rtype: str + +.. py:function:: plot_results(dict_lst, bar_label, title, xlabel, ylabel, xticklabels) + + 根据字典的键值对,以键为横坐标,对应的值为纵坐标,画出柱状图。 + + .. note:: + + 该函数主要调用来画出采样分布或时间比较的柱状图。 + + :param dict_lst: 待画图的字典列表 + :type dict_lst: list + :param bar_label: 每种柱状图对应的名称 + :type bar_label: list + :param title: 整个图的标题 + :type title: str + :param xlabel: 横坐标的名称 + :type xlabel: str + :param ylabel: 纵坐标的名称 + :type ylabel: str + :param xticklabels: 柱状图中每个横坐标的名称 + :type xticklabels: Optional[list] + +.. py:function:: write_running_data(textfile, eg, width, mbqc_time, reference_time) + + 写入电路模拟运行的时间。 + + 由于在许多电路模型模拟案例中,需要比较我们的 ``MBQC`` 模拟思路与 ``Qiskit`` 或量桨平台的电路模型模拟思路的运行时间。因而单独定义了写入文件函数。 + + .. hint:: + + 该函数与 ``read_running_data`` 函数配套使用。 + + .. warning:: + + 在调用该函数之前,需要调用 ``open`` 打开 ``textfile``;在写入结束之后,需要调用 ``close`` 关闭 ``textfile``。 + + :param textfile: 待写入的文件 + :type textfile: TextIOWrapper + :param eg: 当前案例的名称 + :type eg: str + :param width: 电路宽度(比特数) + :type width: float + :param mbqc_time: ``MBQC`` 模拟电路运行时间 + :type mbqc_time: float + :param reference_time: ``Qiskit`` 或量桨平台的 ``UAnsatz`` 电路模型运行时间 + :type reference_time: flaot + +.. py:function:: write_running_data(file_name) + :noindex: + + 读取电路模拟运行的时间。 + + 由于在许多电路模型模拟案例中,需要比较我们的 ``MBQC`` 模拟思路与 ``Qiskit`` 或量桨平台的电路模型模拟思路的运行时间。因而单独定义了读取文件函数读取运行时间,将其处理为一个列表,列表中的两个元素分别为 ``Qiskit`` 或量桨平台的 ``UAnsatz`` 电路模型模拟思路的运行时间 + + .. hint:: + + 该函数与 ``write_running_data`` 函数配套使用。 + + :param file_name: 待读取的文件名 + :type file_name: str + :return: 运行时间列表 + :rtype: list diff --git a/docs_zh_CN/source/paddle_quantum.qinfo.rst b/docs_zh_CN/source/paddle_quantum.qinfo.rst index c54f672..f690b84 100644 --- a/docs_zh_CN/source/paddle_quantum.qinfo.rst +++ b/docs_zh_CN/source/paddle_quantum.qinfo.rst @@ -128,7 +128,7 @@ paddle\_quantum.qinfo :return: 输入的量子态之间的相对熵。 :rtype: Union[np.ndarray, paddle.Tensor] -.. py:function:: random_pauli_str_generator(n, terms=3) +.. py:function:: random_pauli_str_generator(num_qubits, terms=3) 随机生成一个可观测量(observable)的列表( ``list`` )形式。 @@ -136,14 +136,40 @@ paddle\_quantum.qinfo 列表形式为 ``[[0.3, 'x0'], [0.5, 'y0,z2']]`` 。这样一个可观测量是由 调用 ``random_pauli_str_generator(3, terms=2)`` 生成的。 - :param n: 量子比特数量。 - :type n: int + :param num_qubits: 量子比特数量。 + :type num_qubits: int :param terms: 可观测量的项数, 默认为 3。 :type terms: int, optional :return: 随机生成的可观测量的列表形式。 :rtype: List +.. py:function:: pauli_str_convertor(observable: List) + + 在可观测量(observable)中加入系数 1。 + + 一个可观测量 :math:`O=0.3X\otimes I\otimes I+0.5Y\otimes I\otimes Z` 的 + 列表形式为 ``[['z0,x1'], ['z1']]`` 。这样一个可观测量将变化为 + ``[[1, 'z0,x1'], [1, 'z1']]``。 + + :param observable: 在输入的可观测量(observable)中加入系数 1。 + :type observable: List + + :return: 返回加入系数 1 的可观测量(observable)。 + :rtype: List + +.. py:function:: random_hamiltonian_generator(num_qubits, terms=3) + + 随机生成一个哈密顿量(Hamiltonian)。 + + :param num_qubits: 量子比特数量。 + :type n: int + :param terms: 哈密顿量的最高项数, 默认为 3。 + :type terms: int, optional + + :return: 随机生成的哈密顿量。 + :rtype: List + .. py:function:: pauli_str_to_matrix(pauli_str, n) 将输入的可观测量(observable)的列表( ``list`` )形式转换为其矩阵形式。 @@ -186,7 +212,7 @@ paddle\_quantum.qinfo :return: 输入的量子态的 partial transpose。 :rtype: Union[np.ndarray, paddle.Tensor] -.. py:function:: partial_transpose(mat, perm_list, dim_list) +.. py:function:: permute_systems(mat, perm_list, dim_list) 根据输入顺序组合量子系统。 @@ -311,14 +337,14 @@ paddle\_quantum.qinfo 计算输入的菱形范数 - :param channel_repr: 信道对应的表示, ``ChoiRepr`` 或 ``KrausRepr`` 或 ``StinespringRepr`` 或 ``paddle.Tensor``。 - :type channel_repr: Union[ChoiRepr, KrausRepr, StinespringRepr, paddle.Tensor] + :param channel_repr: 信道对应的表示, ``Channel`` 或 ``paddle.Tensor`` 的实例。 + :type channel_repr: Union[Channel, paddle.Tensor] :param dim_io: 输入和输出的维度。 :type dim_io: Union[int, Tuple[int, int]], optional. :param kwargs: 使用cvx所需的参数。 :type kwargs: Any - :raises RuntimeError: ``channel_repr`` 必须是 ``ChoiRepr`` 或 ``KrausRepr`` 或 ``StinespringRepr`` 或 ``paddle.Tensor``。 + :raises RuntimeError: ``channel_repr`` 必须是 ``Channel`` 或 ``paddle.Tensor``。 :raises TypeError: "dim_io" 必须是 "int" 或者 "tuple"。 :warning: 输入的 ``channel_repr`` 不是choi表示,已被转换成 ``ChoiRepr``。 diff --git a/docs_zh_CN/source/paddle_quantum.qml.bert_qtc.rst b/docs_zh_CN/source/paddle_quantum.qml.bert_qtc.rst new file mode 100644 index 0000000..b03c567 --- /dev/null +++ b/docs_zh_CN/source/paddle_quantum.qml.bert_qtc.rst @@ -0,0 +1,180 @@ +paddle\_quantum.qml.bert\_qtc +============================================== + +BERT-量子时序卷积(Quantum Temporal Convolution, QTC)模型 + +.. py:class:: QuantumTemporalConvolution(num_filter, kernel_size, circuit_depth, padding) + + 基类::py:class:`paddle.nn.Layer` + + 量子时序卷积(Quantum Temporal Convolution, QTC)模型的实现。具体细节可以参考:https://arxiv.org/abs/2203.03550 。 + + :param num_filter: 量子时序卷积核的数量。 + :type num_filter: int + :param kernel_size: 量子时序卷积的卷积核大小,它也是对应的量子神经网络所包含的量子比特数量。 + :type kernel_size: int + :param circuit_depth: 量子神经网络中的电路模板的层数。 + :type circuit_depth: int + :param padding: 序列的填充的长度。如果它是 int 型数据,表示左右两端各填充对应长度的值。如果是list类型,则应该是 [pad_left, pad_right],表示左边填充多少、右边填充多少。 + :type padding: int + + .. py:method:: forward(bert_feature) + + 模型的前向执行函数。 + + :param bert_feature: 模型的输入,它是由 BERT 模型对输入文本提取得到的特征。 + :type bert_feature: paddle.Tensor + + :return: 量子时序卷积网络提取得到的特征。 + :rtype: paddle.Tensor + +.. py:class:: Decoder(num_filter, kernel_size, circuit_depth, padding, num_classes, hidden_size) + + 基类::py:class:`paddle.nn.Layer` + + BERT-QTC 模型的解码器模块。它包含量子时序卷积层、全局最大池化层和线性层。 + + :param num_filter: 量子时序卷积核的数量。 + :type num_filter: int + :param kernel_size: 量子时序卷积的卷积核大小,它也是对应的量子神经网络所包含的量子比特数量。 + :type kernel_size: int + :param circuit_depth: 量子神经网络中的电路模板的层数。 + :type circuit_depth: int + :param padding: 序列的填充的长度。如果它是 int 型数据,表示左右两端各填充对应长度的值。如果是list类型,则应该是 [pad_left, pad_right],表示左边填充多少、右边填充多少。 + :type padding: int + :param num_classes: 模型所要分类的类别的数量。 + :type num_classes: int + :param hidden_size: BERT 模型的隐层状态的向量维数。 + :type hidden_size: int + + .. py:method:: forward(bert_feature) + + 模型的前向执行函数。 + + :param bert_feature: 模型的输入,它是由 BERT 模型对输入文本提取得到的特征。 + :type bert_feature: paddle.Tensor + + :return: 模型的预测结果,即对各个类别的概率分数。 + :rtype: paddle.Tensor + +.. py:class:: BERTQTC(bert_model, decoder) + + 基类::py:class:`paddle.nn.Layer` + + BERT-QTC 模型。它包含 BERT 预训练模型和解码器模块。 + + 具体细节可以参考 https://arxiv.org/abs/2203.03550 。 + + :param bert_model: 预训练的 BERT 模型。 + :type bert_model: str + :param decoder: 解码器模块。 + :type decoder: paddle.nn.Layer + + .. py:method:: forward(token_ids) + + 模型的前向执行函数。 + + :param token_ids: 模型的输入,它是文本令牌化后的数字表示。 + :type token_ids: paddle.Tensor + + :return: 模型的预测结果,即对各个类别的概率分数。 + :rtype: paddle.Tensor + +.. py:class:: TextDataset(file_path, bert_model) + :noindex: + + 基类::py:class:`paddle.io.Dataset` + + 实现文本数据集的类。 + + :param file_path: 数据集的文件路径。其里面应该由多行组成。每一行包含文本标签,由制表符或空格分开。 + :type file_path: str + :param bert_model: 预训练的 BERT 模型,用于构建其对应的令牌器(tokenizer)。 + :type bert_model: str + +.. py:function:: train(num_filter, kernel_size, circuit_depth, padding, num_classes, model_name, dataset, batch_size, num_epochs, bert_model, hidden_size, learning_rate, saved_dir, using_validation, early_stopping) + :noindex: + + 训练 BERT-QTC 模型的函数。 + + :param num_filter: 量子时序卷积核的数量。 + :type num_filter: int + :param kernel_size: 量子时序卷积的卷积核大小,它也是对应的量子神经网络所包含的量子比特数量。 + :type kernel_size: int + :param circuit_depth: 量子神经网络中的电路模板的层数。 + :type circuit_depth: int + :param padding: 序列的填充的长度。如果它是 int 型数据,表示左右两端各填充对应长度的值。如果是list类型,则应该是 [pad_left, pad_right],表示左边填充多少、右边填充多少。 + :type padding: int + :param num_classes: 模型所要分类的类别的数量。 + :type num_classes: int + :param model_name: 模型的名字,用于作为保存的模型参数的文件名。 + :type model_name: str + :param dataset: 模型的名字,用于作为保存的模型参数的文件名。 + :type dataset: str + :param batch_size: 数据的批大小。 + :type batch_size: int + :param num_epochs: 训练的轮数。 + :type num_epochs: int + :param bert_model: 预训练的 BERT 模型,默认为 ``bert-base-chinese`` ,即官方的 BERT 中文预训练模型。 + :type bert_model: str + :param hidden_size: BERT 模型的隐层状态的向量维数,默认为 ``768`` 。 + :type hidden_size: int + :param learning_rate: 更新参数的学习率,默认为 ``0.01`` 。 + :type learning_rate: float + :param saved_dir: 训练得到的模型文件的保存路径,默认使用当前目录。 + :type saved_dir: str + :param using_validation: 是否使用验证集。默认为 ``False`` ,即不包含验证集。 + :type using_validation: bool + :param early_stopping: 默认为 ``1000`` ,即如果模型在 1000 次迭代中,在验证集上的 loss 没有提升,则会自动停止训练。 + :type early_stopping: int + +.. py:function:: evaluate(model, data_loader) + :noindex: + + 对模型进行评估。 + + :param model: 训练得到的模型,用于被评估。 + :type model: paddle.nn.Layer + :param data_loader: 用于评估模型的数据加载器。 + :type data_loader: DataLoader + + :return: 返回模型在输入数据上的平均的损失值和平均准确率。 + :rtype: Tuple[float, float] + +.. py:function:: test(model, model_path, test_loader) + :noindex: + + 使用测试集对模型进行测试。 + + :param model: 训练得到的模型,用于被评估。 + :type model: paddle.nn.Layer + :param model_path: 保存的模型参数的文件路径。 + :type model_path: str + :param test_loader: 测试集的数据加载器。 + :type test_loader: DataLoader + +.. py:function:: inference(text, model_path, classes, num_filter, kernel_size, circuit_depth, padding, bert_model, hidden_size) + :noindex: + + 推理函数。使用训练好的模型对输入的图片进行预测。 + + :param text: 要预测的文本内容。 + :type text: str + :param model_path: 保存的模型参数的文件路径。 + :type model_path: str + :param classes: 要预测的文本的类别。 + :type classes: List[str] + :param num_filter: 量子时序卷积核的数量。 + :type num_filter: int + :param kernel_size: 量子时序卷积的卷积核大小,它也是对应的量子神经网络所包含的量子比特数量。 + :type kernel_size: int + :param circuit_depth: 量子神经网络中的电路模板的层数。 + :type circuit_depth: int + :param padding: 序列的填充的长度。如果它是 int 型数据,表示左右两端各填充对应长度的值。如果是list类型,则应该是 [pad_left, pad_right],表示左边填充多少、右边填充多少。 + :type padding: int + :param bert_model: 预训练的 BERT 模型,默认为 ``bert-base-chinese`` ,即官方的 BERT 中文预训练模型。 + :type bert_model: str + :param hidden_size: BERT 模型的隐层状态的向量维数,默认为 ``768`` 。 + + :return: 返回模型预测的类别。 + :rtype: str diff --git a/docs_zh_CN/source/paddle_quantum.qml.qcaan.rst b/docs_zh_CN/source/paddle_quantum.qml.qcaan.rst new file mode 100644 index 0000000..0a22337 --- /dev/null +++ b/docs_zh_CN/source/paddle_quantum.qml.qcaan.rst @@ -0,0 +1,179 @@ +paddle\_quantum.qml.qcaan +============================================== + +量子电路关联对抗网络(Quantum-Circuit Associative Adversarial Network, QCAAN)模型 + +.. py:function:: Data_Load() + + 加载 MNIST 数据集 + + :return: MNIST 数据集 + :rtype: paddle.vision.datasets.MNIST + + +.. py:class:: ConvBlock(shape, in_channels, out_channels, kernel_size=3, stride=1, padding=1, activation=None, normalize=True) + + 基类::py:class:`paddle.nn.Layer` + + 建立神经网络的卷积块。 + 每一个卷积块包含若干卷积层、Silu 激活层、层归一化层;并且卷积块保持空间维度不变,即图片的宽和高不变,只改变通道数。 + + :param shape: 层归一化的形状 + :type shape: List[int] + :param in_channels: 输入通道数 + :type in_channels: int + :param out_channels: 输出通道数 + :type out_channels: int + :param kernel_size: 卷积核的大小 + :type kernel_size: int + :param stride: stride 的规模 + :type stride: int + :param padding: padding 的规模 + :type padding: int + :param activation: 激活函数 + :type activation: nn.Layer + :param normalize: 指示是否使用层归一化的标记 + :type normalize: bool + + .. py:method:: forward(x) + + 前向执行函数 + + :param x: 输入张量 + :type x: paddle.Tensor + + :return: 输出张量 + :rtype: paddle.Tensor + +.. py:class:: Generator(latent_dim=16) + + 基类::py:class:`paddle.nn.Layer` + + 生成器网络 + + :param latent_dim: 隐藏特征维度 + :type latent_dim: int + + .. py:method:: forward(x) + + 前向执行函数 + + :param x: 输入张量 + :type x: paddle.Tensor + + :return: 输出张量 + :rtype: paddle.Tensor + +.. py:class:: Discriminator(latent_dim=16) + + 基类::py:class:`paddle.nn.Layer` + + 判别器网络 + + :param latent_dim: 隐藏特征维度 + :type latent_dim: int + + .. py:method:: forward(x) + + 前向执行函数 + + :param x: 输入张量 + :type x: paddle.Tensor + + :return: 输出张量 + :rtype: paddle.Tensor + + +.. py:function:: generate_pauli_string_list(num_qubits, num_terms) + + 生成测量量子态所需要的可观测量。 + + :param num_qubits: 量子比特的数量。 + :type num_qubits: int + :param num_terms: 生成的可观测量的项数。 + :type num_terms: int + + :return: 返回生成的可观测量。 + :rtype: List[list] + + +.. py:class:: QCBM(num_qubits, num_depths, latent_dim=16) + + 基类::py:class:`paddle.nn.Layer` + + 量子玻尔兹曼机,这里即等价于量子神经网络。 + + :param num_qubits: 量子比特的数量。 + :type num_qubits: int + :param num_depths: complex entangled layers 的层数 + :type num_depths: int + :param latent_dim: 隐藏特征维度 + :type latent_dim: int + + .. py:method:: forward() + + 前向执行函数 + + :return: 输出在一系列哈密顿量上的观测值,即在 Z0, Z1, ..., X0, X1, ..., Y0, Y1, ... + :rtype: paddle.Tensor + + +.. py:function:: prior_sampling(expec_obs, batch_size) + + 模拟从 QCBM 中采样先验概率的过程。 + + :param expec_obs: 一系列观测值组成的向量,长度等于隐藏特征维度 + :type expec_obs: paddle.Tensor + :param batch_size: 一个 batch 中的样本数 + :type batch_size: int + + :return: 采样结果,值在 {-1, 1}中。 + :rtype: paddle.Tensor + + +.. py:function:: train(num_qubits = 8, num_depths = 4, lr_qnn = 0.005, batch_size = 128, latent_dim = 16, epochs= 21, lr_g = 0.0002, lr_d = 0.0002, beta1 = 0.5, beta2 = 0.9, manual_seed = 888) + :noindex: + + 训练 QCAAN 模型的函数。 + + :param num_qubits: 量子电路所包含的量子比特的数量。 + :type num_qubits: int + :param num_depths: complex entangled layers 的层数。 + :type num_depths: int + :param lr_qnn: 更新QNN中参数的学习率。 + :type lr_qnn: paddle.float32 + :param batch_size: 每一步迭代中的批大小。 + :type batch_size: int + :param latent_dim: 隐藏特征维度。 + :type latent_dim: int + :param epochs: 训练模型需要的 epoch 数目。 + :type epochs: int + :param lr_g: 更新生成器的学习率。 + :type lr_g: paddle.float32 + :param lr_d: 更新判别器的学习率。 + :type lr_d: paddle.float32 + :param beta1: 用于生成器和判别器的Adam 中的 beta1 参数。 + :type beta1: paddle.float32 + :param beta2: 用于生成器和判别器的Adam 中的 beta2 参数。 + :type beta2: paddle.float32 + :param manual_seed: 用于可复现的人工种子。 + :type manual_seed: int + + +.. py:function:: model_test(latent_dim = 16, params_path = "params", num_qubits = 8, num_depths = 4, manual_seed = 20230313,) + + 加载训练好的 QCAAN 模型参数,生成一些新图。最后存储这些图片。 + + :param latent_dim: 隐藏特征维度 + :type latent_dim: int + :param params_path: 加载模型参数的路径。 + :type params_path: str + :param num_qubits: 量子电路所包含的量子比特的数量。 + :type num_qubits: int + :param num_depths: complex entangled layers 的层数。 + :type num_depths: int + :param manual_seed: 用于可复现的人工种子。 + :type manual_seed: int + + + diff --git a/docs_zh_CN/source/paddle_quantum.qml.qnnmic.rst b/docs_zh_CN/source/paddle_quantum.qml.qnnmic.rst index da7e084..6eed426 100644 --- a/docs_zh_CN/source/paddle_quantum.qml.qnnmic.rst +++ b/docs_zh_CN/source/paddle_quantum.qml.qnnmic.rst @@ -25,6 +25,7 @@ QNNMIC 模型。 :rtype: paddle.Tensor .. py:function:: train(model_name, num_qubits, num_depths, observables, batch_size: int=20, num_epochs: int=4, learning_rate: float=0.1, dataset: str='SurfaceCrack', saved_dir: str='./', using_validation: bool=False, num_train: int=-1, num_val: int=-1, num_test: int=-1) + :noindex: 训练 QNNMIC 模型。 @@ -56,7 +57,8 @@ QNNMIC 模型。 :type num_test: Optional[int] .. py:function:: inference(image_path: str, num_samples: int, model_path: str, num_qubits: List, num_depths: List, observables: List) - + :noindex: + 使用 QNNMIC 模型进行推理。 :param image_path: 需要推理的数据集。 diff --git a/docs_zh_CN/source/paddle_quantum.qml.qnnqd.rst b/docs_zh_CN/source/paddle_quantum.qml.qnnqd.rst index 5a99c11..f018b44 100644 --- a/docs_zh_CN/source/paddle_quantum.qml.qnnqd.rst +++ b/docs_zh_CN/source/paddle_quantum.qml.qnnqd.rst @@ -25,7 +25,8 @@ QNNQD 模型。 :rtype: paddle.Tensor .. py:function:: train(model_name, num_qubits, num_depths, observables, batch_size: int=20, num_epochs: int=4, learning_rate: float=0.1, dataset: str='SurfaceCrack', saved_dir: str='./', using_validation: bool=False, num_train: int=-1, num_val: int=-1, num_test: int=-1) - + :noindex: + 训练 QNNQD 模型。 :param model_name: 模型的名字,用于保存模型。 @@ -56,8 +57,9 @@ QNNQD 模型。 :type num_test: Optional[int] .. py:function:: inference(image_path: str, num_samples: int, model_path: str, num_qubits: List, num_depths: List, observables: List) + :noindex: - 使用 QNNQD 模型进行推理。 + 使用 QNNQD 模型进行推理。 :param image_path: 需要推理的数据集。 :type image_path: str diff --git a/docs_zh_CN/source/paddle_quantum.qml.qsann.rst b/docs_zh_CN/source/paddle_quantum.qml.qsann.rst index 0b37dc7..02b079a 100644 --- a/docs_zh_CN/source/paddle_quantum.qml.qsann.rst +++ b/docs_zh_CN/source/paddle_quantum.qml.qsann.rst @@ -4,6 +4,7 @@ paddle\_quantum.qml.qsann 量子自注意力神经网络(Quantum Self-Attention Neural Network, QSANN)模型 .. py:function:: generate_observable(num_qubits, num_terms) + :noindex: 生成测量量子态所需要的可观测量。 @@ -57,6 +58,7 @@ paddle\_quantum.qml.qsann :rtype: Dict[str, int] .. py:class:: TextDataset(file_path, word_idx, pad_size) + :noindex: 基类::py:class:`paddle.io.Dataset` @@ -84,7 +86,8 @@ paddle\_quantum.qml.qsann :rtype: list .. py:function:: train(model_name, dataset, num_qubits, num_layers, depth_ebd, depth_query, depth_key, depth_value, batch_size, num_epochs, learning_rate, saved_dir, using_validation, early_stopping) - + :noindex: + 训练 VSQL 模型的函数。 :param model_name: 模型的名字,用于作为保存的模型参数的文件名。 @@ -117,6 +120,7 @@ paddle\_quantum.qml.qsann :type early_stopping: int .. py:function:: evaluate(model, data_loader) + :noindex: 对模型进行评估。 @@ -129,6 +133,7 @@ paddle\_quantum.qml.qsann :rtype: Tuple[float, float] .. py:function:: test(model, model_path, test_loader) + :noindex: 使用测试集对模型进行测试。 @@ -139,7 +144,8 @@ paddle\_quantum.qml.qsann :param test_loader: 测试集的数据加载器。 :type test_loader: list -.. py:function:: inference() +.. py:function:: inference(text, model_path, vocab_path, classes, num_qubits, num_layers, depth_ebd, depth_query, depth_key, depth_value) + :noindex: 推理函数。使用训练好的模型对输入的图片进行预测。 @@ -147,6 +153,10 @@ paddle\_quantum.qml.qsann :type text: str :param model_path: 保存的模型参数的文件路径。 :type model_path: str + :param vocab_path: 词表文件的路径。 + :type vocab_path: str + :param classes: 要预测的文本的类别。 + :type classes: List[str] :param num_qubits: 量子电路所包含的量子比特的数量。 :type num_qubits: int :param num_layers: 自注意力层的层数。 diff --git a/docs_zh_CN/source/paddle_quantum.qml.rst b/docs_zh_CN/source/paddle_quantum.qml.rst index 8882871..025e1ba 100644 --- a/docs_zh_CN/source/paddle_quantum.qml.rst +++ b/docs_zh_CN/source/paddle_quantum.qml.rst @@ -8,7 +8,10 @@ paddle\_quantum.qml .. toctree:: :maxdepth: 4 + paddle_quantum.qml.bert_qtc + paddle_quantum.qml.qcaan paddle_quantum.qml.qnnmic paddle_quantum.qml.qnnqd paddle_quantum.qml.qsann paddle_quantum.qml.vsql + diff --git a/docs_zh_CN/source/paddle_quantum.qml.vsql.rst b/docs_zh_CN/source/paddle_quantum.qml.vsql.rst index b85e507..dc774d6 100644 --- a/docs_zh_CN/source/paddle_quantum.qml.vsql.rst +++ b/docs_zh_CN/source/paddle_quantum.qml.vsql.rst @@ -16,7 +16,8 @@ paddle\_quantum.qml.vsql :rtype: numpy.ndarray .. py:class:: ImageDataset(file_path, num_samples, transform) - + :noindex: + 基类::py:class:`paddle.io.Dataset` 实现图片数据集的类。 @@ -66,7 +67,8 @@ paddle\_quantum.qml.vsql :rtype: paddle.Tensor .. py:function:: train(model_name, num_qubits, num_shadow, classes, batch_size, num_epochs, depth, datasets, saved_dir, learning_rate, using_validation, num_workers, early_stopping, num_train, num_dev, num_test) - + :noindex: + 训练 VSQL 模型的函数。 :param model_name: 模型的名字,用于作为保存的模型参数的文件名。 @@ -103,6 +105,7 @@ paddle\_quantum.qml.vsql :type num_test: int .. py:function:: evaluate(model, data_loader) + :noindex: 对模型进行评估。 @@ -115,6 +118,7 @@ paddle\_quantum.qml.vsql :rtype: Tuple[float, float] .. py:function:: test(model, model_path, test_loader) + :noindex: 使用测试集对模型进行测试。 @@ -126,6 +130,7 @@ paddle\_quantum.qml.vsql :type test_loader: paddle.io.DataLoader .. py:function:: inference(image_path, is_dir, model_path, num_qubits, num_shadow, classes, depth) + :noindex: 推理函数。使用训练好的模型对输入的图片进行预测。 diff --git a/docs_zh_CN/source/paddle_quantum.qpp.laurent.rst b/docs_zh_CN/source/paddle_quantum.qpp.laurent.rst index 3db86c7..f13e83b 100644 --- a/docs_zh_CN/source/paddle_quantum.qpp.laurent.rst +++ b/docs_zh_CN/source/paddle_quantum.qpp.laurent.rst @@ -12,15 +12,6 @@ paddle\_quantum.qpp.laurent :param coef: 劳伦多项式系数的列表,排列为 :math:`\{p_{-L}, ..., p_{-1}, p_0, p_1, ..., p_L\}` :type coef: np.ndarray - .. py:method:: __call__(X) - - 计算P(X)的值 - :param X: 输入X - :type X: Union[int, float, complex] - - :return: P(X) - :rtype: complex - .. py:property:: coef() 以上升顺序给出多项式的系数序列 @@ -44,51 +35,6 @@ paddle\_quantum.qpp.laurent .. py:property:: parity() 给出多项式的宇称 - - .. py:method:: __copy__() - - 复制劳伦多项式 - - :return: 复制后的多项式 - :rtype: Laurent - - .. py:method:: __add__(other) - - 劳伦多项式的相加 - - :param other: 一个标量或一个劳伦多项式 :math:`Q(x) = \sum_{j = -L}^{L} q_{j} X^j` - :type other: Any - - :raises TypeError: 不支持劳伦多项式和others的相加 - - .. py:method:: __mul__(other) - - 劳伦多项式的相乘 - - :param other: 一个标量或一个劳伦多项式 :math:`Q(x) = \sum_{j = -L}^{L} q_{j} X^j` - :type other: Any - - :raises TypeError: 不支持劳伦多项式和others的相乘 - - .. py:method:: __sub__(other) - - 劳伦多项式的相减 - - :param other: 一个标量或一个劳伦多项式 :math:`Q(x) = \sum_{j = -L}^{L} q_{j} X^j` - :type other: Any - - .. py:method:: __eq__(other) - - 劳伦多项式的相等 - - :param other: 一个标量或一个劳伦多项式 :math:`Q(x) = \sum_{j = -L}^{L} q_{j} X^j` - :type other: Any - - :raises TypeError: 不支持劳伦多项式和 ``others`` 的相等 - - .. py:method:: __str__() - - 打印劳伦多项式 .. py:method:: is_parity(p) diff --git a/docs_zh_CN/source/paddle_quantum.qsvt.qsp.rst b/docs_zh_CN/source/paddle_quantum.qsvt.qsp.rst index d3a3228..4e924e9 100644 --- a/docs_zh_CN/source/paddle_quantum.qsvt.qsp.rst +++ b/docs_zh_CN/source/paddle_quantum.qsvt.qsp.rst @@ -94,7 +94,8 @@ paddle\_quantum.qsvt.qsp :rtype: bool .. py:function:: update_polynomial(poly_p, poly_q, phi) - + :noindex: + 计算 :math:`P, Q` 经过一层量子信号处理后的多项式 :math:`\tilde{P}, \tilde{Q}` :param poly_p: 多项式 :math:`P(x)` diff --git a/docs_zh_CN/source/paddle_quantum.state.state.rst b/docs_zh_CN/source/paddle_quantum.state.state.rst index 7403a75..e5504bc 100644 --- a/docs_zh_CN/source/paddle_quantum.state.state.rst +++ b/docs_zh_CN/source/paddle_quantum.state.state.rst @@ -3,7 +3,7 @@ paddle\_quantum.state.state 量子态类的功能实现。 -.. py:class:: State(data, num_qubits=None, backend=None, dtype=None) +.. py:class:: State(data, num_qubits=None, backend=None, dtype=None, override=False) 基类::py:class:`object` @@ -17,6 +17,8 @@ paddle\_quantum.state.state :type backend: paddle_quantum.Backend, optional :param dtype: 量子态的数据类型。默认为 None,使用全局的默认数据类型。 :type dtype: str, optional + :param override: 是否跳过输入校验,仅限于内部开发使用。默认为 ``False``。 + :type override: bool, optional :raises ValueError: 无法识别后端 @@ -24,10 +26,16 @@ paddle\_quantum.state.state 得到量子态的列向量形式。 + :raises ValueError: 后端必须为 StateVector。 + :return: 量子态的列向量形式 + .. py:property:: bra() 得到量子态的行向量形式。 + :raises ValueError: 后端必须为 StateVector。 + :return: 量子态的行向量形式 + .. py:method:: normalize() 得到归一化后量子态 @@ -54,30 +62,6 @@ paddle\_quantum.state.state :return: 返回张量积 :rtype: State - .. py:method:: __matmul__(other) - - 得到与量子态或张量之间的乘积 - - :param other: 给定量子态 - :type other: State - :raises NotImplementedError: 不支持与该量子态进行乘积计算 - :raises ValueError: 无法对两个态向量相乘,请检查使用的后端 - - :return: 返回量子态的乘积 - :rtype: paddle.Tensor - - .. py:method:: __rmatmul__(other) - - 得到与量子态或张量之间的乘积 - - :param other: 给定量子态 - :type other: State - :raises NotImplementedError: 不支持与该量子态进行乘积计算 - :raises ValueError: 无法对两个态向量相乘,请检查使用的后端 - - :return: 返回量子态的乘积 - :rtype: paddle.Tensor - .. py:method:: numpy() 得到量子态的数据的 numpy 形式。 @@ -107,6 +91,15 @@ paddle\_quantum.state.state :return: 一个内容和当前量子态都相同的新的量子态。 :rtype: paddle_quantum.State + .. py:property:: oper_history() + + 储存在QPU后端的算子历史信息 + + :return: 算子的历史信息 + :rtype: List[Dict[str, Union[str, List[int], paddle.Tensor]]] + :raises NotImplementedError: 此属性应仅适用于 QuLeaf 后端。 + :raises ValueError: 无法获取算子历史信息,请先运行电路 + .. py:method:: expec_val(hamiltonian, shots: int) 量子态关于输入的可观测量的期望值。 @@ -120,7 +113,7 @@ paddle\_quantum.state.state :rtype: float - .. py:method:: measure(shots=0, qubits_idx=None, plot=False) + .. py:method:: measure(shots=0, qubits_idx=None, plot=False, record=False) 对量子态进行测量。 @@ -130,84 +123,21 @@ paddle\_quantum.state.state :type qubits_idx: Union[Iterable[int], int], optional :param plot: 是否画图。默认为 Flase,表示不画图。 :type plot: bool, optional - :raises Exception: 测量的次数必须大于0。 + :param record: 是否返回原始的测量结果记录。默认为 Flase,表示不返回。 + :type record: bool, optional + :raises ValueError: 测量的次数必须大于0。 + :raises NotImplementedError: Quleaf后端暂不支持record功能。 :raises NotImplementedError: 所指定的后端必须为量桨已经实现的后端。 :raises NotImplementedError: 输入的量子比特下标有误。 + :raises ValueError: 使用record功能要求测量次数必须大于0。 :return: 测量结果。 :rtype: dict -.. py:function:: _type_fetch(data) - - 获取数据的类型 - - :param data: 输入数据 - :type data: Union[np.ndarray, paddle.Tensor, State] - - :raises ValueError: 输入量子态不支持所选后端 - :raises TypeError: 无法识别输入量子态的数据类型 - - :return: 返回输入量子态的数据类型 - :rtype: str - -.. py:function:: _density_to_vector(rho) - - 将密度矩阵转换为态向量 - - :param rho: 输入的密度矩阵 - :type rho: Union[np.ndarray, paddle.Tensor] - - :raises ValueError: 输出量子态可能不为纯态 - - :return: 返回态向量 - :rtype: Union[np.ndarray, paddle.Tensor] - -.. py:function:: _type_transform(data, output_type) - - 将输入量子态转换成目标类型 - - :param data: 需要转换的数据 - :type data: Union[np.ndarray, paddle.Tensor, State] - :param output_type: 目标数据类型 - :type output_type: str - - :raises ValueError: 输入态不支持转换为目标数据类型 - - :return: 返回目标数据类型的量子态 - :rtype: Union[np.ndarray, paddle.Tensor, State] - -.. py:function:: is_state_vector(vec, eps) - - 检查输入态是否为量子态向量 - - :param vec: 输入的数据 :math:`x` - :type vec: Union[np.ndarray, paddle.Tensor] - :param eps: 容错率 - :type eps: float, optional - - :return: 返回是否满足 :math:`x^\dagger x = 1` ,以及量子比特数目或错误信息 - :rtype: Tuple[bool, int] - - .. note:: - 错误信息为: - * ``-1`` 如果上述公式不成立 - * ``-2`` 如果输入数据维度不为2的幂 - * ``-3`` 如果输入数据不为向量 - -.. py:function:: is_density_matrix(rho, eps) - - 检查输入数据是否为量子态的密度矩阵 - - :param rho: 输入的数据 ``rho`` - :type rho: Union[np.ndarray, paddle.Tensor] - :param eps: 容错率 - :type eps: float, optional + .. py:method:: reset_sequence(target_sequence=None) - :return: 返回输入数据 ``rho`` 是否为迹为1的PSD矩阵,以及量子比特数目或错误信息 - :rtype: Tuple[bool, int] + 根据输入顺序重置量子比特顺序 - .. note:: - 错误信息为: - * ``-1`` 如果 ``rho`` 不为PSD矩阵 - * ``-2`` 如果 ``rho`` 的迹不为1 - * ``-3`` 如果 ``rho`` 的维度不为2的幂 - * ``-4`` 如果 ``rho`` 不为一个方阵 + :param target_sequence: 目标顺序,默认为 ``None``。 + :type target_sequence: Union[List[int],None] + :return: 在输入比特顺序下的量子态 + :rtype: paddle_quantum.state.state.State diff --git a/introduction/PaddleQuantum_Ansatz_CN.ipynb b/introduction/PaddleQuantum_Ansatz_CN.ipynb new file mode 100644 index 0000000..7067887 --- /dev/null +++ b/introduction/PaddleQuantum_Ansatz_CN.ipynb @@ -0,0 +1,568 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 利用量桨的 ansatz 模块构造量子电路\n", + "\n", + "_Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved._" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`ansatz` 是基于量桨推出的用于实现各种电路拟设功能的工具集。`ansatz` 为量子计算领域的研究者提供了一系列的工具,使他们可以通过设计量子电路实现量子算法等任务。同时,`ansatz` 也提供了方便开发者进行功能扩展的方式。目前 `ansatz` 仍在不断完善,您可以将需求和建议通过 GitHub 的 issue 或 pull request 反馈给我们,我们会及时给出回复。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 搭建量子电路" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "量桨提供以下三种方式搭建量子电路:\n", + "- **直接利用量子门构造:** 量子电路可以表示为一些单比特量子旋转门和双比特门的组合,量桨中提供了包含 $R_y, R_x, R_z$ 单比特旋转门、双比特 CNOT 门等在内的多种量子门,具体可参见[量桨 API](https://qml.baidu.com/api/paddle_quantum.ansatz.circuit.html),利用这些量子门我们可以直接搭建量子电路;\n", + "- **通过设置 Oracle 构造:** 除了利用量桨提供的量子门构造量子电路外,对于一些量桨上没有的量子门,我们可以以通过利用酉算子构造 Oracle 再将其放置于电路中的方式搭建量子电路;\n", + "- **通过内置模板构造:** 量桨中提供了多种内置的参数化量子电路模板可以直接用于搭建量子电路,详细模板可参见[量桨 API](https://qml.baidu.com/api/paddle_quantum.ansatz.circuit.html)。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "让我们从具体的例子出发了解量桨中搭建量子电路的方法,下面演示了利用 `ansatz` 中的 `Circuit` 构造量子电路。" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "d:\\programs\\Anaconda\\envs\\pq\\lib\\site-packages\\openfermion\\hamiltonians\\hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "d:\\programs\\Anaconda\\envs\\pq\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "d:\\programs\\Anaconda\\envs\\pq\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import scipy\n", + "import paddle\n", + "from paddle_quantum.gate import RY, RX, RZ\n", + "from paddle_quantum.ansatz import Circuit\n", + "from paddle_quantum.state import ghz_state\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 直接利用量子门构造量子电路" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "下面演示构造单比特量子电路生成量子态 $\\frac{1}{\\sqrt{2}}(\\ket{0}+\\ket{1})$。" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tensor(shape=[2, 1], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(0.7071067690849304+0j)],\n", + " [(0.7071067690849304+0j)]])\n" + ] + } + ], + "source": [ + "# 创建单比特量子电路\n", + "cir = Circuit(1)\n", + "\n", + "# 设置 Hadamard 门\n", + "cir.h(0)\n", + "\n", + "# 输出量子态,量桨中默认输入态为零态\n", + "output_state = cir()\n", + "print(output_state.ket)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 通过设置 Oracle 构造量子电路" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "下面演示利用构造 Oracle 的方式构建电路实现 $e^{-i\\frac{\\phi}{2}Z}$ 的演化过程,设置输入态 $\\ket{\\psi}=\\frac{1}{\\sqrt{2}}(\\ket{0}+\\ket{1})$,则输出量子态为 $e^{-i\\frac{\\phi}{2}Z}\\ket{\\psi}$,其中 $Z$ 为 Pauli $Z$ 算符。" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def oracle_cir(num_qubits: int, phi: float) -> Circuit:\n", + " r\"\"\" 通过设置 Oracle 的方式构造量子电路\n", + " \n", + " Args:\n", + " num_qubits: 量子电路的量子比特数\n", + " phi: 未知参数输入\n", + "\n", + " Returns:\n", + " 利用 Oracle 创建完成的量子电路\n", + " \n", + " \"\"\"\n", + " # 生成酉算子\n", + " z = np.array([[1, 0],\n", + " [0, -1]])\n", + " oracle_unitary = paddle.to_tensor(scipy.linalg.expm(-1j * z * phi / 2))\n", + " # 创建量子电路\n", + " cir_oracle = Circuit(num_qubits)\n", + " # 添加 Oracle\n", + " cir_oracle.oracle(oracle_unitary, 0) \n", + "\n", + " return cir_oracle" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "经过量子电路后的输出态为:\n", + " Tensor(shape=[2, 1], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(0.6893781423568726-0.15734605491161346j)],\n", + " [(0.6893781423568726+0.15734605491161346j)]])\n" + ] + } + ], + "source": [ + "# 设置参数\n", + "PHI = np.pi / 7\n", + "NUM_QUBITS = 1\n", + "PSI = ghz_state(1)\n", + "CIR = oracle_cir(NUM_QUBITS, PHI)\n", + "# 输出量子态\n", + "print('经过量子电路后的输出态为:\\n', CIR(PSI).ket)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 内置模板构造量子电路" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "下面我们演示在量桨中如何利用内置模板搭建量子电路,这里我们选择的是表达能力较强的 `complex_entangled_layer`,其他模板可参见[量桨 API](https://qml.baidu.com/api/paddle_quantum.ansatz.circuit.html)。" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--U----*---------x--\n", + " | | \n", + "--U----x----*----|--\n", + " | | \n", + "--U---------x----*--\n", + " \n" + ] + } + ], + "source": [ + "N = 3 # 设置量子比特数\n", + "D = 1 # 设置内置模板的层数\n", + "\n", + "# 初始化量子电路\n", + "cir_ent_layer = Circuit(N) \n", + "# 搭建内置模板 complex_entangled_layer\n", + "cir_ent_layer.complex_entangled_layer(depth=D)\n", + "# 输出量子电路\n", + "print(cir_ent_layer)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 量子电路的具体构造" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 可视化量子电路" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "上一部分中输出了内置模板的量子电路,下面我们详细介绍在量桨中如何可视化量子电路。量桨提供了两种电路输出方式:`print(your_cir)` 和 `your_cir.plot()`。第一种方式由线条和量子门的符号表示,形式简单,便于展示复杂电路;第二种方式用方框表示量子门,形式直观。我们以生成 GHZ 态的电路为例,展示两种电路输出形式。" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def gen_ghz_cir(num_qubits: int) -> Circuit:\n", + " r\"\"\" 生成 GHZ 态的量子电路\n", + " \n", + " Args:\n", + " num_qubits: 量子电路的量子比特数\n", + "\n", + " Returns:\n", + " 生成 GHZ 态的量子电路\n", + " \n", + " \"\"\" \n", + " # 创建量子电路\n", + " ghz_cir = Circuit(num_qubits)\n", + " # 设置 Hadamard 门\n", + " ghz_cir.h(0)\n", + " # 设置 CNOT 门\n", + " for i in range(1, num_qubits):\n", + " ghz_cir.cnot([0, i])\n", + "\n", + " return ghz_cir" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "下面我们利用构造的电路生成 $3$ 量子比特的 GHZ 态 $\\frac{1}{\\sqrt{2}}(\\ket{000}+\\ket{111})$。" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "经过量子电路后的输出态为:\n", + " Tensor(shape=[8, 1], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(0.7071067690849304+0j)],\n", + " [0j ],\n", + " [0j ],\n", + " [0j ],\n", + " [0j ],\n", + " [0j ],\n", + " [0j ],\n", + " [(0.7071067690849304+0j)]])\n" + ] + } + ], + "source": [ + "# 调用生成 GHZ 态的函数\n", + "ghz_3_cir = gen_ghz_cir(3)\n", + "# 输出量子态,量桨默认输入态为零态\n", + "ghz_3_state = ghz_3_cir()\n", + "print('经过量子电路后的输出态为:\\n', ghz_3_state.ket)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "可视化量子电路的两种方式:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "第一种量子电路输出方式:\n", + "\n", + "--H----*----*--\n", + " | | \n", + "-------x----|--\n", + " | \n", + "------------x--\n", + " \n", + "第二种量子电路输出方式:\n", + "\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 输出量子电路\n", + "print('第一种量子电路输出方式:')\n", + "print()\n", + "print(ghz_3_cir)\n", + "print('第二种量子电路输出方式:\\n')\n", + "ghz_3_cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 量子门的一般性构造" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "接下来,我们以在量子电路中设置单比特 $R_y, R_x, R_z$ 门和两比特 CNOT 门为例,展示如何进行添加或删减量子门的一般性构造。" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "添加量子门后的电路为:\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "删除量子门后的电路为:\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 创建 3 量子比特电路\n", + "cir = Circuit(3)\n", + "# 设置参数并自定义量子门,这里我们选择 Ry, Rx, Rz 门\n", + "param = np.random.rand(2)\n", + "ry_gate = RY(param=param, qubits_idx=[0, 2]) # 参数可选填,默认情况下 RY 类随机生成一组参数\n", + "rx_gate = RX(param=param, qubits_idx=[0, 1])\n", + "rz_gate = RZ(param=param, qubits_idx=[1, 2])\n", + "# 在量子电路中插入量子门\n", + "cir.append(ry_gate)\n", + "cir.append(rx_gate)\n", + "cir.insert(index=2, operator=rz_gate) # index 指定插入的位置,operator 指定插入的量子门\n", + "# 输出量子电路,这里我们选择较直观的 plot 方法\n", + "print('添加量子门后的电路为:')\n", + "cir.plot()\n", + "\n", + "# 在量子电路中删除 Rx 门\n", + "cir.pop(index=1, operator=rx_gate) # index 指定删除的位置,operator 指定删除的量子门,该参数可选择输入\n", + "print('删除量子门后的电路为:')\n", + "cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "除了利用 `append` 这类方法插入量子门外,还可以用下述方式实现量子门的设置:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 创建 3 量子比特电路\n", + "cir = Circuit(3)\n", + "# 设置参数\n", + "theta = np.full([2], np.pi)\n", + "# 设置量子门\n", + "# 单量子比特 Ry 门\n", + "cir.ry(qubits_idx='full', param=theta[0]) # qubits_idx='full' 指定量子门作用在所有编号的量子比特上,单比特量子门的 qubits_idx 默认为 full;param 指定输入参数,默认情况下由 Ry 门随机生成\n", + "# 两量子比特 CNOT 门\n", + "cir.cnot(qubits_idx='linear') # qubits_idx='linear' 指定量子门作用方式为 linear,多比特量子门的 qubits_idx 默认为 cycle\n", + "# 单量子比特 Rx 门\n", + "cir.rx(qubits_idx='even') # qubits_idx='even' 指定量子门作用在编号为偶数的量子比特上,默认为 full;param 指定输入参数,默认情况下由 Rx 门随机生成\n", + "# 两量子比特 CNOT 门\n", + "cir.cnot(qubits_idx='cycle') # qubits_idx='cycle' 指定量子门作用方式为 cycle,多比特量子门的 qubits_idx 默认为 cycle\n", + "# 单量子比特 Rz 门\n", + "cir.rz(qubits_idx='odd', param=theta[1]) # qubits_idx='odd' 指定量子门作用在编号为奇数的量子比特上,默认为 full;param 指定输入参数,默认情况下由 Rz 门随机生成\n", + "# 两量子比特 CNOT 门\n", + "cir.cnot([0, 2]) # qubits_idx 为 list 指定量子门作用在编号为 0 和 2 的量子比特上,其中 0 为控制位 2 为受控位\n", + "# 输出量子电路\n", + "cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "前面提到的构造量子电路都需要给定量子电路大小,即量子比特数,除了这种方式外,量桨还提供了不需要输入量子比特数的动态电路构造方式,下面我们给出一简单示例来展示该类型电路的构造方法。" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cir = Circuit() # 未指定电路大小\n", + "cir.ry([0, 1]) # 电路大小更新为 2\n", + "cir.h() # 以总比特数为 2 设置 Hadamard 门\n", + "cir.plot() # 绘制此时的 2 比特电路\n", + "cir.rx([2, 3]) # 电路大小根据量子门的添加更新为 4\n", + "cir.cnot() # 以总比特数为 4 设置 CNOT 门\n", + "cir.plot() # 绘制更新后的 4 比特电路" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pq", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Ansatz_EN.ipynb b/introduction/PaddleQuantum_Ansatz_EN.ipynb new file mode 100644 index 0000000..7f8c4b9 --- /dev/null +++ b/introduction/PaddleQuantum_Ansatz_EN.ipynb @@ -0,0 +1,571 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Construct Quantum Circuits with Paddle Quantum's ansatz\n", + "\n", + "_Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved._" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`ansatz`, which builds on top of Paddle Quantum, is designed to be a toolkit for implementing various quantum circuits. It provides high level APIs for researchers who are interested in implementing quantum algorithm with quantum circuits. At the same time, `ansatz` also provides a convenient way for developers to extend the functionality. `ansatz` is currently under active development, feel free to join us by opening issues or pull requests." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Construct the quantum circuits" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Paddle Quantum provides the following three ways to build quantum circuits:\n", + "\n", + "- **Direct construction of quantum circuits using quantum gates.** Quantum circuit can be expressed as a combination of single-qubit quantum gates and two-qubit gates. Paddle Quantum provides a variety of quantum gates including $R_y, R_x, R_z$ single-qubit gate, two-qubit CNOT gate, etc. Specific details can see [API of Paddle Quantum](https://qml.baidu.com/api/paddle_quantum.ansatz.circuit.html). Using these quantum gates we can directly to create quantum circuits.\n", + "\n", + "- **Use oracle to construct quantum circuits.** In addition to constructing quantum circuits using quantum gates provided by Paddle Quantum, we can also construct quantum circuits using the oracle of a unitary, then implement it in the circuit. \n", + "\n", + "- **Use built-in circuit templates to construct quantum circuits.** Paddle Quantum provides some built-in circuit templates to make user's life easier. For more templates, see [API of Paddle Quantum](https://qml.baidu.com/api/paddle_quantum.ansatz.circuit.html)." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's start from a specific example to understand the way to construct a quantum circuit in Paddle Quantum. First we import the necessary packages." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "d:\\programs\\Anaconda\\envs\\pq\\lib\\site-packages\\openfermion\\hamiltonians\\hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "d:\\programs\\Anaconda\\envs\\pq\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "d:\\programs\\Anaconda\\envs\\pq\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import scipy\n", + "import paddle\n", + "from paddle_quantum.gate import RY, RX, RZ\n", + "from paddle_quantum.ansatz import Circuit\n", + "from paddle_quantum.state import ghz_state\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Directly construction of quantum circuits using quantum gates." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following code demonstrates the construction of a single-qubit quantum circuit to generate $\\frac{1}{\\sqrt{2}}(\\ket{0}+\\ket{1})$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tensor(shape=[2, 1], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(0.7071067690849304+0j)],\n", + " [(0.7071067690849304+0j)]])\n" + ] + } + ], + "source": [ + "# Create a single qubit circuit\n", + "cir = Circuit(1)\n", + "\n", + "# Set the Hadamard gate\n", + "cir.h(0)\n", + "\n", + "# Output quantum circuit\n", + "output_state = cir()\n", + "print(output_state.ket)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Use oracle to construct quantum circuits" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We use the oracle of $e^{-i\\frac{\\phi}{2}Z}$ to evolve the input state $\\ket{\\psi}=\\frac{1}{\\sqrt{2}}(\\ket{0}+\\ket{1})$. Then the output state is $e^{-i\\frac{\\phi}{2}Z}\\ket{\\psi}$, where $Z$ is Pauli $Z$." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "def oracle_cir(num_qubits: int, phi: float) -> Circuit:\n", + " r\"\"\" Use oracle to construct quantum circuits\n", + " \n", + " Args:\n", + " num_qubits: the number of qubits\n", + " phi: unknown parameter\n", + "\n", + " Returns:\n", + " Circuit\n", + " \n", + " \"\"\" \n", + " # Create the unitary\n", + " z = np.array([[1, 0],\n", + " [0, -1]])\n", + " oracle_unitary = paddle.to_tensor(scipy.linalg.expm(-1j * z * phi / 2))\n", + " # Create a quantum circuit\n", + " cir_oracle = Circuit(num_qubits)\n", + " # Implement the oracle into the circuit \n", + " cir_oracle.oracle(oracle_unitary, 0) \n", + "\n", + " return cir_oracle" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The output state is \n", + " Tensor(shape=[2, 1], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(0.6893781423568726-0.15734605491161346j)],\n", + " [(0.6893781423568726+0.15734605491161346j)]])\n" + ] + } + ], + "source": [ + "# Set parameters\n", + "PHI = np.pi / 7\n", + "NUM_QUBITS = 1\n", + "PSI = ghz_state(1)\n", + "CIR = oracle_cir(NUM_QUBITS, PHI)\n", + "# Output state\n", + "print('The output state is \\n', CIR(PSI).ket)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Use built-in circuit templates to construct quantum circuits" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Here we demonstrate how to build a quantum circuit using built-in circuit templates. We choose the `complex_entangled_layer`. For other templates, see [API of Paddle Quantum](https://qml.baidu.com/api/paddle_quantum.ansatz.circuit.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--U----*---------x--\n", + " | | \n", + "--U----x----*----|--\n", + " | | \n", + "--U---------x----*--\n", + " \n" + ] + } + ], + "source": [ + "N = 3 # The number of qubits\n", + "D = 1 # The depth of the template\n", + "\n", + "# Initialize the quantum circuit\n", + "cir_ent_layer = Circuit(N) \n", + "# Construct complex_entangled_layer\n", + "cir_ent_layer.complex_entangled_layer(depth=D)\n", + "# Print circuit\n", + "print(cir_ent_layer)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Specific circuit construction" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Visualize circuit" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the previous section, we print the built-in template. Now we describe in detail how to visualize the circuit in Paddle Quantum. Two circuit output modes are provided: `print(your_cir)` and `your_cir.plot()`. The first method is represented by lines and symbols, which is simple in form and easy to show complex circuits. The second one is to use a box to represent the quantum gate, the form is more intuitive than the first one. We take a circuit generating the GHZ state as an example in the following to show two circuit output modes." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [], + "source": [ + "def gen_ghz_cir(num_qubits: int) -> Circuit:\n", + " r\"\"\" Quantum circuit to generate GHZ state\n", + " \n", + " Args:\n", + " num_qubits: the number of qubits\n", + "\n", + " Returns:\n", + " Circuit\n", + " \n", + " \"\"\" \n", + " # Create a quantum circuit\n", + " ghz_cir = Circuit(num_qubits)\n", + " # Add the Hadamard gate to the first qubit\n", + " ghz_cir.h(0)\n", + " # Add CNOT gates\n", + " for i in range(1, num_qubits):\n", + " ghz_cir.cnot([0, i])\n", + "\n", + " return ghz_cir" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the constructed circuit to generate $3$-qubit GHZ state $\\frac{1}{\\sqrt{2}}(\\ket{000}+\\ket{111})$." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The output state is\n", + " Tensor(shape=[8, 1], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(0.7071067690849304+0j)],\n", + " [0j ],\n", + " [0j ],\n", + " [0j ],\n", + " [0j ],\n", + " [0j ],\n", + " [0j ],\n", + " [(0.7071067690849304+0j)]])\n" + ] + } + ], + "source": [ + "# Use the function that generates the GHZ state\n", + "ghz_3_cir = gen_ghz_cir(3)\n", + "# Output quantum state\n", + "ghz_3_state = ghz_3_cir()\n", + "print('The output state is\\n', ghz_3_state.ket)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Two ways to visualize quantum circuits:" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "First way to show the circuit:\n", + "\n", + "--H----*----*--\n", + " | | \n", + "-------x----|--\n", + " | \n", + "------------x--\n", + " \n", + "Second way to show the circuit: \n", + "\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Print circuits\n", + "print('First way to show the circuit:')\n", + "print()\n", + "print(ghz_3_cir)\n", + "print('Second way to show the circuit: \\n')\n", + "ghz_3_cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### General construction of quantum gates" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Next, we take $R_y, R_x, R_z$ and CNOT gates as an example to show a general construction of how to add or remove gates." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The quantum circuit after adding gates is: \n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The quantum circuit after removing gates is:\n" + ] + }, + { + "data": { + "image/png": "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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Initialize a 3-qubit quantum circuit\n", + "cir = Circuit(3)\n", + "# Set parameters and customize quantum gates. Here we select Ry, Rx, Rz gates\n", + "param = np.random.rand(2)\n", + "ry_gate = RY(param=param, qubits_idx=[0, 2]) # By default, Ry randomly generates a set of parameters\n", + "rx_gate = RX(param=param, qubits_idx=[0, 1])\n", + "rz_gate = RZ(param=param, qubits_idx=[1, 2])\n", + "# Add quantum gates\n", + "cir.append(ry_gate)\n", + "cir.append(rx_gate)\n", + "cir.insert(index=2, operator=rz_gate) # index specifies where to insert, and operator specifies which quantum gate to insert\n", + "# Print quantum gate\n", + "print('The quantum circuit after adding gates is: ')\n", + "cir.plot()\n", + "\n", + "# Remove Rx gate\n", + "cir.pop(index=1, operator=rx_gate) # index specifies where to remove, and operator specifies which quantum gate to remove\n", + "print('The quantum circuit after removing gates is:')\n", + "cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition to inserting a quantum gate using methods such as `append`, it can also be realized in the following ways:" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Initialize a 3-qubit quantum circuit\n", + "cir = Circuit(3)\n", + "# Set parameters\n", + "theta = np.full([2], np.pi)\n", + "# Add quantum gates\n", + "# Add single-qubit gate Ry \n", + "cir.ry(qubits_idx='full', param=theta[0]) # qubits_idx='full': specifies that all qubits are applied, defaults qubits_idx of the single-qubit gate to 'cycle'. param: parameters of the gates, defaults to None, i.e., randomly generated by Ry gate.\n", + "# Add two-qubit gate CNOT\n", + "cir.cnot(qubits_idx='linear') # qubits_idx='linear': specifies that the implement of the CNOT gate is linear, default qubits_idx of the multi-qubit quantum gate is cycle.\n", + "# Add single qubit gate Rx \n", + "cir.rx(qubits_idx='even') # qubits_idx='even': specifies that even number of qubits are applied, defaults of single-qubit gate to 'cycle'. param: parameters of the gates, defaults to None, i.e., randomly generated by Rx gate.\n", + "# Add two-qubit gate CNOT\n", + "cir.cnot(qubits_idx='cycle') # qubits_idx='cycle': specifies that the implement of the CNOT gate is cycle, default qubits_idx of the multi-qubit quantum gate is cycle.\n", + "# Add single qubit gate Rz\n", + "cir.rz(qubits_idx='odd', param=theta[1]) # qubits_idx='odd': specifies that odd number of qubits are applied, defaults of single-qubit gate to 'cycle'. param: parameters of the gates, defaults to None, i.e., randomly generated by Rz gate.\n", + "# Add two-qubit gate CNOT\n", + "cir.cnot([0, 2]) # qubits_idx is [0, 2] that specifies the CNOT acting on qubits numbered 0 and 2, where 0 is the control qubit and 2 is the target qubit.\n", + "# Print circuit\n", + "cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The quantum circuit construction mentioned above requires a given circuit size, that is, qubit number. In addition to this way, Paddle Quantum also provides a dynamic circuit construction method that does not require input qubit number. The following is a simple example to demonstrate this method." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cir = Circuit() # Do not give a qubit number\n", + "cir.ry([0, 1]) # The size of this circuit is updated to 2\n", + "cir.h() # Set Hadamard gates\n", + "cir.plot() # Draw this 2-qubit circuit\n", + "cir.rx([2, 3]) # The size of this circuit is updated to 4 because of the added Rx gates\n", + "cir.cnot() # Set CNOT gates\n", + "cir.plot() # Draw the updated 4-qubit circuit" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "pq", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Custom_CN.ipynb b/introduction/PaddleQuantum_Custom_CN.ipynb new file mode 100644 index 0000000..f62226e --- /dev/null +++ b/introduction/PaddleQuantum_Custom_CN.ipynb @@ -0,0 +1,338 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 利用 Paddle Quantum 的 `gate` 和 `channel` 模块构建量子操作\n", + "\n", + "_Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved._\n", + "\n", + "量桨的 `gate` 和 `channel` 模块可以用于构建量子操作。它们可以直接作用在一个 `State` 上或者插入到一个量子电路当中。量桨提供了方便的接口可以快速地创建常见的量子操作,用户也可以创建自定义操作。" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "import paddle_quantum\n", + "from paddle_quantum.ansatz import Circuit\n", + "from paddle_quantum.gate.custom import Oracle\n", + "from paddle_quantum.channel import *\n", + "from paddle_quantum.state.common import zero_state\n", + "from paddle_quantum.qinfo import qft_generation, random_channel\n", + "from paddle_quantum.linalg import dagger" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 自定义量子门\n", + "之前,我们已经看到如何创建一个量子门并将其插入到电路中。用户也可以使用 Oracle 类来实现自定义的量子门。\n", + "\n", + "例如,考虑 n 量子比特下的傅里叶逆变换 (Inverse Quantum Fourier Transform, inverse QFT),它是一个酉算符,其矩阵形式为\n", + "\n", + "$$\n", + "\\frac{1}{\\sqrt{N}}\\begin{pmatrix}\n", + " 1 & 1 & 1 & \\ldots & 1 \\\\\n", + " 1 & \\omega^{N-1} & \\omega^{N-2} & \\ldots & \\omega \\\\\n", + " 1 & \\omega^{2(N-1)} & \\omega^{2(N-2)} & \\ldots & \\omega^2 \\\\\n", + " \\ldots & \\ldots & \\ldots & \\ldots & \\ldots \\\\\n", + " 1 & \\omega^{(N-1)(N-1)} & \\omega^{(N-1)(N-2)} & \\ldots & \\omega^{N-1}\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "其中, $N=2^n$ 是系统的维度,$\\omega = e^{2\\pi i/N}$。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "下面的代码创建了一个实现 2 比特傅里叶逆变换的 oracle 。" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "unitary = qft_generation(2) # 通过量桨内置函数得到2比特QFT的矩阵\n", + "unitary = dagger(unitary) # 通过量桨内置函数对矩阵进行共轭转置,得到 inverse QFT 的矩阵 (对于么正矩阵来说,共轭转置就是求逆的过程)\n", + "QFT_inverse = Oracle(unitary)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "它是一个量子门,我们可以把它插入到一个量子电路当中并且打印电路。" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cir = Circuit(3)\n", + "cir.h()\n", + "cir.cnot([0,1])\n", + "cir.append(QFT_inverse) # 插入 oracle \n", + "cir.cnot([2,1])\n", + "cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**注意**:假如需要打印电路,那么它不能是不连续的(比如作用在第 1 和第 3 量子比特上),否则将报错。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "用户可以通过改变 gate_info 的内容去修改打印电路时 oracle 的样式。" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gate_info = {\n", + " 'texname': r'$QFT^{\\dagger}$', # 更改打印的时候 oracle 的名字\n", + " 'plot_width': 1.5, # 调整打印的时候 oracle 的宽度\n", + "}\n", + "# 更新 oracle 的 gate_info\n", + "QFT_inverse.gate_info.update(gate_info)\n", + "# 创建和之前一样的电路\n", + "cir = Circuit(3)\n", + "cir.h()\n", + "cir.cnot([0,1])\n", + "cir.append(QFT_inverse) # 插入 oracle\n", + "cir.cnot([2,1])\n", + "cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "另外一种插入 oracle 的方法是在搭建电路的时候直接使用 `Circuit.oracle`。" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cir=Circuit(3)\n", + "cir.h()\n", + "cir.cnot([0,1])\n", + "# 直接使用 cir.oracle 去构建一个 oracle 门。构建的同时可以给出 gate_info 的自定义内容\n", + "cir.oracle(unitary, qubits_idx=[0,1], latex_name=r'$QFT^{\\dagger}$', plot_width=1.5) \n", + "cir.cnot([2,1])\n", + "cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 量子信道\n", + "\n", + "量桨同时支持构建通用的量子操作,即构建量子信道。\n", + "\n", + "构建信道的方法有两种。一种是通过量桨构建固定模式的信道,或者也可以构建一个自定义信道。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**注意**: `gate` 类可以在 `state_vecotr` 或 `density_matrix` 后端下运行,而 `channel` 只能在 `density_matrix` 后端运行。" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "paddle_quantum.set_backend('density_matrix') # 更改后端为 'density_matrix'" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "例如,我们可以构建一个比特反转信道,然后作用在 0 态上。常用信道的详细列表可参见 [量桨API](https://qml.baidu.com/api/paddle_quantum.channel.common.html)。" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.49999997+0.j 0. +0.j]\n", + " [0. +0.j 0.49999997+0.j]]\n" + ] + } + ], + "source": [ + "bit_flip_channel = BitFlip(prob=0.5, num_qubits=1) # 定义一个单比特比特反转信道,反转概率为 0.5\n", + "input = zero_state(1)\n", + "output = bit_flip_channel(input) # 作用信道在 0 态上\n", + "print(output)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "自定义信道可以通过其 Kraus, Stinespring 或者 Choi 表达式构建。下面我们展示如何使用这三种不同的表达方式构建一个自定义信道。我们使用量桨的内置函数去随机生成这些表达方式。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**注意**: 量桨里对 Choi 矩阵的定义是信道作用在第二个系统上,即\n", + "$$\n", + " J(\\Lambda) = \\sum_{i,j} |i\\rangle\\langle j| \\otimes \\Lambda(|i\\rangle\\langle j|).\n", + "$$\n", + "其中,$\\Lambda$ 表示信道。" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "# 随机生成一组 Kraus 算子\n", + "kraus = random_channel(num_qubits=1, target='Kraus') \n", + "# 通过 Kraus 算子构建信道\n", + "custom_kraus = KrausRepr(kraus)\n", + "\n", + "# 随机生成一个Stinespring 保距映射\n", + "stinespring = random_channel(num_qubits=1, target='Stinespring')\n", + "# 通过 Stinespring 保距映射构建信道\n", + "custom_stinespring = StinespringRepr(stinespring)\n", + "\n", + "# 随机生成一个 Choi 矩阵\n", + "choi = random_channel(num_qubits=1, target='Choi')\n", + "# 通过 Choi 矩阵构建信道\n", + "custom_choi = ChoiRepr(choi)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "之前看到我们可以把一个量子门插入到电路当中,我们同样也可以把一个信道以相同的方法插入到电路当中。不过,目前量桨并不支持打印含有信道的电路。" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [], + "source": [ + " # 默认情况下,信道会作用在第一个比特上。我们可以通过在构建信道的时候给出 qubits_idx 的值来指定它作用在哪个比特上。\n", + "custom_choi = ChoiRepr(choi, qubits_idx=[2])\n", + "cir = Circuit(3)\n", + "cir.append(bit_flip_channel) # 在电路的末尾插入信道\n", + "cir.h()\n", + "cir.insert(index=2, operator = custom_choi) # 在电路指定位置插入一个信道\n", + "cir.bit_flip(0.5, qubits_idx=[2]) # 在构建电路的时候直接构建信道" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "PaddleQu", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.15" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "f5d4b275a355082aa93d1cfb501360a5fbfc9f440cd049520a322ef6c5deb126" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Custom_EN.ipynb b/introduction/PaddleQuantum_Custom_EN.ipynb new file mode 100644 index 0000000..af6d1ef --- /dev/null +++ b/introduction/PaddleQuantum_Custom_EN.ipynb @@ -0,0 +1,340 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Implement quantum operations using Paddle Quantum's `gate` and `channel`\n", + "\n", + "_Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved._\n", + "\n", + "The `gate` and `channel` modules allow basic quantum operations to be defined. They can act on a state object directly or be inserted into a quantum circuit. Paddle Quantum provides a list of common operations but customized ones can also be created." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "import paddle_quantum\n", + "from paddle_quantum.ansatz import Circuit\n", + "from paddle_quantum.gate.custom import Oracle\n", + "from paddle_quantum.channel import *\n", + "from paddle_quantum.state.common import zero_state\n", + "from paddle_quantum.qinfo import qft_generation, random_channel\n", + "from paddle_quantum.linalg import dagger" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Custom gates\n", + "Previously, we've seen how to create a gate object and insert it into a circuit. Users can also implement customized unitary operation using the Oracle class.\n", + "\n", + "For example, consider the n qubit inverse quantum Fourier transform (QFT), it's a unitary operation whose matrix is given by\n", + "\n", + "$$\n", + "\\frac{1}{\\sqrt{N}}\\begin{pmatrix}\n", + " 1 & 1 & 1 & \\ldots & 1 \\\\\n", + " 1 & \\omega^{N-1} & \\omega^{N-2} & \\ldots & \\omega \\\\\n", + " 1 & \\omega^{2(N-1)} & \\omega^{2(N-2)} & \\ldots & \\omega^2 \\\\\n", + " \\ldots & \\ldots & \\ldots & \\ldots & \\ldots \\\\\n", + " 1 & \\omega^{(N-1)(N-1)} & \\omega^{(N-1)(N-2)} & \\ldots & \\omega^{N-1}\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "where $N=2^n$ is the dimension of the Hilbert space and $\\omega = e^{2\\pi i/N}$." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The following code creates an oracle that implements a 2-qubit inverse QFT." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "unitary = qft_generation(2) # obtain matrix for 2-qubit QFT using Paddle Quantum's built-in function\n", + "unitary = dagger(unitary) # obtain matrix for inverse QFT by calculating conjugate transpose of QFT matrix using Paddle Quantum's built-in function\n", + "QFT_inverse = Oracle(unitary)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As a gate object, we can insert it into a circuit and print the circuit. " + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cir = Circuit(3)\n", + "cir.h()\n", + "cir.cnot([0,1])\n", + "cir.append(QFT_inverse) # insert the oracle\n", + "cir.cnot([2,1])\n", + "cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note**: to print the oracle, it must not be disconnected, otherwise error message will be displayed." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n", + "To change how the oracle is printed, users can modify the content of gate_info. Users can change the name of the oracle printed and the width of the gate in the plot." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "gate_info = {\n", + " 'texname': r'$QFT^{\\dagger}$', # change the name of the oracle when printing the circuit\n", + " 'plot_width': 1.5, # change the width of the box representing the oracle\n", + "}\n", + "# update gate_info of the oracle\n", + "QFT_inverse.gate_info.update(gate_info)\n", + "# create the same circuit as before\n", + "cir = Circuit(3)\n", + "cir.h()\n", + "cir.cnot([0,1])\n", + "cir.append(QFT_inverse) # insert the oracle gate\n", + "cir.cnot([2,1])\n", + "cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Another way of inserting an oracle into a circuit is by calling `Circuit.oracle` directly when creating the circuit." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cir=Circuit(3)\n", + "cir.h()\n", + "cir.cnot([0,1])\n", + "# call cir.oracle directly to create an oracle gate, its gate_info can also be specified when creating\n", + "cir.oracle(unitary, qubits_idx=[0,1], latex_name=r'$QFT^{\\dagger}$', plot_width=1.5) \n", + "cir.cnot([2,1])\n", + "cir.plot()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Channel\n", + "\n", + "Paddle Quantum also supports channel as the most general quantum operation.\n", + "\n", + "There are two ways of creating a channel. Users can either create one of the common channels provided by Paddle Quantum, or create a custom channel." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note**: Unlike `gate` object which supports both in `'state_vector'` and `'density_matrix'` backend, `channel` must be used in `'density_matrix'` backend." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "paddle_quantum.set_backend('density_matrix') # set the backend to density matrix" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For example, we can create a bit flip channel and apply it to the zero state. For the full list of common channels, see [API of Paddle Quantum](https://qml.baidu.com/api/paddle_quantum.channel.common.html)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.49999997+0.j 0. +0.j]\n", + " [0. +0.j 0.49999997+0.j]]\n" + ] + } + ], + "source": [ + "bit_flip_channel = BitFlip(prob=0.5, num_qubits=1) # define a single qubit bit flip channel with probability 0.5\n", + "input = zero_state(1)\n", + "output = bit_flip_channel(input) # apply bit flip channel to input zero state\n", + "print(output)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "A custom channel can be created using either its Kraus operators, Stinespring isometry, or Choi matrix. We show how to create a custom channel using these three different representations. We generate them randomly using the built-in function from Paddle Quantum." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Note**: the convention for Choi matrix in PaddleQuantum is that the channel acts on the second system, i.e.\n", + "\n", + "$$\n", + " J(\\Lambda) = \\sum_{i,j} |i\\rangle\\langle j| \\otimes \\Lambda(|i\\rangle\\langle j|).\n", + "$$\n", + "where $\\Lambda$ denotes the channel." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "# generate Kraus operators of a random channel\n", + "kraus = random_channel(num_qubits=1, target='Kraus') \n", + "# create channel using Kraus operators\n", + "custom_kraus = KrausRepr(kraus)\n", + "\n", + "# generate Stinespring isometry of a random channel\n", + "stinespring = random_channel(num_qubits=1, target='Stinespring')\n", + "# create channel using Stinespring isometry\n", + "custom_stinespring = StinespringRepr(stinespring)\n", + "\n", + "# generate Choi matrix of a random channel\n", + "choi = random_channel(num_qubits=1, target='Choi')\n", + "# create channel using Choi matrix\n", + "custom_choi = ChoiRepr(choi)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Channel can also be inserted into a circuit using the same syntax as for gate. However, currently printing circuit containing a channel is not supported." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + " # by default, the channel would act on qubit with index 0, we can specify which qubit it acts on by providing qubits_idx\n", + "custom_choi = ChoiRepr(choi, qubits_idx=[2])\n", + "cir = Circuit(3)\n", + "cir.append(bit_flip_channel) # insert a channel object at the end of the circuit\n", + "cir.h()\n", + "cir.insert(index=2, operator = custom_choi) # insert a channel object at specific position\n", + "cir.bit_flip(0.5, qubits_idx=[2]) # create a channel when building the circuit" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "PaddleQu", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.15" + }, + "orig_nbformat": 4, + "vscode": { + "interpreter": { + "hash": "f5d4b275a355082aa93d1cfb501360a5fbfc9f440cd049520a322ef6c5deb126" + } + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Hamiltonian_CN.ipynb b/introduction/PaddleQuantum_Hamiltonian_CN.ipynb new file mode 100644 index 0000000..a501495 --- /dev/null +++ b/introduction/PaddleQuantum_Hamiltonian_CN.ipynb @@ -0,0 +1,269 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 量桨哈密顿量模块简介\n", + "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*\n", + "\n", + "`Hamiltonian` 模块是量桨封装的与哈密顿量相关的模块。用户可以通过该模块,以泡利字符串的形式快速创建自定义哈密顿量,以及获取哈密顿量的各相关信息。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 哈密顿量的创建\n", + "\n", + "量子系统的哈密顿量是与系统总能量相关的可观测量,在 [变分量子本征值求解器](https://qml.baidu.com/tutorials/quantum-simulation/variational-quantum-eigensolver.html) 和 [利用Product Formula模拟时间演化](https://qml.baidu.com/tutorials/quantum-simulation/hamiltonian-simulation-with-product-formula.html) 等量子模拟算法中有着重要应用。在量子计算中,哈密顿量需要表示成量子计算机能处理的泡利算子张量积求和的形式。比如,如下哈密顿量就是以这种形式来表示的:\n", + "\n", + "$$\n", + "H = Z \\otimes Z \\otimes I + I \\otimes X \\otimes Z\n", + "\\tag{1}\n", + "$$\n", + "\n", + "在 Paddle Quantum 中,用户可通过定义一个包含了多项泡利算子张量积信息的列表来创建哈密顿量,列表中的元素应为哈密顿量中每一项的系数及其表示了该项对应的泡利算符的字符串。如以上哈密顿量$H$中的第一项为$Z \\otimes Z \\otimes I$,对应的系数为$1$,对应的字符串为'Z0, Z1',其中‘Z0’,‘Z1’分别表示该泡利算子作用在第$0$位量子比特和第$1$位量子比特上,这里的单位算符$I$可以被省略。接下来我们可以试着创建以上哈密顿量$H$。 \n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0 Z0, Z1\n", + "1.0 X1, Z2\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import paddle_quantum\n", + "from paddle_quantum import Hamiltonian\n", + "from paddle_quantum.qinfo import random_hamiltonian_generator\n", + "from paddle_quantum.trotter import get_1d_heisenberg_hamiltonian\n", + "\n", + "h = Hamiltonian([[1,'Z0, Z1'], [1,'X1, Z2']])\n", + "print(h)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 哈密顿量支持的操作\n", + "\n", + "Paddle Quantum 中的哈密顿量类 `Hamiltonian` 支持自动合并同类项,加减法,系数乘法,索引以及拆分等操作,如下:" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0 Z0, Z1\n", + "1.0 X1, Z2\n" + ] + } + ], + "source": [ + "h = Hamiltonian([[0.5,'Z0, Z1'], [0.5,'Z1, Z0'], [1,'X1, Z2']], compress = True)\n", + "print(h)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "h1 + h2: \n", + " 1.0 Z0, Z1\n", + "1.0 X1, Z2\n", + "h1 * 2: 2.0 Z0, Z1\n", + "h1: 1.0 Z0, Z1\n" + ] + } + ], + "source": [ + "h1 = Hamiltonian([[1,'Z0, Z1']])\n", + "h2 = Hamiltonian([[1 ,'X1, Z2']])\n", + "h = h1 + h2\n", + "print('h1 + h2: \\n', h)\n", + "print('h1 * 2: ', h1 * 2)\n", + "print('h1: ', h[0])\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 常用方法\n", + "\n", + "`Hamiltonian` 内置的 `decompose_pauli_words()` 和 `decompose_with_sites()` 方法可以将哈密顿量中的各项泡利算符及对应的系数提取出来,分解为更加方便处理的形式。其中,`decompose_pauli_words()` 将哈密顿量分解为两部分,分别为系数列表和对应的泡利字符串 (Pauli strings) 列表。一个$n$比特的泡利算符的泡利字符串表示,是一个由n个来自于集合$\\{'I', 'X', 'Y', 'Z'\\}$的字符组成的字符串。如泡利算符$Z \\otimes Z \\otimes I$的泡利字符串表示为'ZZI'; `decompose_with_sites()`则将哈密顿量分解成三部分,分别是系数列表,泡利字符串的化简形式的列表以及它们分别作用的量子比特下标的列表。如泡利算符$I \\otimes X \\otimes Z$的泡利字符串表示为'IXZ', 进一步的化简形式为'XZ', 由列表[1, 2]来分别标识'X'和'Z'分别作用的量子比特下标。" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pauli words 分解: ([1.0, 1.0], ['ZZI', 'IXZ'])\n", + "Pauli with sites 分解: ([1.0, 1.0], ['ZZ', 'XZ'], [[0, 1], [1, 2]])\n" + ] + } + ], + "source": [ + "print('Pauli words 分解:', h.decompose_pauli_words())\n", + "print('Pauli with sites 分解:', h.decompose_with_sites())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "除此之外,`Hamiltonian` 内置的 `construct_h_matrix()` 方法 还可以创建其在泡利 $Z$ 基底下的矩阵形式:" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[ 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n", + " [ 0.+0.j, -1.+0.j, 0.+0.j, 0.+0.j],\n", + " [ 0.+0.j, 0.+0.j, -1.+0.j, 0.+0.j],\n", + " [ 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]], dtype=complex64)" + ] + }, + "execution_count": 51, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "h1.construct_h_matrix()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 哈密顿量的其他创建方式\n", + "\n", + "除了利用 `Hamiltonian`,用户还可以用量桨 `qinfo` 模块里的 `random_hamiltonian_generator` 函数来生成一个随机哈密顿量。如下,用户可以随机生成一个,作用在$3$个qubit上,总共有$4$项互不对易的泡利算符的哈密顿量:" + ] + }, + { + "cell_type": "code", + "execution_count": 57, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-0.588549459410759 Z0, Z2\n", + "-0.6863539010269364 X0, Z1, Y2\n", + "0.08533003337080869 Y0, X1, Y2\n", + "-0.002948614747939171 Z0, Z1, X2\n" + ] + } + ], + "source": [ + "h_random = random_hamiltonian_generator(num_qubits= 3, terms= 4)\n", + "print(h_random)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "用户还可以利用量桨 `trotter` 模块中的 `get_1d_heisenberg_hamiltonian` 函数来创建一个一维海森堡链的哈密顿量,实现 [一维海森堡链的自旋动力学模拟](https://qml.baidu.com/tutorials/quantum-simulation/simulate-the-spin-dynamics-on-a-heisenberg-chain.html):" + ] + }, + { + "cell_type": "code", + "execution_count": 62, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "系统的哈密顿量为:\n", + "1.0 X0, X1\n", + "2.0 Y0, Y1\n", + "2.0 Z0, Z1\n", + "1.0 X1, X2\n", + "2.0 Y1, Y2\n", + "2.0 Z1, Z2\n", + "1.0 X2, X3\n", + "2.0 Y2, Y3\n", + "2.0 Z2, Z3\n", + "1.0 X3, X4\n", + "2.0 Y3, Y4\n", + "2.0 Z3, Z4\n", + "-0.09133431514782564 Z0\n", + "-0.08305794685805723 Z1\n", + "0.23542270730722192 Z2\n", + "0.502365299254947 Z3\n", + "0.21580198180161436 Z4\n" + ] + } + ], + "source": [ + "h_heisenberg = get_1d_heisenberg_hamiltonian(length=5, j_x=1, j_y=2, j_z=2, h_z=2 * np.random.rand(5) - 1, periodic_boundary_condition=False)\n", + "print('系统的哈密顿量为:')\n", + "print(h_heisenberg)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "paddle_quantum_env", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Hamiltonian_EN.ipynb b/introduction/PaddleQuantum_Hamiltonian_EN.ipynb new file mode 100644 index 0000000..ea6a617 --- /dev/null +++ b/introduction/PaddleQuantum_Hamiltonian_EN.ipynb @@ -0,0 +1,278 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction to the `Hamiltonian` Module in Paddle Quantum\n", + "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*\n", + "\n", + "The `Hamiltonian` module in Paddle Quantum is a module related to Hamiltonians, which allows users to quickly create custom Hamiltonians in the form of Pauli strings and obtain various related information about the Hamiltonians." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Creation of Hamiltonians\n", + "\n", + "The Hamiltonian of a quantum system is an observable related to the total energy of the system and has important applications in quantum simulation algorithms such as the [Variational Quantum Eigensolver](https://qml.baidu.com/tutorials/quantum-simulation/variational-quantum-eigensolver.html) and [Hamiltonian Simulation with Product Formula](https://qml.baidu.com/tutorials/quantum-simulation/hamiltonian-simulation-with-product-formula.html). In quantum computing, the Hamiltonian needs to be represented in the form of a sum of tensor products of Pauli operators that can be processed by a quantum computer. For example, the following Hamiltonian is represented in this form:\n", + "\n", + "$$\n", + "H = Z \\otimes Z \\otimes I + I \\otimes X \\otimes Z\n", + "\\tag{1}\n", + "$$\n", + "\n", + "In Paddle Quantum, users can create Hamiltonians in the form of Pauli strings by defining a list of the coefficients and corresponding Pauli operators for each term in the Hamiltonian. The identity operator $I$ can be omitted in each Pauli operator term. Let's try to create the Hamiltonian above.\n", + "\n", + "In Paddle Quantum, users can create Hamiltonians by defining a list that contains information about multiple tensor products of Pauli operators. Each element of the list should include the coefficient and the string representation of the corresponding Pauli operator. For example, the first term in the Hamiltonian $H$ above is $Z \\otimes Z \\otimes I$, with a coefficient of $1$ and a corresponding string representation of 'Z0, Z1',where 'Z0' and 'Z1' indicate that the Pauli operator acts on the 0-th and 1st qubits, respectively. Here, the identity operator $I$ can be omitted. Let's try to create the Hamiltonian $H$ above.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0 Z0, Z1\n", + "1.0 X1, Z2\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "import paddle_quantum\n", + "from paddle_quantum import Hamiltonian\n", + "from paddle_quantum.qinfo import random_hamiltonian_generator\n", + "from paddle_quantum.trotter import get_1d_heisenberg_hamiltonian\n", + "\n", + "\n", + "h = Hamiltonian([[1,'Z0, Z1'], [1,'X1, Z2']])\n", + "print(h)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Hamiltonian Operations\n", + "\n", + "The `Hamiltonian` class in Paddle Quantum supports operations such as automatic merging of like terms, addition and subtraction, coefficient multiplication, indexing, and splitting, as shown below:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0 Z0, Z1\n", + "1.0 X1, Z2\n" + ] + } + ], + "source": [ + "h = Hamiltonian([[0.5,'Z0, Z1'], [0.5,'Z1, Z0'], [1,'X1, Z2']], compress = True)\n", + "print(h)" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "h1 + h2: \n", + " 1.0 Z0, Z1\n", + "1.0 X1, Z2\n", + "h1 * 2: 2.0 Z0, Z1\n", + "h1: 1.0 Z0, Z1\n" + ] + } + ], + "source": [ + "h1 = Hamiltonian([[1,'Z0, Z1']])\n", + "h2 = Hamiltonian([[1 ,'X1, Z2']])\n", + "h = h1 + h2\n", + "print('h1 + h2: \\n', h)\n", + "print('h1 * 2: ', h1 * 2)\n", + "print('h1: ', h[0])" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Common Methods\n", + "\n", + "The built-in `decompose_pauli_words()` and `decompose_with_sites()` methods in `Hamiltonian` can extract the various Pauli operators and their corresponding coefficients in the Hamiltonian and decompose them into a more convenient form. Among them, decompose_pauli_words() decomposes the Hamiltonian into two parts, a coefficient list and a corresponding Pauli string list. A Pauli string representation of a $n$-qubit Pauli operator is a string of $n$ characters derived from the set $\\{'I', 'X', 'Y', 'Z'\\}$. For example, the Pauli string representation of the Pauli operator $Z \\otimes Z \\otimes I$ is 'ZZI'; decompose_with_sites() decomposes the Hamiltonian into three parts, which are the coefficient list, the simplified form of the Pauli string list, and the list of qubit indices on which they respectively act. For example, the Pauli string representation of the Pauli operator $I \\otimes X \\otimes Z$ is 'IXZ', which further simplifies to 'XZ', and is identified by the list [1, 2] to indicate the qubit indices on which 'X' and 'Z' respectively act.\n", + "\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Pauli words decomposion: ([1.0, 1.0], ['ZZI', 'IXZ'])\n", + "Pauli with sites decomposion: ([1.0, 1.0], ['ZZ', 'XZ'], [[0, 1], [1, 2]])\n" + ] + } + ], + "source": [ + "print('Pauli words decomposion:', h.decompose_pauli_words())\n", + "print('Pauli with sites decomposion:', h.decompose_with_sites())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition, the `construct_h_matrix()` method built in `Hamiltonian` can also create its matrix form in the Pauli Z basis." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "matrix([[ 1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n", + " [ 0.+0.j, -1.+0.j, 0.+0.j, 0.+0.j],\n", + " [ 0.+0.j, 0.+0.j, -1.+0.j, 0.+0.j],\n", + " [ 0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]], dtype=complex64)" + ] + }, + "execution_count": 16, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "h1.construct_h_matrix()" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Other Ways to Create Hamiltonians\n", + "\n", + "In addition to using `Hamiltonian`, users can also use the `random_hamiltonian_generator` function in the `qinfo` module of Paddle Quantum to generate a random Hamiltonian. For example, users can generate a Hamiltonian that acts on 3 qubits and has 4 mutually non-commuting Pauli operators:" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "-0.7669177644685217 Z1, X2\n", + "-0.34974226780994044 Y1, Y2\n", + "0.898612346022807 Y0\n", + "0.9923126285950277 X0, X1, X2\n" + ] + } + ], + "source": [ + "h_random = random_hamiltonian_generator(num_qubits= 3, terms= 4)\n", + "print(h_random)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Users can also use the `get_1d_heisenberg_hamiltonian` function in the `trotter` module of Paddle Quantum to create a Hamiltonian for a one-dimensional Heisenberg chain and simulate the spin dynamics, as shown in [Simulating the Spin Dynamics on a Heisenberg Chain](https://qml.baidu.com/tutorials/quantum-simulation/simulate-the-spin-dynamics-on-a-heisenberg-chain.html):" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "System hamiltonian:\n", + "1.0 X0, X1\n", + "2.0 Y0, Y1\n", + "2.0 Z0, Z1\n", + "1.0 X1, X2\n", + "2.0 Y1, Y2\n", + "2.0 Z1, Z2\n", + "1.0 X2, X3\n", + "2.0 Y2, Y3\n", + "2.0 Z2, Z3\n", + "1.0 X3, X4\n", + "2.0 Y3, Y4\n", + "2.0 Z3, Z4\n", + "-0.4816758416088862 Z0\n", + "0.713595033376984 Z1\n", + "0.5129840224089792 Z2\n", + "-0.5857705588538953 Z3\n", + "0.8340974367670304 Z4\n" + ] + } + ], + "source": [ + "h_heisenberg = get_1d_heisenberg_hamiltonian(length=5, j_x=1, j_y=2, j_z=2, h_z=2 * np.random.rand(5) - 1, periodic_boundary_condition=False)\n", + "print('System hamiltonian:')\n", + "print(h_heisenberg)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "paddle_quantum_env", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Linalg_and_Qinfo_CN.ipynb b/introduction/PaddleQuantum_Linalg_and_Qinfo_CN.ipynb new file mode 100644 index 0000000..363823b --- /dev/null +++ b/introduction/PaddleQuantum_Linalg_and_Qinfo_CN.ipynb @@ -0,0 +1,387 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 量桨线性代数与量子信息模块简介\n", + "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*\n", + "\n", + "`linalg` 和 `qinfo` 模块是量桨封装各类矩阵操作和量子信息相关功能的模块。`linalg` 包含了矩阵的转置、共轭、迹等常用的函数,而 `qinfo` 模块则主要包含了偏迹,各类量子态的熵,保真度,迹距离等常见的量子信息相关的函数。" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 矩阵的常见运算\n", + "\n", + "我们知道量子力学和线性代数有着密不可分的关联,在这里,我们通过简单的例子介绍量桨 `linalg` 模块和飞桨内常见的矩阵相关的运算函数。" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "c:\\Users\\liugeng02\\Anaconda3\\envs\\2023q2\\lib\\site-packages\\openfermion\\hamiltonians\\hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "c:\\Users\\liugeng02\\Anaconda3\\envs\\2023q2\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "c:\\Users\\liugeng02\\Anaconda3\\envs\\2023q2\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], + "source": [ + "import paddle\n", + "import paddle_quantum\n", + "from paddle_quantum.state import State\n", + "from paddle.linalg import eigvals, eig\n", + "from paddle_quantum.linalg import dagger, NKron, density_matrix_random, unitary_random\n", + "from paddle_quantum.qinfo import (\n", + " partial_trace,\n", + " state_fidelity,\n", + " trace_distance,\n", + " von_neumann_entropy,\n", + " relative_entropy,\n", + ")\n", + "\n", + "\n", + "paddle_quantum.set_backend(\"density_matrix\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们先通过量桨内置的函数创建两个随机酉矩阵,在这里两个矩阵A和B均是 `paddle.Tensor` 形式。" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "矩阵A为:\n", + "Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[ (0.2921386957168579-0.1418590545654297j),\n", + " (-0.7422900795936584+0.5861198306083679j)],\n", + " [(0.9016497135162354-0.28558504581451416j),\n", + " (0.28133758902549744-0.1622287780046463j)]])\n", + "\n", + "矩阵B为:\n", + "Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(-0.30973920226097107-0.29339805245399475j),\n", + " (0.8378809690475464+0.34049180150032043j) ],\n", + " [ (0.8848108649253845-0.18732032179832458j) ,\n", + " (0.3566453754901886-0.2341471016407013j) ]])\n" + ] + } + ], + "source": [ + "A = unitary_random(num_qubits=1)\n", + "B = unitary_random(num_qubits=1)\n", + "print(f\"矩阵A为:\\n{A}\\n\")\n", + "print(f\"矩阵B为:\\n{B}\")\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**矩阵乘法**:矩阵乘法A*B有两种实现方式,第一种是使用paddle内部的 `matmul` 函数,第二种是直接使用 `@` 符号代表矩阵乘法。\n", + "\n", + "**矩阵转置**:计算矩阵A的转置可以使用 `A.t()`。\n", + "\n", + "**矩阵共轭**:计算矩阵A的共轭可以使用 `A.conj()` 。\n", + "\n", + "**矩阵的共轭转置**:计算一个矩阵的共轭转置有两种方法,一种是将两步操作分开,先后求取其共轭和转置 `A.conj().t()` ;另一种是直接调用量桨内部的 `dagger` 函数求取共轭转置。\n", + "\n", + "**矩阵的张量积**:矩阵的张量积 $A\\otimes B$ 可以使用 `paddle.kron()` 来计算。\n", + "\n", + "**多个矩阵的张量积**:多个矩阵的张量积可以使用量桨 `linalg` 内的 `NKron()` 来计算。\n", + "\n", + "**矩阵的迹**:对矩阵求迹可以使用 `paddle.trace()` 函数。\n", + "\n", + "**矩阵的偏迹**:对矩阵求偏迹可以使用量桨 `qinfo` 内的 `partial_trace()` 函数。\n", + "\n", + "**矩阵的特征值与特征向量**:矩阵的特征值和特征向量可以使用 `eig` 函数计算,也可以使用 `eigvals` 来单独计算矩阵的特征值。" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "multiplyAB_1 = paddle.matmul(A, B) # 矩阵乘法\n", + "multiplyAB_2 = A @ B # 矩阵乘法\n", + "A_transpose = A.t() # 矩阵的转置\n", + "A_conjugate = A.conj() # 矩阵的共轭\n", + "A_dagger = dagger(A) # 矩阵的共轭转置\n", + "tensor_product_AB = paddle.kron(A, B) # 矩阵的张量积\n", + "tensor_product_ABA = NKron(A, B, A) # 多个矩阵的张量积\n", + "A_trace = paddle.trace(A) # 矩阵的迹\n", + "partial_trace_matrix = partial_trace(tensor_product_AB, dim1=2, dim2=2, A_or_B=2) # 矩阵的偏迹\n", + "eigenvalue, eigenvector = eig(A) # 矩阵的特征值与特征向量" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 量子信息中的常见函数" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们先使用 `linalg` 里的 `density_matrix_random` 创建两个随机单比特量子态。" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "第一个量子态为:\n", + " Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[ (0.8994134664535522+0j) ,\n", + " (-0.28608179092407227-0.09287679195404053j)],\n", + " [(-0.28608179092407227+0.09287679195404053j),\n", + " (0.10058653354644775+0j) ]])\n", + "\n", + "第二个量子态为:\n", + " Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(0.17564187943935394+0j) ,\n", + " (0.32964783906936646-0.1900634616613388j)],\n", + " [(0.32964783906936646+0.1900634616613388j),\n", + " (0.8243581056594849+0j) ]])\n" + ] + } + ], + "source": [ + "state1 = density_matrix_random(1)\n", + "print(f\"第一个量子态为:\\n {state1}\\n\")\n", + "state2 = density_matrix_random(1)\n", + "print(f\"第二个量子态为:\\n {state2}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们利用 `state_fidelity()` 可以获得两个量子态之间保真度。" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "两个量子态之间的保真度为:\n", + "Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,\n", + " [0.29595008])\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "c:\\Users\\liugeng02\\Anaconda3\\envs\\2023q2\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " elif dtype == np.bool:\n" + ] + } + ], + "source": [ + "fidelity = state_fidelity(state1, state2)\n", + "print(f\"两个量子态之间的保真度为:\\n{fidelity}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "值得注意的是,量桨有关量子态的函数兼容多种不同形式的输入,其形式可以是 `paddle.Tensor`, `numpy.ndarray`, 或是 `State`。同时,函数输出的格式与输入格式是匹配的,例如输入 `numpy.ndarray` 形式的数据将会同样获得 `numpy.ndarray` 形式的结果。" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.29595009466850986\n" + ] + } + ], + "source": [ + "# 以numpy.ndarray形式输入\n", + "state1 = state1.numpy()\n", + "state2 = state2.numpy()\n", + "print(state_fidelity(state1, state2))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,\n", + " [0.29595008])\n" + ] + } + ], + "source": [ + "# 以State形式输入\n", + "state1 = State(state1)\n", + "state2 = State(state2)\n", + "print(state_fidelity(state1, state2))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "利用 `trace_distance()` 我们可以计算两个量子态之间的迹距离" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "两个量子态之间的迹距离为:\n", + "Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,\n", + " [0.95520324])\n" + ] + } + ], + "source": [ + "TraceDistance = trace_distance(state1, state2)\n", + "print(f\"两个量子态之间的迹距离为:\\n{TraceDistance}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "使用 `von_neumann_entropy()` 可以计算量子态的冯诺依曼熵" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "量子态的冯诺依曼熵为:\n", + "Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,\n", + " [0.])\n" + ] + } + ], + "source": [ + "v_entropy = von_neumann_entropy(state2)\n", + "print(f\"量子态的冯诺依曼熵为:\\n{v_entropy}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "使用 `relative_entropy()` 可以计算两个量子态的相对熵" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "logm result may be inaccurate, approximate err = 1.2365573141431553e-07\n", + "logm result may be inaccurate, approximate err = 2.1966168634145265e-08\n", + "两个量子态之间的相对熵为:\n", + "Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,\n", + " [23.84987831])\n" + ] + } + ], + "source": [ + "r_entropy = relative_entropy(state1, state2)\n", + "print(f\"两个量子态之间的相对熵为:\\n{r_entropy}\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "2023q2", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Linalg_and_Qinfo_EN.ipynb b/introduction/PaddleQuantum_Linalg_and_Qinfo_EN.ipynb new file mode 100644 index 0000000..46e6939 --- /dev/null +++ b/introduction/PaddleQuantum_Linalg_and_Qinfo_EN.ipynb @@ -0,0 +1,386 @@ +{ + "cells": [ + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Introduction to Linear Algebra and Quantum Information modules of Paddle Quantum\n", + "*Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*\n", + "\n", + "`linalg` and `qinfo` module are Paddle Quantum modules that support operations of matrices and functions of quantum information respectively. `linalg` module provides many matrix operations includeing transpose, conjuagte, tensor product and trace. And `qinfo` module mainly includes partial trace, different quantum entropy, fidelity of quantum states and trace distance, which are functions that related to quantum information theory." + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Common operations of matrix\n", + "\n", + "We know that quantum mechanics has a close connection with linear algebra. Here, we will introduce the common operations of matrix in `linalg` module with simple examples." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "c:\\Users\\liugeng02\\Anaconda3\\envs\\2023q2\\lib\\site-packages\\openfermion\\hamiltonians\\hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "c:\\Users\\liugeng02\\Anaconda3\\envs\\2023q2\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "c:\\Users\\liugeng02\\Anaconda3\\envs\\2023q2\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], + "source": [ + "import paddle\n", + "import paddle_quantum\n", + "from paddle_quantum.state import State\n", + "from paddle.linalg import eigvals, eig\n", + "from paddle_quantum.linalg import dagger, NKron, density_matrix_random, unitary_random\n", + "from paddle_quantum.qinfo import (\n", + " partial_trace,\n", + " state_fidelity,\n", + " trace_distance,\n", + " von_neumann_entropy,\n", + " relative_entropy,\n", + ")\n", + "\n", + "paddle_quantum.set_backend(\"density_matrix\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We first initialize two random unitary matrices through built-in function of Paddle Quantum. The matrix A and B here are both in `paddle.Tensor` format." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Matrix A is:\n", + "Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(-0.008479282259941101-0.3407862186431885j),\n", + " (0.6076244115829468-0.7173460721969604j) ],\n", + " [(-0.3203158378601074-0.8838498592376709j) ,\n", + " (-0.12643268704414368+0.3165784478187561j) ]])\n", + "\n", + "Matrix B is:\n", + "Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(-0.6520524621009827-0.2549170255661011j) ,\n", + " (-0.5733906030654907-0.42552101612091064j)],\n", + " [ (0.5613574981689453+0.44127389788627625j),\n", + " (-0.4174516499042511-0.5620402097702026j) ]])\n" + ] + } + ], + "source": [ + "A = unitary_random(num_qubits=1)\n", + "B = unitary_random(num_qubits=1)\n", + "print(f\"Matrix A is:\\n{A}\\n\")\n", + "print(f\"Matrix B is:\\n{B}\")\n" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**matrix multiplication**:There are two ways to calculate matrix multiplication, the first way is using `matmul` method of Paddle, and the second way is directly using `@`.\n", + "\n", + "**transpose**:The transpose of matrix A can be calculated using `A.t()`.\n", + "\n", + "**conjugate**:The conjugate of matrix A can be calculated using `A.conjugate()`.\n", + "\n", + "**conjugate transpose**:There are two ways to calculate conjugate transpose of a matrix. The first way is calculating the conjugate of the matrix followed by calculating the transpose, using `A.conj().t()`; the second way is directly using `dagger` method of Paddle Quantum.\n", + "\n", + "**tensor product of two matrices**:The tensor product of two matrices can be calculated using `paddle.kron()`.\n", + "\n", + "**tensor product of multiple matrices**:The tensor product of multiple matrices can be calculated using `NKron()` of Paddle Quantum.\n", + "\n", + "**trace of matrix**:The trace of a matrix can be calculated using `paddle.trace()`.\n", + "\n", + "**partial trace of matrix**:The partial trace of a matrix can be calculated using `partial_trace()` of Paddle Quantum.\n", + "\n", + "**eigenvalue and eigenvector of matrix**:The eigenvalues and eigenvectors of a matrix can be calculated using `eig`, and the eigenvalues can be directly calculated using `eigvals`." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "multiplyAB_1 = paddle.matmul(A, B) # matrix multiplication\n", + "multiplyAB_2 = A @ B # matrix multiplication\n", + "A_transpose = A.t() # transpose\n", + "A_conjugate = A.conj() # conjugate\n", + "A_dagger = dagger(A) # conjugate transpose\n", + "tensor_product_AB = paddle.kron(A, B) # tensor product of two matrices\n", + "tensor_product_ABA = NKron(A, B, A) # tensor product of multiple matrices\n", + "A_trace = paddle.trace(A) # trace of the matrix\n", + "partial_trace_matrix = partial_trace(tensor_product_AB, dim1=2, dim2=2, A_or_B=2) # partial trace of matrix\n", + "eigenvalue, eigenvector = eig(A) # eigenvalue and eigenvector of the matrix" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Common functions in quantum information" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We first initialize two random single qubit quantum states with `density_matrix_random`." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The first quantum state is:\n", + " Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(0.5706692337989807+0j) ,\n", + " (0.4849703907966614+0.09904339164495468j)],\n", + " [(0.4849703907966614-0.09904339164495468j),\n", + " (0.4293307662010193+0j) ]])\n", + "\n", + "The second quantum state is:\n", + " Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[ (0.8634329438209534+0j) ,\n", + " (-0.04915342852473259+0.33985358476638794j)],\n", + " [(-0.04915342852473259-0.33985358476638794j),\n", + " (0.13656707108020782+0j) ]])\n" + ] + } + ], + "source": [ + "state1 = density_matrix_random(1)\n", + "print(f\"The first quantum state is:\\n {state1}\\n\")\n", + "state2 = density_matrix_random(1)\n", + "print(f\"The second quantum state is:\\n {state2}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use `state_fidelity()` to calculate the fidelity of two quantum states." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The fidelity is:\n", + "Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,\n", + " [0.75565338])\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "c:\\Users\\liugeng02\\Anaconda3\\envs\\2023q2\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " elif dtype == np.bool:\n" + ] + } + ], + "source": [ + "fidelity = state_fidelity(state1, state2)\n", + "print(f\"The fidelity is:\\n{fidelity}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "It is worth noting that the functions of Paddle Quantum that related to quantum states supports different format of input, including `paddle.Tensor`, `numpy.ndarray`, and `State`. At the same time, the output format is consistent with the input format. For example, the output will be `numpy.ndarray` format if the input is also `numpy.ndarray` format." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.7556533814816342\n" + ] + } + ], + "source": [ + "# Input with numpy.ndarray format\n", + "state1 = state1.numpy()\n", + "state2 = state2.numpy()\n", + "print(state_fidelity(state1, state2))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,\n", + " [0.75565338])\n" + ] + } + ], + "source": [ + "# Input with State format\n", + "state1 = State(state1)\n", + "state2 = State(state2)\n", + "print(state_fidelity(state1, state2))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use `trace_distance` to calculate the trace distance between two quantum states." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The trace distance is:\n", + "Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,\n", + " [0.65497208])\n" + ] + } + ], + "source": [ + "TraceDistance = trace_distance(state1, state2)\n", + "print(f\"The trace distance is:\\n{TraceDistance}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use `von_neumann_entropy()` to calculate the von neumann entropy of a quantum state." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The von veumann entropy of the quantum state is:\n", + "Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,\n", + " [0.00000026])\n" + ] + } + ], + "source": [ + "v_entropy = von_neumann_entropy(state2)\n", + "print(f\"The von veumann entropy of the quantum state is:\\n{v_entropy}\")" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can use `relative_entropy()` to calculate the relative entropy of two quantum states." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "logm result may be inaccurate, approximate err = 3.3328131580525864e-07\n", + "logm result may be inaccurate, approximate err = 2.3121323283812061e-07\n", + "The relative entropy is:\n", + "Tensor(shape=[1], dtype=float32, place=Place(cpu), stop_gradient=True,\n", + " [11.14819717])\n" + ] + } + ], + "source": [ + "r_entropy = relative_entropy(state1, state2)\n", + "print(f\"The relative entropy is:\\n{r_entropy}\")" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "2023q2", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + }, + "orig_nbformat": 4 + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Qchem_Tutorial_CN.ipynb b/introduction/PaddleQuantum_Qchem_Tutorial_CN.ipynb index d6fea60..ad5242c 100644 --- a/introduction/PaddleQuantum_Qchem_Tutorial_CN.ipynb +++ b/introduction/PaddleQuantum_Qchem_Tutorial_CN.ipynb @@ -31,9 +31,24 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/openfermion/hamiltonians/hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import paddle_quantum as pq\n", "from paddle_quantum import qchem as pq_qchem\n", @@ -53,7 +68,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -79,7 +94,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -135,6 +150,23 @@ "完成上面的步骤之后,我们可以调用 `GroundStateSolver` 求解器,并利用 PaddlePaddle 中的优化器来训练参数化量子线路。" ] }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + } + ], + "source": [ + "print(type(mol))" + ] + }, { "cell_type": "code", "execution_count": 5, @@ -154,15 +186,14 @@ "INFO:root:\tlearning_rate: 0.5\n", "INFO:root:\n", "Optimization:\n", - "INFO:root:\tItr 0, loss=-0.32028.\n", - "INFO:root:\tItr 10, loss=-1.02221.\n", - "INFO:root:\tItr 20, loss=-1.12635.\n", - "INFO:root:\tItr 30, loss=-1.13166.\n", - "INFO:root:\tItr 40, loss=-1.13439.\n", - "INFO:root:\tItr 50, loss=-1.13665.\n", - "INFO:root:\tItr 60, loss=-1.13680.\n", - "INFO:root:Optimization converged after 65 iterations.\n", - "INFO:root:The final loss = -1.13705.\n" + "INFO:root:\tItr 0, loss=-0.52172.\n", + "INFO:root:\tItr 10, loss=-1.05356.\n", + "INFO:root:\tItr 20, loss=-1.11600.\n", + "INFO:root:\tItr 30, loss=-1.12634.\n", + "INFO:root:\tItr 40, loss=-1.13320.\n", + "INFO:root:\tItr 50, loss=-1.13628.\n", + "INFO:root:Optimization converged after 58 iterations.\n", + "INFO:root:The final loss = -1.13636.\n" ] } ], @@ -171,7 +202,7 @@ "from paddle.optimizer import Adam\n", "\n", "solver = pq_qchem.GroundStateSolver(Adam, num_iterations=100, tol=1e-5, save_every=10)\n", - "e, psi = solver.solve(mol, cir, learning_rate=0.5)" + "e, psi = solver.solve(cir, mol, learning_rate=0.5)" ] }, { @@ -206,7 +237,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.15" + "version": "3.8.13" }, "vscode": { "interpreter": { diff --git a/introduction/PaddleQuantum_Qchem_Tutorial_EN.ipynb b/introduction/PaddleQuantum_Qchem_Tutorial_EN.ipynb index c87dc4d..77baa7c 100644 --- a/introduction/PaddleQuantum_Qchem_Tutorial_EN.ipynb +++ b/introduction/PaddleQuantum_Qchem_Tutorial_EN.ipynb @@ -26,9 +26,24 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/openfermion/hamiltonians/hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import paddle_quantum as pq\n", "from paddle_quantum import qchem as pq_qchem\n", @@ -48,7 +63,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -74,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -132,7 +147,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -149,16 +164,13 @@ "INFO:root:\tlearning_rate: 0.5\n", "INFO:root:\n", "Optimization:\n", - "INFO:root:\tItr 0, loss=-0.26383.\n", - "INFO:root:\tItr 10, loss=-1.02679.\n", - "INFO:root:\tItr 20, loss=-1.08981.\n", - "INFO:root:\tItr 30, loss=-1.12582.\n", - "INFO:root:\tItr 40, loss=-1.13435.\n", - "INFO:root:\tItr 50, loss=-1.13531.\n", - "INFO:root:\tItr 60, loss=-1.13634.\n", - "INFO:root:\tItr 70, loss=-1.13713.\n", - "INFO:root:Optimization converged after 73 iterations.\n", - "INFO:root:The final loss = -1.13703.\n" + "INFO:root:\tItr 0, loss=-0.47434.\n", + "INFO:root:\tItr 10, loss=-1.05781.\n", + "INFO:root:\tItr 20, loss=-1.10282.\n", + "INFO:root:\tItr 30, loss=-1.11235.\n", + "INFO:root:\tItr 40, loss=-1.11737.\n", + "INFO:root:Optimization converged after 46 iterations.\n", + "INFO:root:The final loss = -1.11891.\n" ] } ], @@ -167,7 +179,7 @@ "from paddle.optimizer import Adam\n", "\n", "solver = pq_qchem.GroundStateSolver(Adam, num_iterations=100, tol=1e-5, save_every=10)\n", - "e, psi = solver.solve(mol, cir, learning_rate=0.5)" + "e, psi = solver.solve(cir, mol, learning_rate=0.5)" ] }, { @@ -201,7 +213,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.15" + "version": "3.8.13" }, "vscode": { "interpreter": { diff --git a/introduction/PaddleQuantum_State_CN.ipynb b/introduction/PaddleQuantum_State_CN.ipynb new file mode 100644 index 0000000..29277fe --- /dev/null +++ b/introduction/PaddleQuantum_State_CN.ipynb @@ -0,0 +1,443 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 利用 Paddle Quantum 的 state 模块操作量子态\n", + "\n", + "_Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved._\n", + "\n", + "`state` 模块是量桨封装的支持量子态(`paddle_quantum.state.State`)相关操作的模块,主要包括了量子态的创建和运算。`state` 模块为用户提供了诸多接口,用于创建、编辑量子态和与量子电路交互、测量。\n", + "\n", + "## 量子态的创建\n", + "用户可以通过已有数据创建量子态,也可通过量桨创建特殊类型的量子态。\n", + "首先我们可以根据已有数据创建量子态。" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Applications/anaconda3/envs/pq/lib/python3.8/site-packages/openfermion/hamiltonians/hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "/Applications/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.+0.j 0.+0.j]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Applications/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/Applications/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " elif dtype == np.bool:\n" + ] + } + ], + "source": [ + "import paddle\n", + "import paddle_quantum as pq\n", + "from paddle_quantum.backend import Backend\n", + "\n", + "state_vec = pq.state.to_state([1, 0])\n", + "print(state_vec)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "也可以通过指定 `backend` 创建密度矩阵。" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.5+0.j 0. +0.j]\n", + " [0. +0.j 0.5+0.j]]\n" + ] + } + ], + "source": [ + "state_density = pq.state.State([[0.5, 0], [0, 0.5]], backend=Backend.DensityMatrix)\n", + "print(state_density)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们也可以通过量桨内置的函数创建特殊类型的量子态。比如创建单比特零态。" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.+0.j 0.+0.j]\n" + ] + } + ], + "source": [ + "print(pq.state.zero_state(num_qubits=1))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "创建两比特随机态。" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-0.0477975 -0.521988j -0.21298088+0.06160466j 0.4515487 +0.19628459j\n", + " 0.625157 +0.20698515j]\n" + ] + } + ], + "source": [ + "print(pq.state.random_state(num_qubits=2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "此外,量桨还支持其它若干特殊量子态的创建,详见[API 文档](https://qml.baidu.com/api/paddle_quantum.state.common.html)。\n", + "\n", + "我们也可以通过一行代码设置全局后端为密度矩阵。当然,我们继续使用默认后端,即态矢量,进行演示。" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1.+0.j 0.+0.j]\n", + " [0.+0.j 0.+0.j]]\n" + ] + } + ], + "source": [ + "pq.set_backend('density_matrix') # 设置全局后端为密度矩阵\n", + "print(pq.state.zero_state(num_qubits=1))\n", + "pq.set_backend('state_vector') # 设置回默认后端" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 量子态的数据\n", + "我们可以通过访问 `data`,`ket`,`bra` 来读取 `State` 中的数据。" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Its data is : Tensor(shape=[2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [(1+0j), 0j ])\n", + "Its ket is : Tensor(shape=[2, 1], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(1+0j)],\n", + " [0j ]])\n", + "Its bra is : Tensor(shape=[1, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(1-0j), -0j ]])\n" + ] + } + ], + "source": [ + "zero_state = pq.state.zero_state(num_qubits=1)\n", + "print('Its data is :', zero_state.data)\n", + "print('Its ket is :', zero_state.ket)\n", + "print('Its bra is :', zero_state.bra)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们也可以通过成员函数 `numpy()` 来输出 `State` 的 `numpy.ndarray` 类型数据。" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.+0.j 0.+0.j]\n" + ] + } + ], + "source": [ + "print(zero_state.numpy())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 量子态的运算\n", + "我们可以通过矩阵乘法 `@` 求两个量子态的乘积。这方便求取量子态的重叠。" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[0j, 0j],\n", + " [0j, 0j]])\n", + "The overlap of state_1 and state_2 is : Tensor(shape=[1], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [0j])\n" + ] + } + ], + "source": [ + "state_1 = pq.state.zero_state(num_qubits=1, backend=Backend.DensityMatrix)\n", + "state_2 = pq.state.to_state([[0, 0], [0, 1]], backend=Backend.DensityMatrix)\n", + "print(state_1 @ state_2)\n", + "print('The overlap of state_1 and state_2 is :', paddle.trace(state_1 @ state_2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "也可以使用 `State.kron()` 求得量子态 $\\rho$ 和 $\\sigma$ 的张量积 $\\rho \\otimes \\sigma$。" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n" + ] + } + ], + "source": [ + "rho = pq.state.zero_state(num_qubits=1)\n", + "sigma = pq.state.to_state([0, 1])\n", + "product_state = rho.kron(sigma)\n", + "print(product_state)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "还可以通过索引或切片的方式对量子态求偏迹。如我们想要获取 $|011\\rangle$ 的第一个比特,和 第二、三个比特的量子态。" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n", + "the state of the first qubit is : [1.+0.j 0.+0.j]\n", + "the state of the second and third qubits is : [0.+0.j 0.+0.j 0.+0.j 1.+0.j]\n" + ] + } + ], + "source": [ + "psi_012 = pq.state.computational_basis(num_qubits=3, index=3)\n", + "print(psi_012)\n", + "\n", + "psi_1 = psi_012[0]\n", + "psi_12 = psi_012[1:]\n", + "print('the state of the first qubit is :', psi_1)\n", + "print('the state of the second and third qubits is :', psi_12)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 量子态的测量与演化\n", + "量子态的成员函数 `State.evolve()` 可以在给定哈密顿量 $H$ 和演化时间 $t$ 的情况下,给出量子态在 $e^{-iHt}$ 演化下的末态。这里我们设置哈密顿量为泡利 $Z$ 矩阵,演化时间 $t=1$。" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.5403023-0.84147096j 0. +0.j ]\n" + ] + } + ], + "source": [ + "state = pq.state.zero_state(num_qubits=1)\n", + "t = 1\n", + "hamiltonian = pq.hamiltonian.Hamiltonian([(1, 'Z0')])\n", + "state.evolve(H=hamiltonian, t=t)\n", + "print(state)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "量子态的成员函数 `State.expec_val()` 可以求取在给定可观测量(哈密顿量)下的期望值。" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0\n" + ] + } + ], + "source": [ + "state = pq.state.zero_state(num_qubits=1)\n", + "observable = pq.hamiltonian.Hamiltonian([(1, 'Z0')])\n", + "print(state.expec_val(hamiltonian=observable))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "量子态的成员函数 `State.measure()` 可以获取在计算基下的测量结果。用户可以设置 `shots` 数值来模拟或令 `shots=0` 求期望,也可以使用 `plot` 参数作图。" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Theoretical value is : {'0': 0.5, '1': 0.5}\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "{'0': 0.5625, '1': 0.4375}" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "state = pq.state.to_state([[0.5, 0], [0, 0.5]], backend=Backend.DensityMatrix)\n", + "print('Theoretical value is :', state.measure(shots=0)) # theoretical value\n", + "state.measure(shots=16, plot=True)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_State_EN.ipynb b/introduction/PaddleQuantum_State_EN.ipynb new file mode 100644 index 0000000..ab5488b --- /dev/null +++ b/introduction/PaddleQuantum_State_EN.ipynb @@ -0,0 +1,447 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Manipulate quantum states via Paddle Quantum's `state` module\n", + "\n", + "_Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved._\n", + "\n", + "The `state` module is a Paddle Quantum module that supports operations related to quantum states (`paddle_quantum.state.State`), mainly including the creation of quantum states and operations. The `state` module provides a number of interfaces for the user to create and edit quantum states and to interact with quantum circuits and measurements.\n", + "\n", + "## Creation of states\n", + "User can create quantum states from existing data, or create special states by Paddle Quantum.\n", + "First we can create quantum states from existing data." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Applications/anaconda3/envs/pq/lib/python3.8/site-packages/openfermion/hamiltonians/hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "/Applications/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.+0.j 0.+0.j]\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Applications/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/Applications/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " elif dtype == np.bool:\n" + ] + } + ], + "source": [ + "import paddle\n", + "import paddle_quantum as pq\n", + "from paddle_quantum.backend import Backend\n", + "\n", + "state_vec = pq.state.to_state([1, 0])\n", + "print(state_vec)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The density matrix can also be created by specifying `backend`." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[0.5+0.j 0. +0.j]\n", + " [0. +0.j 0.5+0.j]]\n" + ] + } + ], + "source": [ + "state_density = pq.state.State([[0.5, 0], [0, 0.5]], backend=Backend.DensityMatrix)\n", + "print(state_density)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also create special types of quantum states by using the functions built into the Paddle Quantum. For example, we can create a single-qubit zero state." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.+0.j 0.+0.j]\n" + ] + } + ], + "source": [ + "print(pq.state.zero_state(num_qubits=1))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Create a 2-qubit random state." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[-0.00128883+0.02999492j 0.26680315-0.47462934j -0.22390576+0.8043244j\n", + " 0.00640717+0.07435807j]\n" + ] + } + ], + "source": [ + "print(pq.state.random_state(num_qubits=2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition, the Paddle Quantum supports the creation of several other special quantum states. More detail can be found in [API ducument](https://qml.baidu.com/api/paddle_quantum.state.common.html). \n", + "\n", + "We can also set the global backend to be density matrix mode with a single line of code. Of course, we continue to use the default backend, i.e., the state vector, for this demonstration." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[[1.+0.j 0.+0.j]\n", + " [0.+0.j 0.+0.j]]\n" + ] + } + ], + "source": [ + "pq.set_backend('density_matrix') # set the global backend as density matrix\n", + "print(pq.state.zero_state(num_qubits=1))\n", + "pq.set_backend('state_vector') # set back to the default backend" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Data of states\n", + "We can read the data in `State` by accessing `data`, `ket`, `bra`." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Its data is : Tensor(shape=[2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [(1+0j), 0j ])\n", + "Its ket is : Tensor(shape=[2, 1], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(1+0j)],\n", + " [0j ]])\n", + "Its bra is : Tensor(shape=[1, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[(1-0j), -0j ]])\n" + ] + } + ], + "source": [ + "zero_state = pq.state.zero_state(num_qubits=1)\n", + "print('Its data is :', zero_state.data)\n", + "print('Its ket is :', zero_state.ket)\n", + "print('Its bra is :', zero_state.bra)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can also use the method `numpy()` to output `numpy.ndarray` type data for `State`." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[1.+0.j 0.+0.j]\n" + ] + } + ], + "source": [ + "print(zero_state.numpy())" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Operations of states\n", + "We can get the product of two quantum states by matrix multiplication `@`, which makes calculating the overlap of two states easy." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Tensor(shape=[2, 2], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [[0j, 0j],\n", + " [0j, 0j]])\n", + "The overlap of state_1 and state_2 is : Tensor(shape=[1], dtype=complex64, place=Place(cpu), stop_gradient=True,\n", + " [0j])\n" + ] + } + ], + "source": [ + "state_1 = pq.state.zero_state(num_qubits=1, backend=Backend.DensityMatrix)\n", + "state_2 = pq.state.to_state([[0, 0], [0, 1]], backend=Backend.DensityMatrix)\n", + "print(state_1 @ state_2)\n", + "print('The overlap of state_1 and state_2 is :', paddle.trace(state_1 @ state_2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "User can also use `State.kron()` to find the tensor product $\\rho \\otimes \\sigma$ of the quantum states $\\rho$ and $\\sigma$." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.+0.j 1.+0.j 0.+0.j 0.+0.j]\n" + ] + } + ], + "source": [ + "rho = pq.state.zero_state(num_qubits=1)\n", + "sigma = pq.state.to_state([0, 1])\n", + "product_state = rho.kron(sigma)\n", + "print(product_state)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can give partial trace on states by slicing or indexing. For example, we want to get the state of the first qubit of $|011\\rangle$ and the state of the last two qubits." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.+0.j 0.+0.j 0.+0.j 1.+0.j 0.+0.j 0.+0.j 0.+0.j 0.+0.j]\n", + "the state of the first qubit is : [1.+0.j 0.+0.j]\n", + "the state of the second and third qubits is : [0.+0.j 0.+0.j 0.+0.j 1.+0.j]\n" + ] + } + ], + "source": [ + "psi_012 = pq.state.computational_basis(num_qubits=3, index=3)\n", + "print(psi_012)\n", + "\n", + "psi_1 = psi_012[0]\n", + "psi_12 = psi_012[1:]\n", + "print('the state of the first qubit is :', psi_1)\n", + "print('the state of the second and third qubits is :',psi_12)" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Measurement and evolution of states\n", + "The method `State.evolve()` of a quantum state can give the final state of the quantum state under $e^{-iHt}$ evolution given the Hamiltonian $H$ and the evolution time $t$. Here we set the Hamiltonian to be the Pauli $Z$ matrix and the evolution time $t=1$." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "[0.5403023-0.84147096j 0. +0.j ]\n" + ] + } + ], + "source": [ + "state = pq.state.zero_state(num_qubits=1)\n", + "t = 1\n", + "hamiltonian = pq.hamiltonian.Hamiltonian([(1, 'Z0')])\n", + "state.evolve(H=hamiltonian, t=t)\n", + "print(state)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The method `State.expec_val()` of states can calculate the expectation under given observables (Hamiltonian)." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "1.0\n" + ] + } + ], + "source": [ + "state = pq.state.zero_state(num_qubits=1)\n", + "observable = pq.hamiltonian.Hamiltonian([(1, 'Z0')])\n", + "print(state.expec_val(hamiltonian=observable))" + ] + }, + { + "attachments": {}, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "`State.measure()` can give the measurement result in the computational basis. The user can set the `shots` value to simulate or make `shots=0` to calculate the expectation, or use the `plot` parameter to make a plot." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Theoretical value is : {'0': 0.5, '1': 0.5}\n" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
    " + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "{'0': 0.5625, '1': 0.4375}" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "state = pq.state.to_state([[0.5, 0], [0, 0.5]], backend=Backend.DensityMatrix)\n", + "print('Theoretical value is :', state.measure(shots=0)) # theoretical value\n", + "state.measure(shots=16, plot=True)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.13" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Training_CN.ipynb b/introduction/PaddleQuantum_Training_CN.ipynb new file mode 100644 index 0000000..68b77ce --- /dev/null +++ b/introduction/PaddleQuantum_Training_CN.ipynb @@ -0,0 +1,390 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 利用量桨训练参数化量子电路\n", + "\n", + "_Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved._" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "变分量子算法(Variational Quantum Algorithms, VQA)是指通过用一个经典优化器来训练一个含参量子电路(Parameterized Quantum Circuit, PQC)来求解特定问题的算法。它可以看作是机器学习在量子计算中的自然类比。因此含参量子线路一般也被称作量子神经网络(Quantum Neural Network, QNN)。\n", + "\n", + "量桨提供了完善易用的工具集来实现对含参量子电路的训练。这里我们以量子态制备为例,介绍如何利用量桨便捷地构建参数化量子电路,设定参数,并通过经典优化器来训练参数化量子电路。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 快速构建量子神经网络" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "利用量桨中的 Circuit 类,我们可以通过复合各种量子门来构建一个量子神经网络。下面我们来看一个具体的例子。" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# 首先导入所需的程序包\n", + "import numpy as np\n", + "import paddle\n", + "from paddle_quantum.ansatz import Circuit\n", + "from paddle_quantum.state import ghz_state\n", + "from paddle_quantum.loss import StateFidelity\n", + "import matplotlib.pyplot as plt\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(1.835)----Rx(5.255)----*--------------x--\n", + " | | \n", + "--Ry(4.561)----Rx(2.712)----x----*---------|--\n", + " | | \n", + "--Ry(3.485)----Rx(1.283)---------x----*----|--\n", + " | | \n", + "--Ry(0.988)----Rx(4.441)--------------x----*--\n", + " \n" + ] + } + ], + "source": [ + "# 创建一个空的量子电路,量子比特数为 4\n", + "cir_1 = Circuit(4)\n", + "\n", + "# 添加一层 Ry 门、一层 Rx 门和一层 CNOT 门\n", + "cir_1.ry() # 默认参数:qubits_idx='full',意为在所有量子比特上都添加这样一个单比特量子门。参数默认是随机初始化的\n", + "cir_1.rx()\n", + "cir_1.cnot() # 默认参数:qubits_idx='cycle',意为在所有两两近邻的量子比特对上都添加这样一个双比特量子门\n", + "\n", + "# 输出量子电路图示\n", + "print(cir_1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在上面这个例子中,量子门默认是以逐层的方式添加到所有量子比特上的,这是量子神经网络常见的构造方式。仿照经典神经网络,每一层量子门可称为一个训练层。如果我们想指定某个量子门作用的量子比特,只需更改 qubits_idx 参数即可。" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(2.957)----*-------\n", + " | \n", + "--Rx(2.106)----x----x--\n", + " | \n", + "--Ry(0.354)---------*--\n", + " \n" + ] + } + ], + "source": [ + "# 创建一个空的量子电路\n", + "cir_2 = Circuit(3)\n", + "\n", + "# 按特定方式添加量子门\n", + "cir_2.ry(qubits_idx='even') # 在编号为偶数的量子比特上都添加这样一个单比特量子门\n", + "cir_2.rx(qubits_idx=1) # 通过指定量子比特编号的方式添加量子门\n", + "cir_2.cnot(qubits_idx=[[0,1],[2,1]]) # 通过指定量子比特编号的方式添加量子门,其中前者为控制位,后者为受控位\n", + "\n", + "# 输出量子电路图示\n", + "print(cir_2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "量桨还内置了一些常见训练层的模板,方便使用者更快速地构建量子神经网络。其他模板可参见[量桨 API](https://qml.baidu.com/api/paddle_quantum.ansatz.circuit.html)。" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(4.225)----*--------------x----Ry(2.909)----*--------------x----U----*--------------x--\n", + " | | | | | | \n", + "--Ry(4.139)----x----*---------|----Ry(5.014)----x----*---------|----U----x----*---------|--\n", + " | | | | | | \n", + "--Ry(5.998)---------x----*----|----Ry(0.292)---------x----*----|----U---------x----*----|--\n", + " | | | | | | \n", + "--Ry(1.065)--------------x----*----Ry(4.375)--------------x----*----U--------------x----*--\n", + " \n" + ] + } + ], + "source": [ + "# 创建一个空的量子电路\n", + "cir_3 = Circuit(4)\n", + "\n", + "# 添加两层内置模板 real_entangled_layer:每层包括一层 Ry 门,一层 CNOT 门\n", + "cir_3.real_entangled_layer(depth=2)\n", + "# 添加一层内置模板 complex_entangled_layer:每层包括一层 U3 门(Rz*Ry*Rz),一层 CNOT 门\n", + "cir_3.complex_entangled_layer(depth=1)\n", + "\n", + "# 输出量子电路\n", + "print(cir_3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 设定量子神经网络中的参数" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "在以上的例子中,量子神经网络中的参数都是默认随机初始化的。我们可以通过访问 param 属性来获取电路中现存的参数数值并保存到一个数组里。" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(5.308)--\n", + " \n", + "--Ry(0.278)--\n", + " \n", + "Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=False,\n", + " [5.30772972, 0.27760327])\n" + ] + } + ], + "source": [ + "# 创建一个空的量子电路\n", + "cir_4 = Circuit(2)\n", + "# 添加一层 Ry 门\n", + "cir_4.ry()\n", + "# 输出量子电路\n", + "print(cir_4)\n", + "# 输出量子电路内可训练参数的取值\n", + "print(cir_4.param)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "此外,我们可以通过执行 update_param() 方法来手动设定一组参数的值。" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(0.100)--\n", + " \n", + "--Ry(0.200)--\n", + " \n", + "Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=False,\n", + " [0.10000000, 0.20000000])\n" + ] + } + ], + "source": [ + "# 创建新的参数数组\n", + "theta_new = paddle.to_tensor([0.1, 0.2], dtype='float32')\n", + "# 更新电路中的参数\n", + "cir_4.update_param(theta_new)\n", + "# 输出量子电路图示\n", + "print(cir_4)\n", + "# 输出量子电路内可训练参数的取值\n", + "print(cir_4.param)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### 用经典优化器训练量子神经网络" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "完成量子神经网络的构建后,我们就可以根据需要定义一个损失函数,并调用经典优化器来训练这个量子神经网络了。这里我们用量子神经网络去学习一个 GHZ 态,损失函数采用保真度距离。" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 0, loss: 0.1734\n", + "iter: 5, loss: 0.1296\n", + "iter: 10, loss: 0.0896\n", + "iter: 15, loss: 0.0548\n", + "iter: 20, loss: 0.0264\n", + "iter: 25, loss: 0.0087\n", + "iter: 30, loss: 0.0084\n", + "iter: 35, loss: 0.0094\n", + "iter: 40, loss: 0.0064\n", + "iter: 45, loss: 0.0008\n", + "iter: 50, loss: 0.0035\n", + "iter: 55, loss: 0.0006\n", + "iter: 60, loss: 0.0016\n", + "iter: 65, loss: 0.0006\n", + "iter: 70, loss: 0.0004\n", + "iter: 75, loss: 0.0001\n", + "iter: 80, loss: 0.0001\n", + "iter: 85, loss: 0.0004\n", + "iter: 90, loss: 0.0002\n", + "iter: 95, loss: 0.0003\n" + ] + } + ], + "source": [ + "# 定义训练的超参数\n", + "ITR = 100 # 训练迭代次数\n", + "LR = 0.02 # 学习率\n", + "\n", + "# 定义电路\n", + "cir = Circuit(4)\n", + "cir.ry()\n", + "cir.rx()\n", + "cir.cnot()\n", + "\n", + "# 定义损失函数的形式,这里选用了量子电路的输出态和 GHZ 态的保真度\n", + "loss_func = StateFidelity(ghz_state(4))\n", + "# 选择经典优化器,通常选用 Adam 优化器\n", + "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=cir.parameters())\n", + "# 创建一个列表记录训练过程\n", + "loss_list = []\n", + "# 开始迭代优化\n", + "for itr in range(ITR):\n", + " # 运行电路,得到输出态,计算损失函数的值\n", + " loss = loss_func(cir())\n", + " # 反向传播,计算梯度\n", + " loss.backward()\n", + " # 最小化损失函数,更新参数\n", + " opt.minimize(loss)\n", + " opt.clear_grad()\n", + " # 记录损失函数的值\n", + " loss_list.append(loss.numpy().item())\n", + " if itr % 5 == 0:\n", + " print(f'iter: {itr}, loss: {loss.numpy().item():.4f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(1.177)----Rx(3.797)----*--------------x--\n", + " | | \n", + "--Ry(2.529)----Rx(5.456)----x----*---------|--\n", + " | | \n", + "--Ry(0.002)----Rx(3.140)---------x----*----|--\n", + " | | \n", + "--Ry(0.221)----Rx(3.953)--------------x----*--\n", + " \n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# 输出训练结束后的参数化量子线路\n", + "print(cir)\n", + "\n", + "# 绘制损失函数随迭代次数的变化曲线\n", + "func = plt.plot(loss_list)\n", + "plt.xlabel('Iterations')\n", + "plt.ylabel('Loss')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "我们可以发现随着训练的进行保真度距离收敛于零附近,这意味着参数化量子电路的输出态已经非常接近目标态,说明我们成功训练出了一个可以制备目标态的量子电路。" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/introduction/PaddleQuantum_Training_EN.ipynb b/introduction/PaddleQuantum_Training_EN.ipynb new file mode 100644 index 0000000..f11d018 --- /dev/null +++ b/introduction/PaddleQuantum_Training_EN.ipynb @@ -0,0 +1,390 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Use Paddle Quantum to train a PQC\n", + "\n", + "_Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved._" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Variational Quantum Algorithms (VQA) refers to algorithms that solve specific problems by training a parameterized quantum circuit (PQC) using a classical optimizer. It can be seen as a natural analogy of machine learning in quantum computing. Therefore, a PQC is also referred to as a quantum neural network (QNN).\n", + "\n", + "Paddle Quantum provides a comprehensive and easy-to-use toolkit for training PQCs. Using Paddle Quantum, we take quantum state preparation as an example to introduce how to conveniently build a PQC, set parameters, and train the PQC using a classical optimizer." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Construct a QNN" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Using the Circuit class in Paddle Quantum, we can construct a QNN by composing various quantum gates. Let's take a concrete example below." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [], + "source": [ + "# import packages\n", + "import numpy as np\n", + "import paddle\n", + "from paddle_quantum.ansatz import Circuit\n", + "from paddle_quantum.state import ghz_state\n", + "from paddle_quantum.loss import StateFidelity\n", + "import matplotlib.pyplot as plt\n", + "import warnings\n", + "warnings.filterwarnings(\"ignore\")" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(1.332)----Rx(5.582)----*--------------x--\n", + " | | \n", + "--Ry(6.031)----Rx(1.548)----x----*---------|--\n", + " | | \n", + "--Ry(5.681)----Rx(4.597)---------x----*----|--\n", + " | | \n", + "--Ry(4.998)----Rx(6.073)--------------x----*--\n", + " \n" + ] + } + ], + "source": [ + "# construct a blank quantum circuit on 4 qubits\n", + "cir_1 = Circuit(4)\n", + "\n", + "# add a layer of Ry, Rx and CNOT gates\n", + "cir_1.ry() # default:qubits_idx='full',i.e., add such a single-qubit quantum gate to all qubits. The training parameters are initialized randomly\n", + "cir_1.rx()\n", + "cir_1.cnot() # default:qubits_idx='cycle',i.e., add such a two-qubit quantum gate to all pairs of neighboring qubits\n", + "\n", + "# print the constructed circuit\n", + "print(cir_1)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the example above, quantum gates are added to all qubits by default in a layer-wise manner, which is a common method for constructing QNNs. Similar to classical neural networks, each layer of quantum gates can be referred to as a training layer. If we want to specify the qubits on which a certain quantum gate acts, we can simply change the qubits_idx parameter." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(2.892)----*-------\n", + " | \n", + "--Rx(3.203)----x----x--\n", + " | \n", + "--Ry(6.145)---------*--\n", + " \n" + ] + } + ], + "source": [ + "# construct a blank quantum circuit\n", + "cir_2 = Circuit(3)\n", + "\n", + "# add quantum gates in a specific way\n", + "cir_2.ry(qubits_idx='even') # add such a single-qubit quantum gate to all even-numbered qubits\n", + "cir_2.rx(qubits_idx=1) # add quantum gates by specifying the qubit index\n", + "cir_2.cnot(qubits_idx=[[0,1],[2,1]]) # add quantum gates by specifying the qubit indices, where the former is the control qubit and the latter is the target qubit\n", + "\n", + "# print the constructed circuit\n", + "print(cir_2)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Paddle Quantum also provides built-in templates for common training layers, which make it easier for users to quickly construct QNNs. Other templates can be found in the [Paddle Quantum API](https://qml.baidu.com/api/paddle_quantum.ansatz.circuit.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(5.156)----*--------------x----Ry(3.702)----*--------------x----U----*--------------x--\n", + " | | | | | | \n", + "--Ry(0.102)----x----*---------|----Ry(5.598)----x----*---------|----U----x----*---------|--\n", + " | | | | | | \n", + "--Ry(4.582)---------x----*----|----Ry(0.862)---------x----*----|----U---------x----*----|--\n", + " | | | | | | \n", + "--Ry(3.816)--------------x----*----Ry(2.835)--------------x----*----U--------------x----*--\n", + " \n" + ] + } + ], + "source": [ + "# construct a blank quantum circuit\n", + "cir_3 = Circuit(4)\n", + "\n", + "# add two layers of the built-in template real_entangled_layer: each layer contains a layer of Ry gates and a layer of CNOT gates\n", + "cir_3.real_entangled_layer(depth=2)\n", + "# add one layer of the built-in template complex_entangled_layer: each layer contains a layer of U3 gates and a layer of CNOT gates\n", + "cir_3.complex_entangled_layer(depth=1)\n", + "\n", + "# print the constructed circuit\n", + "print(cir_3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Set parameters in QNNs" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the above example, the parameters in the QNN are initialized randomly by default. We can retrieve the values of the existing parameters in the circuit and store them in an array by accessing the param property." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(3.633)--\n", + " \n", + "--Ry(4.663)--\n", + " \n", + "Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=False,\n", + " [3.63321853, 4.66316223])\n" + ] + } + ], + "source": [ + "# construct a blank quantum circuit\n", + "cir_4 = Circuit(2)\n", + "# add a layer of Ry gates\n", + "cir_4.ry()\n", + "# print the constructed circuit\n", + "print(cir_4)\n", + "# print the values of the parameters in the circuit\n", + "print(cir_4.param)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In addition, we can manually set the values of the parameters in the circuit by executing the update_param() method." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(0.100)--\n", + " \n", + "--Ry(0.200)--\n", + " \n", + "Tensor(shape=[2], dtype=float32, place=Place(cpu), stop_gradient=False,\n", + " [0.10000000, 0.20000000])\n" + ] + } + ], + "source": [ + "# create an array of new parameters\n", + "theta_new = paddle.to_tensor([0.1, 0.2], dtype='float32')\n", + "# update the parameters in the circuit\n", + "cir_4.update_param(theta_new)\n", + "# print the constructed circuit\n", + "print(cir_4)\n", + "# print the values of the parameters in the circuit\n", + "print(cir_4.param)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Use a classical optimizer to train a QNN" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "After constructing the QNN, we can define a loss function as needed and call the classical optimizer to train this QNN. Here we use QNNs to learn a GHZ state, and use the fidelity distance as the loss function." + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 0, loss: 0.0379\n", + "iter: 5, loss: 0.0226\n", + "iter: 10, loss: 0.0126\n", + "iter: 15, loss: 0.0065\n", + "iter: 20, loss: 0.0032\n", + "iter: 25, loss: 0.0014\n", + "iter: 30, loss: 0.0005\n", + "iter: 35, loss: 0.0003\n", + "iter: 40, loss: 0.0003\n", + "iter: 45, loss: 0.0003\n", + "iter: 50, loss: 0.0002\n", + "iter: 55, loss: 0.0001\n", + "iter: 60, loss: 0.0000\n", + "iter: 65, loss: 0.0001\n", + "iter: 70, loss: 0.0000\n", + "iter: 75, loss: 0.0000\n", + "iter: 80, loss: 0.0000\n", + "iter: 85, loss: 0.0000\n", + "iter: 90, loss: 0.0000\n", + "iter: 95, loss: 0.0000\n" + ] + } + ], + "source": [ + "# define the hyperparameters in the training\n", + "ITR = 100 # training iteration number\n", + "LR = 0.02 # learning rate\n", + "\n", + "# define a PQC\n", + "cir = Circuit(4)\n", + "cir.ry()\n", + "cir.rx()\n", + "cir.cnot()\n", + "\n", + "# define the form of the loss function. Here we use the fidelity distance between the output state from the circuit and the GHZ state\n", + "loss_func = StateFidelity(ghz_state(4))\n", + "# choose a classical optimizer, where we usually use Adam\n", + "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=cir.parameters())\n", + "# create a list to record the training process\n", + "loss_list = []\n", + "# start iteration of optimization\n", + "for itr in range(ITR):\n", + " # run the circuit, get the output state, compute the loss value\n", + " loss = loss_func(cir())\n", + " # backward propagating,compute the gradient\n", + " loss.backward()\n", + " # minimize the loss function, update the parameters\n", + " opt.minimize(loss)\n", + " opt.clear_grad()\n", + " # record the loss value\n", + " loss_list.append(loss.numpy().item())\n", + " if itr % 5 == 0:\n", + " print(f'iter: {itr}, loss: {loss.numpy().item():.4f}')" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "--Ry(5.709)----Rx(3.130)----*--------------x--\n", + " | | \n", + "--Ry(4.281)----Rx(0.462)----x----*---------|--\n", + " | | \n", + "--Ry(3.437)----Rx(-0.01)---------x----*----|--\n", + " | | \n", + "--Ry(0.000)----Rx(3.140)--------------x----*--\n", + " \n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# output the PQC after training\n", + "print(cir)\n", + "\n", + "# plot the loss value as a function of the iteration number\n", + "func = plt.plot(loss_list)\n", + "plt.xlabel('Iterations')\n", + "plt.ylabel('Loss')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can find that the fidelity distance converges near zero as the training proceeds, which means that the output state of the PQC is very close to the target state, and hence we have successfully trained a quantum circuit that can prepare the target state." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.16" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/paddle_quantum/QAOA/example/main.py b/paddle_quantum/QAOA/example/main.py index 973b812..fd10c59 100644 --- a/paddle_quantum/QAOA/example/main.py +++ b/paddle_quantum/QAOA/example/main.py @@ -36,7 +36,7 @@ options = { if __name__ == "__main__": - n = 4 + num_acted_qubits = 4 paddle.seed(SEED) p = 4 # number of layers in the circuit @@ -56,7 +56,7 @@ if __name__ == "__main__": # construct the Hamiltonian H_D_list = maxcut_hamiltonian(E) - H_D_matrix = pauli_str_to_matrix(H_D_list, n) + H_D_matrix = pauli_str_to_matrix(H_D_list, num_acted_qubits) H_D_diag = np.diag(H_D_matrix).real H_max = np.max(H_D_diag) diff --git a/paddle_quantum/__init__.py b/paddle_quantum/__init__.py index 1e2d697..527846c 100644 --- a/paddle_quantum/__init__.py +++ b/paddle_quantum/__init__.py @@ -14,8 +14,17 @@ # limitations under the License. r""" -Paddle Quantum Library. +Paddle Quantum +============== + +[Paddle Quantum](https://qml.baidu.com) is a quantum machine learning (QML) toolkit +developed based on Baidu PaddlePaddle. It supports easy-to-use quantum neural +networks (QNN) construction and training, provides combinatorial optimization, +quantum chemistry and other cutting-edge quantum applications. + +See [online API](https://qml.baidu.com/api) for complete documentation. """ + import os os.environ["PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION"]="python" from .backend import Backend @@ -25,6 +34,7 @@ from .base import set_device, get_device from .base import set_dtype, get_dtype from .base import set_backend, get_backend from .hamiltonian import Hamiltonian +from .ansatz import Circuit from . import ansatz from . import channel from . import gate @@ -34,7 +44,7 @@ from . import mbqc from . import operator from . import base from . import dataset -#from . import finance +from . import finance from . import fisher from . import gradtool from . import hamiltonian @@ -47,4 +57,4 @@ from . import visual from . import qchem name = 'paddle_quantum' -__version__ = '2.3.0' +__version__ = '2.4.0' diff --git a/paddle_quantum/ansatz/__init__.py b/paddle_quantum/ansatz/__init__.py index 480ca9a..89ae943 100644 --- a/paddle_quantum/ansatz/__init__.py +++ b/paddle_quantum/ansatz/__init__.py @@ -19,4 +19,5 @@ The module that contains the various ansatzes. from .container import Sequential from .circuit import Circuit +from .layer import Layer from .vans import VAns diff --git a/paddle_quantum/ansatz/circuit.py b/paddle_quantum/ansatz/circuit.py index 4a4f490..16b4ad9 100644 --- a/paddle_quantum/ansatz/circuit.py +++ b/paddle_quantum/ansatz/circuit.py @@ -20,23 +20,22 @@ The source file of the Circuit class. import warnings import paddle from .container import Sequential +from .layer import Layer, SuperpositionLayer, WeakSuperpositionLayer, LinearEntangledLayer +from .layer import RealBlockLayer, RealEntangledLayer, ComplexBlockLayer, ComplexEntangledLayer, QAOALayer from ..gate import Gate, H, S, Sdg, T, Tdg, X, Y, Z, P, RX, RY, RZ, U3 from ..gate import CNOT, CX, CY, CZ, SWAP from ..gate import CP, CRX, CRY, CRZ, CU, RXX, RYY, RZZ -from ..gate import MS, CSWAP, Toffoli +from ..gate import MS, CSWAP, CCX from ..gate import UniversalTwoQubits, UniversalThreeQubits from ..gate import Oracle, ControlOracle -from ..gate import SuperpositionLayer, WeakSuperpositionLayer, LinearEntangledLayer -from ..gate import RealBlockLayer, RealEntangledLayer, ComplexBlockLayer, ComplexEntangledLayer -from ..gate import QAOALayer -from ..gate import AmplitudeEncoding from ..channel import BitFlip, PhaseFlip, BitPhaseFlip, AmplitudeDamping, GeneralizedAmplitudeDamping, PhaseDamping from ..channel import Depolarizing, GeneralizedDepolarizing, PauliChannel, ResetChannel, ThermalRelaxation -from ..channel import MixedUnitaryChannel, KrausRepr -from ..intrinsic import _get_float_dtype +from ..channel import MixedUnitaryChannel, Channel, ChoiRepr, KrausRepr, StinespringRepr +from ..intrinsic import _get_float_dtype, _format_qubits_idx, _cnot_idx_fetch from ..state import zero_state from ..operator import Collapse from typing import Union, Iterable, Optional, Dict, List, Tuple +import paddle_quantum as pq from paddle_quantum import State, get_backend, get_dtype, Backend from math import pi import numpy as np @@ -59,8 +58,15 @@ class Circuit(Sequential): # whether the circuit is a dynamic quantum circuit self.__isdynamic = num_qubits is None - # alias for ccx + # alias self.toffoli = self.ccx + self.cx = self.cnot + + # preparing cnot index in 'cycle' case + if num_qubits is not None and num_qubits > 1: + cnot_qubits_idx = _format_qubits_idx("cycle", num_qubits, num_acted_qubits=2) + self.__cnot_cycle_idx = _cnot_idx_fetch(num_qubits=num_qubits, qubits_idx=cnot_qubits_idx) + @property def num_qubits(self) -> int: @@ -93,10 +99,11 @@ class Circuit(Sequential): """ grad_list = [] for param in self.parameters(): - assert param.grad is not None, 'the gradient is None, run the backward first before calling this property,' + \ - ' otherwise check where the gradient chain is broken' - grad_list.append(paddle.flatten(param.grad)) - return paddle.concat(grad_list).numpy() + assert param.grad is not None, ( + 'The gradient is None, run the backward first before calling this property, ' + 'otherwise check where the gradient chain is broken.') + grad_list.append(param.grad.numpy().flatten()) + return np.concatenate(grad_list) def update_param(self, theta: Union[paddle.Tensor, np.ndarray, float], idx: int = None) -> None: r"""Replace parameters of all/one layer(s) by ``theta``. @@ -125,7 +132,8 @@ class Circuit(Sequential): param = paddle.create_parameter( shape=param.shape, dtype='float32', - default_initializer=paddle.nn.initializer.Assign(theta[:num_param].reshape(param.shape)), + default_initializer=paddle.nn.initializer.Assign( + theta[:num_param].reshape(param.shape)), ) setattr(layer, 'theta', param) @@ -133,11 +141,12 @@ class Circuit(Sequential): return theta = theta[num_param:] elif isinstance(idx, int): - assert idx < len(self.sublayers()), f"the index is out of range, expect below {len(self.sublayers())}" + assert idx < len(self.sublayers( + )), f"the index is out of range, expect below {len(self.sublayers())}" layer = self.sublayers()[idx] - assert theta.shape == paddle.concat([paddle.flatten(param) for param in layer.parameters()]).shape, \ - "the shape of input parameters is not correct," + assert theta.shape == paddle.concat([paddle.flatten(param) for param in layer.parameters()]).shape, ( + "The shape of input parameters is not correct.") for name, _ in layer.named_parameters(): param = getattr(layer, name) @@ -146,7 +155,8 @@ class Circuit(Sequential): param = paddle.create_parameter( shape=param.shape, dtype='float32', - default_initializer=paddle.nn.initializer.Assign(theta[:num_param].reshape(param.shape)), + default_initializer=paddle.nn.initializer.Assign( + theta[:num_param].reshape(param.shape)), ) setattr(layer, 'theta', param) @@ -163,26 +173,43 @@ class Circuit(Sequential): for layer in self.sublayers(): for name, _ in layer.named_parameters(): param = getattr(layer, name) - param.stop_gradient = True + param.stop_gradient = True setattr(layer, 'theta', param) - def randomize_param(self, low: float = 0, high: Optional[float] = 2 * pi) -> None: - r"""Randomize parameters of the circuit in a range from low to high. + def randomize_param(self, arg0: float = 0, arg1: float = 2 * pi, initializer_type: str= 'Uniform') -> None: + r"""Randomize parameters of the circuit based on the initializer. Current we only support Uniform and Normal initializer. + + A detail introduction can be found in https://www.paddlepaddle.org.cn/documentation/docs/zh/api/paddle/nn/initializer/Uniform_en.html Args: - low: Lower bound. - high: Upper bound. + arg0: first argument of the initializer. Defaults to 0. + arg1: first argument of the initializer. Defaults to 2 * pi. + initializer_type: The type of the initializer. Defaults to 'Uniform'. """ + assert initializer_type in ["Uniform", "Normal"], ( + "The initializer should be Uniform or Normal." + ) + for layer in self.sublayers(): for name, _ in layer.named_parameters(): param = getattr(layer, name) - param = paddle.create_parameter( - shape=param.shape, - dtype=param.dtype, - default_initializer=paddle.nn.initializer.Uniform(low=low, high=high), - ) - setattr(layer, 'theta', param) + if initializer_type == 'Uniform': + param = paddle.create_parameter( + shape=param.shape, + dtype=param.dtype, + default_initializer=paddle.nn.initializer.Uniform( + low=arg0, high=arg1), + ) + setattr(layer, 'theta', param) + elif initializer_type == 'Normal': + param = paddle.create_parameter( + shape=param.shape, + dtype=param.dtype, + default_initializer=paddle.nn.initializer.Normal( + mean=arg0, std=arg1), + ) + setattr(layer, 'theta', param) def __num_qubits_update(self, qubits_idx: Union[Iterable[int], int, str]) -> None: r"""Update ``self.num_qubits`` according to ``qubits_idx``, or report error. @@ -191,8 +218,9 @@ class Circuit(Sequential): qubits_idx: Input qubit indices of a quantum gate. """ num_qubits = self.__num_qubits - if isinstance(qubits_idx, str): - assert num_qubits is not None, "The qubit idx cannot be full when the number of qubits is unknown" + if isinstance(qubits_idx, str) or qubits_idx is None: + assert num_qubits is not None, \ + f"The qubit idx cannot be a string or None when the number of qubits is unknown: received {qubits_idx}" return if isinstance(qubits_idx, Iterable): @@ -204,12 +232,13 @@ class Circuit(Sequential): self.__num_qubits = max_idx + 1 return - assert max_idx + 1 <= num_qubits or self.__isdynamic, \ - f"The circuit is not a dynamic quantum circuit. Invalid input qubit idx: {max_idx} num_qubit: {self.__num_qubits}" + assert max_idx + 1 <= num_qubits or self.__isdynamic, ( + "The circuit is not a dynamic quantum circuit. " + f"Invalid input qubit idx: {max_idx} num_qubit: {self.__num_qubits}") self.__num_qubits = int(max(max_idx + 1, num_qubits)) def h( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1 ) -> None: r"""Add single-qubit Hadamard gates. @@ -225,14 +254,13 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append(H(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(H(qubits_idx, self.num_qubits, depth)) def s( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1 ) -> None: r"""Add single-qubit S gates. @@ -248,15 +276,13 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - S(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(S(qubits_idx, self.num_qubits, depth)) def sdg( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1 ) -> None: r"""Add single-qubit S dagger (S inverse) gates. @@ -272,15 +298,13 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ self.__num_qubits_update(qubits_idx) - self.append( - Sdg(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(Sdg(qubits_idx, self.num_qubits, depth)) def t( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1 ) -> None: r"""Add single-qubit T gates. @@ -295,15 +319,13 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - T(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(T(qubits_idx, self.num_qubits, depth)) def tdg( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1 ) -> None: r"""Add single-qubit T dagger (T inverse) gates. @@ -319,15 +341,13 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - Tdg(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) - + self.append(Tdg(qubits_idx, self.num_qubits, depth)) + def x( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1 ) -> None: r"""Add single-qubit X gates. @@ -341,15 +361,13 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - X(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(X(qubits_idx, self.num_qubits, depth)) def y( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1 ) -> None: r"""Add single-qubit Y gates. @@ -364,15 +382,13 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - Y(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(Y(qubits_idx, self.num_qubits, depth)) def z( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1 ) -> None: r"""Add single-qubit Z gates. @@ -387,15 +403,13 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - Z(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(Z(qubits_idx, self.num_qubits, depth)) def p( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add single-qubit P gates. @@ -411,17 +425,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append( - P(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth, param, param_sharing)) + self.append(P(qubits_idx, self.num_qubits, depth, param, param_sharing)) def rx( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add single-qubit rotation gates about the x-axis. @@ -437,17 +449,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(RX(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(RX(qubits_idx, self.num_qubits, depth, param, param_sharing)) def ry( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add single-qubit rotation gates about the y-axis. @@ -463,17 +473,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(RY(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(RY(qubits_idx, self.num_qubits, depth, param, param_sharing)) def rz( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: Optional[int] = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add single-qubit rotation gates about the z-axis. @@ -489,17 +497,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(RZ(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(RZ(qubits_idx, self.num_qubits, depth, param, param_sharing)) def u3( - self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], int, str] = 'full', depth: int = 1, param: Union[paddle.Tensor, Iterable[float]] = None, param_sharing: bool = False ) -> None: r"""Add single-qubit rotation gates. @@ -518,17 +524,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(U3(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(U3(qubits_idx, self.num_qubits, depth, param, param_sharing)) def cnot( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1 ) -> None: r"""Add CNOT gates. @@ -549,29 +553,16 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - CNOT(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) - - def cx( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1 - ) -> None: - r"""Same as cnot. - - Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. - depth: Number of layers. Defaults to 1. - """ - self.__num_qubits_update(qubits_idx) - self.append( - CX(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + if qubits_idx == "cycle" and not self.__isdynamic: + self.append(CNOT(qubits_idx, self.num_qubits, depth, self.__cnot_cycle_idx)) + else: + self.append(CNOT(qubits_idx, self.num_qubits, depth)) def cy( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1 ) -> None: r"""Add controlled Y gates. @@ -592,15 +583,13 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - CY(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(CY(qubits_idx, self.num_qubits, depth)) def cz( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], str] = 'linear', depth: int = 1 ) -> None: r"""Add controlled Z gates. @@ -620,16 +609,14 @@ class Circuit(Sequential): \end{align} Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'linear'. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - CZ(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(CZ(qubits_idx, self.num_qubits, depth)) def swap( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], str] = 'linear', depth: int = 1 ) -> None: r"""Add SWAP gates. @@ -648,16 +635,14 @@ class Circuit(Sequential): \end{align} Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'linear'. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - SWAP(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(SWAP(qubits_idx, self.num_qubits, depth)) def cp( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add controlled P gates. @@ -678,17 +663,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(CP(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(CP(qubits_idx, self.num_qubits, depth, param, param_sharing)) def crx( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add controlled rotation gates about the x-axis. @@ -710,17 +693,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(CRX(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(CRX(qubits_idx, self.num_qubits, depth, param, param_sharing)) def cry( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add controlled rotation gates about the y-axis. @@ -742,17 +723,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(CRY(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(CRY(qubits_idx, self.num_qubits, depth, param, param_sharing)) def crz( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add controlled rotation gates about the z-axis. @@ -774,17 +753,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(CRZ(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(CRZ(qubits_idx, self.num_qubits, depth, param, param_sharing)) def cu( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add controlled single-qubit rotation gates. @@ -806,17 +783,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(CU(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(CU(qubits_idx, self.num_qubits, depth, param, param_sharing)) def rxx( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], str] = 'linear', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add RXX gates. @@ -836,18 +811,16 @@ class Circuit(Sequential): \end{align} Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'linear'. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(RXX(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(RXX(qubits_idx, self.num_qubits, depth, param, param_sharing)) def ryy( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], str] = 'linear', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add RYY gates. @@ -867,18 +840,16 @@ class Circuit(Sequential): \end{align} Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'linear'. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(RYY(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(RYY(qubits_idx, self.num_qubits, depth, param, param_sharing)) def rzz( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], str] = 'linear', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add RZZ gates. @@ -898,18 +869,16 @@ class Circuit(Sequential): \end{align} Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'linear'. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(RZZ(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(RZZ(qubits_idx, self.num_qubits, depth, param, param_sharing)) def ms( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1 ) -> None: r"""Add Mølmer-Sørensen (MS) gates. @@ -929,15 +898,13 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - MS(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(MS(qubits_idx, self.num_qubits, depth)) def cswap( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1 ) -> None: r"""Add CSWAP (Fredkin) gates. @@ -961,17 +928,15 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - CSWAP(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(CSWAP(qubits_idx, self.num_qubits, depth)) def ccx( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1 ) -> None: - r"""Add CCX gates. + r"""Add CCX (Toffoli) gates. The matrix form of such a gate is: @@ -992,39 +957,35 @@ class Circuit(Sequential): Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - Toffoli(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.append(CCX(qubits_idx, self.num_qubits, depth)) def universal_two_qubits( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add universal two-qubit gates. One of such a gate requires 15 parameters. Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. """ self.__num_qubits_update(qubits_idx) - self.append(UniversalTwoQubits(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(UniversalTwoQubits( + qubits_idx, self.num_qubits, depth, param, param_sharing)) def universal_three_qubits( - self, qubits_idx: Union[Iterable[int], str] = 'cycle', num_qubits: int = None, depth: int = 1, + self, qubits_idx: Union[Iterable[int], str] = 'cycle', depth: int = 1, param: Union[paddle.Tensor, float] = None, param_sharing: bool = False ) -> None: r"""Add universal three-qubit gates. One of such a gate requires 81 parameters. Args: qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'cycle'. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. param: Parameters of the gates. Defaults to None. param_sharing: Whether gates in the same layer share a parameter. Defaults to False. @@ -1033,12 +994,11 @@ class Circuit(Sequential): ValueError: The ``param`` must be paddle.Tensor or float. """ self.__num_qubits_update(qubits_idx) - self.append(UniversalThreeQubits(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - depth, param, param_sharing)) + self.append(UniversalThreeQubits( + qubits_idx, self.num_qubits, depth, param, param_sharing)) def oracle( - self, oracle: paddle.tensor, qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int], - num_qubits: int = None, depth: int = 1, + self, oracle: paddle.tensor, qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int], depth: int = 1, gate_name: Optional[str] = 'O', latex_name: Optional[str] = None, plot_width: Optional[float] = None ) -> None: """Add an oracle gate. @@ -1046,22 +1006,21 @@ class Circuit(Sequential): Args: oracle: Unitary oracle to be implemented. qubits_idx: Indices of the qubits on which the gates are applied. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. gate_name: name of this oracle. latex_name: latex name of this oracle, default to be the gate name. plot_width: width of this gate in circuit plot, default to be proportional with the gate name. """ self.__num_qubits_update(qubits_idx) - gate_info = {'gatename': gate_name, - 'texname': f"${gate_name}$" if latex_name is None else latex_name, - 'plot_width': 0.6 * len(gate_name) if plot_width is None else plot_width} - self.append(Oracle(oracle, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits, depth, gate_info)) + gate_info = { + 'gatename': gate_name, + 'texname': f"${gate_name}$" if latex_name is None else latex_name, + 'plot_width': 0.6 * len(gate_name) if plot_width is None else plot_width} + self.append(Oracle( + oracle, qubits_idx, self.num_qubits, depth, gate_info)) def control_oracle( - self, oracle: paddle.Tensor, qubits_idx: Union[Iterable[Iterable[int]], Iterable[int]], - num_qubits: int = None, depth: int = 1, + self, oracle: paddle.Tensor, qubits_idx: Union[Iterable[Iterable[int]], Iterable[int]], depth: int = 1, gate_name: Optional[str] = 'O', latex_name: Optional[str] = None, plot_width: Optional[float] = None ) -> None: """Add a controlled oracle gate. @@ -1069,26 +1028,25 @@ class Circuit(Sequential): Args: oracle: Unitary oracle to be implemented. qubits_idx: Indices of the qubits on which the gates are applied. - num_qubits: Total number of qubits. Defaults to None. depth: Number of layers. Defaults to 1. gate_name: name of this oracle. latex_name: latex name of this oracle, default to be the gate name. plot_width: width of this gate in circuit plot, default to be proportional with the gate name. """ self.__num_qubits_update(qubits_idx) - gate_info = {'gatename': f"c{gate_name}", - 'texname': f"${gate_name}$" if latex_name is None else latex_name, - 'plot_width': 0.6 * len(gate_name) if plot_width is None else plot_width} - self.append(ControlOracle(oracle, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits, depth, gate_info)) - - def collapse(self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None, + gate_info = { + 'gatename': f"c{gate_name}", + 'texname': f"${gate_name}$" if latex_name is None else latex_name, + 'plot_width': 0.6 * len(gate_name) if plot_width is None else plot_width} + self.append(ControlOracle( + oracle, qubits_idx, self.num_qubits, depth, gate_info)) + + def collapse(self, qubits_idx: Union[Iterable[int], int, str] = 'full', desired_result: Union[int, str] = None, if_print: bool = False, measure_basis: Union[Iterable[paddle.Tensor], str] = 'z') -> None: r""" Args: qubits_idx: list of qubits to be collapsed. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to ``None``. desired_result: The desired result you want to collapse. Defaults to ``None`` meaning randomly choose one. if_print: whether print the information about the collapsed state. Defaults to ``False``. measure_basis: The basis of the measurement. The quantum state will collapse to the corresponding eigenstate. @@ -1101,169 +1059,160 @@ class Circuit(Sequential): When desired_result is `None`, Collapse does not support gradient calculation """ self.__num_qubits_update(qubits_idx) - self.append(Collapse(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, - desired_result, if_print, measure_basis)) + self.append(Collapse( + qubits_idx, self.num_qubits, desired_result, if_print, measure_basis)) def superposition_layer( - self, qubits_idx: Iterable[int] = 'full', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Iterable[int] = None, depth: int = 1 ) -> None: r"""Add layers of Hadamard gates. Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``None``. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - SuperpositionLayer(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) - + self.extend( + SuperpositionLayer(qubits_idx, self.num_qubits, depth)) + def weak_superposition_layer( - self, qubits_idx: Iterable[int] = 'full', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Iterable[int] = None, depth: int = 1 ) -> None: r"""Add layers of Ry gates with a rotation angle :math:`\pi/4`. Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``None``. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - WeakSuperpositionLayer(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) - + self.extend( + WeakSuperpositionLayer(qubits_idx, self.num_qubits, depth)) + def linear_entangled_layer( - self, qubits_idx: Iterable[int] = 'full', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Iterable[int] = None, depth: int = 1 ) -> None: r"""Add linear entangled layers consisting of Ry gates, Rz gates, and CNOT gates. Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``None``. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - LinearEntangledLayer(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.extend( + LinearEntangledLayer(qubits_idx, self.num_qubits, depth)) def real_entangled_layer( - self, qubits_idx: Iterable[int] = 'full', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Iterable[int] = None, depth: int = 1 ) -> None: r"""Add strongly entangled layers consisting of Ry gates and CNOT gates. Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``None``. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - RealEntangledLayer(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.extend( + RealEntangledLayer(qubits_idx, self.num_qubits, depth)) def complex_entangled_layer( - self, qubits_idx: Iterable[int] = 'full', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Iterable[int] = None, depth: int = 1 ) -> None: r"""Add strongly entangled layers consisting of single-qubit rotation gates and CNOT gates. Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``None``. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - ComplexEntangledLayer(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.extend( + ComplexEntangledLayer(qubits_idx, self.num_qubits, depth)) def real_block_layer( - self, qubits_idx: Iterable[int] = 'full', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Iterable[int] = None, depth: int = 1 ) -> None: r"""Add weakly entangled layers consisting of Ry gates and CNOT gates. Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``None``. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - RealBlockLayer(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) - + self.extend( + RealBlockLayer(qubits_idx, self.num_qubits, depth)) + def complex_block_layer( - self, qubits_idx: Iterable[int] = 'full', num_qubits: int = None, depth: int = 1 + self, qubits_idx: Iterable[int] = None, depth: int = 1 ) -> None: r"""Add weakly entangled layers consisting of single-qubit rotation gates and CNOT gates. Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. + qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``None``. depth: Number of layers. Defaults to 1. """ self.__num_qubits_update(qubits_idx) - self.append( - ComplexBlockLayer(qubits_idx, self.num_qubits if num_qubits is None else num_qubits, depth)) + self.extend( + ComplexBlockLayer(qubits_idx, self.num_qubits, depth)) + + def qaoa_layer(self, edges: Iterable, nodes: Iterable, depth: Optional[int] = 1) -> None: + # TODO: see qaoa layer in layer.py + self.__num_qubits_update(edges) + self.__num_qubits_update(nodes) + self.extend(QAOALayer(edges, nodes, depth)) def bit_flip( - self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None + self, prob: Union[paddle.Tensor, float], + qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add bit flip channels. Args: prob: Probability of a bit flip. qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) - self.append(BitFlip(prob, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) + self.append(BitFlip(prob, qubits_idx, self.num_qubits)) def phase_flip( - self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', - num_qubits: int = None + self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add phase flip channels. Args: prob: Probability of a phase flip. qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) self.append(PhaseFlip(prob, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) + self.num_qubits)) def bit_phase_flip( - self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', - num_qubits: int = None + self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add bit phase flip channels. Args: prob: Probability of a bit phase flip. qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) - self.append(BitPhaseFlip(prob, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) + self.append(BitPhaseFlip(prob, qubits_idx, self.num_qubits)) def amplitude_damping( - self, gamma: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None + self, gamma: Union[paddle.Tensor, float], + qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add amplitude damping channels. Args: gamma: Damping probability. qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) - self.append(AmplitudeDamping(gamma, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) + self.append(AmplitudeDamping(gamma, qubits_idx, self.num_qubits)) def generalized_amplitude_damping( self, gamma: Union[paddle.Tensor, float], prob: Union[paddle.Tensor, float], - qubits_idx: Union[Iterable[int], int, str] = 'full', - num_qubits: int = None + qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add generalized amplitude damping channels. @@ -1271,90 +1220,74 @@ class Circuit(Sequential): gamma: Damping probability. Its value should be in the range :math:`[0, 1]`. prob: Excitation probability. Its value should be in the range :math:`[0, 1]`. qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) - self.append(GeneralizedAmplitudeDamping(gamma, prob, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) - + self.append(GeneralizedAmplitudeDamping( + gamma, prob, qubits_idx, self.num_qubits)) + def phase_damping( - self, gamma: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', - num_qubits: int = None + self, gamma: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add phase damping channels. Args: gamma: Parameter of the phase damping channel. qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) - self.append(PhaseDamping(gamma, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) + self.append(PhaseDamping(gamma, qubits_idx, self.num_qubits)) def depolarizing( - self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', - num_qubits: int = None + self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add depolarizing channels. Args: prob: Parameter of the depolarizing channel. qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) - self.append(Depolarizing(prob, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) - + self.append(Depolarizing(prob, qubits_idx, self.num_qubits)) + def generalized_depolarizing( - self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str], - num_qubits: int = None + self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] ) -> None: r"""Add a general depolarizing channel. Args: prob: Probabilities corresponding to the Pauli basis. qubits_idx: Indices of the qubits on which the channel is applied. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) - self.append(PauliChannel(prob, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) + self.append(GeneralizedDepolarizing(prob, qubits_idx, self.num_qubits)) def pauli_channel( - self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', - num_qubits: int = None + self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add Pauli channels. Args: prob: Probabilities corresponding to the Pauli X, Y, and Z operators. qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) - self.append(PauliChannel(prob, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) - + self.append(PauliChannel(prob, qubits_idx, self.num_qubits)) + def reset_channel( - self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', - num_qubits: int = None + self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add reset channels. Args: prob: Probabilities of resetting to :math:`|0\rangle` and to :math:`|1\rangle`. qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) - self.append(ResetChannel(prob, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) + self.append(ResetChannel(prob, qubits_idx, self.num_qubits)) def thermal_relaxation( - self, const_t: Union[paddle.Tensor, Iterable[float]], exec_time: Union[paddle.Tensor, float], - qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None + self, const_t: Union[paddle.Tensor, Iterable[float]], exec_time: Union[paddle.Tensor, float], + qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add thermal relaxation channels. @@ -1362,66 +1295,74 @@ class Circuit(Sequential): const_t: :math:`T_1` and :math:`T_2` relaxation time in microseconds. exec_time: Quantum gate execution time in the process of relaxation in nanoseconds. qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. """ self.__num_qubits_update(qubits_idx) - self.append(ThermalRelaxation(const_t, exec_time, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) + self.append( + ThermalRelaxation(const_t, exec_time, qubits_idx, self.num_qubits)) def mixed_unitary_channel( - self, num_unitary: Union[paddle.Tensor, int], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None + self, num_unitary: Union[paddle.Tensor, int], + qubits_idx: Union[Iterable[int], int, str] = 'full' ) -> None: r"""Add mixed random unitary channels Args: num_unitary: The amount of random unitaries to be generated. qubits_idx: Indices of the qubits on which the channels act. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to ``None``. """ self.__num_qubits_update(qubits_idx) - self.append(MixedUnitaryChannel(num_unitary, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) + self.append(MixedUnitaryChannel(num_unitary, qubits_idx, self.num_qubits)) + + def choi_channel( + self, choi_repr: Iterable[paddle.Tensor], + qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] + ) -> None: + r"""Add custom channels in the Choi representation. - def kraus_repr( + Args: + choi_repr: Choi representation of this channel. + qubits_idx: Indices of the qubits on which the channels are applied. + """ + self.__num_qubits_update(qubits_idx) + self.append(ChoiRepr(choi_repr, qubits_idx, self.num_qubits)) + + def kraus_channel( self, kraus_oper: Iterable[paddle.Tensor], - qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int], - num_qubits: int = None + qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] ) -> None: r"""Add custom channels in the Kraus representation. Args: - kraus_oper: Kraus operators of this channel. - qubits_idx: Indices of the qubits on which the channels are applied. Defaults to 'full'. - num_qubits: Total number of qubits. Defaults to None. + kraus_oper: Kraus representation of this channel. + qubits_idx: Indices of the qubits on which the channels are applied. """ self.__num_qubits_update(qubits_idx) - self.append(KrausRepr(kraus_oper, qubits_idx, - self.num_qubits if num_qubits is None else num_qubits)) + self.append(KrausRepr(kraus_oper, qubits_idx, self.num_qubits)) - def qaoa_layer(self, edges: Iterable, nodes: Iterable, depth: Optional[int] = 1) -> None: - # TODO: see qaoa layer in layer.py - self.__num_qubits_update(edges) - self.__num_qubits_update(nodes) - self.append(QAOALayer(edges, nodes, depth)) - - def unitary_matrix(self, num_qubits: Optional[int] = None) -> paddle.Tensor: - r"""Get the unitary matrix form of the circuit. + def stinespring_channel( + self, stinespring_repr: Iterable[paddle.Tensor], + qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] + ) -> None: + r"""Add custom channels in the Stinespring representation. Args: - num_qubits: Total number of qubits. Defaults to None. + stinespring_repr: Stinespring representation of this channel. + qubits_idx: Indices of the qubits on which the channels are applied. + """ + self.__num_qubits_update(qubits_idx) + self.append( + StinespringRepr(stinespring_repr, qubits_idx, self.num_qubits)) + + def unitary_matrix(self) -> paddle.Tensor: + r"""Get the unitary matrix form of the circuit. Returns: Unitary matrix form of the circuit. """ - if num_qubits is None: - num_qubits = self.__num_qubits - else: - assert num_qubits >= self.__num_qubits - backend = get_backend() self.to(backend=Backend.UnitaryMatrix) - unitary = State(paddle.eye(2 ** num_qubits).cast(get_dtype()), - backend=Backend.UnitaryMatrix) + unitary = State(paddle.eye( + 2 ** self.num_qubits).cast(get_dtype()), backend=Backend.UnitaryMatrix) for layer in self._sub_layers.values(): unitary = layer(unitary) self.to(backend=backend) @@ -1429,21 +1370,45 @@ class Circuit(Sequential): @property def gate_history(self) -> List[Dict[str, Union[str, List[int], paddle.Tensor]]]: - r""" list of gates information of circuit + r"""List of gates information of circuit Returns: history of quantum gates of circuit """ gate_history = [] - for gate in self.sublayers(): - if gate.gate_info['gatename'] is None: - raise NotImplementedError(f"Gate {type(gate)} has no gate name and hence cannot be recorded into history.") + for op in self.sublayers(): + if isinstance(op, Layer): + gate_history.extend(op.gate_history) else: - gate.gate_history_generation() - gate_history.extend(gate.gate_history) + if op.gate_info['gatename'] is None: + raise NotImplementedError( + f"{type(op)} has no gate name and hence cannot be recorded into history.") + op.gate_history_generation() + gate_history.extend(op.gate_history) return gate_history + @property + def depth(self) -> int: + r"""Depth of gate sequences. + + Returns: + depth of this circuit + + Note: + The measurement is omitted, and all gates are assumed to have depth 1. + See Niel's answer in the [StackExchange](https://quantumcomputing.stackexchange.com/a/5772). + + """ + qubit_depth = np.array([0] * self.num_qubits) + for gate_info in self.gate_history: + qubits_idx = gate_info['which_qubits'] + if isinstance(qubits_idx, int): + qubit_depth[qubits_idx] += 1 + else: + qubit_depth[qubits_idx] = np.max(qubit_depth[qubits_idx]) + 1 + return int(np.max(qubit_depth)) + def __count_history(self, history): # Record length of each section length = [5] @@ -1454,7 +1419,6 @@ class Circuit(Sequential): qubit_max = max(qubit) # Record section number for each gate gate = [] - for current_gate in history: # Single-qubit gates with no params to print if current_gate['gate'] in {'h', 's', 't', 'x', 'y', 'z', 'u', 'sdg', 'tdg'}: @@ -1474,15 +1438,17 @@ class Circuit(Sequential): if qubit[curr_qubit] > qubit_max: length.append(5) qubit_max = qubit[curr_qubit] - elif current_gate['gate'] in {'cnot', 'swap', 'rxx', 'ryy', 'rzz', 'ms', - 'cy', 'cz', 'cu', 'cp', 'crx', 'cry', 'crz', - 'cswap', 'ccx'}: + elif current_gate['gate'] in { + 'cnot', 'swap', 'rxx', 'ryy', 'rzz', 'ms', + 'cy', 'cz', 'cu', 'cp', 'crx', 'cry', 'crz', 'cswap', 'ccx' + }: a = max(current_gate['which_qubits']) b = min(current_gate['which_qubits']) ind = max(qubit[b: a + 1]) gate.append(ind) - if length[ind] < 13 and current_gate['gate'] in {'rxx', 'ryy', 'rzz', - 'cp', 'crx', 'cry', 'crz'}: + if length[ind] < 13 and current_gate['gate'] in { + 'rxx', 'ryy', 'rzz', 'cp', 'crx', 'cry', 'crz' + }: length[ind] = 13 for j in range(b, a + 1): qubit[j] = ind + 1 @@ -1498,7 +1464,7 @@ class Circuit(Sequential): Returns: list of gate history on each qubit - + Note: The entry ``qubit_history[i][j][0/1]`` returns the gate information / gate index of the j-th gate applied on the i-th qubit. @@ -1513,22 +1479,21 @@ class Circuit(Sequential): history_qubit[j].append([i, idx]) return history_qubit - def __str__(self) -> str: + def __str__(self): history = self.gate_history num_qubits = self.__num_qubits length, gate = self.__count_history(history) # Ignore the unused section total_length = sum(length) - 5 - - print_list = [['-' if i % 2 == 0 else ' '] * + print_list = [['-' if i % 2 == 0 else ' '] * total_length for i in range(num_qubits * 2)] - for i, current_gate in enumerate(history): if current_gate['gate'] in {'h', 's', 't', 'x', 'y', 'z', 'u'}: # Calculate starting position ind of current gate sec = gate[i] ind = sum(length[:sec]) - print_list[current_gate['which_qubits'] * 2][ind + length[sec] // 2] = current_gate['gate'].upper() + print_list[current_gate['which_qubits'] * 2][ind + + length[sec] // 2] = current_gate['gate'].upper() elif current_gate['gate'] in {'sdg'}: sec = gate[i] ind = sum(length[:sec]) @@ -1552,20 +1517,23 @@ class Circuit(Sequential): print_list[line][ind + 2] = 'R' print_list[line][ind + 3] = current_gate['gate'][1] print_list[line][ind + 4] = '(' - print_list[line][ind + 5: ind + 10] = format(float(param.numpy()), '.3f')[:5] + print_list[line][ind + 5: ind + + 10] = format(float(param.numpy()), '.3f')[:5] print_list[line][ind + 10] = ')' # Two-qubit gates elif current_gate['gate'] in {'cnot', 'swap', 'rxx', 'ryy', 'rzz', 'ms', 'cz', 'cy', - 'cu', 'crx', 'cry', 'crz'}: + 'cu', 'cp', 'crx', 'cry', 'crz'}: sec = gate[i] ind = sum(length[:sec]) cqubit = current_gate['which_qubits'][0] tqubit = current_gate['which_qubits'][1] if current_gate['gate'] in {'cnot', 'swap', 'cy', 'cz', 'cu'}: print_list[cqubit * 2][ind + length[sec] // 2] = \ - '*' if current_gate['gate'] in {'cnot', 'cy', 'cz', 'cu'} else 'x' + '*' if current_gate['gate'] in {'cnot', + 'cy', 'cz', 'cu'} else 'x' print_list[tqubit * 2][ind + length[sec] // 2] = \ - 'x' if current_gate['gate'] in {'swap', 'cnot'} else current_gate['gate'][1] + 'x' if current_gate['gate'] in { + 'swap', 'cnot'} else current_gate['gate'][1] elif current_gate['gate'] == 'ms': for qubit in {cqubit, tqubit}: print_list[qubit * 2][ind + length[sec] // 2 - 1] = 'M' @@ -1576,19 +1544,31 @@ class Circuit(Sequential): param = current_gate['theta'] for line in {cqubit * 2, tqubit * 2}: print_list[line][ind + 2] = 'R' - print_list[line][ind + 3: ind + 5] = current_gate['gate'][1:3].lower() + print_list[line][ind + 3: ind + + 5] = current_gate['gate'][1:3].lower() print_list[line][ind + 5] = '(' - print_list[line][ind + 6: ind + 10] = format(float(param.numpy()), '.2f')[:4] + print_list[line][ind + 6: ind + + 10] = format(float(param.numpy()), '.2f')[:4] print_list[line][ind + 10] = ')' elif current_gate['gate'] in {'crx', 'cry', 'crz'}: - # param = self.__param[current_gate['theta'][2 if current_gate['gate'] == 'crz' else 0]] param = current_gate['theta'] print_list[cqubit * 2][ind + length[sec] // 2] = '*' print_list[tqubit * 2][ind + 2] = 'R' print_list[tqubit * 2][ind + 3] = current_gate['gate'][2] print_list[tqubit * 2][ind + 4] = '(' - print_list[tqubit * 2][ind + 5: ind + 10] = format(float(param.numpy()), '.3f')[:5] + print_list[tqubit * 2][ind + 5: ind + + 10] = format(float(param.numpy()), '.3f')[:5] + print_list[tqubit * 2][ind + 10] = ')' + elif current_gate['gate'] == 'cp': + param = current_gate['theta'] + print_list[cqubit * 2][ind + length[sec] // 2] = '*' + print_list[tqubit * 2][ind + 2] = ' ' + print_list[tqubit * 2][ind + 3] = 'P' + print_list[tqubit * 2][ind + 4] = '(' + print_list[tqubit * 2][ind + 5: ind + + 10] = format(float(param.numpy()), '.3f')[:5] print_list[tqubit * 2][ind + 10] = ')' + start_line = min(cqubit, tqubit) end_line = max(cqubit, tqubit) for k in range(start_line * 2 + 1, end_line * 2): @@ -1623,21 +1603,23 @@ class Circuit(Sequential): print_list[cqubit2 * 2][ind + length[sec] // 2] = '*' print_list[tqubit * 2][ind + length[sec] // 2] = 'X' else: - raise NotImplementedError(f"Not support to print the gate {current_gate['gate']}.") + raise NotImplementedError( + f"Not support to print the gate {current_gate['gate']}.") print_list = list(map(''.join, print_list)) return_str = '\n'.join(print_list) return return_str - - def plot(self, - save_path: Optional[str] = None, - dpi: Optional[int] = 100, - show: Optional[bool] = True, - output: Optional[bool] = False, - scale: Optional[float] = 1.0, - tex: Optional[bool] = False, - ) -> Union[None, matplotlib.figure.Figure]: + + def plot( + self, + save_path: Optional[str] = None, + dpi: Optional[int] = 100, + show: Optional[bool] = True, + output: Optional[bool] = False, + scale: Optional[float] = 1.0, + tex: Optional[bool] = False, + ) -> Union[None, matplotlib.figure.Figure]: r'''display the circuit using matplotlib Args: @@ -1646,11 +1628,11 @@ class Circuit(Sequential): show: whether execute ``plt.show()`` output: whether return the ``matplotlib.figure.Figure`` instance scale: scale coefficient of figure, default to 1.0 - tex: a bool flag which controls latex fonts of gate display, default to ``False``. + tex: a bool flag which controls latex fonts of gate display, default to ``False``. Returns: a ``matplotlib.figure.Figure`` instance or ``None`` depends on ``output`` - + Note: Using ``plt.show()`` may cause a distortion, but it will not happen in the figure saved. If the depth is too long, there will be some patches unable to display. @@ -1659,56 +1641,61 @@ class Circuit(Sequential): https://matplotlib.org/stable/gallery/text_labels_and_annotations/tex_demo.html for more details. ''' - _fig = _circuit_plot(self, dpi=dpi, scale=scale, tex = tex) - - if save_path: - plt.savefig(save_path, dpi=dpi,) - - if show: # whether display in window + _fig = _circuit_plot(self, dpi=dpi, scale=scale, tex=tex) + if save_path: + plt.savefig(save_path, dpi=dpi, ) + if show: # whether display in window plt.show() + if output: + return _fig # return the ``matplotlib.pyplot.figure`` instance - if output: - return _fig # return the ``matplotlib.pyplot.figure`` instance - def extend(self, cir): r""" extend for quantum circuit - + Args: cir: a Circuit or a Sequential - + Returns: concatenation of two quantum circuits - """ if isinstance(cir, Circuit): if self.__num_qubits is None: self.__num_qubits = cir.num_qubits else: - self.__num_qubits = self.__num_qubits if cir.num_qubits is None else max(self.__num_qubits, cir.num_qubits) + self.__num_qubits = self.__num_qubits if cir.num_qubits is None else max(self.__num_qubits, + cir.num_qubits) super().extend(cir) elif isinstance(cir, Sequential): super().extend(cir) else: raise TypeError("the input type must be Circuit or Sequential") - + def forward(self, state: Optional[State] = None) -> State: r""" forward the input - + Args: state: initial state - + Returns: output quantum state - """ assert self.__num_qubits is not None, "Information about num_qubits is required before running the circuit" - + if state is None: state = zero_state(self.__num_qubits, self.backend, self.dtype) else: assert self.__num_qubits == state.num_qubits, \ f"num_qubits does not agree: expected {self.__num_qubits}, received {state.num_qubits}" - - return super().forward(state) - - + + if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: + state.oper_history = self.oper_history + return state + + state = state.clone() + state.is_swap_back = False + state = super().forward(state) + + # reset state in the original qubit sequence + state.reset_sequence() + state.is_swap_back = True + return state diff --git a/paddle_quantum/ansatz/container.py b/paddle_quantum/ansatz/container.py index 28f138d..c7e67b6 100644 --- a/paddle_quantum/ansatz/container.py +++ b/paddle_quantum/ansatz/container.py @@ -18,32 +18,33 @@ The source file of the Sequential class. """ import collections -from paddle_quantum import Operator -from typing import Optional, Union, Iterable, Any, List +import warnings +import paddle +import paddle_quantum as pq +from typing import Optional, Union, Iterable, Any, List, Dict -class Sequential(Operator): +class Sequential(pq.Operator): r"""Sequential container. Args: *operators: initial operators ready to be a sequential - + Note: Sublayers will be added to this container in the order of argument in the constructor. The argument passed to the constructor can be iterable Layers or iterable name Layer pairs. - """ - def __init__(self, *operators: Operator): + def __init__(self, *operators: pq.Operator): super().__init__() self.index = 0 - if len(operators) > 0 and isinstance(operators[0], (list, tuple)): + if operators and isinstance(operators[0], (list, tuple)): for name, oper in operators: self.add_sublayer(name, oper) else: for idx, oper in enumerate(operators): self.add_sublayer(str(idx), oper) - def __getitem__(self, name: Union[str, slice]) -> Operator: + def __getitem__(self, name: Union[str, slice]) -> pq.Operator: if isinstance(name, slice): return self.__class__(*(list(self._sub_layers.values())[name])) if isinstance(name, str): @@ -56,8 +57,8 @@ class Sequential(Operator): raise IndexError(f'index {name:s} is out of range') return self._sub_layers[str(name)] - def __setitem__(self, name: Any, layer: Operator) -> None: - assert isinstance(layer, Operator) + def __setitem__(self, name: Any, layer: pq.Operator) -> None: + assert isinstance(layer, pq.Operator) setattr(self, str(name), layer) def __delitem__(self, name: Any) -> None: @@ -68,7 +69,7 @@ class Sequential(Operator): def __iter__(self): return self - def __next__(self) -> Union[Operator, StopIteration]: + def __next__(self) -> Union[pq.Operator, StopIteration]: if self.index < len(self._sub_layers): oper = self._sub_layers[str(self.index)] self.index += 1 @@ -78,30 +79,54 @@ class Sequential(Operator): def __len__(self): return len(self._sub_layers) + + @property + def oper_history(self) -> List[Dict[str, Union[str, List[int], paddle.Tensor]]]: + r"""Return the operator history of this Sequential + """ + oper_history = [] + for op in self.sublayers(): + if isinstance(op, pq.gate.ParamGate): + oper_history.append({ + 'name': op.__class__.__name__, + 'qubits_idx': op.qubits_idx, + 'depth': op.depth, + 'param': op.theta, + 'param_sharing': op.param_sharing + }) + elif hasattr(op, 'qubits_idx'): + oper_history.append({ + 'name': op.__class__.__name__, + 'qubits_idx': op.qubits_idx, + 'depth': op.depth if hasattr(op, 'depth') else 1 + }) + else: + warnings.warn( + f"Cannot recognize the operator: expected an operator with attribute qubits_idx, received {type(op)}.", UserWarning) + oper_history.append(None) + return oper_history - def append(self, operator: Union[Iterable, Operator]) -> None: + # TODO: append only a operator, don't allow to append a list of operators + def append(self, operator: Union[Iterable, pq.Operator]) -> None: r""" append an operator - + Args: operator: operator with a name or just an operator - """ - if isinstance(operator, Operator): + if isinstance(operator, pq.Operator): idx = len(self._sub_layers) self.add_sublayer(str(idx), operator) elif isinstance(operator, Iterable): name, oper = operator self.add_sublayer(name, oper) - - def extend(self, operators: List[Operator]) -> None: + def extend(self, operators: List[pq.Operator]) -> None: r""" append a list of operators - + Args: operator: list of operators - """ - if len(operators) > 0 and isinstance(operators[0], (list, tuple)): + if operators and isinstance(operators[0], (list, tuple)): for name, oper in operators: self.add_sublayer(name, oper) else: @@ -109,16 +134,15 @@ class Sequential(Operator): for idx, oper in enumerate(operators): self.add_sublayer(str(idx + origin_len), oper) - def insert(self, index: int, operator: Operator) -> None: + def insert(self, index: int, operator: pq.Operator) -> None: r""" insert an operator at ``index`` - + Args: index: index to be inserted operator: an operator - """ new_operators = collections.OrderedDict() - assert index <= len(self._sub_layers), 'the index ' + str(index) + ' should be no more than ' + str(len(self._sub_layers)) + assert index <= len(self._sub_layers), f'the index {index} should be no more than {len(self._sub_layers)}' if index == len(self._sub_layers): self.append(operator) for idx, name in enumerate(self._sub_layers): @@ -128,7 +152,7 @@ class Sequential(Operator): if isinstance(operator, (list, tuple)): name, oper = operator new_operators[name] = oper - elif isinstance(operator, Operator): + elif isinstance(operator, pq.Operator): new_operators[str(index)] = operator if name.isdigit(): new_operators[str(int(name) + 1)] = self._sub_layers[name] @@ -140,16 +164,15 @@ class Sequential(Operator): new_operators[name] = self._sub_layers[name] self._sub_layers = new_operators - def pop(self, index: int = None, operator: Optional[Operator] = None): + def pop(self, index: int = None, operator: Optional[pq.Operator] = None): r""" remove the operator at ``index`` or matched with ``operator`` - + Args: index: at which the operator will be popped operator: matched with which the operator will be popped - """ if index is not None: - assert index < len(self._sub_layers), 'the index ' + str(index) + ' should be less than ' + str(len(self._sub_layers)) + assert index < len(self._sub_layers), f'the index {index} should be less than {len(self._sub_layers)}' if isinstance(index, int): index = str(index) operator = self._sub_layers[index] @@ -167,17 +190,16 @@ class Sequential(Operator): else: new_operators[name] = self._sub_layers[name] self._sub_layers = new_operators - + def forward(self, state: Any) -> Any: r""" forward the input - + Args: state: initial state - + Returns: output state - - """ + """ for layer in self._sub_layers.values(): state = layer(state) return state diff --git a/paddle_quantum/ansatz/layer.py b/paddle_quantum/ansatz/layer.py new file mode 100644 index 0000000..3260e94 --- /dev/null +++ b/paddle_quantum/ansatz/layer.py @@ -0,0 +1,332 @@ +# !/usr/bin/env python3 +# Copyright (c) 2022 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +r""" +The source file of the class for quantum circuit templates. +""" + +import matplotlib +import numpy as np +from typing import Iterable, List, Union, Tuple, Dict + +from .container import Sequential +from ..gate import H, RX, RY, RZ, U3, CNOT +from ..intrinsic import _cnot_idx_fetch, _inverse_gather_for_dm + + +__all__ = ['Layer', 'SuperpositionLayer', 'LinearEntangledLayer', 'RealEntangledLayer', 'ComplexEntangledLayer', + 'RealBlockLayer', 'QAOALayer', 'QAOALayerWeighted'] + + +def _qubits_idx_filter(qubits_idx: Union[List[int], str], num_qubits: int) -> List[int]: + r"""Check the validity of ``qubits_idx`` and ``num_qubits``. + + Args: + qubits_idx: Indices of qubits. + num_qubits: Total number of qubits. + + Raises: + RuntimeError: You must specify ``qubits_idx`` or ``num_qubits`` to instantiate the class. + ValueError: The ``qubits_idx`` must be ``Iterable`` or ``None``. + + Returns: + Checked indices of qubits. + """ + if qubits_idx is None or qubits_idx == 'full': + if num_qubits is None: + raise RuntimeError( + "You must specify qubits_idx or num_qubits to instantiate the class.") + return list(range(num_qubits)) + elif isinstance(qubits_idx, Iterable): + assert len(np.array(qubits_idx).shape) == 1, \ + "The input qubit index must be a list of int for layers." + qubits_idx = list(qubits_idx) + assert len(qubits_idx) > 1, \ + f"Requires more than 1 qubit for a layer to act on: received length {len(qubits_idx)}" + assert len(qubits_idx) == len(set(qubits_idx)), \ + f"Layers do not allow repeated indices: received {qubits_idx}" + return qubits_idx + + raise ValueError(f"The qubits_idx must be a list of int or None: received {type(qubits_idx)}") + + +class Layer(Sequential): + r"""Base class for Layers. + + Args: + qubits_idx: Indices of the qubits on which this layer is applied. + num_qubits: Total number of qubits. + depth: Number of layers. + + Note: + A Circuit instance needs to extend this Layer instance to be used in a circuit. + + """ + def __init__(self, qubits_idx: Union[Iterable[int], str], num_qubits: int, depth: int = 1): + self.num_qubits = num_qubits + self.qubits_idx = _qubits_idx_filter(qubits_idx, num_qubits) + self.depth = depth + super().__init__() + + @property + def gate_history(self): + r""" list of gates information of this layer + + Returns: + history of quantum gates + """ + gate_history = [] + for op in self.sublayers(): + if op.gate_info['gatename'] is None: + raise NotImplementedError( + f"{type(op)} has no gate name and hence cannot be recorded into history.") + op.gate_history_generation() + gate_history.extend(op.gate_history) + return gate_history + + +class SuperpositionLayer(Layer): + r"""Layers of Hadamard gates. + + Args: + qubits_idx: Indices of the qubits on which the layer is applied. + Defaults to ``None`` i.e. applied on all qubits. + num_qubits: Total number of qubits. Defaults to ``None``. + depth: Number of layers. Defaults to ``1``. + """ + def __init__( + self, qubits_idx: Union[Iterable[int], str] = None, num_qubits: int = None, depth: int = 1 + ): + super().__init__(qubits_idx, num_qubits, depth) + self.append(H(self.qubits_idx, num_qubits, depth)) + + +class WeakSuperpositionLayer(Layer): + r"""Layers of Ry gates with a rotation angle :math:`\pi/4`. + + Args: + qubits_idx: Indices of the qubits on which the layer is applied. + Defaults to ``None`` i.e. applied on all qubits. + num_qubits: Total number of qubits. Defaults to ``None``. + depth: Number of layers. Defaults to ``1``. + """ + def __init__( + self, qubits_idx: Union[Iterable[int], str] = None, num_qubits: int = None, depth: int = 1 + ): + super().__init__(qubits_idx, num_qubits, depth) + self.append(RY(self.qubits_idx, num_qubits, depth, np.pi / 4, param_sharing=True)) + + +class LinearEntangledLayer(Layer): + r"""Linear entangled layers consisting of Ry gates, Rz gates, and CNOT gates. + + Args: + qubits_idx: Indices of the qubits on which the layer is applied. + Defaults to ``None`` i.e. applied on all qubits. + num_qubits: Total number of qubits. Defaults to ``None``. + depth: Number of layers. Defaults to ``1``. + """ + def __init__( + self, qubits_idx: Union[Iterable[int], str] = None, num_qubits: int = None, depth: int = 1 + ): + super().__init__(qubits_idx, num_qubits, depth) + assert len(self.qubits_idx)>1, 'acted qubits need more than 1' + num_acted_qubits = len(self.qubits_idx) + acted_list = [(self.qubits_idx[idx], self.qubits_idx[idx+1]) for idx in range(num_acted_qubits-1)] + cnot_idx = _cnot_idx_fetch(num_qubits=self.num_qubits, qubits_idx=acted_list) + + for _ in range(self.depth): + self.append(RY(self.qubits_idx)) + self.append(CNOT(qubits_idx=acted_list, cnot_idx=cnot_idx)) + self.append(RZ(self.qubits_idx)) + self.append(CNOT(qubits_idx=acted_list, cnot_idx=cnot_idx)) + + +class RealEntangledLayer(Layer): + r"""Strongly entangled layers consisting of Ry gates and CNOT gates. + + Note: + The mathematical representation of this layer of quantum gates is a real unitary matrix. + This ansatz is from the following paper: https://arxiv.org/pdf/1905.10876.pdf. + + Args: + qubits_idx: Indices of the qubits on which the layer is applied. + Defaults to ``None`` i.e. applied on all qubits. + num_qubits: Total number of qubits. Defaults to ``None``. + depth: Number of layers. Defaults to ``1``. + """ + def __init__( + self, qubits_idx: Union[Iterable[int], str] = None, num_qubits: int = None, depth: int = 1 + ): + super().__init__(qubits_idx, num_qubits, depth) + assert len(self.qubits_idx)>1, 'acted qubits need more than 1' + acted_list = [(self.qubits_idx[idx], self.qubits_idx[(idx + 1) % len(self.qubits_idx)]) + for idx in range(len(self.qubits_idx))] + cnot_idx = _cnot_idx_fetch(num_qubits=self.num_qubits, qubits_idx=acted_list) + + for _ in range(self.depth): + self.append(RY(self.qubits_idx)) + self.append(CNOT(qubits_idx=acted_list, cnot_idx=cnot_idx)) + + +class ComplexEntangledLayer(Layer): + r"""Strongly entangled layers consisting of single-qubit rotation gates and CNOT gates. + + Note: + The mathematical representation of this layer of quantum gates is a complex unitary matrix. + This ansatz is from the following paper: https://arxiv.org/abs/1804.00633. + + Args: + qubits_idx: Indices of the qubits on which the layer is applied. + Defaults to ``None`` i.e. applied on all qubits. + num_qubits: Total number of qubits. Defaults to ``None``. + depth: Number of layers. Defaults to ``1``. + """ + def __init__( + self, qubits_idx: Union[Iterable[int], str] = None, num_qubits: int = None, depth: int = 1 + ): + super().__init__(qubits_idx, num_qubits, depth) + assert len(self.qubits_idx)>1, 'acted qubits need more than 1' + acted_list = [(self.qubits_idx[idx], self.qubits_idx[(idx + 1) % len(self.qubits_idx)]) + for idx in range(len(self.qubits_idx))] + cnot_idx = _cnot_idx_fetch(num_qubits=self.num_qubits, qubits_idx=acted_list) + + for _ in range(self.depth): + self.append(U3(self.qubits_idx)) + self.append(CNOT(qubits_idx=acted_list, cnot_idx=cnot_idx)) + + +class RealBlockLayer(Layer): + r"""Weakly entangled layers consisting of Ry gates and CNOT gates. + + Note: + The mathematical representation of this layer of quantum gates is a real unitary matrix. + + Args: + qubits_idx: Indices of the qubits on which the layer is applied. + Defaults to ``None`` i.e. applied on all qubits. + num_qubits: Total number of qubits. Defaults to ``None``. + depth: Number of layers. Defaults to ``1``. + """ + def __init__( + self, qubits_idx: Union[Iterable[int], str] = None, num_qubits: int = None, depth: int = 1 + ): + super().__init__(qubits_idx, num_qubits, depth) + assert len(self.qubits_idx)>1, 'acted qubits need more than 1' + num_acted_qubits = len(self.qubits_idx) + if num_acted_qubits % 2 == 0: + for _ in range(self.depth): + self.__add_real_layer([0, num_acted_qubits - 1]) + self.__add_real_layer([1, num_acted_qubits - 2]) if num_acted_qubits > 2 else None + else: + for _ in range(self.depth): + self.__add_real_layer([0, num_acted_qubits - 2]) + self.__add_real_layer([1, num_acted_qubits - 1]) + + def __add_real_layer(self, position: List) -> None: + cnot_acted_list = [[self.qubits_idx[i], self.qubits_idx[i+1]] for i in range(position[0], position[1], 2)] + ry_acted_list = [] + for i in range(position[0], position[1], 2): + ry_acted_list.extend((self.qubits_idx[i], self.qubits_idx[i+1])) + self.append(RY(ry_acted_list)) + self.append(CNOT(cnot_acted_list)) + self.append(RY(ry_acted_list)) + + +class ComplexBlockLayer(Layer): + r"""Weakly entangled layers consisting of single-qubit rotation gates and CNOT gates. + + Note: + The mathematical representation of this layer of quantum gates is a complex unitary matrix. + + Args: + qubits_idx: Indices of the qubits on which the layer is applied. + Defaults to ``None`` i.e. applied on all qubits. + num_qubits: Total number of qubits. Defaults to ``None``. + depth: Number of layers. Defaults to ``1``. + """ + def __init__(self, qubits_idx: Union[Iterable[int], str] = None, num_qubits: int = None, depth: int = 1): + super().__init__(qubits_idx, num_qubits, depth) + assert len(self.qubits_idx)>1, 'acted qubits need more than 1' + num_acted_qubits = len(self.qubits_idx) + if num_acted_qubits % 2 == 0: + for _ in range(self.depth): + self.__add_complex_layer([0, num_acted_qubits - 1]) + if num_acted_qubits > 2: + self.__add_complex_layer([1, num_acted_qubits - 2]) + else: + for _ in range(self.depth): + self.__add_complex_layer([0, num_acted_qubits - 2]) + self.__add_complex_layer([1, num_acted_qubits - 1]) + + def __add_complex_layer(self, position: List[int]) -> None: + cnot_acted_list = [[self.qubits_idx[i], self.qubits_idx[i+1]] for i in range(position[0], position[1], 2)] + u3_acted_list = [] + for i in range(position[0], position[1], 2): + u3_acted_list.extend((self.qubits_idx[i], self.qubits_idx[i+1])) + self.append(U3(u3_acted_list)) + self.append(CNOT(cnot_acted_list)) + self.append(U3(u3_acted_list)) + + +class QAOALayer(Layer): + r""" QAOA driving layers + + Note: + this layer only works for MAXCUT problem + + Args: + edges: edges of the graph + nodes: nodes of the graph + depth: depth of layer + + """ + # TODO: only for maxcut now + def __init__( + self, edges: Iterable, nodes: Iterable, depth: int = 1 + ): + Sequential.__init__(self) + self.edges, self.nodes, self.depth = edges, nodes, depth + + for _ in range(self.depth): + for node0, node1 in self.edges: + self.append(CNOT([node0, node1])) + self.append(RZ(node1)) + self.append(CNOT([node0, node1])) + self.append(RX(self.nodes)) + + +class QAOALayerWeighted(Layer): + r""" QAOA driving layers with weights + + Args: + edges: edges of the graph with weights + nodes: nodes of the graph with weights + depth: depth of layer + + """ + def __init__( + self, edges: Dict[Tuple[int, int], float], nodes: Dict[int, float], depth: int = 1 + ) -> None: + Sequential.__init__(self) + self.edges, self.nodes, self.depth = edges.keys(), nodes.keys(), depth + + for _ in range(self.depth): + for node0, node1 in self.edges: + self.append(CNOT([node0, node1])) + self.append(RZ(node1)) + self.append(CNOT([node0, node1])) + self.append(RZ(self.nodes)) + self.append(RX(self.nodes)) diff --git a/paddle_quantum/ansatz/vans.py b/paddle_quantum/ansatz/vans.py index afb57a0..e2280d6 100644 --- a/paddle_quantum/ansatz/vans.py +++ b/paddle_quantum/ansatz/vans.py @@ -51,7 +51,7 @@ def cir_decompose(cir: Circuit, trainable: Optional[bool] = False) -> Circuit: continue if trainable: - param = param.reshape([1] + param.shape) + param = param.reshape([1] + [1] + param.shape) param = paddle.create_parameter( shape=param.shape, dtype=param.dtype, default_initializer=paddle.nn.initializer.Assign(param)) diff --git a/paddle_quantum/backend/density_matrix.py b/paddle_quantum/backend/density_matrix.py index 33c3208..44bbd8e 100644 --- a/paddle_quantum/backend/density_matrix.py +++ b/paddle_quantum/backend/density_matrix.py @@ -18,7 +18,8 @@ The source file of the density_matrix backend. """ import paddle -from typing import List, Iterable, Union +import paddle_quantum as pq +from typing import List, Iterable, Union, Tuple def unitary_transformation( @@ -70,10 +71,12 @@ def unitary_transformation( shape.append(2 ** (2 * num_qubits - last_idx - 1)) state = paddle.reshape(state, shape) state = paddle.transpose( - state, list(range(0, num_higher_dims)) + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] + state, list(range(0, num_higher_dims)) + + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] ) state = paddle.reshape( - state, higher_dims.copy() + [2 ** num_acted_qubits, 2 ** (2 * num_qubits - num_acted_qubits)] + state, higher_dims.copy() + + [2 ** num_acted_qubits, 2 ** (2 * num_qubits - num_acted_qubits)] ) state = paddle.matmul(gate, state) swap_ops.reverse() @@ -87,7 +90,8 @@ def unitary_transformation( shape.append(2 ** (2 * num_qubits - last_idx - 1)) state = paddle.reshape(state, shape) state = paddle.transpose( - state, list(range(0, num_higher_dims)) + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] + state, list(range(0, num_higher_dims)) + + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] ) swap_ops.reverse() for idx, swap_op in enumerate(swap_ops): @@ -102,10 +106,13 @@ def unitary_transformation( shape.append(2 ** (2 * num_qubits - last_idx - 1)) state = paddle.reshape(state, shape) state = paddle.transpose( - state, list(range(0, num_higher_dims)) + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] + state, list(range(0, num_higher_dims)) + + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] ) state = paddle.reshape( - state, higher_dims.copy() + [2 ** num_qubits, 2 ** num_acted_qubits, 2 ** (num_qubits - num_acted_qubits)] + state, higher_dims.copy() + + [2 ** num_qubits, 2 ** num_acted_qubits, + 2 ** (num_qubits - num_acted_qubits)] ) # gate_dagger = paddle.conj(paddle.t(gate)) # state = paddle.einsum('abc,bx->axc', state, gate_dagger) @@ -123,8 +130,51 @@ def unitary_transformation( shape.append(2 ** (2 * num_qubits - last_idx - 1)) state = paddle.reshape(state, shape) state = paddle.transpose( - state, list(range(0, num_higher_dims)) + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] + state, list(range(0, num_higher_dims)) + + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] ) - state = paddle.reshape(state, higher_dims.copy() + [2 ** num_qubits, 2 ** num_qubits]) + state = paddle.reshape(state, higher_dims.copy() + + [2 ** num_qubits, 2 ** num_qubits]) return state + + +def unitary_transformation_without_swapback( + state: paddle.Tensor, gate: List[paddle.Tensor], qubit_idx: List[int], num_qubits: int, qubit_sequence: List[int] +) -> Tuple[paddle.Tensor, List[int]]: + r"""The function of unitary transformation in the mode of density matrix. + + Args: + state: The input quantum state. + gate: The gate that represents the unitary transformation. + qubit_idx: The indices of the qubits on which the gate is acted. + num_qubits: The number of the qubits in the input quantum state. + qubit_sequence: The sequence of qubit indices at this moment. + + Returns: + The transformed quantum state. + """ + # The order of the tensor in paddle is less than 10. + higher_dims = state.shape[:-2] + gate = pq.intrinsic._gate_tensor(gate) + + # generate swap_list + num_acted_qubits = len(qubit_idx) + seq_for_acted = qubit_idx + \ + [x for x in qubit_sequence if x not in qubit_idx] + perm_map = pq.intrinsic._perm_of_list(qubit_sequence, seq_for_acted) + + # mat multiplication + state = pq.intrinsic._base_transpose_for_dm(state, perm=perm_map) + state = paddle.reshape(state, higher_dims.copy( + ) + [2 ** num_acted_qubits, 2 ** (2 * num_qubits - num_acted_qubits)]) + state = paddle.matmul(gate, state) + + state = paddle.reshape(state, higher_dims.copy( + ) + [2 ** num_qubits, 2 ** num_acted_qubits, 2 ** (num_qubits - num_acted_qubits)]) + gate_dagger = paddle.conj(gate) + state = paddle.matmul(gate_dagger, state) + + state = paddle.reshape(state, higher_dims.copy() + + [2 ** num_qubits, 2 ** num_qubits]) + return state, seq_for_acted diff --git a/paddle_quantum/backend/quleaf.py b/paddle_quantum/backend/quleaf.py index 8430d4c..17d9609 100644 --- a/paddle_quantum/backend/quleaf.py +++ b/paddle_quantum/backend/quleaf.py @@ -23,8 +23,9 @@ import numpy as np import paddle import QCompute import re +import paddle_quantum as pq from QCompute import MeasureZ, RX, RY -import paddle_quantum +from typing import Optional, List BACKEND = 'local_baidu_sim2' TOKEN = None @@ -75,11 +76,30 @@ def get_quleaf_token() -> str: return TOKEN -def _act_gates_to_state(gate_history: list, quleaf_state: QCompute.QEnv, param_all: list) -> QCompute.QEnv: +single_qubit_gates = { + 'S': QCompute.S, 'T': QCompute.T, 'Sdg': QCompute.SDG, 'Tdg': QCompute.TDG, + 'H': QCompute.H, 'X': QCompute.X, 'Y': QCompute.Y, 'Z': QCompute.Z, + 'U3': QCompute.U, 'RX': QCompute.RX, 'RY': QCompute.RY, 'RZ': QCompute.RZ +} +multi_qubits_gates = { + 'CNOT': QCompute.CX, 'CX': QCompute.CX, 'CY': QCompute.CY, 'CZ': QCompute.CZ, 'SWAP': QCompute.SWAP, + 'CU': QCompute.CU, 'CRX': QCompute.CRX, 'CRY': QCompute.CRY, 'CRZ': QCompute.CRZ, + 'CSWAP': QCompute.CSWAP, 'CCX': QCompute.CCX +} +fixed_gates = {'S', 'T', 'Sdg', 'Tdg', 'H', 'X', 'Y', 'Z', 'CNOT', 'CX', 'CY', 'CZ', 'SWAP', 'CSWAP', 'CCX'} +parameterized_gates = {'U3', 'RX', 'RY', 'RZ', 'CU', 'CRX', 'CRY', 'CRZ'} + + +# TODO: need to check whether the logic is right when the param_sharing is True. +def _act_gates_to_state( + oper_history: List[dict], quleaf_state: QCompute.QEnv, + _gate_idx: Optional[int] = None, _depth_idx: Optional[int] = None, _qubits_idx: Optional[int] = None, + _param_idx: Optional[int] = None, _param_shift_val: Optional[int] = None +) -> QCompute.QEnv: r"""The function to act the quantum gate to the quantum state in the QuLeaf backend. Args: - gate_history: The history of quantum gate, which records the type, parameters and qubits index of the gates. + oper_history: The history of quantum gate, which records the type, parameters and qubits index of the gates. quleaf_state: The quantum state in QuLeaf. param_all: All the parameters in the gates. @@ -89,69 +109,62 @@ def _act_gates_to_state(gate_history: list, quleaf_state: QCompute.QEnv, param_a Returns: The acted quantum state. """ - single_qubit_gates = { - 's': QCompute.S, 't': QCompute.T, 'sdg': QCompute.SDG, 'tdg': QCompute.TDG, - 'h': QCompute.H, 'x': QCompute.X, 'y': QCompute.Y, 'z': QCompute.Z, - 'u3': QCompute.U, 'rx': QCompute.RX, 'ry': QCompute.RY, 'rz': QCompute.RZ - } - multi_qubits_gates = { - 'cnot': QCompute.CX, 'cx': QCompute.CX, 'cy': QCompute.CY, 'cz': QCompute.CZ, 'swap': QCompute.SWAP, - 'cu': QCompute.CU, 'crx': QCompute.CRX, 'cry': QCompute.CRY, 'crz': QCompute.CRZ, - 'cswap': QCompute.CSWAP, 'ccx': QCompute.CCX - } - for gate in gate_history: - gate_name = gate['gate_name'] + for gate_idx, gate_info in enumerate(oper_history): + gate_name = gate_info['name'] if gate_name in single_qubit_gates: gate_func = single_qubit_gates[gate_name] - fixed_gate = ['s', 't', 'sdg', 'tdg', 'h', 'x', 'y', 'z'] - if gate_name in fixed_gate: - for _ in range(0, gate['depth']): - for qubit_idx in gate['qubits_idx']: + if gate_name in fixed_gates: + for _ in range(gate_info['depth']): + for qubit_idx in gate_info['qubits_idx']: gate_func(quleaf_state.Q[qubit_idx]) - elif gate_name == 'u': - for depth_idx in range(0, gate['depth']): - for idx, qubit_idx in enumerate(gate['qubits_idx']): - if gate['param_sharing']: - param_idx = gate['param'][depth_idx] + elif gate_name == 'U3': + for depth_idx in range(gate_info['depth']): + for idx, qubit_idx in enumerate(gate_info['qubits_idx']): + if gate_info['param_sharing']: + param = gate_info['param'][depth_idx].tolist() else: - param_idx = gate['param'][depth_idx][idx] - gate_param = [param_all[idx] for idx in param_idx] - gate_func(*gate_param)(quleaf_state.Q[qubit_idx]) + param = gate_info['param'][depth_idx][idx].tolist() + if gate_idx == _gate_idx and depth_idx == _depth_idx and idx == _qubits_idx: + param[_param_idx] += _param_shift_val + gate_func(*param)(quleaf_state.Q[qubit_idx]) else: - for depth_idx in range(0, gate['depth']): - for idx, qubit_idx in enumerate(gate['qubits_idx']): - if gate['param_sharing']: - param_idx = gate['param'][depth_idx] + # Single qubit parameterized quantum gate + for depth_idx in range(gate_info['depth']): + for idx, qubit_idx in enumerate(gate_info['qubits_idx']): + if gate_info['param_sharing']: + param = gate_info['param'][depth_idx][0].item() else: - param_idx = gate['param'][depth_idx][idx] - gate_func(param_all[param_idx])(quleaf_state.Q[qubit_idx]) + param = gate_info['param'][depth_idx][idx][0].item() + if gate_idx == _gate_idx and depth_idx == _depth_idx and idx == _qubits_idx: + param += _param_shift_val + gate_func(param)(quleaf_state.Q[qubit_idx]) elif gate_name in multi_qubits_gates: gate_func = multi_qubits_gates[gate_name] - fixed_gate = ['cnot', 'cx', 'cy', 'cz', 'swap', 'cswap', 'ccx'] - if gate_name in fixed_gate: - for _ in range(0, gate['depth']): - for qubits_idx in gate['qubits_idx']: - qubit_list = [quleaf_state.Q[qubit_idx] for qubit_idx in qubits_idx] - gate_func(*qubit_list) - elif gate_name == 'cu': - for depth_idx in range(0, gate['depth']): - for idx, qubits_idx in enumerate(gate['qubits_idx']): - if gate['param_sharing']: - param_idx = gate['param'][depth_idx] + if gate_name in fixed_gates: + for _ in range(gate_info['depth']): + for qubits_idx in gate_info['qubits_idx']: + gate_func(*[quleaf_state.Q[qubit_idx] for qubit_idx in qubits_idx]) + elif gate_name == 'CU': + for depth_idx in range(gate_info['depth']): + for idx, qubits_idx in enumerate(gate_info['qubits_idx']): + if gate_info['param_sharing']: + param = gate_info['param'][depth_idx].tolist() else: - param_idx = gate['param'][depth_idx][idx] - gate_param = [param_all[idx] for idx in param_idx] - qubit_list = [quleaf_state.Q[qubit_idx] for qubit_idx in qubits_idx] - gate_func(*gate_param)(*qubit_list) + param = gate_info['param'][depth_idx][idx].tolist() + if gate_idx == _gate_idx and depth_idx == _depth_idx and idx == _qubits_idx: + param[_param_idx] += _param_shift_val + gate_func(*param)(*[quleaf_state.Q[qubit_idx] for qubit_idx in qubits_idx]) else: - for depth_idx in range(0, gate['depth']): - for idx, qubits_idx in enumerate(gate['qubits_idx']): - if gate['param_sharing']: - param_idx = gate['param'][0] + # CRx, CRy, CRz + for depth_idx in range(gate_info['depth']): + for idx, qubits_idx in enumerate(gate_info['qubits_idx']): + if gate_info['param_sharing']: + param = gate_info['param'][depth_idx][0].item() else: - param_idx = gate['param'][depth_idx][idx] - qubit_list = [quleaf_state.Q[qubit_idx] for qubit_idx in qubits_idx] - gate_func(param_all[param_idx])(*qubit_list) + param = gate_info['param'][depth_idx][idx][0].item() + if gate_idx == _gate_idx and depth_idx == _depth_idx and idx == _qubits_idx: + param += _param_shift_val + gate_func(param)(*[quleaf_state.Q[qubit_idx] for qubit_idx in qubits_idx]) else: raise NotImplementedError return quleaf_state @@ -183,51 +196,30 @@ def _expec_val_on_quleaf(state: 'QCompute.QEnv', coeff: 'float', pauli_str: 'str qubit_idx = int(pauli_term[1:]) observed_qubits.append(qubit_idx) if pauli_matrix == 'x': - RY(-np.pi / 2)(_state.Q[qubit_idx]) + RY(-math.pi / 2)(_state.Q[qubit_idx]) elif pauli_matrix == 'y': - RX(np.pi / 2)(_state.Q[qubit_idx]) - elif pauli_matrix == 'z': - pass - else: + RX(math.pi / 2)(_state.Q[qubit_idx]) + elif pauli_matrix != 'z': raise ValueError("Cannot recognize the pauli words of the hamiltonian.") MeasureZ(*_state.Q.toListPair()) counts = _state.commit(shots, fetchMeasure=True)['counts'] filtered_counts = [(counts[key], [key[-idx - 1] for idx in observed_qubits]) for key in counts] - val = coeff * sum([((-1) ** key.count('1')) * val / shots for val, key in filtered_counts]) - return val - - -def _get_param_for_gate_list(gate_history: list) -> list: - r"""Get the all parameters from the gate list. - - Args: - gate_history: The gate history, it is automatically generated. - - Returns: - The list of the parameters. - """ - param_for_gate_list = [] - num_param_in_gate = { - 'rx': 1, 'ry': 1, 'rz': 1, 'u3': 3, - 'crx': 1, 'cry': 1, 'crz': 1, 'cu': 1, - } - for gate in gate_history: - gate_name = gate['gate_name'] - if gate_name in num_param_in_gate: - num_param = np.array(gate['param']).size - for _ in range(0, num_param): - param_for_gate_list.append(gate_name) - return param_for_gate_list + return coeff * sum( + ( + ((-1) ** key.count('1')) * val / shots + for val, key in filtered_counts + ) + ) class ExpecValOp(paddle.autograd.PyLayer): @staticmethod def forward( ctx: paddle.autograd.PyLayerContext, - param: paddle.Tensor, - state: 'paddle_quantum.State', - hamiltonian: 'paddle_quantum.Hamiltonian', - shots: int, + state: 'pq.State', + hamiltonian: 'pq.Hamiltonian', + shots: paddle.Tensor, + *parameters ) -> paddle.Tensor: r"""The forward function to compute the expectation value of the observable in the QuLeaf Backend. @@ -237,28 +229,28 @@ class ExpecValOp(paddle.autograd.PyLayer): state: The quantum state to be measured. hamiltonian: The observable. shots: The number of measurement shots. + *parameters: The parameters in the parameterized quantum circuit. Returns: The expectation value of the observable for the input state. """ - ctx.save_for_backward(param) + dtype = shots.dtype + shots = int(shots.item()) + ctx.save_for_backward(*parameters) quleaf_state = copy.deepcopy(state.data) + oper_history = state.oper_history ctx.quleaf_state = quleaf_state - gate_history = state.gate_history - ctx.gate_history = gate_history + ctx.oper_history = oper_history ctx.hamiltonian = hamiltonian ctx.shots = shots - state.gate_history = [] - state.param_list = [] - state.num_param = 0 - param_all = param.tolist() + ctx.dtype = dtype _state = copy.deepcopy(quleaf_state) - acted_state = _act_gates_to_state(gate_history, _state, param_all) + acted_state = _act_gates_to_state(oper_history, _state, parameters) expec_val = 0 for coeff, pauli_str in hamiltonian.pauli_str: _state = copy.deepcopy(acted_state) expec_val += _expec_val_on_quleaf(_state, coeff, pauli_str, shots) - expec_val = paddle.to_tensor([expec_val], dtype=param.dtype) + expec_val = paddle.to_tensor([expec_val], dtype=dtype) return expec_val @staticmethod @@ -272,20 +264,19 @@ class ExpecValOp(paddle.autograd.PyLayer): Returns: The gradient of the parameters for the quantum gates. """ - param, = ctx.saved_tensor() - param_all = param.tolist() + parameters = ctx.saved_tensor() + dtype = ctx.dtype quleaf_state = ctx.quleaf_state - gate_history = ctx.gate_history + oper_history = ctx.oper_history hamiltonian = ctx.hamiltonian shots = ctx.shots - param_for_gate_list = _get_param_for_gate_list(gate_history) - assert len(param_for_gate_list) == len(param_all) - def expec_val_shift(param_idx: int, param_shift: float) -> float: - param_temp = copy.deepcopy(param_all) - param_temp[param_idx] += param_shift + def expec_val_shift( + _gate_idx: int, _depth_idx: int, _qubits_idx: int, _param_idx: int, param_shift_val: float + ) -> float: _state = copy.deepcopy(quleaf_state) - acted_state = _act_gates_to_state(gate_history, _state, param_temp) + acted_state = _act_gates_to_state( + oper_history, _state, _gate_idx, _depth_idx, _qubits_idx, _param_idx, param_shift_val) expec_val = 0 for coeff, pauli_str in hamiltonian.pauli_str: _state = copy.deepcopy(acted_state) @@ -293,9 +284,10 @@ class ExpecValOp(paddle.autograd.PyLayer): # expec_val = paddle.to_tensor([expec_val], dtype=expec_val_grad.dtype) return expec_val - def general_param_shift(param_idx: int) -> float: - gate_name = param_for_gate_list[param_idx] - if gate_name in ['crx', 'cry', 'crz', 'cu']: + def general_param_shift( + gate_name: str, _gate_idx: int, _depth_idx: int, _qubits_idx: int, _param_idx: int + ) -> float: + if gate_name in {'CRX', 'CRY', 'CRZ', 'CU'}: coeff_list = [ 1 / (16 * math.pow(math.sin(math.pi / 8), 2)), -1 / (16 * math.pow(math.sin(3 * math.pi / 8), 2)), @@ -304,7 +296,9 @@ class ExpecValOp(paddle.autograd.PyLayer): ] shift_list = [math.pi / 2, 3 * math.pi / 2, 5 * math.pi / 2, 7 * math.pi / 2] grad_terms = map( - lambda coeff, shift: coeff * expec_val_shift(param_idx, shift), + lambda coeff, shift_val: coeff * expec_val_shift( + _gate_idx, _depth_idx, _qubits_idx, _param_idx, shift_val + ), coeff_list, shift_list ) grad = sum(grad_terms) @@ -312,15 +306,28 @@ class ExpecValOp(paddle.autograd.PyLayer): coeff1 = 0.5 coeff2 = -0.5 grad = ( - coeff1 * expec_val_shift(param_idx, math.pi / 2) + - coeff2 * expec_val_shift(param_idx, 3 * math.pi / 2) + coeff1 * expec_val_shift(_gate_idx, _depth_idx, _qubits_idx, _param_idx, math.pi / 2) + + coeff2 * expec_val_shift(_gate_idx, _depth_idx, _qubits_idx, _param_idx, 3 * math.pi / 2) ) return grad - param_grad = np.zeros(param.size) - for idx in range(0, param_grad.size): - param_grad[idx] = general_param_shift(idx) - param_grad = np.reshape(param_grad, param.shape) - param_grad = paddle.to_tensor(param_grad, dtype=param.dtype) - param_grad = expec_val_grad * param_grad - return param_grad + params_idx = 0 + params_grad = [None] + for gate_idx, gate_info in enumerate(oper_history): + gate_name = gate_info['name'] + if gate_name not in parameterized_gates: + continue + if parameters[params_idx].stop_gradient is True: + params_grad.append(None) + params_idx += 1 + continue + shape = parameters[params_idx].shape + param_grad = np.zeros(shape=shape) + for _depth_idx in range(shape[0]): + for _qubits_idx in range(shape[1]): + for _param_idx in range(shape[2]): + grad = general_param_shift(gate_name, gate_idx, _depth_idx, _qubits_idx, _param_idx) + param_grad[_depth_idx, _qubits_idx, _param_idx] += grad + params_grad.append(expec_val_grad * paddle.to_tensor(param_grad, dtype=dtype)) + params_idx += 1 + return params_grad diff --git a/paddle_quantum/backend/state_vector.py b/paddle_quantum/backend/state_vector.py index 3da9636..b60e1e6 100644 --- a/paddle_quantum/backend/state_vector.py +++ b/paddle_quantum/backend/state_vector.py @@ -18,7 +18,9 @@ The source file of the state_vector backend. """ import paddle -from typing import List, Iterable, Union +import numpy as np +import paddle_quantum as pq +from typing import List, Iterable, Union, Tuple def unitary_transformation( @@ -38,10 +40,10 @@ def unitary_transformation( # The order of the tensor in paddle is less than 10. higher_dims = state.shape[:-1] num_higher_dims = len(higher_dims) - + if not isinstance(qubit_idx, Iterable): qubit_idx = [qubit_idx] - + # generate swap_list num_acted_qubits = len(qubit_idx) origin_seq = list(range(0, num_qubits)) @@ -69,9 +71,11 @@ def unitary_transformation( shape.append(2 ** (num_qubits - last_idx - 1)) state = paddle.reshape(state, shape) state = paddle.transpose( - state, list(range(0, num_higher_dims)) + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] + state, list(range(0, num_higher_dims)) + + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] ) - state = paddle.reshape(state, higher_dims.copy() + [2 ** num_acted_qubits, 2 ** (num_qubits - num_acted_qubits)]) + state = paddle.reshape(state, higher_dims.copy( + ) + [2 ** num_acted_qubits, 2 ** (num_qubits - num_acted_qubits)]) state = paddle.matmul(gate, state) swap_ops.reverse() for swap_op in swap_ops: @@ -84,8 +88,43 @@ def unitary_transformation( shape.append(2 ** (num_qubits - last_idx - 1)) state = paddle.reshape(state, shape) state = paddle.transpose( - state, list(range(0, num_higher_dims)) + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] + state, list(range(0, num_higher_dims)) + + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] ) state = paddle.reshape(state, higher_dims.copy() + [2 ** num_qubits]) return state + + +def unitary_transformation_without_swapback( + state: paddle.Tensor, gate: List[paddle.Tensor], qubit_idx: List[int], num_qubits: int, qubit_sequence: List[int] +) -> Tuple[paddle.Tensor, List[int]]: + r"""The function of unitary transformation in the mode of state vector. + + Args: + state: The input quantum state. + gate: The list of gates that represents the unitary transformation. + qubit_idx: The list of indices of the qubits on which the gate is acted. + num_qubits: The number of the qubits in the input quantum state. + qubit_sequence: The sequence of qubit indices at this moment. + + Returns: + The transformed quantum state. + """ + # The order of the tensor in paddle is less than 10. + higher_dims = state.shape[:-1] + gate = pq.intrinsic._gate_tensor(gate) + + # generate base index order + num_acted_qubits = len(qubit_idx) + seq_for_acted = qubit_idx + \ + [x for x in qubit_sequence if x not in qubit_idx] + perm_map = pq.intrinsic._perm_of_list(qubit_sequence, seq_for_acted) + state = pq.intrinsic._base_transpose(state, perm_map) + + # matrix multiplication + state = paddle.reshape(state, higher_dims.copy( + ) + [2 ** num_acted_qubits, 2 ** (num_qubits - num_acted_qubits)]) + state = paddle.matmul(gate, state) + state = paddle.reshape(state, higher_dims.copy() + [2 ** num_qubits]) + return state, seq_for_acted diff --git a/paddle_quantum/backend/unitary_matrix.py b/paddle_quantum/backend/unitary_matrix.py index a614908..7ff2697 100644 --- a/paddle_quantum/backend/unitary_matrix.py +++ b/paddle_quantum/backend/unitary_matrix.py @@ -20,7 +20,6 @@ The source file of the unitary_matrix backend. import paddle from typing import List, Iterable, Union - def unitary_transformation( state: paddle.Tensor, gate: paddle.Tensor, qubit_idx: Union[List[int], int], num_qubits: int ) -> paddle.Tensor: @@ -91,3 +90,5 @@ def unitary_transformation( ) state = paddle.reshape(state, higher_dims.copy() + [2 ** num_qubits, 2 ** num_qubits]) return state + +# TODO Update same tensor contraction logic \ No newline at end of file diff --git a/paddle_quantum/base.py b/paddle_quantum/base.py index b44b8fb..c1d0e63 100644 --- a/paddle_quantum/base.py +++ b/paddle_quantum/base.py @@ -97,7 +97,7 @@ def get_dtype() -> 'str': class Operator(paddle.nn.Layer): - r"""The basic class to implement the quantum operation. + r"""The basic class to implement the operation in Paddle Quantum. Args: backend: The backend implementation of the operator. @@ -106,20 +106,25 @@ class Operator(paddle.nn.Layer): Defaults to ``None``, which means to use the default data type. name_scope: Prefix name used by the operator to name parameters. Defaults to ``None``. """ - def __init__(self, backend: Optional[paddle_quantum.Backend] = None, dtype: Optional[str] = None, - name_scope: Optional[str] = None): + def __init__( + self, backend: Optional[paddle_quantum.Backend] = None, + dtype: Optional[str] = None, name_scope: Optional[str] = None + ): if dtype is None: super().__init__(name_scope) else: super().__init__(name_scope, dtype) self.dtype = dtype if dtype is not None else get_dtype() - if backend == paddle_quantum.Backend.StateVector: - self.backend = backend - elif backend == paddle_quantum.Backend.DensityMatrix: - self.backend = backend - elif backend is None: - self.backend = get_backend() + self.backend = backend if backend is not None else get_backend() + + def __setattr__(self, name, value): + super().__setattr__(name, value) + if isinstance(value, Operator): + if value.backend is None: + value.backend = get_backend() if self.backend is None else self.backend + if value.dtype is None: + value.dtype = get_dtype() if self.dtype is None else self.dtype def to(self, backend: Optional[paddle_quantum.Backend] = None, device: Optional[str] = None, dtype: Optional[str] = None, blocking: Optional[str] = None): diff --git a/paddle_quantum/channel/__init__.py b/paddle_quantum/channel/__init__.py index 9a900ec..d5c6b3b 100644 --- a/paddle_quantum/channel/__init__.py +++ b/paddle_quantum/channel/__init__.py @@ -19,5 +19,5 @@ The module of the quantum channels. from .base import Channel from .common import * -from .custom import ChoiRepr, KrausRepr, StinespringRepr +from .custom import * from .representation import * diff --git a/paddle_quantum/channel/base.py b/paddle_quantum/channel/base.py index fc0d304..a7e79e0 100644 --- a/paddle_quantum/channel/base.py +++ b/paddle_quantum/channel/base.py @@ -17,86 +17,306 @@ r""" The source file of the basic class for the quantum channels. """ -from typing import Any, Optional, List +import warnings +import math +from typing import Any, Optional, Union, List, Iterable, Callable import paddle +import paddle_quantum as pq +from . import functional from ..base import Operator, get_backend, get_dtype from ..backend import Backend +from ..intrinsic import _get_float_dtype, _format_qubits_idx class Channel(Operator): r"""Basic class for quantum channels. Args: + type_repr: type of a representation. should be ``'Choi'``, ``'Kraus'``, ``'Stinespring'``. + representation: the representation of this channel. Defaults to ``None`` i.e. not specified. + qubits_idx: indices of the qubits on which this channel acts on. Defaults to ``None``. + i.e. list(range(num_acted_qubits)). + num_qubits: total number of qubits. Defaults to ``None``. + check_legality: whether check the completeness of the representation if provided. Defaults to ``True``. + num_acted_qubits: the number of qubits that this channel acts on. Defaults to ``None``. backend: Backend on which the channel is executed. Defaults to ``None``. dtype: Type of data. Defaults to ``None``. name_scope: Prefix name used by the layer to name parameters. If prefix is "my_layer", parameter name in - MyLayer can be "my_layer_0.w_n", where "w" is the parameter base name and "n" is an unique suffix - auto-generated. If ``None``, prefix name will be snake cased class name. Defaults to ``None``. + MyLayer can be "my_layer_0.w_n", where "w" is the parameter base name and "n" is an unique suffix auto-generated. + If ``None``, prefix name will be snake cased class name. Defaults to ``None``. + + Raises: + ValueError: Unsupported channel representation for ``type_repr``. + NotImplementedError: The noisy channel can only run in density matrix mode. + TypeError: Unexpected data type for Channel representation. + + Note: + If ``representation`` is given, then ``num_acted_qubits`` will be determined by ``representation``, no matter + ``num_acted_qubits`` is ``None`` or not. """ def __init__( - self, backend: Backend = None, dtype: str = None, name_scope: str = None + self, type_repr: str, representation: Union[paddle.Tensor, List[paddle.Tensor]] = None, + qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] = None, + num_qubits: int = None, check_legality: bool = True, num_acted_qubits: int = None, + backend: Backend = None, dtype: str = None, name_scope: str = None ) -> None: super().__init__(backend, dtype, name_scope) + assert representation is not None or num_acted_qubits is not None, ( + "Received None for representation and num_acted_qubits: " + "either one of them must be specified to initialize a Channel instance.") + type_repr = type_repr.capitalize() + if type_repr not in ['Choi', 'Kraus', 'Stinespring']: + raise ValueError( + "Unsupported channel representation:" + f"require 'Choi', 'Kraus' or 'Stinespring', not {type_repr}") + + if representation is None: + assert num_acted_qubits is not None, ( + "Received None for representation and num_acted_qubits: " + "either one of them must be specified to initialize a Channel instance.") + elif type_repr == 'Choi': + num_acted_qubits = self.__choi_init(representation, check_legality) + elif type_repr == 'Kraus': + num_acted_qubits = self.__kraus_init(representation, check_legality) + elif type_repr == 'Stinespring': + num_acted_qubits = self.__stinespring_init(representation, check_legality) + + if qubits_idx is None: + self.qubits_idx = list(range(num_acted_qubits)) + else: + self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits) + self.type_repr = type_repr + self.num_acted_qubits = num_acted_qubits + + def __choi_init(self, choi_repr: paddle.Tensor, check_legality: bool) -> int: + r"""Initialize channel for type_repr as ``'Choi'`` + """ + if self.backend != Backend.DensityMatrix: + raise NotImplementedError( + "The noisy channel can only run in density matrix mode.") + + if not isinstance(choi_repr, paddle.Tensor): + raise TypeError( + f"Unexpected data type for Choi representation: expected paddle.Tensor, received {type(choi_repr)}") + choi_repr = choi_repr.cast(self.dtype) + + num_acted_qubits = int(math.log2(choi_repr.shape[0]) / 2) + if check_legality: + # TODO: need to add more sanity check for choi + assert 2 ** (2 * num_acted_qubits) == choi_repr.shape[0], \ + "The shape of Choi representation should be the integer power of 4: check your inputs." + + self.__choi_repr = choi_repr + return num_acted_qubits + + def __kraus_init(self, kraus_repr: Union[paddle.Tensor, List[paddle.Tensor]], check_legality: bool) -> int: + r"""Initialize channel for type_repr as ``'Kraus'`` + """ + if self.backend != Backend.DensityMatrix: + raise NotImplementedError( + "The noisy channel can only run in density matrix mode.") + + complex_dtype = self.dtype + if isinstance(kraus_repr, paddle.Tensor): + kraus_repr = [kraus_repr.cast(complex_dtype)] + elif isinstance(kraus_repr, List): + kraus_repr = [oper.cast(complex_dtype) for oper in kraus_repr] + else: + raise TypeError( + "Unexpected data type for Kraus representation: " + f"expected paddle.Tensor or its List, received {type(kraus_repr)}" + ) + dimension = kraus_repr[0].shape[0] + num_acted_qubits = int(math.log2(dimension)) + assert 2 ** num_acted_qubits == dimension, \ + "The length of oracle should be integer power of 2." + + # sanity check + if check_legality: + oper_sum = paddle.zeros([dimension, dimension]).cast(complex_dtype) + for oper in kraus_repr: + oper_sum = oper_sum + paddle.conj(oper.T) @ oper + err = paddle.norm(paddle.abs(oper_sum - paddle.eye(dimension).cast(complex_dtype))).item() + if err > min(1e-6 * dimension * len(kraus_repr), 0.01): + warnings.warn( + f"\nThe input data may not be a Kraus representation of a channel: norm(sum(E * E^d) - I) = {err}.", + UserWarning) - def to(self, backend: Optional[str] = None, device: Optional[str] = None, - dtype: Optional[str] = None, blocking: Optional[str] = None) -> None: + self.__kraus_repr = kraus_repr + return num_acted_qubits + + def __stinespring_init(self, stinespring_repr: paddle.Tensor, check_legality: bool) -> int: + r"""Initialize channel for type_repr as ``'Stingspring'`` + """ + if self.backend != Backend.DensityMatrix: + raise NotImplementedError( + "The noisy channel can only run in density matrix mode.") + + stinespring_repr = stinespring_repr.cast(self.dtype) + num_acted_qubits = int(math.log2(stinespring_repr.shape[1])) + + # sanity check + if check_legality: + # TODO: need to add more sanity check for stinespring + dim_ancilla = stinespring_repr.shape[0] // stinespring_repr.shape[1] + dim_act = stinespring_repr.shape[1] + assert dim_act * dim_ancilla == stinespring_repr.shape[0], \ + 'The width of stinespring matrix should be the factor of its height' + + self.__stinespring_repr = stinespring_repr + return num_acted_qubits + + def to( + self, backend: Optional[str] = None, device: Optional[str] = None, + dtype: Optional[str] = None, blocking: Optional[str] = None + ) -> None: super().to(device, dtype, blocking) # TODO: to be implemented raise NotImplementedError - def forward(self, *inputs: Any, **kwargs: Any) -> None: - raise NotImplementedError - - def __setattr__(self, name, value): - super().__setattr__(name, value) - if isinstance(value, Channel): - if value.backend is None: - value.backend = get_backend() if self.backend is None else self.backend - if value.dtype is None: - value.dtype = get_dtype() if self.dtype is None else self.dtype - @property def choi_repr(self) -> paddle.Tensor: r"""Choi representation of a channel - + Returns: - a tensor with shape :math:`[d_\text{out}^2, d_\text{in}^2]`, where :math:`d_\text{in/out}` is the input/output - dimension of this channel - + a tensor with shape :math:`[d_\text{out}^2, d_\text{in}^2]`, where :math:`d_\text{in/out}` is + the input/output dimension of this channel + Raises: - Cannot return the Choi representation of a general channel: use ChoiRepr instead to specify your channel - + ValueError: Need to specify the Choi representation in this Channel instance. """ - raise NotImplementedError( - "Cannot return the Choi representation of a general channel: use ChoiRepr instead to specify your channel") - + type_repr = self.type_repr + if type_repr == 'Kraus': + return _kraus_to_choi(self.__kraus_repr) + elif type_repr == 'Choi': + if self.__choi_repr is None: + raise ValueError( + "Need to specify the Choi representation in this Channel instance.") + return self.__choi_repr + elif type_repr == 'Stinespring': + return _stinespring_to_choi(self.__stinespring_repr) + else: + raise ValueError("Cannot recognize the type_repr, it should be ``'Choi'``, ``'Kraus'``, ``'Stinespring'``.") + @property def kraus_repr(self) -> List[paddle.Tensor]: r"""Kraus representation of a channel - + Returns: - a list of tensors with shape :math:`[d_\text{out}, d_\text{in}]`, where :math:`d_\text{in/out}` is the input/output - dimension of this channel - + a list of tensors with shape :math:`[d_\text{out}, d_\text{in}]`, where :math:`d_\text{in/out}` is + the input/output dimension of this channel + Raises: - Cannot return the Kraus representation of a general channel: use KrausRepr instead to specify your channel - + ValueError: Need to specify the Kraus representation in this Channel instance. """ - raise NotImplementedError( - "Cannot return the Kraus representation of a general channel: use KrausRepr instead to specify your channel") - + type_repr = self.type_repr + if type_repr == 'Kraus': + if self.__kraus_repr is None: + raise ValueError( + "Need to specify the Kraus representation in this Channel instance.") + return self.__kraus_repr + elif type_repr == 'Choi': + return _choi_to_kraus(self.__choi_repr, tol=1e-6) + elif type_repr == 'Stinespring': + return _stinespring_to_kraus(self.__stinespring_repr) + else: + raise ValueError("Cannot recognize the type_repr, it should be ``'Choi'``, ``'Kraus'``, ``'Stinespring'``.") + @property def stinespring_repr(self) -> paddle.Tensor: r"""Stinespring representation of a channel - + Returns: - a tensor with shape :math:`[r * d_\text{out}, d_\text{in}]`, where :math:`r` is the rank of this channel and + a tensor with shape :math:`[r * d_\text{out}, d_\text{in}]`, where :math:`r` is the rank of this channel and :math:`d_\text{in/out}` is the input/output dimension of this channel - + Raises: - Cannot return the Stinespring representation of a general channel: use StinespringRepr instead to specify your channel - + ValueError: Need to specify the Stinespring representation in this Channel instance. """ - raise NotImplementedError( - "Cannot return the Stinespring representation of a general channel: use StinespringRepr instead to specify your channel") + type_repr = self.type_repr + if type_repr == 'Kraus': + return _kraus_to_stinespring(self.__kraus_repr) + elif type_repr == 'Choi': + return _choi_to_stinespring(self.__choi_repr, tol=1e-6) + elif type_repr == 'Stinespring': + if self.__stinespring_repr is None: + raise ValueError( + "Need to specify the Stinespring representation in this Channel instance.") + return self.__stinespring_repr + else: + raise ValueError("Cannot recognize the type_repr, it should be ``'Choi'``, ``'Kraus'``, ``'Stinespring'``.") + + def forward(self, state: pq.State) -> pq.State: + if state.backend == Backend.QuLeaf: + raise NotImplementedError + type_repr = self.type_repr + for qubits_idx in self.qubits_idx: + if type_repr in ['Gate', 'Kraus']: + state = functional.kraus_repr(state, self.kraus_repr, qubits_idx, self.dtype, self.backend) + elif type_repr == 'Choi': + state = functional.choi_repr(state, self.choi_repr, qubits_idx, self.dtype, self.backend) + else: + state = functional.stinespring_repr(state, self.stinespring_repr, qubits_idx, self.dtype, self.backend) + return state + + +def _choi_to_kraus(choi_repr: paddle.Tensor, tol: float) -> List[paddle.Tensor]: + r"""Transform the Choi representation to the Kraus representation + """ + ndim = int(math.sqrt(choi_repr.shape[0])) + w, v = paddle.linalg.eigh(choi_repr) + + # add abs to make eigvals safe + w = paddle.abs(w) + l_cut = 0 + for l in range(len(w) - 1, -1, -1): + if paddle.sum(paddle.abs(w[l:])) / paddle.sum(paddle.abs(w)) > 1 - tol: + l_cut = l + break + return [(v * paddle.sqrt(w))[:, l].reshape([ndim, ndim]).T for l in range(l_cut, ndim**2)] + + +def _choi_to_stinespring(choi_repr: paddle.Tensor, tol: float) -> List[paddle.Tensor]: + r"""Transform the Choi representation to the Stinespring representation + """ + # TODO: need a more straightforward transformation + return _kraus_to_stinespring(_choi_to_kraus(choi_repr, tol)) + + +def _kraus_to_choi(kraus_repr: List[paddle.Tensor]) -> paddle.Tensor: + r"""Transform the Kraus representation to the Choi representation + """ + ndim = kraus_repr[0].shape[0] + kraus_oper_tensor = paddle.reshape( + paddle.concat([paddle.kron(x, x.conj().T) for x in kraus_repr]), + shape=[len(kraus_repr), ndim, -1] + ) + choi_repr = paddle.sum(kraus_oper_tensor, axis=0).reshape([ndim for _ in range(4)]).transpose([2, 1, 0, 3]) + return choi_repr.transpose([0, 2, 1, 3]).reshape([ndim * ndim, ndim * ndim]) + + +def _kraus_to_stinespring(kraus_repr: List[paddle.Tensor]) -> paddle.Tensor: + r"""Transform the Kraus representation to the Stinespring representation + """ + j_dim = len(kraus_repr) + i_dim = kraus_repr[0].shape[0] + kraus_oper_tensor = paddle.concat(kraus_repr).reshape([j_dim, i_dim, -1]) + stinespring_repr = kraus_oper_tensor.transpose([1, 0, 2]) + return stinespring_repr.reshape([i_dim * j_dim, i_dim]) + + +def _stinespring_to_choi(stinespring_repr: paddle.Tensor) -> paddle.Tensor: + r"""Transform the Stinespring representation to the Choi representation + """ + # TODO: need a more straightforward transformation + return _kraus_to_choi(_stinespring_to_kraus(stinespring_repr)) + + +def _stinespring_to_kraus(stinespring_repr: paddle.Tensor) -> List[paddle.Tensor]: + r"""Transform the Stinespring representation to the Kraus representation + """ + i_dim = stinespring_repr.shape[1] + j_dim = stinespring_repr.shape[0] // i_dim + kraus_oper = stinespring_repr.reshape([i_dim, j_dim, i_dim]).transpose([1, 0, 2]) + return [kraus_oper[j] for j in range(j_dim)] diff --git a/paddle_quantum/channel/common.py b/paddle_quantum/channel/common.py index 31bdb3a..d450d33 100644 --- a/paddle_quantum/channel/common.py +++ b/paddle_quantum/channel/common.py @@ -17,15 +17,22 @@ r""" The source file of the classes for common quantum channels. """ +import numpy as np import paddle -from .custom import KrausRepr +from .base import Channel from ..intrinsic import _format_qubits_idx from ..qinfo import kraus_unitary_random -from .representation import * +from ..state import State +from .representation import ( + bit_flip_kraus, phase_flip_kraus, bit_phase_flip_kraus, + amplitude_damping_kraus, generalized_amplitude_damping_kraus, phase_damping_kraus, + depolarizing_kraus, generalized_depolarizing_kraus, pauli_kraus, reset_kraus, + thermal_relaxation_kraus, replacement_choi +) from typing import Union, Iterable -class BitFlip(KrausRepr): +class BitFlip(Channel): r"""A collection of bit flip channels. Such a channel's Kraus operators are @@ -44,10 +51,10 @@ class BitFlip(KrausRepr): self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - super().__init__(bit_flip_kraus(prob), qubits_idx, num_qubits, check_complete=False) - + super().__init__('kraus', bit_flip_kraus(prob), qubits_idx, num_qubits, check_legality=False) -class PhaseFlip(KrausRepr): + +class PhaseFlip(Channel): r"""A collection of phase flip channels. Such a channel's Kraus operators are @@ -66,10 +73,10 @@ class PhaseFlip(KrausRepr): self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - super().__init__(phase_flip_kraus(prob), qubits_idx, num_qubits, check_complete=False) + super().__init__('kraus', phase_flip_kraus(prob), qubits_idx, num_qubits, check_legality=False) -class BitPhaseFlip(KrausRepr): +class BitPhaseFlip(Channel): r"""A collection of bit phase flip channels. Such a channel's Kraus operators are @@ -88,10 +95,10 @@ class BitPhaseFlip(KrausRepr): self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - super().__init__(bit_phase_flip_kraus(prob), qubits_idx, num_qubits, check_complete=False) + super().__init__('kraus', bit_phase_flip_kraus(prob), qubits_idx, num_qubits, check_legality=False) -class AmplitudeDamping(KrausRepr): +class AmplitudeDamping(Channel): r"""A collection of amplitude damping channels. Such a channel's Kraus operators are @@ -118,10 +125,10 @@ class AmplitudeDamping(KrausRepr): self, gamma: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - super().__init__(amplitude_damping_kraus(gamma), qubits_idx, num_qubits, check_complete=False) + super().__init__('kraus', amplitude_damping_kraus(gamma), qubits_idx, num_qubits, check_legality=False) -class GeneralizedAmplitudeDamping(KrausRepr): +class GeneralizedAmplitudeDamping(Channel): r"""A collection of generalized amplitude damping channels. Such a channel's Kraus operators are @@ -147,10 +154,11 @@ class GeneralizedAmplitudeDamping(KrausRepr): self, gamma: Union[paddle.Tensor, float], prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - super().__init__(generalized_amplitude_damping_kraus(gamma, prob), qubits_idx, num_qubits, check_complete=False) + super().__init__( + 'kraus', generalized_amplitude_damping_kraus(gamma, prob), qubits_idx, num_qubits, check_legality=False) -class PhaseDamping(KrausRepr): +class PhaseDamping(Channel): r"""A collection of phase damping channels. Such a channel's Kraus operators are @@ -177,10 +185,10 @@ class PhaseDamping(KrausRepr): self, gamma: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - super().__init__(phase_damping_kraus(gamma), qubits_idx, num_qubits, check_complete=False) + super().__init__('kraus', phase_damping_kraus(gamma), qubits_idx, num_qubits, check_legality=False) -class Depolarizing(KrausRepr): +class Depolarizing(Channel): r"""A collection of depolarizing channels. Such a channel's Kraus operators are @@ -208,10 +216,10 @@ class Depolarizing(KrausRepr): self, prob: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - super().__init__(depolarizing_kraus(prob), qubits_idx, num_qubits, check_complete=False) + super().__init__('kraus', depolarizing_kraus(prob), qubits_idx, num_qubits, check_legality=False) -class GeneralizedDepolarizing(KrausRepr): +class GeneralizedDepolarizing(Channel): r"""A generalized depolarizing channel. Such a channel's Kraus operators are @@ -220,23 +228,26 @@ class GeneralizedDepolarizing(KrausRepr): E_0 = \sqrt{1-(D - 1)p/D} I, \text{ where } D = 4^n, \\ E_k = \sqrt{p/D} \sigma_k, \text{ for } 0 < k < D. - + Args: prob: probability :math:`p`. Its value should be in the range :math:`[0, 1]`. qubits_idx: Indices of the qubits on which the channels act, the length of which is :math:`n`. + Defaults to be ``None``. num_qubits: Total number of qubits. Defaults to ``None``. - """ def __init__( self, prob: Union[paddle.Tensor, float], - qubits_idx: Union[Iterable[int], int, str], num_qubits: int = None + qubits_idx: Union[Iterable[int], int, str] = None, num_qubits: int = None ): - num_acted_qubits = np.size(np.array(qubits_idx)).item() - super().__init__(generalized_depolarizing_kraus(prob, num_acted_qubits), - qubits_idx, num_qubits, check_complete=False) + num_acted_qubits = np.size(np.array(qubits_idx)) + if qubits_idx is None: + qubits_idx = 'full' if num_acted_qubits == 1 else 'cycle' + super().__init__( + 'kraus', generalized_depolarizing_kraus(prob, num_acted_qubits), + qubits_idx, num_qubits, check_legality=False) -class PauliChannel(KrausRepr): +class PauliChannel(Channel): r"""A collection of Pauli channels. Args: @@ -252,10 +263,10 @@ class PauliChannel(KrausRepr): self, prob: Union[paddle.Tensor, Iterable[float]], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - super().__init__(pauli_kraus(prob), qubits_idx, num_qubits, check_complete=False) + super().__init__('kraus', pauli_kraus(prob), qubits_idx, num_qubits, check_legality=False) -class ResetChannel(KrausRepr): +class ResetChannel(Channel): r"""A collection of reset channels. Such a channel reset the state to :math:`|0\rangle` with a probability of p and to :math:`|1\rangle` with @@ -298,10 +309,10 @@ class ResetChannel(KrausRepr): self, prob: Union[paddle.Tensor, Iterable[float]], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - super().__init__(reset_kraus(prob), qubits_idx, num_qubits, check_complete=False) + super().__init__('kraus', reset_kraus(prob), qubits_idx, num_qubits, check_legality=False) -class ThermalRelaxation(KrausRepr): +class ThermalRelaxation(Channel): r"""A collection of thermal relaxation channels. Such a channel simulates the mixture of the :math:`T_1` and the :math:`T_2` processes on superconducting devices. @@ -319,13 +330,16 @@ class ThermalRelaxation(KrausRepr): self, const_t: Union[paddle.Tensor, Iterable[float]], exec_time: Union[paddle.Tensor, float], qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - super().__init__(thermal_relaxation_kraus(const_t, exec_time), qubits_idx, num_qubits, check_complete=False) + super().__init__( + 'kraus', thermal_relaxation_kraus(const_t, exec_time), + qubits_idx, num_qubits, check_legality=False) -class MixedUnitaryChannel(KrausRepr): +class MixedUnitaryChannel(Channel): r"""A collection of single-qubit mixed unitary channels. Such a channel's Kraus operators are randomly generated unitaries times related probabilities + .. math:: N(\rho) = \sum_{i} p_{i} U_{i} \rho U_{i}^{\dagger} @@ -336,13 +350,37 @@ class MixedUnitaryChannel(KrausRepr): num_qubits: Total number of qubits. Defaults to ``None``. Note: - The probability distribution of unitaries is set to be uniform distribution. + The probability distribution of unitaries is set to be uniform distribution. """ def __init__( self, num_unitary: int, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ): - #TODO: increase the number of acting qubits, currently only support 1 - super().__init__(kraus_unitary_random(1, num_unitary), - _format_qubits_idx(qubits_idx, num_qubits, 1), - num_qubits, check_complete=False) + # TODO: increase the number of acting qubits, currently only support 1 + super().__init__( + 'kraus', kraus_unitary_random(1, num_unitary), + _format_qubits_idx(qubits_idx, num_qubits, 1), num_qubits, check_legality=False) + + +class ReplacementChannel(Channel): + r"""A collection of quantum replacement channels. + + For a quantum state :math:`\sigma`, the corresponding replacement channel :math:`R` is defined as + + .. math:: + + R(\rho) = \text{tr}(\rho)\sigma + + Args: + sigma: The state to be replaced. + qubits_idx: Indices of the qubits on which the channels act, the length of which is :math:`n`. + Defaults to be ``None``. + num_qubits: Total number of qubits. Defaults to ``None``. + """ + def __init__( + self, sigma: State, + qubits_idx: Union[Iterable[int], int, str] = None, num_qubits: int = None + ): + if qubits_idx is None: + qubits_idx = list(range(sigma.num_qubits)) + super().__init__('choi', replacement_choi(sigma), qubits_idx, num_qubits) diff --git a/paddle_quantum/channel/custom.py b/paddle_quantum/channel/custom.py index 0891ab9..a9e386b 100644 --- a/paddle_quantum/channel/custom.py +++ b/paddle_quantum/channel/custom.py @@ -35,65 +35,16 @@ class ChoiRepr(Channel): Args: choi_repr: Choi operator of this channel. - qubits_idx: Indices of the qubits on which this channel acts. + qubits_idx: Indices of the qubits on which this channel acts. Defaults to ``None``. num_qubits: Total number of qubits. Defaults to ``None``. - - Raises: - NotImplementedError: The noisy channel can only run in density matrix mode. - """ def __init__( self, choi_repr: paddle.Tensor, - qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int], + qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] = None, num_qubits: int = None ): - super().__init__() - num_acted_qubits = int(math.log2(choi_repr.shape[0]) / 2) - assert 2 ** (2 * num_acted_qubits) == choi_repr.shape[0], "The length of oracle should be integer power of 2." - - #TODO: need to add sanity check for choi - self.__choi_repr = choi_repr - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits) - - if self.backend != Backend.DensityMatrix: - raise NotImplementedError( - "The noisy channel can only run in density matrix mode.") - - @property - def choi_repr(self) -> paddle.Tensor: - r"""Choi representation - """ - return self.__choi_repr - - @property - def kraus_repr(self) -> List[paddle.Tensor]: - r"""Kraus representation - """ - return _choi_to_kraus(self.__choi_repr, tol=1e-6) - - @property - def stinespring_repr(self) -> paddle.Tensor: - r"""Stinespring representation - """ - return _choi_to_stinespring(self.__choi_repr, tol=1e-6) - - def to_kraus(self) -> 'KrausRepr': - r"""Convert to Kraus representation of this chanel - """ - return KrausRepr(self.kraus_repr, qubits_idx=self.qubits_idx) - - def to_stinespring(self) -> 'StinespringRepr': - r"""Convert to Stinespring representation of this chanel - """ - return StinespringRepr(self.stinespring_repr, qubits_idx=self.qubits_idx) - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for qubits_idx in self.qubits_idx: - state = functional.choi_repr(state, self.__choi_repr, qubits_idx, self.dtype, self.backend) - return state + super().__init__('choi', choi_repr, qubits_idx, num_qubits) class KrausRepr(Channel): @@ -101,90 +52,15 @@ class KrausRepr(Channel): Args: kraus_repr: list of Kraus operators of this channel. - qubits_idx: Indices of the qubits on which this channel acts. + qubits_idx: Indices of the qubits on which this channel acts. Defaults to ``None``. num_qubits: Total number of qubits. Defaults to ``None``. - check_complete: whether check the kraus representation is valid. Defaults to be ``True``. - Set to ``False`` only if the data correctness is guaranteed. - - Raises: - NotImplementedError: The noisy channel can only run in density matrix mode. - """ def __init__( - self, kraus_repr: Union[paddle.Tensor, List[paddle.Tensor]], qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int], - num_qubits: int = None, check_complete: bool = True + self, kraus_repr: Union[paddle.Tensor, List[paddle.Tensor]], + qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] = None, + num_qubits: int = None ): - super().__init__() - num_acted_qubits = int(math.log2(kraus_repr[0].shape[0])) - assert 2 ** num_acted_qubits == kraus_repr[0].shape[0], "The length of oracle should be integer power of 2." - - # kraus operation formalize - self.__kraus_repr = [oper.cast(self.dtype) for oper in kraus_repr] if isinstance(kraus_repr, List) else [kraus_repr.cast(self.dtype)] - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits) - - # sanity check - if check_complete: - dimension = 2 ** num_acted_qubits - oper_sum = paddle.zeros([dimension, dimension]).cast(self.dtype) - for oper in self.__kraus_repr: - oper_sum = oper_sum + oper @ paddle.conj(oper.T) - err = paddle.norm(paddle.abs(oper_sum - paddle.eye(dimension).cast(self.dtype))).item() - if err > min(1e-6 * dimension * len(kraus_repr), 0.01): - warnings.warn( - f"\nThe input data may not be a Kraus representation of a channel: norm(sum(E * E^d) - I) = {err}.", UserWarning) - - if self.backend != Backend.DensityMatrix: - raise NotImplementedError( - "The noisy channel can only run in density matrix mode.") - - def __matmul__(self, other: 'KrausRepr') -> 'KrausRepr': - r"""Composition between channels with Kraus representations - - """ - assert self.qubits_idx == other.qubits_idx, \ - f"Two channels should have the same qubit indices to composite: received {self.qubits_idx} and {other.qubits_idx}" - if not isinstance(other, KrausRepr): - raise NotImplementedError( - f"does not support the composition between KrausRepr and {type(other)}") - new_kraus_oper = [] - for this_kraus in self.kraus_oper: - new_kraus_oper.extend([this_kraus @ other_kraus for other_kraus in other.kraus_oper]) - return KrausRepr(new_kraus_oper, self.qubits_idx) - - @property - def choi_repr(self) -> paddle.Tensor: - r"""Choi representation - """ - return _kraus_to_choi(self.__kraus_repr) - - @property - def kraus_repr(self) -> List[paddle.Tensor]: - r"""Kraus representation - """ - return self.__kraus_repr - - @property - def stinespring_repr(self) -> paddle.Tensor: - r"""Stinespring representation - """ - return _kraus_to_stinespring(self.__kraus_repr) - - def to_choi(self) -> 'ChoiRepr': - r"""Convert to Choi representation of this chanel - """ - return ChoiRepr(self.choi_repr, qubits_idx=self.qubits_idx) - - def to_stinespring(self) -> 'StinespringRepr': - r"""Convert to Stinespring representation of this chanel - """ - return StinespringRepr(self.stinespring_repr, qubits_idx=self.qubits_idx) - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for qubits_idx in self.qubits_idx: - state = functional.kraus_repr(state, self.__kraus_repr, qubits_idx, self.dtype, self.backend) - return state + super().__init__('kraus', kraus_repr, qubits_idx, num_qubits) class StinespringRepr(Channel): @@ -192,122 +68,13 @@ class StinespringRepr(Channel): Args: stinespring_mat: Stinespring matrix that represents this channel. - qubits_idx: Indices of the qubits on which this channel acts. + qubits_idx: Indices of the qubits on which this channel acts. Defaults to ``None``. num_qubits: Total number of qubits. Defaults to ``None``. - - Raises: - NotImplementedError: The noisy channel can only run in density matrix mode. - """ def __init__( self, stinespring_mat: paddle.Tensor, - qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int], + qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] = None, num_qubits: int = None ): - super().__init__() - num_acted_qubits = int(math.log2(stinespring_mat.shape[1])) - dim_ancilla = stinespring_mat.shape[0] // stinespring_mat.shape[1] - dim_act = stinespring_mat.shape[1] - assert dim_act * dim_ancilla == stinespring_mat.shape[0], 'The width of stinespring matrix should be the factor of its height' - - #TODO: need to add sanity check for stinespring - self.__stinespring_repr = stinespring_mat - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits) - - if self.backend != Backend.DensityMatrix: - raise NotImplementedError( - "The noisy channel can only run in density matrix mode.") - - @property - def choi_repr(self) -> paddle.Tensor: - r"""Choi representation - """ - return _stinespring_to_choi(self.__stinespring_repr) - - @property - def kraus_repr(self) -> List[paddle.Tensor]: - r"""Kraus representation - """ - return _stinespring_to_kraus(self.__stinespring_repr) - - @property - def stinespring_repr(self) -> paddle.Tensor: - r"""Stinespring representation - """ - return self.__stinespring_repr - - def to_choi(self) -> 'ChoiRepr': - r"""Convert to Choi representation of this chanel - """ - return ChoiRepr(self.choi_repr, qubits_idx=self.qubits_idx) - - def to_kraus(self) -> 'KrausRepr': - r"""Convert to Kraus representation of this chanel - """ - return KrausRepr(self.kraus_repr, qubits_idx=self.qubits_idx) - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for qubits_idx in self.qubits_idx: - state = functional.stinespring_repr(state, self.__stinespring_repr, qubits_idx, self.dtype, self.backend) - return state - - -def _choi_to_kraus(choi_repr: paddle.Tensor, tol: float) -> List[paddle.Tensor]: - r"""Transform the Choi representation to the Kraus representation - """ - ndim = int(math.sqrt(choi_repr.shape[0])) - w, v = paddle.linalg.eigh(choi_repr) - - # add abs to make eigvals safe - w = paddle.abs(w) - l_cut = 0 - for l in range(len(w) - 1, -1, -1): - if paddle.sum(paddle.abs(w[l:])) / paddle.sum(paddle.abs(w)) > 1 - tol: - l_cut = l - break - return [(v * paddle.sqrt(w))[:, l].reshape([ndim, ndim]).T for l in range(l_cut, ndim**2)] - - -def _choi_to_stinespring(choi_repr: paddle.Tensor, tol: float) -> List[paddle.Tensor]: - r"""Transform the Choi representation to the Stinespring representation - """ - # TODO: need a more straightforward transformation - return _kraus_to_stinespring(_choi_to_kraus(choi_repr, tol)) - - -def _kraus_to_choi(kraus_repr: List[paddle.Tensor]) -> paddle.Tensor: - r"""Transform the Kraus representation to the Choi representation - """ - ndim = kraus_repr[0].shape[0] - kraus_oper_tensor = paddle.concat([paddle.kron(x, x.conj().T) for x in kraus_repr]).reshape([len(kraus_repr), ndim, -1]) - choi_repr = paddle.sum(kraus_oper_tensor, axis=0).reshape([ndim for _ in range(4)]).transpose([2, 1, 0, 3]) - return choi_repr.transpose([0, 2, 1, 3]).reshape([ndim * ndim, ndim * ndim]) - - -def _kraus_to_stinespring(kraus_repr: List[paddle.Tensor]) -> paddle.Tensor: - r"""Transform the Kraus representation to the Stinespring representation - """ - j_dim = len(kraus_repr) - i_dim = kraus_repr[0].shape[0] - kraus_oper_tensor = paddle.concat(kraus_repr).reshape([j_dim, i_dim, -1]) - stinespring_repr = kraus_oper_tensor.transpose([1, 0, 2]) - return stinespring_repr.reshape([i_dim * j_dim, i_dim]) - - -def _stinespring_to_choi(stinespring_repr: paddle.Tensor) -> paddle.Tensor: - r"""Transform the Stinespring representation to the Choi representation - """ - # TODO: need a more straightforward transformation - return _kraus_to_choi(_stinespring_to_kraus(stinespring_repr)) - - -def _stinespring_to_kraus(stinespring_repr: paddle.Tensor) -> List[paddle.Tensor]: - r"""Transform the Stinespring representation to the Kraus representation - """ - i_dim = stinespring_repr.shape[1] - j_dim = stinespring_repr.shape[0] // i_dim - kraus_oper = stinespring_repr.reshape([i_dim, j_dim, i_dim]).transpose([1, 0, 2]) - return [kraus_oper[j] for j in range(j_dim)] + super().__init__('stinespring', stinespring_mat, qubits_idx, num_qubits) diff --git a/paddle_quantum/channel/representation.py b/paddle_quantum/channel/representation.py index 0a1a9d8..8697c2a 100644 --- a/paddle_quantum/channel/representation.py +++ b/paddle_quantum/channel/representation.py @@ -23,6 +23,7 @@ import paddle from ..base import get_dtype from ..intrinsic import _zero, _one, _get_float_dtype from ..linalg import pauli_basis_generation +from ..state import State from typing import List, Union @@ -37,10 +38,10 @@ def bit_flip_kraus(prob: Union[float, np.ndarray, paddle.Tensor], dtype: str = N Args: prob: probability :math:`p`. dtype: data type. Defaults to be ``None``. - + Returns: a list of Kraus operators - + """ dtype = get_dtype() if dtype is None else dtype prob = prob if isinstance(prob, paddle.Tensor) else paddle.to_tensor(prob, dtype=_get_float_dtype(dtype)) @@ -66,14 +67,13 @@ def phase_flip_kraus(prob: Union[float, np.ndarray, paddle.Tensor], dtype: str = E_0 = \sqrt{1 - p} I, E_1 = \sqrt{p} Z. - + Args: prob: probability :math:`p`. dtype: data type. Defaults to be ``None``. - + Returns: a list of Kraus operators - """ dtype = get_dtype() if dtype is None else dtype prob = prob if isinstance(prob, paddle.Tensor) else paddle.to_tensor(prob, dtype=_get_float_dtype(dtype)) @@ -99,14 +99,13 @@ def bit_phase_flip_kraus(prob: Union[float, np.ndarray, paddle.Tensor], dtype: s E_0 = \sqrt{1 - p} I, E_1 = \sqrt{p} Y. - + Args: prob: probability :math:`p`. dtype: data type. Defaults to be ``None``. - + Returns: a list of Kraus operators - """ dtype = get_dtype() if dtype is None else dtype prob = prob if isinstance(prob, paddle.Tensor) else paddle.to_tensor(prob, dtype=_get_float_dtype(dtype)) @@ -117,7 +116,7 @@ def bit_phase_flip_kraus(prob: Union[float, np.ndarray, paddle.Tensor], dtype: s ], [ _zero(dtype), -1j * paddle.sqrt(prob), - 1j * -paddle.sqrt(prob), _zero(dtype), + 1j * paddle.sqrt(prob), _zero(dtype), ] ] for idx, oper in enumerate(kraus_oper): @@ -140,14 +139,13 @@ def amplitude_damping_kraus(gamma: Union[float, np.ndarray, paddle.Tensor], dtyp 0 & \sqrt{\gamma} \\ 0 & 0 \end{bmatrix}. - + Args: gamma: coefficient :math:`\gamma`. dtype: data type. Defaults to be ``None``. - + Returns: a list of Kraus operators - """ dtype = get_dtype() if dtype is None else dtype gamma = gamma if isinstance(gamma, paddle.Tensor) else paddle.to_tensor(gamma, dtype=_get_float_dtype(dtype)) @@ -166,8 +164,10 @@ def amplitude_damping_kraus(gamma: Union[float, np.ndarray, paddle.Tensor], dtyp return kraus_oper -def generalized_amplitude_damping_kraus(gamma: Union[float, np.ndarray, paddle.Tensor], - prob: Union[float, np.ndarray, paddle.Tensor], dtype: str = None) -> List[paddle.Tensor]: +def generalized_amplitude_damping_kraus( + gamma: Union[float, np.ndarray, paddle.Tensor], + prob: Union[float, np.ndarray, paddle.Tensor], dtype: str = None +) -> List[paddle.Tensor]: r"""Kraus representation of a generalized amplitude damping channel with form .. math:: @@ -176,15 +176,14 @@ def generalized_amplitude_damping_kraus(gamma: Union[float, np.ndarray, paddle.T E_1 = \sqrt{p} \begin{bmatrix} 0 & \sqrt{\gamma} \\ 0 & 0 \end{bmatrix},\\ E_2 = \sqrt{1-p} \begin{bmatrix} \sqrt{1-\gamma} & 0 \\ 0 & 1 \end{bmatrix}, E_3 = \sqrt{1-p} \begin{bmatrix} 0 & 0 \\ \sqrt{\gamma} & 0 \end{bmatrix}. - + Args: gamma: coefficient :math:`\gamma`. prob: probability :math:`p`. dtype: data type. Defaults to be ``None``. - + Returns: a list of Kraus operators - """ dtype = get_dtype() if dtype is None else dtype float_dtype = _get_float_dtype(dtype) @@ -228,14 +227,13 @@ def phase_damping_kraus(gamma: Union[float, np.ndarray, paddle.Tensor], dtype: s 0 & 0 \\ 0 & \sqrt{\gamma} \end{bmatrix}. - + Args: gamma: coefficient :math:`\gamma`. dtype: data type. Defaults to be ``None``. - + Returns: a list of Kraus operators - """ dtype = get_dtype() if dtype is None else dtype gamma = gamma if isinstance(gamma, paddle.Tensor) else paddle.to_tensor(gamma, dtype=_get_float_dtype(dtype)) @@ -263,14 +261,13 @@ def depolarizing_kraus(prob: Union[float, np.ndarray, paddle.Tensor], dtype: str E_1 = \sqrt{p/4} X, E_2 = \sqrt{p/4} Y, E_3 = \sqrt{p/4} Z. - + Args: prob: probability :math:`p`. dtype: data type. Defaults to be ``None``. - + Returns: a list of Kraus operators - """ dtype = get_dtype() if dtype is None else dtype prob = prob if isinstance(prob, paddle.Tensor) else paddle.to_tensor(prob, dtype=_get_float_dtype(dtype)) @@ -299,42 +296,42 @@ def depolarizing_kraus(prob: Union[float, np.ndarray, paddle.Tensor], dtype: str def generalized_depolarizing_kraus(prob: float, num_qubits: int, dtype: str = None) -> List[paddle.Tensor]: r"""Kraus representation of a generalized depolarizing channel with form - + .. math:: E_0 = \sqrt{1-(D - 1)p/D} I, \text{ where } D = 4^n, E_k = \sqrt{p/D} \sigma_k, \text{ for } 0 < k < D. - + Args: prob: probability :math:`p`. num_qubits: number of qubits :math:`n` of this channel. dtype: data type. Defaults to be ``None``. - + Returns: a list of Kraus operators - """ dtype = get_dtype() if dtype is None else dtype prob = prob if isinstance(prob, paddle.Tensor) else paddle.to_tensor(prob, dtype=_get_float_dtype(dtype)) - + basis = [ele.cast(dtype) * (2 ** num_qubits + 0j) for ele in pauli_basis_generation(num_qubits)] I, other_elements = basis[0], basis[1:] - + dim = 4 ** num_qubits - return ([I * (paddle.sqrt(1 - (dim - 1) * prob / dim) + 0j)] + - [ele * (paddle.sqrt(prob / dim) + 0j) for ele in other_elements]) + return ( + [I * (paddle.sqrt(1 - (dim - 1) * prob / dim) + 0j)] + + [ele * (paddle.sqrt(prob / dim) + 0j) for ele in other_elements] + ) def pauli_kraus(prob: Union[List[float], np.ndarray, paddle.Tensor], dtype: str = None) -> List[paddle.Tensor]: r"""Kraus representation of a pauli channel - + Args: prob: a list of three probabilities corresponding to X, Y, Z gate :math:`p`. dtype: data type. Defaults to be ``None``. - + Returns: a list of Kraus operators - """ dtype = get_dtype() if dtype is None else dtype float_dtype = _get_float_dtype(dtype) @@ -343,7 +340,7 @@ def pauli_kraus(prob: Union[List[float], np.ndarray, paddle.Tensor], dtype: str prob_sum = paddle.sum(prob) assert prob_sum <= 1, \ f"The sum of input probabilities should not be greater than 1: received {prob_sum.item()}" - prob_i = paddle.sqrt(1 - prob_sum) + prob_i = 1 - prob_sum kraus_oper = [ [ paddle.sqrt(prob_i).cast(dtype), _zero(dtype), @@ -400,7 +397,6 @@ def reset_kraus(prob: Union[List[float], np.ndarray, paddle.Tensor], dtype: str Returns: a list of Kraus operators - """ dtype = get_dtype() if dtype is None else dtype float_dtype = _get_float_dtype(dtype) @@ -437,8 +433,10 @@ def reset_kraus(prob: Union[List[float], np.ndarray, paddle.Tensor], dtype: str return kraus_oper -def thermal_relaxation_kraus(const_t: Union[List[float], np.ndarray, paddle.Tensor], - exec_time: Union[List[float], np.ndarray, paddle.Tensor], dtype: str = None) -> List[paddle.Tensor]: +def thermal_relaxation_kraus( + const_t: Union[List[float], np.ndarray, paddle.Tensor], + exec_time: Union[List[float], np.ndarray, paddle.Tensor], dtype: str = None +) -> List[paddle.Tensor]: r"""Kraus representation of a thermal relaxation channel Args: @@ -448,15 +446,19 @@ def thermal_relaxation_kraus(const_t: Union[List[float], np.ndarray, paddle.Tens Returns: a list of Kraus operators. - """ dtype = get_dtype() if dtype is None else dtype float_dtype = _get_float_dtype(dtype) + const_t = const_t.cast(float_dtype) if isinstance(const_t, paddle.Tensor) else paddle.to_tensor(const_t, dtype=float_dtype) t1, t2 = const_t[0], const_t[1] + assert t2 <= t1, \ + f"The relaxation time T2 and T1 must satisfy T2 <= T1: received T2 {t2} and T1{t1}" + exec_time = exec_time.cast(float_dtype) / 1000 if isinstance(exec_time, paddle.Tensor) else paddle.to_tensor(exec_time / 1000, dtype=float_dtype) prob_reset = 1 - paddle.exp(-exec_time / t1) prob_z = (1 - prob_reset) * (1 - paddle.exp(-exec_time / t2) * paddle.exp(exec_time / t1)) / 2 + prob_z = _zero(float_dtype) if paddle.abs(prob_z) <= 0 else prob_z prob_i = 1 - prob_reset - prob_z kraus_oper = [ [ @@ -478,4 +480,25 @@ def thermal_relaxation_kraus(const_t: Union[List[float], np.ndarray, paddle.Tens ] for idx, oper in enumerate(kraus_oper): kraus_oper[idx] = paddle.reshape(paddle.concat(oper), [2, 2]) - return kraus_oper \ No newline at end of file + return kraus_oper + + +def replacement_choi(sigma: Union[np.ndarray, paddle.Tensor, State], dtype: str = None) -> paddle.Tensor: + r"""Choi representation of a replacement channel + + Args: + sigma: output state of this channel. + dtype: data type. Defaults to be ``None``. + + Returns: + a Choi operator. + """ + dtype = get_dtype() if dtype is None else dtype + + # sanity check + sigma = sigma if isinstance(sigma, State) else State(sigma) + sigma.to('density_matrix') + sigma = sigma.data + + dim = sigma.shape[0] + return paddle.kron(paddle.eye(dim), sigma).cast(dtype) diff --git a/paddle_quantum/data_analysis/power_flow.py b/paddle_quantum/data_analysis/power_flow.py new file mode 100644 index 0000000..a54ca3e --- /dev/null +++ b/paddle_quantum/data_analysis/power_flow.py @@ -0,0 +1,626 @@ +# !/usr/bin/env python3 +# Copyright (c) 2020 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +r""" +Power Flow model +""" + +import csv +import numpy as np +import os +import warnings +import logging +from typing import Optional, List, Tuple, Callable, Union +warnings.filterwarnings('ignore') +os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python' +import toml +from tqdm import tqdm +import paddle +from paddle_quantum.gate import * +from paddle_quantum.state import * +from paddle_quantum.linalg import * +from paddle_quantum.data_analysis.vqls import _preprocess, _postprocess, VQLS + +class Bus: + r""" + The class of buses in power flow model. + + Args: + data: A list of data of the bus. + name: The name of the bus. + + """ + + def __init__(self, data: List[float], name: str): + self.busIndex = int(data[0]-1) + self.type = int(data[3]) + self.voltage = float(data[4]) + self.theta = float(data[5]) + self.PLi = float(data[6]) + self.QLi = float(data[7]) + self.PGi = float(data[8]) + self.QGi = float(data[9]) + self.Qmin = float(data[12]) + self.Qmax = float(data[13]) + self.v_final = self.voltage + self.theta_final = self.theta + self.name = name + + + @property + def V(self) -> complex: + r""" + Calculate the voltage of the bus. + + Returns: + Return the voltage of the bus. + """ + return self.v_final * np.exp(self.theta_final * 1j) + + +class Branch: + r""" + The class of branch between different buses in power system. + + Args: + branchIndex: The index of the branch. + fromBus: The index of tap bus of the branch. + toBus: The index of Z bus of the branch. + data: A list of data of the branch. + + """ + def __init__(self, branchIndex: int, fromBus: int, toBus: int, data: List[float]): + self.branchIndex = branchIndex + self.fromBus = fromBus + self.toBus = toBus + self.r = float(data[6]) + self.x = float(data[7]) + self.b_half = float(data[8]) + self.x_prime = 1 + self.z = self.r + self.x * 1j + self.y = 1 / self.z + self.b = self.b_half * 1j + +class Grid: + r""" + The class of power grid. + + Args: + buses: The list of all buses in the grid. + branches: The list of all braches in the grid. + Mva_base: Mva base of power system. + + """ + def __init__(self, buses: List[Bus], branches: List[Branch], Mva_base: float): + self.buses = buses + self.branches = branches + self.Mva_base = Mva_base + self.Y = np.zeros((self.bus_num, self.bus_num), dtype=complex) + self.branches_num = len(self.branches) + self._Y_matrix() + self.Pl = np.vstack([bus.PLi for bus in self.buses]) + self.Ql = np.vstack([bus.QLi for bus in self.buses]) + self.Pg = np.vstack([bus.PGi for bus in self.buses]) + self.Qg = np.vstack([bus.QGi for bus in self.buses]) + self.P_diff = self.Pg - self.Pl + self.Q_diff = self.Qg - self.Ql + + + @property + def bus_num(self) -> int: + r""" + Get the number of buses in the power system. + + Returns: + Return the number of buses. + """ + return len(self.buses) + + def get_bus_by_number(self, number: int) -> Bus: + r""" + Get the bus with given number. + + Args: + number: The bus number. + + Returns: + Return the bus with given number. + + Raises: + NameError: No bus with given number. + """ + for bus in self.buses: + if bus.busIndex == number-1: + return bus + raise NameError("No bus with number %d." % number) + + def get_branch_by_number(self, number: int) -> Branch: + r""" + Get the branch with given number. + + Args: + number: The branch number. + + Returns: + Return the branch with given number. + + Raises: + NameError: No branch with given number. + """ + for branch in self.branches: + if branch.branchIndex == number: + return branch + raise NameError("No branch with number %d." % number) + + def get_branches_by_bus(self, busNumber: int) -> List[Branch]: + r""" + Get branches of the bus with given bus number. + + Args: + number: The bus number. + + Returns: + Return the branches of the bus with given bus number. + + """ + branches = [branch for branch in self.branches if + (branch.toBus.busIndex == busNumber-1 or branch.fromBus.busIndex == busNumber-1)] + return branches + + @property + def pq_buses(self): + pq_buses = [bus for bus in self.buses if bus.type == 0 or bus.type==1] + return pq_buses + + @property + def pv_buses(self): + pv_buses = [bus for bus in self.buses if bus.type == 2] + return pv_buses + + def _Y_matrix(self): + """ + Generate Y matrix. + + Returns: + Return the Y matrix of the model. + """ + for k in range(self.branches_num): + branch = self.branches[k] + fromBus = branch.fromBus.busIndex + toBus = branch.toBus.busIndex + self.Y[fromBus, toBus] -= branch.y/branch.x_prime + self.Y[toBus, fromBus] = self.Y[fromBus, toBus] + + for m in range(self.bus_num): + for n in range(self.branches_num): + branch = self.branches[n] + if branch.fromBus.busIndex == m: + self.Y[m, m] += branch.y/(branch.x_prime**2) + elif branch.toBus.busIndex == m: + self.Y[m, m] += branch.y + + def _calculate_pf(self): + Vt = np.vstack([bus.V for bus in self.buses]).reshape((self.bus_num, -1)) + self.I = np.matmul(self.Y, Vt) + Iij = np.zeros((self.bus_num, self.bus_num), dtype=complex) + Sij = np.zeros((self.bus_num, self.bus_num), dtype=complex) + + self.Im = abs(self.I) + self.Ia = np.angle(self.I) + + for bus in self.buses: + m = bus.busIndex # bus index + branches = self.get_branches_by_bus(bus.busIndex+1) + for branch in branches: + if branch.fromBus.busIndex == m: + p = branch.toBus.busIndex # index to + if m != p: + Iij[m,p] = -(branch.fromBus.V - branch.toBus.V * branch.x_prime) * self.Y[m,p]/(branch.x_prime ** 2) + branch.b_half / (branch.x_prime ** 2) * branch.fromBus.V + Iij[p,m] = - (branch.toBus.V - branch.fromBus.V / branch.x_prime) * self.Y[p,m] + branch.b_half * branch.toBus.V + else: + p = branch.fromBus.busIndex # index from + if m != p: + Iij[m,p] = - (branch.toBus.V - branch.fromBus.V / branch.x_prime) * self.Y[p,m] + branch.b_half * branch.toBus.V + Iij[p,m] = - (branch.fromBus.V - branch.toBus.V) * self.Y[m,p] / ( + branch.x_prime ** 2) + branch.b_half / (branch.x_prime ** 2) * branch.fromBus.V + + self.Iij = Iij + self.Iijr = np.real(Iij) + self.Iiji = np.imag(Iij) + + # branch powerflows + for m in range(self.bus_num): + for n in range(self.bus_num): + if n != m: + Sij[m,n] = self.buses[m].V * np.conj(self.Iij[m, n]) * self.Mva_base + + self.Sij = Sij + self.Pij = np.real(Sij) + self.Qij = np.imag(Sij) + + # branch losses + Lij = np.zeros(self.branches_num, dtype=complex) + for branch in self.branches: + m = branch.branchIndex - 1 + p = branch.fromBus.busIndex + q = branch.toBus.busIndex + Lij[m] = Sij[p, q] + Sij[q, p] + + self.Lij = Lij + self.Lpij = np.real(Lij) + self.Lqij = np.imag(Lij) + + # Bus power injection + Si = np.zeros(self.bus_num, dtype=complex) + for i in range(self.bus_num): + for k in range(self.bus_num): + Si[i] += np.conj(self.buses[i].V) * self.buses[k].V * self.Y[i, k] * self.Mva_base + + self.Si = Si + self.Pi = np.real(Si) + self.Qi = -np.imag(Si) + self.Pg = self.Pi.reshape([-1,1]) + self.Pl.reshape([-1,1]) + self.Qg = self.Qi.reshape([-1,1]) + self.Ql.reshape([-1,1]) + + def powerflow(self, threshold, minIter: int, maxIter: int, depth: int, iterations: int, LR: float, gamma: Optional[float]=0): + r""" + Power flow solving process. + + Args: + threshold: Threshold for loss value to end optmization for power flow. + minIter: Minimum number of iterations of power flow optimization. + maxIter: Maximum number of iteration of power flow optimization. + depth: The depth of quantum ansatz circuit. + iterations: Number of optimization cycles of quantum circuit. + LR: The learning rate of the optimizer. + gamma: Threshold for loss value to end optimization for quantum circuit early, default is 0. + + """ + tol=1 + self.iter = 0 + P_diff = self.P_diff / self.Mva_base + Q_diff = self.Q_diff / self.Mva_base + G = np.real(self.Y) + B = np.imag(self.Y) + angles = np.zeros((self.bus_num,1)) + pv_num = len(self.pv_buses) + pq_num = len(self.pq_buses) + self.tolerances = [] + + logging.basicConfig( + filename='./power_flow.log', + filemode='w', + format='%(asctime)s %(levelname)s %(message)s', + level=logging.INFO + ) + + msg = f"Input parameters:" + logging.info(msg) + msg = f'Error threshold for power flow: {threshold}' + logging.info(msg) + msg = f'Minimum number of iterations of power flow: {minIter}' + logging.info(msg) + msg = f'Maximum number of iterations of power flow: {maxIter}' + logging.info(msg) + msg = f"Depth of ansatz circuit: {depth}" + logging.info(msg) + msg = f"Learning rate: {LR}" + logging.info(msg) + msg = f"Number of iterations for optimizing quantum circuits: {iterations}" + logging.info(msg) + + if gamma == 0: + msg = f"No threshold value was given to quantum circuit optimization." + else: + msg = f"Threshold value for quantum circuit optimization: {gamma}" + logging.info(msg) + + while self.iter < minIter or (tol > threshold and self.iter < maxIter): + self.iter += 1 + + msg = f"Start iteration {self.iter} for power flow optimization" + logging.info(msg) + + P = np.zeros((self.bus_num, 1)) + Q = np.zeros((self.bus_num, 1)) + + #calculate P and Q + for bus in self.buses: + i = bus.busIndex + for k in range(self.bus_num): + P[i] += bus.v_final*self.buses[k].v_final*(G[i, k]*np.cos(angles[i]-angles[k]) + B[i,k]*np.sin(angles[i]-angles[k])) + Q[i] += bus.v_final*self.buses[k].v_final*(G[i, k]*np.sin(angles[i]-angles[k]) - B[i,k]*np.cos(angles[i]-angles[k])) + self.P = P + + #calculate gap between current injective voltage and target voltage + dP_all = P_diff - P + dQ_all = Q_diff - Q + k = 0 + dQ = np.zeros((pq_num, 1)) + for bus in self.pq_buses: + i = bus.busIndex + if bus.type == 0 or bus.type==1: + dQ[k] = dQ_all[i] + k += 1 + dP = dP_all[1:self.bus_num] + Mismatch = np.vstack((dP, dQ)) + + # calculate Jacobian matrix. + # H_mat is the derivative of P with respect to angles + H_mat = np.zeros((self.bus_num-1, self.bus_num-1)) + for i in range(self.bus_num-1): + m = i + 1 + for k in range(self.bus_num-1): + n = k + 1 + if n == m: + H_mat[i,k] += -Q[m] + H_mat[i,k] += -self.buses[m].v_final**2*B[m,m] + else: + H_mat[i,k] = self.buses[m].v_final*self.buses[n].v_final*(G[m,n]*np.sin(angles[m]-angles[n]) - B[m,n]*np.cos(angles[m]-angles[n])) + self.H_mat = H_mat + + #N_mat is the derivative of P with respect to V + N_mat = np.zeros((self.bus_num-1, pq_num)) + for i in range(self.bus_num-1): + m = i + 1 + for k in range(pq_num): + n = self.pq_buses[k].busIndex + if n == m: + N_mat[i,k] += P[m] + N_mat[i,k] += self.buses[m].v_final**2*G[m,m] + else: + N_mat[i,k] = self.buses[m].v_final*self.buses[n].v_final*(G[m,n]*np.cos(angles[m]-angles[n]) + B[m,n]*np.sin(angles[m]-angles[n])) + self.N_mat = N_mat + + + #M_mat is the derivative of Q with respect to angles + M_mat = np.zeros((pq_num, self.bus_num-1)) + for i in range(pq_num): + m = self.pq_buses[i].busIndex + for k in range(self.bus_num-1): + n = k + 1 + if n == m: + M_mat[i,k] += P[m] + M_mat[i,k] += -self.buses[m].v_final**2*G[m,m] + else: + M_mat[i,k] = self.buses[m].v_final*self.buses[n].v_final*(-G[m,n]*np.cos(angles[m]-angles[n]) - B[m,n]*np.sin(angles[m]-angles[n])) + self.M_mat = M_mat + + #L_mat is the derivative of Q with respect to V + L_mat = np.zeros((pq_num, pq_num)) + for i in range(pq_num): + m = self.pq_buses[i].busIndex + for k in range(pq_num): + n = self.pq_buses[k].busIndex + if n == m: + L_mat[i,k] += Q[m] + L_mat[i,k] += -self.buses[m].v_final**2*B[m,m] + else: + L_mat[i,k] = self.buses[m].v_final*self.buses[n].v_final*(G[m,n]*np.sin(angles[m]-angles[n]) - B[m,n]*np.cos(angles[m]-angles[n])) + self.L_mat = L_mat + + self.J = np.vstack((np.hstack((H_mat, N_mat)), np.hstack((M_mat, L_mat)))) + + # Calculate the reverse of J and increment of data + + + msg = f"Start optmization for quantum circuit" + logging.info(msg) + X = compute(self.J,Mismatch[:,0], depth, iterations, LR, gamma).real + self.X = X + dTheta = X[0:self.bus_num-1] + dV = X[self.bus_num-1:] + msg = f"End optmization for quantum circuit" + logging.info(msg) + + + #update Angles and Voltages + #angles[0] is the angle of the slack bus + + for i in range(1,self.bus_num): + angles[i]+= dTheta[i-1] + + k=0 + for i in range(1, self.bus_num): + if self.buses[i].type == 0 or self.buses[i].type == 1: + self.buses[i].v_final += dV[k].item()*self.buses[i].v_final + k += 1 + self.buses[i].theta_final = angles[i].item() + + tol = max(abs(Mismatch)) + self.tolerances.append(tol[0]) + self.voltage = [self.buses[i].v_final for i in range(self.bus_num)] + self.theta_final = [self.buses[i].theta_final for i in range(self.bus_num)] + + msg = f"End iteration {self.iter} for power flow optimization, current error is {tol[0]}" + logging.info(msg) + + #calculate the power flow + self._calculate_pf() + + def printResults(self): + r""" + Print the result of power flow. + """ + + print("Power Flow:") + print() + print('| Bus | Bus | V | Angle | Injection | Generation | Load |') + print('| No | Name | pu | Degree | MW | MVar | MW | Mvar | MW | MVar |') + for i in range(self.bus_num): + print(f'| %3g |{self.buses[i].name}| %8.3f | %8.3f | %8.3f | %8.3f | %8.3f | %8.3f |%8.3f | %8.3f |' % (i+1, self.buses[i].v_final, self.buses[i].theta_final, self.Pi[i], self.Qi[i], self.Pg[i], self.Qg[i], self.Pl[i], self.Ql[i])) + + print('----------------------------------------------------------------------------------------------------------') + print() + print("Network and losses:") + print() + print('| From | To | P | Q | From | To | P | Q | Branch Loss |') + print('| Bus | Bus | MW | MVar | Bus | Bus | MW | MVar | MW | MVar |') + for i in range(self.branches_num): + p = self.branches[i].fromBus.busIndex + q = self.branches[i].toBus.busIndex + print('| %5g | %5g | %9.2f | %9.2f | %5g | %5g | %9.2f | %9.2f | %9.2f | %9.2f |' % (p+1, q+1, self.Pij[p,q], self.Qij[p,q], q+1, p+1, self.Pij[q,p], self.Qij[q,p], self.Lpij[i], self.Lqij[i])) + print('----------------------------------------------------------------------------------------------------------') + print() + print('Total active power losses: {active_power:.2f}, Total reactive power losses: {reactive_power:.2f}'.format(active_power=sum(self.Lpij).item(), reactive_power=sum(self.Lqij).item())) + + def saveResults(self): + r""" + Save the result of power flow. + """ + + with open("pf_result.txt","w") as r: + r.write("Power Flow:") + r.write("\n") + r.write('| Bus | Bus | V | Angle | Injection | Generation | Load |\n') + r.write('| No | Name | pu | Degree | MW | MVar | MW | Mvar | MW | MVar |\n') + for i in range(self.bus_num): + r.write(f'| %3g |{self.buses[i].name}| %8.3f | %8.3f | %8.3f | %8.3f | %8.3f | %8.3f |%8.3f | %8.3f |\n' % (i+1, self.buses[i].v_final, self.buses[i].theta_final, self.Pi[i], self.Qi[i], self.Pg[i], self.Qg[i], self.Pl[i], self.Ql[i])) + + r.write('----------------------------------------------------------------------------------------------------------\n') + r.write("Network and losses:\n") + r.write('| From | To | P | Q | From | To | P | Q | Branch Loss |\n') + r.write('| Bus | Bus | MW | MVar | Bus | Bus | MW | MVar | MW | MVar |\n') + for i in range(self.branches_num): + p = self.branches[i].fromBus.busIndex + q = self.branches[i].toBus.busIndex + r.write('| %5g | %5g | %9.2f | %9.2f | %5g | %5g | %9.2f | %9.2f | %9.2f | %9.2f |\n' % (p+1, q+1, self.Pij[p,q], self.Qij[p,q], q+1, p+1, self.Pij[q,p], self.Qij[q,p], self.Lpij[i], self.Lqij[i])) + r.write('---------------------------------------------------------------------------------------------------------\n') + r.write('Total active power losses: {active_power:.2f}, Total reactive power losses: {reactive_power:.2f}\n'.format(active_power=sum(self.Lpij).item(), reactive_power=sum(self.Lqij).item())) + +def compute(A: np.ndarray, b: np.ndarray, depth: int, iterations: int, LR: float, gamma: Optional[float]=0) -> np.ndarray: + r""" + Solve the branchar equation Ax=b. + + Args: + A: Input matrix. + b: Input vector. + depth: Depth of ansatz circuit. + iterations: Number of iterations for optimization. + LR: Learning rate of optimizer. + gamma: Extra option to end optimization early if loss is below this value. Default to '0'. + + Returns: + Return the vector x that solves Ax=b. + + Raises: + ValueError: A is not a square matrix. + ValueError: dimension of A and b don't match. + ValueError: A is a singular matrix hence there's no unique solution. + """ + # check dimension of input and invertibility of A + if A.shape[0] != A.shape[1]: + raise ValueError("A is not a square matrix") + if len(A) != len(b): + raise ValueError("dimension of A and b don't match") + if np.linalg.det(A) == 0: + raise ValueError("A cannot be inverted") + + + b_rescale, num_qubits, list_A, coefficients_real, coefficients_img, original_dim, scale = _preprocess(A=A,b=b) + vqls = VQLS(num_qubits=num_qubits, A=list_A, coefficients_real=coefficients_real, coefficients_img=coefficients_img, b=b_rescale, depth=depth) + opt = paddle.optimizer.Adam(learning_rate=LR, parameters=vqls.parameters()) + + for itr in tqdm(range(1, iterations + 1)): + loss = vqls() + loss.backward() + opt.minimize(loss) + opt.clear_grad() + if itr % 10 == 0: + msg = ( + f"Iter:{itr:5d}, Loss:{loss.item(): 3.5f}" + ) + logging.info(msg) + if loss.item() Grid: + r""" + Transfer the data file to power grid. + + Args: + file_name: The file name of power system data. + + Returns: + Return the power grid. + """ + with open(file_name) as all_data: + data_read = csv.reader(all_data) + data = list(data_read) + + # Initialize a list that contain the positions of '-999' + cuts=[] + for i in range(len(data)): + if data[i-1][0][:4] == '-999': + cuts.append(i-1) + # Delete the last element + del(cuts[-1]) + + # Mva Base + Mva_base = float(data[0][0][31:36]) + + # Data preprocess + for i in range(2,cuts[0]): + data[i].append(data[i][0][5:17]) + data[i][0]=data[i][0][:5]+data[i][0][17:] + + # Extract buses data + bus = [] + bus_name = [] + bus_num = cuts[0] - 2 + for i in range(2,cuts[0]): + bus.append(data[i][0]) + bus_name.append(data[i][1]) + + bus_data = np.arange(bus_num*17,dtype=float).reshape(bus_num,17) + for i in range(bus_num): + bus_data[i] = np.fromstring(bus[i],dtype=float,sep=' ') + + + # Extract branches data + branch_num = cuts[1]-cuts[0]-2 + branch = [] + for i in range(cuts[0]+2,cuts[1]): + branch.append(data[i]) + + branch_data = np.arange(branch_num*21,dtype=float).reshape(branch_num,21) + for i in range(branch_num): + branch_data[i] = np.fromstring(branch[i][0],dtype=float,sep=' ') + + # Creating a list of buses + bus_list = [] + for i in range(bus_num): + n = bus_data[i] + bus_list.append(Bus(n,name=bus_name[i])) + + # Creating a list of branches + branch_list= [] + for i in range(branch_num): + b = branch_data[i] + branch_list.append(Branch(i+1,bus_list[int(b[0]-1)],bus_list[int(b[1]-1)],b)) + + grid = Grid(buses=bus_list, branches=branch_list, Mva_base=Mva_base) + return grid + +if __name__ == '__main__': + exit(0) \ No newline at end of file diff --git a/paddle_quantum/data_analysis/rand_num.py b/paddle_quantum/data_analysis/rand_num.py new file mode 100644 index 0000000..65fe8e7 --- /dev/null +++ b/paddle_quantum/data_analysis/rand_num.py @@ -0,0 +1,134 @@ +# !/usr/bin/env python3 +# Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +import os +import logging +import paddle_quantum as pq +from QCompute import BackendName +import paddle +from math import log + +r""" +Quantum random number generator. +""" + +def random_number_generation( + bit_len: int, + backend: str = 'local_baidu_sim2', + token: str = None, + extract: bool = False, + security: float = 1e-8, + min_entr_1: float = 0.9, + min_entr_2: float = 0.9, + log_path: str = None): + r""" + An encapsuled method of the random number generation, + referring to the paper https://arxiv.org/abs/1311.5322. + + Args: + bit_len: the count of numbers you needed + backend: the physical processor, including + 'local_baidu_sim2', + 'cloud_baidu_sim2_water', + 'cloud_baidu_sim2_earth', + 'cloud_baidu_sim2_thunder', + 'cloud_baidu_sim2_heaven', + 'cloud_baidu_sim2_wind', + 'cloud_baidu_sim2_lake', + 'cloud_aer_at_bd', + 'cloud_baidu_qpu_qian', + 'cloud_iopcas', + 'cloud_ionapm', + 'service_ubqc'. + token: user's token for cloud service + extract: whether to use extractor for post-process + security: security parameters + min_entr_1: the min-entropy of hardware 1 + min_entr_2: the min-entropy of hardware 2 + log_path: the save path of log file + """ + + # logger configuration + if not log_path: + log_path = './qrng.log' + logger = logging.Logger(name='logger_random_number_generation') + logger_file_handler = logging.FileHandler(log_path) + logger_file_handler.setFormatter(logging.Formatter(r'%(levelname)s %(asctime)s %(message)s')) + logger_file_handler.setLevel(logging.INFO) + logger.addHandler(logger_file_handler) + + # environment configuration + logger.info('QRNG Initializing...') + os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python' + pq.set_backend('quleaf') + pq.backend.quleaf.set_quleaf_backend(backend) + if backend not in (BackendName.LocalBaiduSim2, 'local_baidu_sim2'): + assert token, 'Cloud service needs token!' + pq.backend.quleaf.set_quleaf_token(token) + + # calculation + logger.info('Parameters:') + logger.info(f' Target bit length: {bit_len}') + logger.info(f' Backend: {backend}') + logger.info(f' Extractor state: {extract}') + bit_string = [] + if not extract: + cir = pq.ansatz.Circuit(num_qubits=1) + cir.h() + output_state = cir() + for _ in range(bit_len): + result = list(list(output_state.measure(shots=1,))[0]) + bit_string.append(int(result[0])) + + logger.info('Processing...') + logger.info(f'Output: {bit_string}') + return bit_string + + else: + logger.info(f' Security parameter: {security}') + logger.info(f' Min-entropy-1: {min_entr_1}') + logger.info(f' Min-entropy-2: {min_entr_2}') + logger.info('Computing raw bits needed') + shots = int((bit_len-1-2*log(security))/(min_entr_1 + min_entr_2 - 1)) # raw bit length needed + logger.info(f' Raw bit length: {shots}') + print('need raw bit length: {shots}') + + cir = pq.ansatz.Circuit(num_qubits=2) + cir.h() + output_state = cir() + + bit_string1 = [] + bit_string2 = [] + for _ in range(shots): + bit1, bit2 = list(list(output_state.measure(shots=1))[0]) + bit_string1.append(int(bit1[0])) + bit_string2.append(int(bit2[0])) + + logger.info(f' Bit string on hardware-1: {bit_string1}') + logger.info(f' Bit string on hardware-2: {bit_string2[:shots-1]}') + logger.info('Processing...') + + string_vec1 = paddle.to_tensor(bit_string1, dtype='float32') + string_vec2 = paddle.to_tensor(bit_string2[:shots-1], dtype='float32') + + topelitz = [] + for i in range(bit_len): + topelitz.append(string_vec2[bit_len-1-i:shots-1-i]) + topelitz = paddle.concat((paddle.to_tensor(topelitz), paddle.ones((bit_len, bit_len))), axis=1) + extract = paddle.matmul(string_vec1.unsqueeze(axis=0), topelitz.t()) + result = paddle.to_tensor(extract.squeeze() % 2, dtype='int64').tolist() + + logger.info(f'Output: {result}') + return result diff --git a/paddle_quantum/data_analysis/vqls.py b/paddle_quantum/data_analysis/vqls.py index ad2649a..8095377 100644 --- a/paddle_quantum/data_analysis/vqls.py +++ b/paddle_quantum/data_analysis/vqls.py @@ -148,8 +148,8 @@ def hadamard_overlap_test(phi: State, b: State, An: paddle.Tensor, Am: paddle.Te # Return the real part cir = Circuit(2*num_qubits + 1) cir.h([0]) - cir.control_oracle(An, range(num_qubits + 1), num_qubits=num_qubits+1) - cir.control_oracle(Am.conj().T, [0]+list(range(num_qubits+1, 2*num_qubits+1)), num_qubits=num_qubits+1) + cir.control_oracle(An, range(num_qubits + 1)) + cir.control_oracle(Am.conj().T, [0]+list(range(num_qubits+1, 2*num_qubits+1))) for idx in range(num_qubits): cir.cnot([idx+1, idx+1+num_qubits]) cir.h(range(num_qubits+1)) @@ -181,8 +181,8 @@ def hadamard_overlap_test(phi: State, b: State, An: paddle.Tensor, Am: paddle.Te # Return the imaginary part cir = Circuit(2*num_qubits + 1) cir.h([0]) - cir.control_oracle(An, range(num_qubits + 1), num_qubits=num_qubits+1) - cir.control_oracle(Am.conj().T, [0]+list(range(num_qubits+1, 2*num_qubits+1)), num_qubits=num_qubits+1) + cir.control_oracle(An, range(num_qubits + 1)) + cir.control_oracle(Am.conj().T, [0]+list(range(num_qubits+1, 2*num_qubits+1))) for idx in range(num_qubits): cir.cnot([idx+1,idx+1+num_qubits]) cir.rz(qubits_idx=0, param=-np.pi/2) diff --git a/paddle_quantum/data_analysis/vqr.py b/paddle_quantum/data_analysis/vqr.py index 4c0949e..7b0b0ef 100644 --- a/paddle_quantum/data_analysis/vqr.py +++ b/paddle_quantum/data_analysis/vqr.py @@ -43,8 +43,9 @@ import warnings # paddle libs import paddle import paddle_quantum as pq -from paddle_quantum.ansatz import Circuit -from paddle_quantum.state import State, _type_fetch, _type_transform +from ..ansatz import Circuit +from ..state import State +from ..intrinsic import _type_fetch, _type_transform from paddle_quantum.loss import Measure # format figures diff --git a/paddle_quantum/finance/__init__.py b/paddle_quantum/finance/__init__.py index 0d68e5a..790e061 100644 --- a/paddle_quantum/finance/__init__.py +++ b/paddle_quantum/finance/__init__.py @@ -23,4 +23,4 @@ from .finance import( portfolio_diversification_hamiltonian, arbitrage_opportunities_hamiltonian ) -from .pricing import qae_alg, qae_cir, qmc_alg, EuroOptionEstimator +from .pricing import qae_alg, qae_cir, qmc_alg, EuroOptionEstimator, CreditRiskAnalyzer diff --git a/paddle_quantum/finance/pricing.py b/paddle_quantum/finance/pricing.py index 4814205..2629862 100644 --- a/paddle_quantum/finance/pricing.py +++ b/paddle_quantum/finance/pricing.py @@ -14,23 +14,28 @@ # limitations under the License. r""" -Tools for QMC and option pricing. +Tools for QMC, option pricing and credit analysis. """ -import logging import math import numpy as np -import paddle +from scipy.special import erf, erfinv +import paddle from paddle_quantum.ansatz import Circuit -from paddle_quantum.intrinsic import get_dtype -from paddle_quantum.linalg import dagger +from paddle_quantum.intrinsic import get_dtype, _get_float_dtype +from paddle_quantum.linalg import dagger, NKron from paddle_quantum.loss import Measure from paddle_quantum.qinfo import grover_generation, qft_generation -from typing import Tuple, Callable, List +from functools import reduce +import operator + +import logging +from itertools import product +from typing import Tuple, Callable, List, Union, Optional -__all__ = ['qae_cir', 'qae_alg', 'qmc_alg', 'EuroOptionEstimator'] +__all__ = ['qae_cir', 'qae_alg', 'qmc_alg', 'EuroOptionEstimator', 'CreditRiskAnalyzer'] def qae_cir(oracle: paddle.Tensor, num_ancilla: int) -> Circuit: @@ -85,13 +90,14 @@ def qae_alg(oracle: paddle.Tensor, num_ancilla: int) -> Tuple[Circuit, paddle.Te """ complex_dtype = get_dtype() + float_dtype = _get_float_dtype(complex_dtype) op_M = Measure() aux_reg = list(range(num_ancilla)) oracle = oracle.cast(complex_dtype) cir = qae_cir(oracle, num_ancilla) state = cir() - measured_result = paddle.argmax(op_M(state, qubits_idx=aux_reg)) + measured_result = paddle.argmax(op_M(state, qubits_idx=aux_reg)).cast(float_dtype) estimated_sin = paddle.abs(paddle.sin(measured_result / (2 ** num_ancilla) * math.pi)) return cir, estimated_sin @@ -182,14 +188,12 @@ class EuroOptionEstimator(object): degree_of_estimation: degree of price estimation. Defaults to be ``5``. Note: - Option price is evaluated under - the `Black-Scholes-Merton model `_. - + Option price is evaluated under the [Black-Scholes-Merton model](https://en.wikipedia.org/wiki/Black%E2%80%93Scholes_model). """ def __init__(self, initial_price: float, strike_price: float, interest_rate: float, volatility: float, maturity_date: float, - degree_of_estimation: int = 5) -> None: + degree_of_estimation: Optional[int] = 5) -> None: logging.basicConfig( filename='./euro_pricing.log', @@ -251,7 +255,7 @@ class EuroOptionEstimator(object): f" retrieve estimation result {estimated_expectance:<.5f} from QMC algorithm.") return estimated_expectance - def plot(self, dpi: int = 100) -> None: + def plot(self, dpi: int = 200) -> None: r"""Plot the quantum circuit used in pricing. Args: @@ -262,3 +266,292 @@ class EuroOptionEstimator(object): raise UserWarning( "You need to estimate the option first before plotting the circuit.") self.__cir.plot(dpi=dpi) + + +def __u_t(list_output: np.ndarray) -> paddle.Tensor: + num_assets, size = list_output.shape + complex_dtype = get_dtype() + + def reflection(x: float) -> np.ndarray: + return np.array([[math.sqrt(1 - x), math.sqrt(x)], + [math.sqrt(x), -1 * math.sqrt(1 - x)]], dtype=complex_dtype) + + def ket_bra(j: int) -> np.ndarray: + mat = np.zeros([size, size]) + mat[j, j] += 1 + return mat + + mat = sum(np.kron(NKron(*[reflection(list_output[k, j]) for k in range(num_assets)]), + ket_bra(j)) for j in range(size)) + + return paddle.to_tensor(mat, dtype=complex_dtype) + +def __u_comp(lgd_list: List[int], y: float) -> paddle.Tensor: + num_assets = len(lgd_list) + dimension = 2 ** num_assets + complex_dtype = get_dtype() + + def threshold_matrix(x: float) -> np.ndarray: + x = np.binary_repr(x, width=num_assets) + loss = sum(int(x[i]) * lgd_list[i] for i in range(num_assets)) + return np.array([[1, 0], [0, -1]]) if loss > y else np.array([[0, 1], [1, 0]]) + + def ket_bra(j: int) -> np.ndarray: + mat = np.zeros([dimension, dimension]) + mat[j, j] += 1 + return mat + + mat = sum(np.kron(threshold_matrix(j), ket_bra(j)) for j in range(dimension)) + return paddle.to_tensor(mat, dtype=complex_dtype) + +def cra_oracle(prob: np.ndarray, param: np.ndarray, lgd: List[int], threshold: float) -> paddle.Tensor: + r"""Construct the oracle for credit risk analysis. + + Args: + prob: probability distribution of the latent random variable + param: parameters for Bernoulli variables of assets + lgd: losses given default (LGD) of assets + threshold: guessed VaR + + Returns: + The grover operator ready to be placed into QAE circuit. + + """ + num_sample, num_assets = len(prob), len(lgd) + Up = __u_p(prob) + Ut = __u_t(param) + A = Ut @ paddle.kron(paddle.eye(2 ** num_assets), Up) + Uc = __u_comp(lgd, threshold) + return paddle.kron(Uc, paddle.eye(num_sample)) @ paddle.kron(paddle.eye(2), A) + +class CreditRiskAnalyzer(object): + r"""Simulator for credit risk analysis (CRA) speeded up by quantum algorithms + + Args: + num_assets: number of assets. + base_default_prob: basic default probabilities of assets. + sensitivity: sensitivities of assets. + lgd: losses given default (LGD) of assets. + confidence_level: level of confidence of computed result. + degree_of_simulation: degree of simulation of CRA, determining the number of samples of the latent variable. Defaults to be ``4``. + even_sample: whether sample the latent variable by evenly-spaced probability. Defaults to be ``True``. + + Note: + CRA is simulated under the model given by [Tarca & Silvio](https://arxiv.org/abs/1412.1183). + That is, the latent random variable for the market is assumed to follow a standard normal distribution. + + + """ + def __init__(self, num_assets: int, base_default_prob: np.ndarray, sensitivity: np.ndarray, + lgd: np.ndarray, confidence_level: float, + degree_of_simulation: Optional[int] = 4, even_sample: Optional[bool] = True) -> None: + logging.basicConfig( + filename='./risk_analysis.log', + filemode='w', + format='%(asctime)s %(levelname)s %(message)s', + level=logging.INFO + ) + base_default_prob, sensitivity, lgd = np.array(base_default_prob), np.array(sensitivity), np.array(lgd) + self.__assert_and_log(num_assets, base_default_prob, sensitivity, lgd, confidence_level) + + # generate latent variable + num_samples = 2 ** degree_of_simulation + logging.info( + f"Taking {num_samples} samples from the normal distribution." + ) + outcome_z_list = self.__quantile_normal(np.linspace(1 / num_samples, 1, num_samples, endpoint=False)) \ + if even_sample else np.linspace(-2, 2, num_samples) + prob_z_list = self.__pdf_normal(outcome_z_list) + prob_z_list /= sum(prob_z_list) + + # generate Bernoulli variables + bernoulli_param_list = np.zeros([num_assets, num_samples]) + for k, j in product(range(num_assets), range(num_samples)): + bernoulli_param_list[k, j] = self.__prob_generation(outcome_z_list[j], base_default_prob[k], sensitivity[k]) + logging.info( + f"Bernoulli random variables of {num_assets} assets are created." + ) + + self.prob_z_list = prob_z_list + self.bernoulli_param_list = bernoulli_param_list + self.lgd = lgd + self.confidence_level = confidence_level + self.__log_exact() + + logging.info( + f"{1 + num_assets + degree_of_simulation + 6} qubits are required to execute quantum algorithms." + ) + + def estimate_var(self) -> float: + r"""Estimate VaR using the QAE algorithm. + + Returns: + the estimated Value at Risk of these credit assets + + """ + return self.__bisection_search() + + def __assert_and_log(self, num_assets: int, + base_default_prob: np.ndarray, sensitivity: np.ndarray, + lgd: np.ndarray, confidence_level: float) -> None: + r"""Assert and log the input data of this model. + """ + logging.info( + f"Received the following information of {num_assets} assets:" + ) + + np.set_printoptions(precision=4) + assert base_default_prob.size == num_assets, \ + f"The shape of input default_prob is incorrect: received {base_default_prob.shape}, expect {[num_assets]}." + logging.info( + f" list of default probabilities {base_default_prob}," + ) + assert all(base_default_prob >= 0) and all(base_default_prob <= 1), \ + "The data of input default_prob is incorrect: data must be within [0, 1]." + + assert sensitivity.size == num_assets, \ + f"The shape of input sensitivity is incorrect: received {sensitivity.shape}, expect {[num_assets]}." + logging.info( + f" list of sensitivities {sensitivity}," + ) + assert all(sensitivity >= 0) and all(sensitivity <= 1), \ + "The data of input sensitivity is incorrect: data must be within [0, 1]." + + assert lgd.size == num_assets, \ + f"The shape of input lgd is incorrect: received {lgd.shape}, expect {[num_assets]}." + logging.info( + f" list of losses given default {lgd}." + ) + + assert 0 <= confidence_level <= 1, \ + f"The level of confidence must be within [0, 1]: received {confidence_level :.2f}" + confidence_level = np.array(confidence_level) + logging.info( + f"Assets are analyzed with level of confidence {confidence_level * 100} %." + ) + + def __log_exact(self) -> None: + r"""Log the exact values of VaR and CVaR of these assets. + """ + num_assets = len(self.lgd) + logging.info( + f"Exact values of some properties of these {num_assets} assets:" + ) + + # generate random variable of total loss + default_prob_list = self.bernoulli_param_list @ self.prob_z_list + adhere_prob_list = (1 - self.bernoulli_param_list) @ self.prob_z_list + outcome_list = [np.binary_repr(x, num_assets) for x in range(2 ** num_assets)] + + value_list = [sum(int(outcome[i]) * self.lgd[i] for i in range(num_assets)) + for outcome in outcome_list] + prob_list = [reduce(operator.mul, [adhere_prob_list[i] if outcome[i] == '0' else default_prob_list[i] + for i in range(num_assets)], 1) for outcome in outcome_list] + logging.info( + f" expected loss: {np.dot(prob_list, value_list) :.5f}" + ) + + # sort two lists by value_list + prob_list = np.array([x for _, x in sorted(zip(value_list, prob_list))]) + value_list = np.array(sorted(value_list)) + cdf_list = self.__cdf_variable(prob_list, value_list, value_list) + + # compute the exact values + exact_var = min(value_list[cdf_list >= self.confidence_level]) + logging.info( + f" Value at Risk: {exact_var :.5f}" + ) + + prob_var = self.__cdf_variable(prob_list, value_list, float(exact_var)) + logging.info( + f" probability to be lower than VaR: {prob_var :.5f}" + ) + + # TODO: add the estimation of CVaR using quantum algorithms + # indices = value_list > exact_var + # exact_cvar = np.dot(prob_list[indices], value_list[indices]) / sum(prob_list[indices]) + # logging.info( + # f" Conditional Value at Risk: {exact_cvar :.5f}" + # ) + + def __pdf_normal(self, x: Union[float, np.ndarray]) -> Union[float, np.ndarray]: + r"""Apply the pdf of normal distribution. + """ + return 1 / math.sqrt(2 * math.pi) * np.exp(-0.5 * (x ** 2)) + + def __cdf_normal(self,x: Union[float, np.ndarray]) -> Union[float, np.ndarray]: + r"""Apply the cdf of normal distribution. + """ + return 0.5 * (1 + erf(x / math.sqrt(2))) + + def __quantile_normal(self,prob: Union[float, np.ndarray]) -> Union[float, np.ndarray]: + r"""Apply the quantile of normal distribution. + """ + return math.sqrt(2) * erfinv(2 * prob - 1) + + def __prob_generation(self, z: float, base_default_prob: float, sensitivity: float) -> float: + r""" Calculate the parameter of the Bernoulli variable of a given asset. + """ + rho, rho_0 = sensitivity, base_default_prob + return self.__cdf_normal((self.__quantile_normal(rho_0) - math.sqrt(rho) * z) / math.sqrt(1 - rho)) + + def __cdf_variable(self, distribution: np.ndarray, outcome: np.ndarray, + x: Union[float, np.ndarray]) -> Union[float, np.ndarray]: + r"""Calculate Pr(X <= x) given the description of X. + """ + return sum(distribution[outcome <= x]) if isinstance(x, float) else \ + np.array([sum(distribution[outcome <= i]) for i in x]) + + def __eval_prob(self, guess_var: int) -> float: + r"""Evaluate the probability that the total loss is less than ``guess_var`` + """ + logging.info( + f" Setting up Grover operator with guessed VaR {guess_var}" + ) + grover = cra_oracle(self.prob_z_list, self.bernoulli_param_list, self.lgd, guess_var) + + logging.info( + " Running QAE algorithm..." + ) + guess_amplitude = qae_alg(grover, 6)[1].item() + return guess_amplitude ** 2 + + def __bisection_search(self) -> float: + r"""Bisection method to search the minimum loss of assets that happens with probability greater than ``confidence_level``. + """ + confidence_level = self.confidence_level + print("-----------------------------------------------------------------------------------") + print(f"Begin bisection search for VaR with confidence level >= {confidence_level * 100:.1f}%.") + print("-----------------------------------------------------------------------------------") + print("Lower guess: level Middle guess: level Upper guess: level ") + + low_guess, up_guess = -1, math.floor(np.sum(np.abs(self.lgd)).item()) + low_prob, up_prob = 0, 1 + logging.info( + "Starting classical bisection search..." + ) + + while up_guess > low_guess + 1: + # extract middle index + mid_guess = int((low_guess + up_guess) // 2) + mid_prob = self.__eval_prob(mid_guess) + + # print message + print(" %2d : %.3f %2d : %.3f %2d : %.3f " % + (low_guess, low_prob, mid_guess, mid_prob, up_guess, up_prob)) + + # update lower or upper guess + if mid_prob < confidence_level: + low_guess, low_prob = mid_guess, mid_prob + else: + up_guess, up_prob = mid_guess, mid_prob + + final_guess, final_prob = [up_guess, up_prob] if mid_prob < confidence_level else \ + [mid_guess, mid_prob] + print("-----------------------------------------------------------------------------------") + print(f"Estimated VaR is {final_guess} with confidence level {final_prob * 100:.1f}%.") + print("-----------------------------------------------------------------------------------") + logging.info( + f"Receive VaR {final_guess} with confidence level {final_prob}." + ) + return final_guess diff --git a/paddle_quantum/gate/__init__.py b/paddle_quantum/gate/__init__.py index b35a55e..c39747d 100644 --- a/paddle_quantum/gate/__init__.py +++ b/paddle_quantum/gate/__init__.py @@ -20,17 +20,14 @@ The module of the quantum gates. from . import functional from .base import Gate, ParamGate from .clifford import Clifford, compose_clifford_circuit -from .single_qubit_gate import H, S, Sdg, T, Tdg, X, Y, Z, P, RX, RY, RZ, U3 -from .multi_qubit_gate import CNOT, CX, CY, CZ, SWAP -from .multi_qubit_gate import CP, CRX, CRY, CRZ, CU, RXX, RYY, RZZ -from .multi_qubit_gate import MS, CSWAP, Toffoli -from .multi_qubit_gate import UniversalTwoQubits, UniversalThreeQubits -from .custom import Oracle, ControlOracle -from .layer import SuperpositionLayer, WeakSuperpositionLayer -from .layer import LinearEntangledLayer, RealEntangledLayer, ComplexEntangledLayer -from .layer import RealBlockLayer, ComplexBlockLayer -from .layer import QAOALayer +from .custom import Oracle, ControlOracle, ParamOracle from .encoding import BasisEncoding from .encoding import AmplitudeEncoding from .encoding import AngleEncoding from .encoding import IQPEncoding +from .matrix import * +from .multi_qubit_gate import CNOT, CX, CY, CZ, SWAP +from .multi_qubit_gate import CP, CRX, CRY, CRZ, CU, RXX, RYY, RZZ +from .multi_qubit_gate import MS, CSWAP, Toffoli, CCX +from .multi_qubit_gate import UniversalTwoQubits, UniversalThreeQubits +from .single_qubit_gate import H, S, Sdg, T, Tdg, X, Y, Z, P, RX, RY, RZ, U3 diff --git a/paddle_quantum/gate/base.py b/paddle_quantum/gate/base.py index 9df7509..62cba82 100644 --- a/paddle_quantum/gate/base.py +++ b/paddle_quantum/gate/base.py @@ -17,61 +17,139 @@ r""" The source file of the basic class for the quantum gates. """ -import paddle -import paddle_quantum -from typing import Union, List, Iterable, Optional, Any +import copy +import math +import matplotlib +import warnings +from typing import Union, Iterable, Any, List, Callable -from paddle_quantum.gate.functional.single_qubit_gate import x -from ..intrinsic import _get_float_dtype -from math import pi +import paddle +import paddle_quantum as pq +from .functional.base import simulation from .functional.visual import _base_gate_display, _base_param_gate_display -import matplotlib +from ..backend import Backend +from ..base import get_backend, get_dtype, Operator +from ..channel import Channel +from ..channel.base import _kraus_to_choi, _kraus_to_stinespring +from ..intrinsic import _get_float_dtype, _format_param_shape, _format_qubits_idx + -class Gate(paddle_quantum.Operator): +class Gate(Channel): r"""Base class for quantum gates. Args: - depth: Number of layers. Defaults to 1. - backend: Backend on which the gates are executed. Defaults to None. - dtype: Type of data. Defaults to None. + matrix: the matrix of this gate. Defaults to ``None`` i.e. not specified. + qubits_idx: indices of the qubits on which this gate acts on. Defaults to ``None``. + i.e. list(range(num_acted_qubits)). + depth: Number of layers. Defaults to ``1``. + gate_info: information of this gate that will be placed into the gate history or plotted by a Circuit. + Defaults to ``None``. + num_qubits: total number of qubits. Defaults to ``None``. + check_legality: whether check the completeness of the matrix if provided. Defaults to ``True``. + num_acted_qubits: the number of qubits that this gate acts on. Defaults to ``None``. + backend: Backend on which the gates are executed. Defaults to ``None``. + dtype: Type of data. Defaults to ``None``. name_scope: Prefix name used by the layer to name parameters. If prefix is "my_layer", parameter name in - MyLayer can be "my_layer_0.w_n", where "w" is the parameter base name and "n" is an unique suffix - auto-generated. If ``None``, prefix name will be snake cased class name. Defaults to ``None``. + MyLayer can be "my_layer_0.w_n", where "w" is the parameter base name and "n" is an unique suffix + auto-generated. If None, prefix name will be snake cased class name. Defaults to ``None``. """ + def __init__( - self, depth: int = 1, backend: paddle_quantum.Backend = None, dtype: str = None, name_scope: str = None + self, matrix: paddle.Tensor = None, qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] = None, + depth: int = 1, gate_info: dict = None, num_qubits: int = None, + check_legality: bool = True, num_acted_qubits: int = None, + backend: pq.Backend = None, dtype: str = None, name_scope: str = None ): - super().__init__(backend, dtype, name_scope) + Operator.__init__(self, backend=backend, + dtype=dtype, name_scope=name_scope) + self.type_repr = 'Gate' + assert matrix is not None or num_acted_qubits is not None, ( + "Received None for matrix and num_acted_qubits: " + "either one of them must be specified to initialize a Gate instance.") + if matrix is not None: + num_acted_qubits = self.__gate_init(matrix, check_legality) + if qubits_idx is None: + self.qubits_idx = [0] if num_acted_qubits == 1 else [ + list(range(num_acted_qubits))] + else: + self.qubits_idx = _format_qubits_idx( + qubits_idx, num_qubits, num_acted_qubits) + self.num_acted_qubits = num_acted_qubits + self.num_qubits = num_qubits self.depth = depth - self.gate_info = { - 'gatename': None, - 'texname': None, - 'plot_width': None, + default_gate_info = { + 'gatename': 'O', + 'texname': r'$O$', + 'plot_width': 0.9, } - - def forward(self, *inputs, **kwargs): - raise NotImplementedError + if gate_info is not None: + default_gate_info.update(gate_info) + self.gate_info = default_gate_info + self.__matrix = matrix if matrix is None else matrix.cast(self.dtype) + + def __gate_init(self, gate_matrix: paddle.Tensor, check_legality: bool) -> int: + r"""Initialize channel for type_repr as ``'Gate'`` + """ + complex_dtype = self.dtype + gate_matrix = gate_matrix.cast(complex_dtype) + + if not isinstance(gate_matrix, paddle.Tensor): + raise TypeError( + f"Unexpected data type for quantum gate: expected paddle.Tensor, received {type(gate_matrix)}") + + dimension = gate_matrix.shape[0] + + if check_legality: + err = paddle.norm( + paddle.abs(gate_matrix @ paddle.conj(gate_matrix.T) - + paddle.cast(paddle.eye(dimension), complex_dtype)) + ).item() + if err > min(1e-6 * dimension, 0.01): + warnings.warn( + f"\nThe input gate matrix may not be a unitary: norm(U * U^d - I) = {err}.", UserWarning) + num_acted_qubits = int(math.log2(dimension)) + + self.__kraus_repr = [gate_matrix] + return num_acted_qubits + + @property + def matrix(self) -> paddle.Tensor: + r"""Unitary matrix of this gate + + Raises: + ValueError: Need to specify the matrix form in this Gate instance. + + """ + if self.__matrix is None: + raise ValueError( + "Need to specify the matrix form in this Gate instance.") + return self.__matrix - def __setattr__(self, name, value): - super().__setattr__(name, value) - if isinstance(value, paddle_quantum.Operator): - if value.backend is None: - value.backend = paddle_quantum.get_backend() if self.backend is None else self.backend - if value.dtype is None: - value.dtype = paddle_quantum.get_dtype() if self.dtype is None else self.dtype + @property + def choi_repr(self) -> paddle.Tensor: + return _kraus_to_choi(self.kraus_repr) + + @property + def kraus_repr(self) -> List[paddle.Tensor]: + return [self.matrix] + + @property + def stinespring_repr(self) -> paddle.Tensor: + return _kraus_to_stinespring(self.kraus_repr) def gate_history_generation(self) -> None: r""" determine self.gate_history - + """ gate_history = [] for _ in range(self.depth): for qubit_idx in self.qubits_idx: - gate_info = {'gate': self.gate_info['gatename'], 'which_qubits': qubit_idx, 'theta': None} + gate_info = { + 'gate': self.gate_info['gatename'], 'which_qubits': qubit_idx, 'theta': None} gate_history.append(gate_info) self.gate_history = gate_history - - def set_gate_info(self, **kwargs: Any) -> None: + + def set_gate_info(self, **kwargs: Any) -> None: r'''the interface to set `self.gate_info` Args: @@ -79,70 +157,166 @@ class Gate(paddle_quantum.Operator): ''' self.gate_info.update(kwargs) - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float) -> float: r'''The display function called by circuit instance when plotting. Args: ax: the ``matplotlib.axes.Axes`` instance x: the start horizontal position - + Returns: the total width occupied - + Note: Users could overload this function for custom display. ''' return _base_gate_display(self, ax, x) + def _single_qubit_combine_with_threshold6(self, state: pq.State, matrices: List[paddle.Tensor]) -> pq.State: + r""" + Combines single-qubit gates in a circuit with 6-qubit threshold and updates the state accordingly. + + Args: + state: The current state, represented as a `pq.State` object. + matrices: A list of `paddle.Tensor` objects representing the single-qubit gates to be combined. + + Returns: + The updated state after the single-qubit gates have been combined, represented as a `pq.State` object. + """ + threshold_qubits = 6 + tensor_times = len(self.qubits_idx) // threshold_qubits + tensor_left = len(self.qubits_idx) % threshold_qubits + for threshold_idx in range(tensor_times): + idx_st = threshold_idx * threshold_qubits + idx_end = (threshold_idx + 1) * threshold_qubits + state = simulation( + state, matrices[idx_st:idx_end], self.qubits_idx[idx_st:idx_end]) + if tensor_left > 0: + idx_st = tensor_times * threshold_qubits + state = simulation( + state, matrices[idx_st:], self.qubits_idx[idx_st:]) + return state + + def forward(self, state: pq.State) -> pq.State: + for _ in range(self.depth): + matrices = [self.matrix for _ in self.qubits_idx] + + if self.num_acted_qubits == 1: + state = self._single_qubit_combine_with_threshold6( + state=state, matrices=matrices) + else: + for param_idx, qubit_idx in enumerate(self.qubits_idx): + state = simulation( + state, matrices[param_idx:param_idx + 1], qubit_idx) + return state + class ParamGate(Gate): - r""" Base class for quantum parameterized gates - + r"""Base class for quantum parameterized gates. + + Args: + generator: function that generates the unitary matrix of this gate. + param: input parameters of quantum parameterized gates. Defaults to ``None`` i.e. randomized. + qubits_idx: indices of the qubits on which this gate acts on. Defaults to ``None``. + i.e. list(range(num_acted_qubits)). + depth: number of layers. Defaults to ``1``. + num_acted_param: the number of parameters required for a single operation. + param_sharing: whether all operations are shared by the same parameter set. + gate_info: information of this gate that will be placed into the gate history or plotted by a Circuit. + Defaults to ``None``. + num_qubits: total number of qubits. Defaults to ``None``. + check_legality: whether check the completeness of the matrix if provided. Defaults to ``True``. + num_acted_qubits: the number of qubits that this gate acts on. Defaults to ``None``. + backend: Backend on which the gates are executed. Defaults to ``None``. + dtype: Type of data. Defaults to ``None``. + name_scope: Prefix name used by the layer to name parameters. If prefix is "my_layer", parameter name in + MyLayer can be "my_layer_0.w_n", where "w" is the parameter base name and "n" is an unique suffix + auto-generated. If None, prefix name will be snake cased class name. Defaults to ``None``. """ + + def __init__( + self, generator: Callable[[paddle.Tensor], paddle.Tensor], + param: Union[paddle.Tensor, float, List[float]] = None, + depth: int = 1, num_acted_param: int = 1, param_sharing: bool = False, + qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] = None, gate_info: dict = None, + num_qubits: int = None, check_legality: bool = True, num_acted_qubits: int = None, + backend: pq.Backend = None, dtype: str = None, name_scope: str = None + ): + # if num_acted_qubits is unknown, generate an example matrix to run Gate.__init__ + ex_matrix = generator(paddle.randn( + [num_acted_param], dtype)) if num_acted_qubits is None else None + + super().__init__(ex_matrix, qubits_idx, depth, gate_info, num_qubits, check_legality, num_acted_qubits, + backend=backend, dtype=dtype, name_scope=name_scope) + + param_shape = _format_param_shape( + self.depth, self.qubits_idx, num_acted_param, param_sharing) + self.param_sharing = param_sharing + self.theta_generation(param, param_shape) + self.__generator = generator + + @property + def matrix(self) -> Union[paddle.Tensor, List[paddle.Tensor]]: + matrices_list = [] + for depth_idx in range(self.depth): + if self.param_sharing: + matrices_list.append(self.__generator(self.theta[depth_idx])) + else: + matrices_list.extend( + self.__generator(self.theta[depth_idx, param_idx]) + for param_idx, _ in enumerate(self.qubits_idx) + ) + return matrices_list[0] if len(matrices_list) == 1 else matrices_list + + @property + def kraus_repr(self) -> List[paddle.Tensor]: + matrix = self.matrix + assert not isinstance(matrix, List), \ + f"Cannot generate Kraus representation for multiple matrices: received number of matrices {len(matrix)}" + return [matrix] + def theta_generation(self, param: Union[paddle.Tensor, float, List[float]], param_shape: List[int]) -> None: - """ determine self.theta, and create parameter if necessary + r""" determine self.theta, and create parameter if necessary Args: param: input theta param_shape: shape for theta - + Note: In the following cases ``param`` will be transformed to a parameter: - - ``param`` is None + - ``param`` is ``None`` In the following cases ``param`` will be added to the parameter list: - ``param`` is a ParamBase In the following cases ``param`` will keep unchanged: - ``param`` is a Tensor but not a ParamBase - ``param`` is a float or a list of floats - """ - float_dtype = _get_float_dtype(self.dtype) - + if param is None: theta = self.create_parameter( shape=param_shape, dtype=float_dtype, - default_initializer=paddle.nn.initializer.Uniform(low=0, high=2 * pi) + default_initializer=paddle.nn.initializer.Uniform( + low=0, high=2 * math.pi) ) self.add_parameter('theta', theta) - elif isinstance(param, paddle.fluid.framework.ParamBase): - assert param.shape == param_shape, f"received: {str(param.shape)} expect: {param_shape}" + assert param.shape == param_shape, \ + f"Shape assertion failed for input parameter: receive {str(param.shape)}, expect {param_shape}" + assert param.dtype == (paddle.float32 if float_dtype == 'float32' else paddle.float64), \ + f"Dtype assertion failed for input parameter: receive {param.dtype}, expect {float_dtype}" self.add_parameter('theta', param) - elif isinstance(param, paddle.Tensor): - param = param.reshape(param_shape) + param = param.reshape(param_shape).cast(float_dtype) self.theta = param - elif isinstance(param, (int, float)): self.theta = paddle.ones(param_shape, dtype=float_dtype) * param - - else: # when param is a list of float - self.theta = paddle.to_tensor(param, dtype=float_dtype).reshape(param_shape) + else: # when param is a list of float + self.theta = paddle.to_tensor( + param, dtype=float_dtype).reshape(param_shape) def gate_history_generation(self) -> None: r""" determine self.gate_history when gate is parameterized - """ gate_history = [] for depth_idx in range(self.depth): @@ -151,21 +325,44 @@ class ParamGate(Gate): param = self.theta[depth_idx] else: param = self.theta[depth_idx][idx] - gate_info = {'gate': self.gate_info['gatename'], 'which_qubits': qubit_idx, 'theta': param} + gate_info = { + 'gate': self.gate_info['gatename'], 'which_qubits': qubit_idx, 'theta': param} gate_history.append(gate_info) self.gate_history = gate_history - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: r'''The display function called by circuit instance when plotting. Args: ax: the ``matplotlib.axes.Axes`` instance x: the start horizontal position - + Returns: the total width occupied - + Note: Users could overload this function for custom display. ''' - return _base_param_gate_display(self, ax, x) \ No newline at end of file + return _base_param_gate_display(self, ax, x) + + def forward(self, state: pq.State) -> pq.State: + for depth_idx in range(self.depth): + param_matrices = [] + if self.param_sharing: + param_matrix = self.__generator(self.theta[depth_idx]) + param_matrix = paddle.cast(param_matrix, self.dtype) + param_matrices = [param_matrix for _ in self.qubits_idx] + else: + for param_idx in range(len(self.qubits_idx)): + param_matrix = self.__generator( + self.theta[depth_idx, param_idx]) + param_matrix = paddle.cast(param_matrix, self.dtype) + param_matrices.append(param_matrix) + if self.num_acted_qubits == 1: + state = self._single_qubit_combine_with_threshold6( + state=state, matrices=param_matrices) + else: + for param_idx, qubit_idx in enumerate(self.qubits_idx): + state = simulation( + state, param_matrices[param_idx:param_idx + 1], qubit_idx) + return state diff --git a/paddle_quantum/gate/custom.py b/paddle_quantum/gate/custom.py index c562a4d..912c7f5 100644 --- a/paddle_quantum/gate/custom.py +++ b/paddle_quantum/gate/custom.py @@ -20,14 +20,14 @@ The source file of the oracle class and the control oracle class. import math import matplotlib import paddle +from typing import Callable, List, Union, Iterable import warnings import paddle_quantum as pq from . import functional -from .base import Gate -from ..intrinsic import _format_qubits_idx -from typing import Union, Iterable +from .base import Gate, ParamGate from .functional.visual import _c_oracle_like_display, _oracle_like_display +from ..intrinsic import _format_qubits_idx class Oracle(Gate): @@ -40,36 +40,10 @@ class Oracle(Gate): depth: Number of layers. Defaults to ``1``. """ def __init__( - self, oracle: paddle.Tensor, qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int], + self, oracle: paddle.Tensor, qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] = None, num_qubits: int = None, depth: int = 1, gate_info: dict = None ): - super().__init__(depth) - complex_dtype = pq.get_dtype() - oracle = oracle.cast(complex_dtype) - - dimension = oracle.shape[0] - err = paddle.norm(paddle.abs(oracle @ paddle.conj(oracle.T) - paddle.cast(paddle.eye(dimension), complex_dtype))).item() - if err > min(1e-6 * dimension, 0.01): - warnings.warn( - f"\nThe input oracle may not be a unitary: norm(U * U^d - I) = {err}.", UserWarning) - - num_acted_qubits = int(math.log2(dimension)) - self.oracle = oracle - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits) - - self.gate_info = { - 'gatename': 'O', - 'texname': r'$O$', - 'plot_width': 0.6, - } - if gate_info: - self.gate_info.update(gate_info) - - def forward(self, state: pq.State) -> pq.State: - for _ in range(self.depth): - for qubits_idx in self.qubits_idx: - state = functional.oracle(state, self.oracle, qubits_idx, self.backend) - return state + super().__init__(oracle, qubits_idx, depth, gate_info, num_qubits) def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: return _oracle_like_display(self, ax, x) @@ -88,38 +62,47 @@ class ControlOracle(Gate): self, oracle: paddle.Tensor, qubits_idx: Union[Iterable[Iterable[int]], Iterable[int]], num_qubits: int = None, depth: int = 1, gate_info: dict = None ) -> None: - super().__init__(depth) - complex_dtype = pq.get_dtype() - oracle = oracle.cast(complex_dtype) + complex_dtype = oracle.dtype dimension = oracle.shape[0] - err = paddle.norm(paddle.abs(oracle @ paddle.conj(oracle.T) - paddle.cast(paddle.eye(dimension), complex_dtype))).item() - if err > min(1e-6 * dimension, 0.01): - warnings.warn( - f"\nThe input oracle may not be a unitary: norm(U * U^d - I) = {err}.", UserWarning) - - num_acted_qubits = int(math.log2(dimension)) oracle = ( - paddle.kron(paddle.to_tensor([[1.0, 0], [0, 0]], dtype=complex_dtype), paddle.eye(2 ** num_acted_qubits)) + + paddle.kron(paddle.to_tensor([[1.0, 0], [0, 0]], dtype=complex_dtype), paddle.eye(dimension).cast(complex_dtype)) + paddle.kron(paddle.to_tensor([[0.0, 0], [0, 1]], dtype=complex_dtype), oracle) ) - num_acted_qubits += 1 - self.oracle = oracle - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits) - self.gate_info = { + default_gate_info = { 'gatename': 'cO', 'texname': r'$O$', 'plot_width': 0.6, } - if gate_info: - self.gate_info.update(gate_info) - - def forward(self, state: pq.State) -> pq.State: - for _ in range(self.depth): - for qubits_idx in self.qubits_idx: - state = functional.oracle(state, self.oracle, qubits_idx, self.backend) - return state + if gate_info is not None: + default_gate_info.update(gate_info) + super().__init__(oracle, qubits_idx, depth, gate_info, num_qubits) def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: return _c_oracle_like_display(self, ax, x) + + +class ParamOracle(ParamGate): + """An parameterized oracle as a gate + + Args: + generator: function that generates the oracle. + param: input parameters of quantum parameterized gates. Defaults to ``None`` i.e. randomized. + qubits_idx: indices of the qubits on which this gate acts on. Defaults to ``None`` i.e. list(range(num_qubits)). + depth: number of layers. Defaults to ``1``. + num_acted_param: the number of parameters required for a single operation. + param_sharing: whether all operations are shared by the same parameter set. + gate_info: information of this gate that will be placed into the gate history or plotted by a Circuit. + Defaults to ``None``. + num_qubits: total number of qubits. Defaults to ``None``. + + """ + def __init__( + self, generator: Callable[[paddle.Tensor], paddle.Tensor], + param: Union[paddle.Tensor, float, List[float]] = None, + depth: int = 1, num_acted_param: int = 1, param_sharing: bool = False, + qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int] = None, + gate_info: dict = None, num_qubits: int = None + ): + super().__init__(generator, param, depth, num_acted_param, param_sharing, qubits_idx, gate_info, num_qubits) diff --git a/paddle_quantum/gate/encoding.py b/paddle_quantum/gate/encoding.py index 2ff2820..2ec0b0d 100644 --- a/paddle_quantum/gate/encoding.py +++ b/paddle_quantum/gate/encoding.py @@ -18,14 +18,15 @@ The source file of the classes for quantum encoding. """ import paddle -import paddle_quantum -from paddle_quantum.gate import functional -from .base import Gate -from paddle_quantum.intrinsic import _get_float_dtype, _format_qubits_idx +import paddle_quantum as pq +from .functional.base import simulation +from .matrix import x_gate, h_gate, cnot_gate, rx_gate, ry_gate, rz_gate +from ..base import Operator +from ..intrinsic import _get_float_dtype, _format_qubits_idx from typing import Iterable, Optional, Union -class BasisEncoding(Gate): +class BasisEncoding(Operator): r"""Basis encoding gate for encoding input classical data into quantum states. In basis encoding, the input classical data can only consist of 0's and 1's. If the input data are 1101, @@ -36,34 +37,40 @@ class BasisEncoding(Gate): qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'full'``. num_qubits: Total number of qubits. Defaults to ``None``. """ + + __x = x_gate('complex128') + def __init__( self, qubits_idx: Union[Iterable[int], int, str] = 'full', num_qubits: int = None ) -> None: super().__init__() self.num_qubits = num_qubits self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.gate_info['gatename'] = 'BasisEnc' + self.gate_info = { + 'gatename': 'BasisEnc', + 'texname': r'$\text{BasisEnc}$', + 'plot_width': 1.5, + } - def forward(self, feature: paddle.Tensor, state: 'paddle_quantum.State' = None) -> 'paddle_quantum.State': + def forward(self, feature: paddle.Tensor, state: pq.State = None) -> pq.State: + x = BasisEncoding.__x.cast(self.dtype) if state is None: - state = paddle_quantum.state.zero_state(self.num_qubits) + state = pq.state.zero_state(self.num_qubits) feature = paddle.cast(feature, 'int32') gate_history = [] for idx, element in enumerate(feature): if element: - state = functional.x(state, self.qubits_idx[idx], self.dtype, self.backend) + state = simulation(state, [x], self.qubits_idx[idx]) gate_history.append({'gate': 'x', 'which_qubits': self.qubits_idx[idx], 'theta': None}) self.gate_history = gate_history return state def gate_history_generation(self) -> None: if self.gate_history is None: - raise RuntimeError("you must forward the encoding to receive the gate history") - pass - + raise RuntimeError("you must forward the encoding to receive the gate history") -class AmplitudeEncoding(Gate): +class AmplitudeEncoding(Operator): r"""Amplitude encoding gate for encoding input classical data into quantum states. Args: @@ -78,9 +85,13 @@ class AmplitudeEncoding(Gate): super().__init__() self.num_qubits = num_qubits self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.gate_info['gatename'] = 'AmpEnc' + self.gate_info = { + 'gatename': 'AmpEnc', + 'texname': r'$\text{AmpEnc}$', + 'plot_width': 1.5, + } - def forward(self, feature: paddle.Tensor) -> 'paddle_quantum.State': + def forward(self, feature: paddle.Tensor) -> pq.State: def calc_location(location_of_bits_list): if len(location_of_bits_list) <= 1: result_list = [0, location_of_bits_list[0]] @@ -88,7 +99,7 @@ class AmplitudeEncoding(Gate): current_tmp = location_of_bits_list[0] inner_location_of_qubits_list = calc_location(location_of_bits_list[1:]) current_list_len = len(inner_location_of_qubits_list) - for each in range(0, current_list_len): + for each in range(current_list_len): inner_location_of_qubits_list.append(inner_location_of_qubits_list[each] + current_tmp) result_list = inner_location_of_qubits_list return result_list @@ -105,7 +116,7 @@ class AmplitudeEncoding(Gate): # Get the specific position of the code, denoted by sequence number (list) location_of_qubits_list = encoding_location_list(self.qubits_idx) # Classical data preprocessing - feature = paddle.cast(feature, _get_float_dtype(paddle_quantum.get_dtype())) + feature = paddle.cast(feature, _get_float_dtype(pq.get_dtype())) feature = paddle.flatten(feature) length = paddle.norm(feature, p=2) # Normalization @@ -113,19 +124,23 @@ class AmplitudeEncoding(Gate): # Create a quantum state with all zero amplitudes data = paddle.zeros((2 ** self.num_qubits,), feature.dtype) # The value of the encoded amplitude is filled into the specified qubits - for idx in range(0, len(feature)): + for idx in range(len(feature)): data[location_of_qubits_list[idx]] = feature[idx] - data = paddle.cast(data, dtype=paddle_quantum.get_dtype()) - if self.backend == paddle_quantum.Backend.DensityMatrix: + data = paddle.cast(data, dtype=pq.get_dtype()) + if self.backend == pq.Backend.DensityMatrix: data = paddle.unsqueeze(data, axis=1) - data = paddle.matmul(data, paddle_quantum.linalg.dagger(data)) - elif self.backend != paddle_quantum.Backend.StateVector: + data = paddle.matmul(data, pq.linalg.dagger(data)) + elif self.backend != pq.Backend.StateVector: raise ValueError("the mode should be state_vector or density_matrix") - encoding_state = paddle_quantum.state.to_state(data, self.num_qubits) + encoding_state = pq.state.to_state(data, self.num_qubits) return encoding_state + + def gate_history_generation(self) -> None: + if self.gate_history is None: + raise RuntimeError("you must forward the encoding to receive the gate history") -class AngleEncoding(Gate): +class AngleEncoding(Operator): r"""Angle encoding gate for encoding input classical data into quantum states. Args: @@ -146,34 +161,34 @@ class AngleEncoding(Gate): self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) if encoding_gate == 'rx': - self.encoding_gate = functional.rx + self.encoding_gate = rx_gate elif encoding_gate == 'ry': - self.encoding_gate = functional.ry + self.encoding_gate = ry_gate elif encoding_gate == 'rz': - self.encoding_gate = functional.rz + self.encoding_gate = rz_gate self.encoding_gate_name = encoding_gate - feature = paddle.cast(feature, _get_float_dtype(paddle_quantum.get_dtype())) + feature = paddle.cast(feature, _get_float_dtype(pq.get_dtype())) feature = paddle.flatten(feature) self.feature = feature - self.gate_info['gatename'] = 'AngleEnc' + self.gate_info = { + 'gatename': 'AngleEnc', + 'texname': r'$\text{AngleEnc}$', + 'plot_width': 1.5, + } def forward( - self, state: 'paddle_quantum.State' = None, invert: bool = False - ) -> 'paddle_quantum.State': + self, state: pq.State = None, invert: bool = False + ) -> pq.State: gate_history = [] if state is None: - state = paddle_quantum.state.zero_state(self.num_qubits) - if invert: - feature = -1 * self.feature - else: - feature = self.feature + state = pq.state.zero_state(self.num_qubits) + feature = -1 * self.feature if invert else self.feature + for idx, element in enumerate(feature): - state = self.encoding_gate( - state, element[0], self.qubits_idx[idx], - dtype=self.dtype, backend=self.backend - ) + param_matrix = self.encoding_gate(element[0]) + state = simulation(state, [param_matrix], self.qubits_idx[idx]) gate_history.append({'gate': self.encoding_gate_name, 'which_qubits': self.qubits_idx[idx], 'theta': element[0]}) self.gate_history = gate_history return state @@ -181,10 +196,9 @@ class AngleEncoding(Gate): def gate_history_generation(self) -> None: if self.gate_history is None: raise RuntimeError("you must forward the encoding to receive the gate history") - pass -class IQPEncoding(Gate): +class IQPEncoding(Operator): r"""IQP style encoding gate for encoding input classical data into quantum states. Args: @@ -193,75 +207,88 @@ class IQPEncoding(Gate): num_qubits: Total number of qubits. Defaults to ``None``. num_repeat: Number of encoding layers. Defaults to ``1``. """ + + __cnot = cnot_gate('complex128') + __h = h_gate('complex128') + def __init__( self, feature: paddle.Tensor, qubits_idx: Optional[Iterable[Iterable[int]]] = None, num_qubits: Optional[int] = None, num_repeat: Optional[int] = 1, ) -> None: super().__init__() - self.qubits_idx = [list(idx) for idx in qubits_idx] + self.num_repeat = num_repeat self.num_qubits = num_qubits if feature is not None: - feature = paddle.cast(feature, _get_float_dtype(paddle_quantum.get_dtype())) + feature = paddle.cast(feature, _get_float_dtype(pq.get_dtype())) feature = paddle.flatten(feature) self.feature = feature - - self.gate_info['gatename'] = 'IQPEnc' + + if qubits_idx is None: + assert num_qubits is not None, \ + f"Number of qubits must be known to create default patterns: received {num_qubits}" + qubits_idx = [] + for idx0 in range(num_qubits): + qubits_idx.extend([idx0, idx1] for idx1 in range(idx0 + 1, num_qubits)) + + self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) + + self.gate_info = { + 'gatename': 'IQPEnc', + 'texname': r'$\text{IQPEnc}$', + 'plot_width': 1.5, + } def forward( - self, state: paddle_quantum.State = None, invert: Optional[bool] = False - ) -> paddle_quantum.State: + self, state: pq.State = None, invert: Optional[bool] = False + ) -> pq.State: gate_history = [] + h, cnot = IQPEncoding.__h.cast(self.dtype), IQPEncoding.__cnot.cast(self.dtype) if state is None: - state = paddle_quantum.state.zero_state(self.num_qubits) - for _ in range(0, self.num_repeat): + state = pq.state.zero_state(self.num_qubits) + for _ in range(self.num_repeat): if invert: for qubits_idx in self.qubits_idx: - state = functional.cnot(state, qubits_idx, dtype=self.dtype, backend=self.backend) - state = functional.rz( - state, -self.feature[qubits_idx[0]] * self.feature[qubits_idx[1]], qubits_idx[1], - dtype=self.dtype, backend=self.backend - ) - state = functional.cnot(state, qubits_idx, dtype=self.dtype, backend=self.backend) - - gate_history.append({'gate': 'cnot', 'which_qubits': qubits_idx, 'theta': None}) - gate_history.append({'gate': 'rz', 'which_qubits': qubits_idx[1], - 'theta': -self.feature[qubits_idx[0]] * self.feature[qubits_idx[1]]}) - gate_history.append({'gate': 'cnot', 'which_qubits': qubits_idx, 'theta': None}) + rz_param = -self.feature[qubits_idx[0]] * self.feature[qubits_idx[1]] + state = simulation(state, [cnot], qubits_idx) + state = simulation(state, [rz_gate(rz_param)], qubits_idx[1]) + state = simulation(state, [cnot], qubits_idx) + + gate_history.extend([ + {'gate': 'cnot', 'which_qubits': qubits_idx, 'theta': None}, + {'gate': 'rz', 'which_qubits': qubits_idx[1], 'theta': rz_param}, + {'gate': 'cnot', 'which_qubits': qubits_idx, 'theta': None}]) - for idx in range(0, self.feature.size): - state = functional.rz(state, -self.feature[idx], idx, dtype=self.dtype, backend=self.backend) + for idx in range(self.feature.size): + state = simulation(state, [rz_gate(-self.feature[idx])], idx) gate_history.append({'gate': 'rz', 'which_qubits': idx, 'theta': -self.feature[idx]}) - - for idx in range(0, self.feature.size): - state = functional.h(state, idx, dtype=self.dtype, backend=self.backend) + + for idx in range(self.feature.size): + state = simulation(state, [h], idx) gate_history.append({'gate': 'h', 'which_qubits': idx, 'theta': None}) else: - for idx in range(0, self.feature.size): - state = functional.h(state, idx, dtype=self.dtype, backend=self.backend) + for idx in range(self.feature.size): + state = simulation(state, [h], idx) gate_history.append({'gate': 'h', 'which_qubits': idx, 'theta': None}) - - for idx in range(0, self.feature.size): - state = functional.rz(state, self.feature[idx], idx, dtype=self.dtype, backend=self.backend) + + for idx in range(self.feature.size): + state = simulation(state, [rz_gate(self.feature[idx])], idx) gate_history.append({'gate': 'rz', 'which_qubits': idx, 'theta': self.feature[idx]}) - + for qubits_idx in self.qubits_idx: - state = functional.cnot(state, qubits_idx, dtype=self.dtype, backend=self.backend) - state = functional.rz( - state, self.feature[qubits_idx[0]] * self.feature[qubits_idx[1]], qubits_idx[1], - dtype=self.dtype, backend=self.backend - ) - state = functional.cnot(state, qubits_idx, dtype=self.dtype, backend=self.backend) - - gate_history.append({'gate': 'cnot', 'which_qubits': qubits_idx, 'theta': None}) - gate_history.append({'gate': 'rz', 'which_qubits': qubits_idx[1], - 'theta': self.feature[qubits_idx[0]] * self.feature[qubits_idx[1]]}) - gate_history.append({'gate': 'cnot', 'which_qubits': qubits_idx, 'theta': None}) + rz_param = self.feature[qubits_idx[0]] * self.feature[qubits_idx[1]] + state = simulation(state, [cnot], qubits_idx) + state = simulation(state, [rz_gate(rz_param)], qubits_idx[1]) + state = simulation(state, [cnot], qubits_idx) + gate_history.extend([ + {'gate': 'cnot', 'which_qubits': qubits_idx, 'theta': None}, + {'gate': 'rz', 'which_qubits': qubits_idx[1], 'theta': rz_param}, + {'gate': 'cnot', 'which_qubits': qubits_idx, 'theta': None}]) + self.gate_history = gate_history return state def gate_history_generation(self) -> None: if self.gate_history is None: raise RuntimeError("you must forward the encoding to receive the gate history") - pass \ No newline at end of file diff --git a/paddle_quantum/gate/functional/__init__.py b/paddle_quantum/gate/functional/__init__.py index f4f5d03..1217ba7 100644 --- a/paddle_quantum/gate/functional/__init__.py +++ b/paddle_quantum/gate/functional/__init__.py @@ -17,35 +17,4 @@ r""" The module that contains the functions of various quantum gates. """ -from .single_qubit_gate import h -from .single_qubit_gate import s -from .single_qubit_gate import sdg -from .single_qubit_gate import t -from .single_qubit_gate import tdg -from .single_qubit_gate import x -from .single_qubit_gate import y -from .single_qubit_gate import z -from .single_qubit_gate import p -from .single_qubit_gate import rx -from .single_qubit_gate import ry -from .single_qubit_gate import rz -from .single_qubit_gate import u3 -from .multi_qubit_gate import cnot -from .multi_qubit_gate import cx -from .multi_qubit_gate import cy -from .multi_qubit_gate import cz -from .multi_qubit_gate import swap -from .multi_qubit_gate import cp -from .multi_qubit_gate import crx -from .multi_qubit_gate import cry -from .multi_qubit_gate import crz -from .multi_qubit_gate import cu -from .multi_qubit_gate import rxx -from .multi_qubit_gate import ryy -from .multi_qubit_gate import rzz -from .multi_qubit_gate import ms -from .multi_qubit_gate import cswap -from .multi_qubit_gate import toffoli -from .multi_qubit_gate import universal_two_qubits -from .multi_qubit_gate import universal_three_qubits -from .multi_qubit_gate import oracle +from .base import simulation diff --git a/paddle_quantum/gate/functional/base.py b/paddle_quantum/gate/functional/base.py index d84ad52..4f4cbf4 100644 --- a/paddle_quantum/gate/functional/base.py +++ b/paddle_quantum/gate/functional/base.py @@ -17,37 +17,106 @@ r""" The source file of the basic function for quantum gates. """ +import copy import paddle -import paddle_quantum +import paddle_quantum as pq from ...backend import state_vector from ...backend import density_matrix from ...backend import unitary_matrix from typing import Union, List -def simulation( - state: paddle_quantum.State, gate: paddle.Tensor, qubit_idx: Union[int, List[int]], - num_qubits: int, backend: paddle_quantum.Backend -) -> 'paddle.Tensor': +def simulation(state: pq.State, gate: List[paddle.Tensor], qubit_idx: Union[int, List[int]]) -> pq.State: r"""Apply the gate on the input state. Args: state: Input state. - gate: Gate to be executed. + gate: List of Gates to be executed. qubit_idx: Indices of the qubits on which the gate is applied. - num_qubits: Total number of qubits. - backend: Backend on which the simulation is run. Returns: Output state. """ if isinstance(qubit_idx, int): qubit_idx = [qubit_idx] - if backend == paddle_quantum.Backend.StateVector: - return state_vector.unitary_transformation(state.data, gate, qubit_idx, num_qubits) - elif backend == paddle_quantum.Backend.DensityMatrix: - return density_matrix.unitary_transformation(state.data, gate, qubit_idx, num_qubits) - elif backend == paddle_quantum.Backend.UnitaryMatrix: - return unitary_matrix.unitary_transformation(state.data, gate, qubit_idx, num_qubits) + + if state.is_swap_back: + if len(gate) > 1: + for gate_i in range(len(gate)): + state = __simulation_with_swapback( + state, gate[gate_i], qubit_idx[gate_i]) + else: + state = __simulation_with_swapback(state, gate[0], qubit_idx) + return state + + return __simulation_without_swapback(state, gate, qubit_idx) + + +def __simulation_with_swapback( + state: pq.State, gate: paddle.Tensor, qubit_idx: List[int] +) -> pq.State: + r"""Apply the gate on the input state (old logic). + + Args: + state: Input state. + gate: Gate to be executed. + qubit_idx: Indices of the qubits on which the gate is applied. + + Returns: + Output state. + """ + num_qubits, backend = state.num_qubits, state.backend + data = state.data + + if backend == pq.Backend.StateVector: + data = state_vector.unitary_transformation( + data, gate, qubit_idx, num_qubits) + elif backend == pq.Backend.DensityMatrix: + data = density_matrix.unitary_transformation( + data, gate, qubit_idx, num_qubits) + elif backend == pq.Backend.UnitaryMatrix: + data = unitary_matrix.unitary_transformation( + data, gate, qubit_idx, num_qubits) else: - return NotImplementedError + raise NotImplementedError + + state = copy.copy(state) + state.data = data + return state + + +def __simulation_without_swapback( + state: pq.State, gate: List[paddle.Tensor], qubit_idx: List[int] +) -> pq.State: + r"""Apply the gate on the input state (new logic). + + Args: + state: Input state. + gate: List of Gates to be executed. + qubit_idx: Indices of the qubits on which the gate is applied. + + Returns: + Output state. + """ + num_qubits, backend = state.num_qubits, state.backend + data = state.data + qubit_sequence = state.qubit_sequence + + if backend == pq.Backend.StateVector: + data, qubit_sequence = state_vector.unitary_transformation_without_swapback( + data, gate, qubit_idx, num_qubits, qubit_sequence) + elif backend == pq.Backend.DensityMatrix: + data, qubit_sequence = density_matrix.unitary_transformation_without_swapback( + data, gate, qubit_idx, num_qubits, qubit_sequence) + else: + if len(gate) > 1: + for gate_i in range(len(gate)): + data = unitary_matrix.unitary_transformation( + data, gate[gate_i], qubit_idx[gate_i], num_qubits) + else: + data = unitary_matrix.unitary_transformation( + data, gate[0], qubit_idx, num_qubits) + + state.data = data + state.qubit_sequence = qubit_sequence + return state diff --git a/paddle_quantum/gate/functional/multi_qubit_gate.py b/paddle_quantum/gate/functional/multi_qubit_gate.py deleted file mode 100644 index 55b2c75..0000000 --- a/paddle_quantum/gate/functional/multi_qubit_gate.py +++ /dev/null @@ -1,554 +0,0 @@ -# !/usr/bin/env python3 -# Copyright (c) 2022 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. - -r""" -The source file of the functions for multi-qubit quantum gates. -""" - -import math -import paddle -import paddle_quantum -from paddle_quantum.intrinsic import _zero, _one -from .single_qubit_gate import h, s, ry, rz, u3 -from .base import simulation - - -def cnot(state: paddle_quantum.State, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a CNOT gate on the input state. - - Args: - state: Input state. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 0, 1], - [0, 0, 1, 0], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -cx = cnot - - -def cy(state: paddle_quantum.State, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a controlled Y gate on the input state. - - Args: - state: Input state. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 0, -1j], - [0, 0, 1j, 0], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def cz(state: paddle_quantum.State, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a controlled Z gate on the input state. - - Args: - state: Input state. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0, 0, 0], - [0, 1, 0, 0], - [0, 0, 1, 0], - [0, 0, 0, -1], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def swap(state: paddle_quantum.State, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a SWAP gate on the input state. - - Args: - state: Input state. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0, 0, 0], - [0, 0, 1, 0], - [0, 1, 0, 0], - [0, 0, 0, 1], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def cp(state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a controlled P gate on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - _one(dtype), _zero(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), _one(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), _zero(dtype), _one(dtype), _zero(dtype), - _zero(dtype), _zero(dtype), _zero(dtype), paddle.cos(theta).cast(dtype) + 1j * paddle.sin(theta).cast(dtype), - ] - gate = paddle.reshape(paddle.concat(gate), [4, 4]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def crx(state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a controlled rotation gate about the x-axis on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - _one(dtype), _zero(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), _one(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), _zero(dtype), paddle.cos(theta / 2).cast(dtype), -1j * paddle.sin(theta / 2).cast(dtype), - _zero(dtype), _zero(dtype), -1j * paddle.sin(theta / 2).cast(dtype), paddle.cos(theta / 2).cast(dtype), - ] - gate = paddle.reshape(paddle.concat(gate), [4, 4]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def cry(state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a controlled rotation gate about the y-axis on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - _one(dtype), _zero(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), _one(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), _zero(dtype), paddle.cos(theta / 2).cast(dtype), (-paddle.sin(theta / 2)).cast(dtype), - _zero(dtype), _zero(dtype), paddle.sin(theta / 2).cast(dtype), paddle.cos(theta / 2).cast(dtype), - ] - gate = paddle.reshape(paddle.concat(gate), [4, 4]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def crz(state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a controlled rotation gate about the z-axis on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - param1 = paddle.cos(theta / 2).cast(dtype) - 1j * paddle.sin(theta / 2).cast(dtype) - param2 = paddle.cos(theta / 2).cast(dtype) + 1j * paddle.sin(theta / 2).cast(dtype) - gate = [ - _one(dtype), _zero(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), _one(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), _zero(dtype), param1, _zero(dtype), - _zero(dtype), _zero(dtype), _zero(dtype), param2, - ] - gate = paddle.reshape(paddle.concat(gate), [4, 4]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def cu(state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a controlled single-qubit rotation gate on the input state. - - Args: - state: Input state. - theta: Parameters of the gate. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - # theta is theta[0], phi is theta[1], lambda is theta[2] - param1 = paddle.cos(theta[0] / 2).cast(dtype) - param2 = (paddle.cos(theta[2]).cast(dtype) + 1j * paddle.sin(theta[2]).cast(dtype)) * \ - (-paddle.sin(theta[0] / 2)).cast(dtype) - param3 = (paddle.cos(theta[1]).cast(dtype) + 1j * paddle.sin(theta[1]).cast(dtype)) * \ - paddle.sin(theta[0] / 2).cast(dtype) - param4 = (paddle.cos(theta[1] + theta[2]).cast(dtype) + 1j * paddle.sin(theta[1] + theta[2]).cast(dtype)) * \ - paddle.cos(theta[0] / 2).cast(dtype) - gate = [ - _one(dtype), _zero(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), _one(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), _zero(dtype), param1, param2, - _zero(dtype), _zero(dtype), param3, param4, - ] - gate = paddle.reshape(paddle.concat(gate), [4, 4]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def rxx(state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply an RXX gate on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - param1 = paddle.cos(theta / 2).cast(dtype) - param2 = -1j * paddle.sin(theta / 2).cast(dtype) - gate = [ - param1, _zero(dtype), _zero(dtype), param2, - _zero(dtype), param1, param2, _zero(dtype), - _zero(dtype), param2, param1, _zero(dtype), - param2, _zero(dtype), _zero(dtype), param1, - ] - gate = paddle.reshape(paddle.concat(gate), [4, 4]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def ryy(state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply an RYY gate on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - param1 = paddle.cos(theta / 2).cast(dtype) - param2 = -1j * paddle.sin(theta / 2).cast(dtype) - param3 = 1j * paddle.sin(theta / 2).cast(dtype) - gate = [ - param1, _zero(dtype), _zero(dtype), param3, - _zero(dtype), param1, param2, _zero(dtype), - _zero(dtype), param2, param1, _zero(dtype), - param3, _zero(dtype), _zero(dtype), param1, - ] - gate = paddle.reshape(paddle.concat(gate), [4, 4]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def rzz(state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply an RZZ gate on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - param1 = paddle.cos(theta / 2).cast(dtype) - 1j * paddle.sin(theta / 2).cast(dtype) - param2 = paddle.cos(theta / 2).cast(dtype) + 1j * paddle.sin(theta / 2).cast(dtype) - gate = [ - param1, _zero(dtype), _zero(dtype), _zero(dtype), - _zero(dtype), param2, _zero(dtype), _zero(dtype), - _zero(dtype), _zero(dtype), param2, _zero(dtype), - _zero(dtype), _zero(dtype), _zero(dtype), param1, - ] - gate = paddle.reshape(paddle.concat(gate), [4, 4]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def ms(state: paddle_quantum.State, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a Mølmer-Sørensen (MS) gate on the input state. - - Args: - state: Input state. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - val1 = 1 / math.sqrt(2) - val2 = 1j / math.sqrt(2) - gate = [ - [val1, 0, 0, val2], - [0, val1, val2, 0], - [0, val2, val1, 0], - [val2, 0, 0, val1], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def cswap(state: paddle_quantum.State, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a CSWAP (Fredkin) gate on the input state. - - Args: - state: Input state. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0, 0, 0, 0, 0, 0, 0], - [0, 1, 0, 0, 0, 0, 0, 0], - [0, 0, 1, 0, 0, 0, 0, 0], - [0, 0, 0, 1, 0, 0, 0, 0], - [0, 0, 0, 0, 1, 0, 0, 0], - [0, 0, 0, 0, 0, 0, 1, 0], - [0, 0, 0, 0, 0, 1, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 1], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def toffoli(state: paddle_quantum.State, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a Toffoli gate on the input state. - - Args: - state: Input state. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0, 0, 0, 0, 0, 0, 0], - [0, 1, 0, 0, 0, 0, 0, 0], - [0, 0, 1, 0, 0, 0, 0, 0], - [0, 0, 0, 1, 0, 0, 0, 0], - [0, 0, 0, 0, 1, 0, 0, 0], - [0, 0, 0, 0, 0, 1, 0, 0], - [0, 0, 0, 0, 0, 0, 0, 1], - [0, 0, 0, 0, 0, 0, 1, 0], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def universal_two_qubits( - state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend -) -> paddle_quantum.State: - r"""Apply a universal two-qubit gate on the input state. - - Args: - state: Input state. - theta: Parameters of the gate. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - idx0, idx1 = qubit_idx - state = u3(state, theta[[0, 1, 2]], idx0, dtype, backend) - state = u3(state, theta[[3, 4, 5]], idx1, dtype, backend) - state = cnot(state, [idx1, idx0], dtype, backend) - state = rz(state, theta[6], idx0, dtype, backend) - state = ry(state, theta[7], idx1, dtype, backend) - state = cnot(state, [idx0, idx1], dtype, backend) - state = ry(state, theta[8], idx1, dtype, backend) - state = cnot(state, [idx1, idx0], dtype, backend) - state = u3(state, theta[[9, 10, 11]], idx0, dtype, backend) - state = u3(state, theta[[12, 13, 14]], idx1, dtype, backend) - return state - - -def universal_three_qubits( - state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: list, dtype: str, backend: paddle_quantum.Backend -) -> paddle_quantum.State: - r"""Apply a universal three-qubit gate on the input state. - - Args: - state: Input state. - theta: Parameters of the gate. - qubit_idx: Indices of the qubits on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - idx0, idx1, idx2 = qubit_idx - psi = paddle.reshape(theta[:60], shape=[4, 15]) - phi = paddle.reshape(theta[60:], shape=[7, 3]) - - def __block_u(_state: paddle_quantum.State, _theta: paddle.Tensor) -> paddle_quantum.State: - _state = cnot(_state, [idx1, idx2], dtype, backend) - _state = ry(_state, _theta[0], idx1, dtype, backend) - _state = cnot(_state, [idx0, idx1], dtype, backend) - _state = ry(_state, _theta[1], idx1, dtype, backend) - _state = cnot(_state, [idx0, idx1], dtype, backend) - _state = cnot(_state, [idx1, idx2], dtype, backend) - _state = h(_state, idx2, dtype, backend) - _state = cnot(_state, [idx1, idx0], dtype, backend) - _state = cnot(_state, [idx0, idx2], dtype, backend) - _state = cnot(_state, [idx1, idx2], dtype, backend) - _state = rz(_state, _theta[2], idx2, dtype, backend) - _state = cnot(_state, [idx1, idx2], dtype, backend) - _state = cnot(_state, [idx0, idx2], dtype, backend) - return _state - - def __block_v(_state: paddle_quantum.State, _theta: paddle.Tensor) -> paddle_quantum.State: - _state = cnot(_state, [idx2, idx0], dtype, backend) - _state = cnot(_state, [idx1, idx2], dtype, backend) - _state = cnot(_state, [idx2, idx1], dtype, backend) - _state = ry(_state, _theta[0], idx2, dtype, backend) - _state = cnot(_state, [idx1, idx2], dtype, backend) - _state = ry(_state, _theta[1], idx2, dtype, backend) - _state = cnot(_state, [idx1, idx2], dtype, backend) - _state = s(_state, idx2, dtype, backend) - _state = cnot(_state, [idx2, idx0], dtype, backend) - _state = cnot(_state, [idx0, idx1], dtype, backend) - _state = cnot(_state, [idx1, idx0], dtype, backend) - _state = h(_state, idx2, dtype, backend) - _state = cnot(_state, [idx0, idx2], dtype, backend) - _state = rz(_state, _theta[2], idx2, dtype, backend) - _state = cnot(_state, [idx0, idx2], dtype, backend) - return _state - - state = universal_two_qubits(state, psi[0], [idx0, idx1], dtype, backend) - state = u3(state, phi[0, 0:3], idx2, dtype, backend) - state = __block_u(state, phi[1]) - state = universal_two_qubits(state, psi[1], [idx0, idx1], dtype, backend) - state = u3(state, phi[2, 0:3], idx2, dtype, backend) - state = __block_v(state, phi[3]) - state = universal_two_qubits(state, psi[2], [idx0, idx1], dtype, backend) - state = u3(state, phi[4, 0:3], idx2, dtype, backend) - state = __block_u(state, phi[5]) - state = universal_two_qubits(state, psi[3], [idx0, idx1], dtype, backend) - state = u3(state, phi[6, 0:3], idx2, dtype, backend) - return state - - -def oracle( - state: paddle_quantum.State, oracle: 'paddle.Tensor', qubit_idx: list, backend: paddle_quantum.Backend -) -> paddle_quantum.State: - r"""Apply an oracle gate on the input state. - - Args: - state: Input state. - oracle: Oracle to be executed. - qubit_idx: Indices of the qubits on which the gate is applied. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - state_data = simulation(state, oracle, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state diff --git a/paddle_quantum/gate/functional/single_qubit_gate.py b/paddle_quantum/gate/functional/single_qubit_gate.py deleted file mode 100644 index ab0b3f5..0000000 --- a/paddle_quantum/gate/functional/single_qubit_gate.py +++ /dev/null @@ -1,350 +0,0 @@ -# !/usr/bin/env python3 -# Copyright (c) 2022 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. - -r""" -The source file of the functions for single-qubit quantum gates. -""" - -import math -import paddle -import paddle_quantum -from .base import simulation -from paddle_quantum.intrinsic import _get_float_dtype, _zero, _one - - -def h(state: paddle_quantum.State, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a Hadamard gate on the input state. - - Args: - state: Input state. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - element = 1 / math.sqrt(2) - gate = [ - [element, element], - [element, -element], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def s(state: paddle_quantum.State, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply an S gate on the input state. - - Args: - state: Input state. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0], - [0, 1j], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def sdg(state: paddle_quantum.State, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply an S dagger (inverse S) gate on the input state. - - Args: - state: Input state. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0], - [0, -1j], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def t(state: paddle_quantum.State, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a T gate on the input state. - - Args: - state: Input state. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0], - [0, math.cos(math.pi / 4) + math.sin(math.pi / 4) * 1j], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - -def tdg(state: paddle_quantum.State, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a T dagger (inverse T) gate on the input state. - - Args: - state: Input state. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0], - [0, math.cos(math.pi/4) - math.sin(math.pi/4) * 1j], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - -def x(state: paddle_quantum.State, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply an X gate on the input state. - - Args: - state: Input state. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [0, 1], - [1, 0], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def y(state: paddle_quantum.State, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a Y gate on the input state. - - Args: - state: Input state. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [0, -1j], - [1j, 0], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def z(state: paddle_quantum.State, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend) -> paddle_quantum.State: - r"""Apply a Z gate on the input state. - - Args: - state: Input state. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - [1, 0], - [0, -1], - ] - gate = paddle.to_tensor(gate, dtype=dtype) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def p( - state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend -) -> paddle_quantum.State: - r"""Apply a P gate on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - _one(dtype), _zero(dtype), - _zero(dtype), paddle.cos(theta).cast(dtype) + 1j * paddle.sin(theta).cast(dtype), - ] - gate = paddle.reshape(paddle.concat(gate), [2, 2]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def rx( - state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend -) -> paddle_quantum.State: - r"""Apply a single-qubit rotation gate about the x-axis on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - paddle.cos(theta / 2).cast(dtype), -1j * paddle.sin(theta / 2).cast(dtype), - -1j * paddle.sin(theta / 2).cast(dtype), paddle.cos(theta / 2).cast(dtype), - ] - gate = paddle.reshape(paddle.concat(gate), [2, 2]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def ry( - state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend -) -> paddle_quantum.State: - r"""Apply a single-qubit rotation gate about the y-axis on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - paddle.cos(theta / 2).cast(dtype), (-paddle.sin(theta / 2)).cast(dtype), - paddle.sin(theta / 2).cast(dtype), paddle.cos(theta / 2).cast(dtype), - ] - gate = paddle.reshape(paddle.concat(gate), [2, 2]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def rz( - state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend -) -> paddle_quantum.State: - r"""Apply a single-qubit rotation gate about the z-axis on the input state. - - Args: - state: Input state. - theta: Parameter of the gate. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - gate = [ - paddle.cos(theta / 2).cast(dtype) - 1j * paddle.sin(theta / 2).cast(dtype), _zero(dtype), - _zero(dtype), paddle.cos(theta / 2).cast(dtype) + 1j * paddle.sin(theta / 2).cast(dtype), - ] - gate = paddle.reshape(paddle.concat(gate), [2, 2]) - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state - - -def u3( - state: paddle_quantum.State, theta: paddle.Tensor, qubit_idx: int, dtype: str, backend: paddle_quantum.Backend -) -> paddle_quantum.State: - r"""Apply a single-qubit rotation gate on the input state. - - Args: - state: Input state. - theta: Parameters of the gate. - qubit_idx: Index of the qubit on which the gate is applied. - dtype: Type of data. - backend: Backend on which the simulation is run. - - Returns: - Output state. - """ - # theta is theta[0], phi is theta[1], lambda is theta[2] - gate_real = [ - paddle.cos(theta[0] / 2), - -paddle.cos(theta[2]) * paddle.sin(theta[0] / 2), - paddle.cos(theta[1]) * paddle.sin(theta[0] / 2), - paddle.cos(theta[1] + theta[2]) * paddle.cos(theta[0] / 2), - ] - gate_real = paddle.reshape(paddle.concat(gate_real), [2, 2]) - - gate_imag = [ - paddle.to_tensor(0, dtype=_get_float_dtype(dtype)), - -paddle.sin(theta[2]) * paddle.sin(theta[0] / 2), - paddle.sin(theta[1]) * paddle.sin(theta[0] / 2), - paddle.sin(theta[1] + theta[2]) * paddle.cos(theta[0] / 2), - ] - gate_imag = paddle.reshape(paddle.concat(gate_imag), [2, 2]) - - gate = gate_real + 1j * gate_imag - state_data = simulation(state, gate, qubit_idx, state.num_qubits, backend) - transformed_state = state.clone() - transformed_state.data = state_data - return transformed_state diff --git a/paddle_quantum/gate/functional/visual.py b/paddle_quantum/gate/functional/visual.py index 82a1817..aad1530 100644 --- a/paddle_quantum/gate/functional/visual.py +++ b/paddle_quantum/gate/functional/visual.py @@ -272,6 +272,7 @@ def _is_continuous_list(qubits_idx: List[int]) -> bool: def _not_exist_intersection(list_a: List[float], list_b: List[float]) -> bool: r'''Check whether there is an overlap in ``List_a`` and ``List_b``. + Args: List_a: a list with two elements List_b: a list with two elements @@ -285,6 +286,20 @@ def _not_exist_intersection(list_a: List[float], list_b: List[float]) -> bool: return max_a+max_b-min_a-min_b < max_ab-min_ab +def _index_no_intersection_(index_list: List[List[int]]): + r'''Check whether there is an overlap in ``index_list``, + which is a List of the List with two interger. + + Args: + index_list: List of the List with two interger + ''' + for i in range(len(index_list)): + for j in range(i+1, len(index_list)): + if not _not_exist_intersection(index_list[i], index_list[j]): + return False + return True + + def _base_gate_display(gate, ax: matplotlib.axes.Axes, x: float,) -> float: r'''The display function for single qubit base gate. @@ -493,12 +508,16 @@ def _cnot_display(gate, ax: matplotlib.axes.Axes, x: float,) -> float: x_start = x h = __CIRCUIT_PLOT_PARAM['circuit_height'] w = __CIRCUIT_PLOT_PARAM['scale'] * gate.gate_info['plot_width'] + parallel = _index_no_intersection_(gate.qubits_idx) for _ in range(gate.depth): for act_qubits in gate.qubits_idx: x_c = x + 0.5 * w _patch_display(ax, x_c, act_qubits[0]*h, mode='.') _patch_display(ax, x_c, act_qubits[1]*h, mode='+') _vertical_line_display(ax, x_c, act_qubits[0]*h, act_qubits[1]*h) + if not parallel: + x += w + if parallel: x += w return x - x_start @@ -517,12 +536,16 @@ def _swap_display(gate, ax: matplotlib.axes.Axes, x: float,) -> float: x_start = x h = __CIRCUIT_PLOT_PARAM['circuit_height'] w = __CIRCUIT_PLOT_PARAM['scale'] * gate.gate_info['plot_width'] + parallel = _index_no_intersection_(gate.qubits_idx) for _ in range(gate.depth): for act_qubits in gate.qubits_idx: x_c = x + 0.5 * w _patch_display(ax, x_c, act_qubits[0]*h, mode='x') _patch_display(ax, x_c, act_qubits[1]*h, mode='x') _vertical_line_display(ax, x_c, act_qubits[0]*h, act_qubits[1]*h) + if not parallel: + x += w + if parallel: x += w return x - x_start @@ -577,240 +600,3 @@ def _tofolli_display(gate, ax: matplotlib.axes.Axes, x: float,) -> float: _vertical_line_display(ax, x_c, min(act_qubits)*h, max(act_qubits)*h) x += w return x - x_start - - -def _linear_entangled_layer_display(gate, ax: matplotlib.axes.Axes, x: float,) -> float: - r'''The display function for ``linear entangled layer`` gate. - - Args: - gate: the ``paddle_quantum.gate.Gate`` instance - ax: the ``matplotlib.axes.Axes`` instance - x: the start horizontal position - - Returns: - the total width occupied - ''' - x_start = x - h = __CIRCUIT_PLOT_PARAM['circuit_height'] - block_w = __CIRCUIT_PLOT_PARAM['scale'] * gate.gate_info['plot_width'] - dot_w = __CIRCUIT_PLOT_PARAM['node_width'] - - for depth in range(gate.depth): - for param_idx, act_qubits in enumerate(gate.qubits_idx): # `ry` layer - _single_qubit_gate_display(ax, x, act_qubits*h, h, block_w, - f'$R_y({float(gate.theta[depth][param_idx][0]):.2f})$') - x += block_w - - for idx in range(len(gate.qubits_idx)-1): # `cnot` layer - act_qubits = [gate.qubits_idx[idx], gate.qubits_idx[idx + 1]] - x_c = x + 0.5 * dot_w - _patch_display(ax, x_c, act_qubits[0]*h, mode='.') - _patch_display(ax, x_c, act_qubits[1]*h, mode='+') - _vertical_line_display(ax, x_c, act_qubits[0]*h, act_qubits[1]*h) - x += dot_w - - for param_idx, act_qubits in enumerate(gate.qubits_idx): # `rz` layer - _single_qubit_gate_display(ax, x, act_qubits*h, h, block_w, - f'$R_z({float(gate.theta[depth][param_idx][1]):.2f})$') - x += block_w - - for idx in range(len(gate.qubits_idx)-1): # `cnot` layer - act_qubits = [gate.qubits_idx[idx], gate.qubits_idx[idx + 1]] - x_c = x + 0.5 * dot_w - _patch_display(ax, x_c, act_qubits[0]*h, mode='.') - _patch_display(ax, x_c, act_qubits[1]*h, mode='+') - _vertical_line_display(ax, x_c, act_qubits[0]*h, act_qubits[1]*h) - x += dot_w - return x - x_start - - -def _cr_entangled_layer_display(gate, ax: matplotlib.axes.Axes, x: float,) -> float: - r'''The display function for ``complex or real entangled layer`` gate. - - Args: - gate: the ``paddle_quantum.gate.Gate`` instance - ax: the ``matplotlib.axes.Axes`` instance - x: the start horizontal position - - Returns: - the total width occupied - ''' - tex_name = gate.gate_info['texname'] - x_start = x - h = __CIRCUIT_PLOT_PARAM['circuit_height'] - block_w = __CIRCUIT_PLOT_PARAM['scale'] * gate.gate_info['plot_width'] - dot_w = __CIRCUIT_PLOT_PARAM['node_width'] - - if tex_name == '$REntLayer$': # define the tex name generator for deferent gates - def _name_generator(theta): - return f'$R_y({float(theta):.2f})$' - elif tex_name == '$CEntLayer$': - def _name_generator(theta): - name = '$U(' - for value in theta: - name += f'{float(value):.2f},' - name = name.strip(',') - name += ')$' - return name - - for depth in range(gate.depth): - for param_idx, act_qubits in enumerate(gate.qubits_idx): - _single_qubit_gate_display(ax, x, act_qubits*h, h, block_w, - _name_generator(gate.theta[depth][param_idx])) - x += block_w - for idx in range(len(gate.qubits_idx)): - act_qubits = [gate.qubits_idx[idx], gate.qubits_idx[(idx + 1) % len(gate.qubits_idx)]] - x_c = x + 0.5 * dot_w - _patch_display(ax, x_c, act_qubits[0]*h, mode='.') - _patch_display(ax, x_c, act_qubits[1]*h, mode='+') - _vertical_line_display(ax, x_c, act_qubits[0]*h, act_qubits[1]*h) - x += dot_w - return x - x_start - - -def _cr_block_layer_display(gate, ax: matplotlib.axes.Axes, x: float,) -> float: - r'''The display function for ``complex or real block layer`` gate. - - Args: - gate: the ``paddle_quantum.gate.Gate`` instance - ax: the ``matplotlib.axes.Axes`` instance - x: the start horizontal position - - Returns: - the total width occupied - ''' - x_start = x - h = __CIRCUIT_PLOT_PARAM['circuit_height'] - block_w = __CIRCUIT_PLOT_PARAM['scale'] * gate.gate_info['plot_width'] - tex_name = gate.gate_info['texname'] - dot_w = __CIRCUIT_PLOT_PARAM['node_width'] - - if tex_name == '$RBLayer$': - def _add_block(ax, x, theta, pos): # add a block including 4 `ry` and 1 `cnot` - _single_qubit_gate_display(ax, x, pos[0]*h, h, block_w, - tex_name=f'$R_y({float(theta[0]):.2f})$') - _single_qubit_gate_display(ax, x, pos[1]*h, h, block_w, - tex_name=f'$R_y({float(theta[1]):.2f})$') - _single_qubit_gate_display(ax, x+block_w+dot_w, pos[0]*h, h, block_w, - tex_name=f'$R_y({float(theta[2]):.2f})$') - _single_qubit_gate_display(ax, x+block_w+dot_w, pos[1]*h, h, block_w, - tex_name=f'$R_y({float(theta[3]):.2f})$') - _patch_display(ax, x+block_w+0.5*dot_w, pos[0]*h, mode='.') - _patch_display(ax, x+block_w+0.5*dot_w, pos[1]*h, mode='+') - _vertical_line_display(ax, x+block_w+0.5*dot_w, pos[0]*h, pos[1]*h) - - elif tex_name == '$CBLayer$': - def _add_block(ax, x, theta, pos,): # add a block including 4 `u3` and 1 `cnot` - _single_qubit_gate_display(ax, x, pos[0]*h, h, block_w, - tex_name=f'$U({float(theta[0]):.2f},\ - {float(theta[1]):.2f},{float(theta[2]):.2f})$') - _single_qubit_gate_display(ax, x, pos[1]*h, h, block_w, - tex_name=f'$U({float(theta[3]):.2f},\ - {float(theta[4]):.2f},{float(theta[5]):.2f})$') - _single_qubit_gate_display(ax, x+block_w+dot_w, pos[0]*h, h, block_w, - tex_name=f'$U({float(theta[6]):.2f},\ - {float(theta[7]):.2f},{float(theta[8]):.2f})$') - _single_qubit_gate_display(ax, x+block_w+dot_w, pos[1]*h, h, block_w, - tex_name=f'$U({float(theta[9]):.2f},\ - {float(theta[10]):.2f},{float(theta[11]):.2f})$') - _patch_display(ax, x+block_w+0.5*dot_w, pos[0]*h, mode='.') - _patch_display(ax, x+block_w+0.5*dot_w, pos[1]*h, mode='+') - _vertical_line_display(ax, x+block_w+0.5*dot_w, pos[0]*h, pos[1]*h) - - def _get_display_layer(): # arrange the order of block and compress - display_layer = [] - num_theta_layer = [0, 0] - act_qubits = gate.qubits_idx - for layer in range(2): - indices = [] - for i in range(1, len(act_qubits), 2): - indices.append([act_qubits[i-1], act_qubits[i]]) - while len(indices) > 0: - indcs_list = [indices.pop(0)] - num_theta_layer[layer] += 1 - for _ in range(len(indices)): - candidate = indices.pop(0) - if all(_not_exist_intersection(indcs, candidate) for indcs in indcs_list): - indcs_list.append(candidate) - else: - indices.append(candidate) - display_layer.append(indcs_list) - act_qubits = act_qubits[1:] - return display_layer, num_theta_layer - - def _add_layer(ax, x, theta, pos_list,): # add block into layer - plotted_list = [] - for pos in pos_list: - _add_block(ax, x, theta[int((gate.qubits_idx.index(pos[0])) / 2)], pos,) - plotted_list.extend(list(range(min(pos), max(pos)+1))) - - display_layer, num_theta_layer = _get_display_layer() # get layers - for depth in range(gate.depth): - for num_theta, layer in enumerate(display_layer): - if num_theta < num_theta_layer[0]: # get parameters - _add_layer(ax, x, gate.theta[depth, :int((len(gate.qubits_idx)) / 2)], layer) - else: - _add_layer(ax, x, gate.theta[depth, int((len(gate.qubits_idx)) / 2):], layer) - x += 2 * block_w + dot_w - return x - x_start - - -def _qaoa_layer_display(gate, ax: matplotlib.axes.Axes, x: float,) -> float: - r'''The display function for ``qaoa layer`` gate. - - Args: - gate: the ``paddle_quantum.gate.Gate`` instance - ax: the ``matplotlib.axes.Axes`` instance - x: the start horizontal position - - Returns: - the total width occupied - ''' - - x_start = x - h = __CIRCUIT_PLOT_PARAM['circuit_height'] - block_w = __CIRCUIT_PLOT_PARAM['scale'] * gate.gate_info['plot_width'] - dot_w = __CIRCUIT_PLOT_PARAM['node_width'] - - def _get_display_layer(): # arrange the order of block and compress - indices = gate.edges - display_layer = [] - while len(indices) > 0: - indcs_list = [indices.pop(0)] - for _ in range(len(indices)): - candidate = indices.pop(0) - if all(_not_exist_intersection(indcs, candidate) for indcs in indcs_list): - indcs_list.append(candidate) - else: - indices.append(candidate) - display_layer.append(indcs_list) - return display_layer - - def _add_block(ax, x, theta, pos): # add a block including 2 `cnot` and 1 `rz` - _single_qubit_gate_display(ax, x+dot_w, pos[1]*h, h, block_w, tex_name=f'$R_z({float(theta):.2f})$') - _patch_display(ax, x+0.5*dot_w, pos[0]*h, mode='.') - _patch_display(ax, x+0.5*dot_w, pos[1]*h, mode='+') - _vertical_line_display(ax, x+0.5*dot_w, pos[0]*h, pos[1]*h) - _patch_display(ax, x+block_w+1.5*dot_w, pos[0]*h, mode='.') - _patch_display(ax, x+block_w+1.5*dot_w, pos[1]*h, mode='+') - _vertical_line_display(ax, x+block_w+1.5*dot_w, pos[0]*h, pos[1]*h) - - def _add_layer(axis, x, theta, pos_list): # add block into layer - plotted_list = [] - for pos in pos_list: - _add_block(axis, x, theta, pos) - plotted_list.extend(list(range(min(pos), max(pos)+1))) - - x_start = x - gamma = gate.theta[:gate.depth] - beta = gate.theta[gate.depth:] - display_layer = _get_display_layer() - - for depth in range(gate.depth): - for layer in display_layer: - _add_layer(ax, x, gamma[depth], layer) - x += block_w + 2 * dot_w - for y in gate.nodes: - _single_qubit_gate_display(ax, x, y*h, h, block_w, tex_name=f'$R_x({float(beta[depth]):.2f})$') - x += block_w - return x - x_start diff --git a/paddle_quantum/gate/layer.py b/paddle_quantum/gate/layer.py deleted file mode 100644 index 9dcf9df..0000000 --- a/paddle_quantum/gate/layer.py +++ /dev/null @@ -1,656 +0,0 @@ -# !/usr/bin/env python3 -# Copyright (c) 2022 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. -# -# Licensed under the Apache License, Version 2.0 (the "License"); -# you may not use this file except in compliance with the License. -# You may obtain a copy of the License at -# -# http://www.apache.org/licenses/LICENSE-2.0 -# -# Unless required by applicable law or agreed to in writing, software -# distributed under the License is distributed on an "AS IS" BASIS, -# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -# See the License for the specific language governing permissions and -# limitations under the License. - -r""" -The source file of the class for quantum circuit templates. -""" - -import math -import numpy as np -import paddle -import paddle_quantum -from paddle_quantum.gate import functional -from paddle_quantum.intrinsic import _get_float_dtype -from .base import Gate -from typing import Iterable, List, Union, Tuple, Dict -import matplotlib -from .functional.visual import ( _linear_entangled_layer_display, _cr_block_layer_display, _qaoa_layer_display,_cr_entangled_layer_display) - -def qubits_idx_filter(qubits_idx: Union[Iterable[int], str], num_qubits: int) -> List[Iterable[int]]: - r"""Check the validity of ``qubits_idx`` and ``num_qubits``. - - Args: - qubits_idx: Indices of qubits. - num_qubits: Total number of qubits. - - Raises: - RuntimeError: You must specify ``qubits_idx`` or ``num_qubits`` to instantiate the class. - ValueError: The ``qubits_idx`` must be ``Iterable`` or ``'full'``. - - Returns: - Checked indices of qubits. - """ - if qubits_idx == 'full': - if num_qubits is None: - raise RuntimeError("You must specify qubits_idx or num_qubits to instantiate the class.") - return list(range(0, num_qubits)) - elif isinstance(qubits_idx, Iterable): - return list(qubits_idx) - else: - raise ValueError("The param qubits_idx must be iterable or full") - - -class SuperpositionLayer(Gate): - r"""Layers of Hadamard gates. - - Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to ``None``. - depth: Number of layers. Defaults to ``1``. - """ - def __init__( - self, qubits_idx: Union[Iterable[int], str] = 'full', num_qubits: int = None, depth: int = 1 - ): - super().__init__(depth) - self.qubits_idx = qubits_idx_filter(qubits_idx, num_qubits) - self.gate_info = { - 'gatename': 'SupLayer', - 'texname': r'$H$', - 'plot_width': 0.4, - } - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - state = functional.h(state, qubit_idx, self.dtype, self.backend) - return state - - def gate_history_generation(self): - gate_history = [] - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - gate_info = {'gate': 'h', 'which_qubits': qubit_idx, 'theta': None} - gate_history.append(gate_info) - self.gate_history = gate_history - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return super().display_in_circuit(ax, x) - - - -class WeakSuperpositionLayer(Gate): - r"""Layers of Ry gates with a rotation angle :math:`\pi/4`. - - Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to ``None``. - depth: Number of layers. Defaults to ``1``. - """ - def __init__( - self, qubits_idx: Union[Iterable[int], str] = 'full', num_qubits: int = None, depth: int = 1 - ): - super().__init__(depth) - self.qubits_idx = qubits_idx_filter(qubits_idx, num_qubits) - self.gate_info = { - 'gatename': 'WSupLayer', - 'texname': r'$R_y(\pi/4)$', - 'plot_width': 0.9, - } - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - theta = paddle.to_tensor([np.pi / 4]) - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - state = functional.ry(state, theta, qubit_idx, self.dtype, self.backend) - return state - - def gate_history_generation(self): - gate_history = [] - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - gate_info = {'gate': 'ry', 'which_qubits': qubit_idx, 'theta': paddle.to_tensor([np.pi / 4])} - gate_history.append(gate_info) - self.gate_history = gate_history - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return super().display_in_circuit(ax, x) - - -class LinearEntangledLayer(Gate): - r"""Linear entangled layers consisting of Ry gates, Rz gates, and CNOT gates. - - Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to ``None``. - depth: Number of layers. Defaults to ``1``. - """ - def __init__( - self, qubits_idx: Union[Iterable[int], str] = 'full', num_qubits: int = None, depth: int = 1 - ): - super().__init__(depth) - self.qubits_idx = qubits_idx_filter(qubits_idx, num_qubits) - - float_dtype = _get_float_dtype(self.dtype) - param_shape = [self.depth] + list(np.shape(self.qubits_idx)) + [2] - initializer = paddle.nn.initializer.Uniform(low=0, high=2 * math.pi) - theta = self.create_parameter( - shape=param_shape, - dtype=float_dtype, - default_initializer=initializer - ) - self.add_parameter('theta', theta) - self.gate_info = { - 'gatename': 'LEntLayer', - 'texname': r'$LEntLayer$', - 'plot_width': 0.9, - } - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - for depth_idx in range(0, self.depth): - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.ry( - state, self.theta[depth_idx, param_idx, 0], qubit_idx, self.dtype, self.backend) - for idx in range(0, len(self.qubits_idx) - 1): - state = functional.cnot( - state, [self.qubits_idx[idx], self.qubits_idx[idx + 1]], self.dtype, self.backend) - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.rz( - state, self.theta[depth_idx, param_idx, 1], qubit_idx, self.dtype, self.backend) - for idx in range(0, len(self.qubits_idx) - 1): - state = functional.cnot( - state, [self.qubits_idx[idx], self.qubits_idx[idx + 1]], self.dtype, self.backend) - return state - - def gate_history_generation(self): - gate_history = [] - qubits_idx = self.qubits_idx - for depth_idx in range(0, self.depth): - for idx, qubit_idx in enumerate(qubits_idx): - gate_history.append({'gate': 'ry', 'which_qubits': qubit_idx, 'theta': self.theta[depth_idx][idx][0]}) - - for idx in range(0, len(qubits_idx) - 1): - gate_history.append({'gate': 'cnot', 'which_qubits': [qubits_idx[idx], qubits_idx[idx + 1]], 'theta': None}) - - for idx, qubit_idx in enumerate(qubits_idx): - gate_history.append({'gate': 'rz', 'which_qubits': qubit_idx, 'theta': self.theta[depth_idx][idx][1]}) - - for idx in range(0, len(qubits_idx) - 1): - gate_history.append({'gate': 'cnot', 'which_qubits': [qubits_idx[idx], qubits_idx[idx + 1]], 'theta': None}) - self.gate_history = gate_history - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _linear_entangled_layer_display(self, ax, x) - - -class RealEntangledLayer(Gate): - r"""Strongly entangled layers consisting of Ry gates and CNOT gates. - - Note: - The mathematical representation of this layer of quantum gates is a real unitary matrix. - This ansatz is from the following paper: https://arxiv.org/pdf/1905.10876.pdf. - - Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to ``None``. - depth: Number of layers. Defaults to ``1``. - """ - def __init__( - self, qubits_idx: Union[Iterable[int], str] = 'full', num_qubits: int = None, depth: int = 1 - ): - super().__init__(depth) - self.qubits_idx = qubits_idx_filter(qubits_idx, num_qubits) - assert len(self.qubits_idx) > 1, 'you need at least 2 qubits' - - float_dtype = _get_float_dtype(self.dtype) - param_shape = [self.depth] + list(np.shape(self.qubits_idx)) - initializer = paddle.nn.initializer.Uniform(low=0, high=2 * math.pi) - theta = self.create_parameter( - shape=param_shape, - dtype=float_dtype, - default_initializer=initializer - ) - self.add_parameter('theta', theta) - self.gate_info = { - 'gatename': 'REntLayer', - 'texname': r'$REntLayer$', - 'plot_width': 0.9, - } - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - for depth_idx in range(0, self.depth): - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.ry( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - for qubit_idx in range(0, len(self.qubits_idx)): - state = functional.cnot( - state, [self.qubits_idx[qubit_idx], self.qubits_idx[(qubit_idx + 1) % len(self.qubits_idx)]], - self.dtype, self.backend) - return state - - def gate_history_generation(self): - gate_history = [] - qubits_idx = self.qubits_idx - for depth_idx in range(0, self.depth): - for idx, qubit_idx in enumerate(qubits_idx): - gate_history.append({'gate': 'ry', 'which_qubits': qubit_idx, 'theta': self.theta[depth_idx][idx]}) - - for idx in range(0, len(qubits_idx)): - gate_history.append({ - 'gate': 'cnot', - 'which_qubits': [qubits_idx[idx], qubits_idx[(idx + 1) % len(qubits_idx)]], - 'theta': None - }) - self.gate_history = gate_history - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _cr_entangled_layer_display(self, ax, x) - - - - -class ComplexEntangledLayer(Gate): - r"""Strongly entangled layers consisting of single-qubit rotation gates and CNOT gates. - - Note: - The mathematical representation of this layer of quantum gates is a complex unitary matrix. - This ansatz is from the following paper: https://arxiv.org/abs/1804.00633. - - Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to ``None``. - depth: Number of layers. Defaults to ``1``. - """ - def __init__( - self, qubits_idx: Union[Iterable[int], str] = 'full', num_qubits: int = None, depth: int = 1 - ): - super().__init__(depth) - self.qubits_idx = qubits_idx_filter(qubits_idx, num_qubits) - assert len(self.qubits_idx) > 1, 'you need at least 2 qubits' - - float_dtype = _get_float_dtype(self.dtype) - param_shape = [self.depth] + list(np.shape(self.qubits_idx)) + [3] - initializer = paddle.nn.initializer.Uniform(low=0, high=2 * math.pi) - theta = self.create_parameter( - shape=param_shape, dtype=float_dtype, - default_initializer=initializer - ) - self.add_parameter('theta', theta) - self.gate_info = { - 'gatename': 'CEntLayer', - 'texname': r'$CEntLayer$', - 'plot_width': 1.65, - } - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - for depth_idx in range(0, self.depth): - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.u3( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - for qubit_idx in range(0, len(self.qubits_idx)): - state = functional.cnot( - state, [self.qubits_idx[qubit_idx], self.qubits_idx[(qubit_idx + 1) % len(self.qubits_idx)]], - self.dtype, self.backend) - return state - - def gate_history_generation(self): - gate_history = [] - qubits_idx = self.qubits_idx - for depth_idx in range(0, self.depth): - for idx, qubit_idx in enumerate(qubits_idx): - gate_history.append({'gate': 'u', 'which_qubits': qubit_idx, 'theta': self.theta[depth_idx][idx]}) - - for idx in range(0, len(qubits_idx)): - gate_history.append({ - 'gate': 'cnot', - 'which_qubits': [qubits_idx[idx], qubits_idx[(idx + 1) % len(qubits_idx)]], - 'theta': None - }) - self.gate_history = gate_history - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _cr_entangled_layer_display(self, ax, x) - - - -class RealBlockLayer(Gate): - r"""Weakly entangled layers consisting of Ry gates and CNOT gates. - - Note: - The mathematical representation of this layer of quantum gates is a real unitary matrix. - - Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to ``None``. - depth: Number of layers. Defaults to ``1``. - """ - def __init__( - self, qubits_idx: Union[Iterable[int], str] = 'full', num_qubits: int = None, depth: int = 1 - ): - super().__init__(depth) - self.qubits_idx = qubits_idx_filter(qubits_idx, num_qubits) - assert len(self.qubits_idx) > 1, 'you need at least 2 qubits' - - float_dtype = _get_float_dtype(self.dtype) - # TODO: currently do not support multiple dimensions of qubits_idx - param_shape = [self.depth] + [len(self.qubits_idx) - 1] + [4] - initializer = paddle.nn.initializer.Uniform(low=0, high=2 * math.pi) - theta = self.create_parameter( - shape=param_shape, - dtype=float_dtype, - default_initializer=initializer - ) - self.add_parameter('theta', theta) - self.gate_info = { - 'gatename': 'RBLayer', - 'texname': r'$RBLayer$', - 'plot_width': 0.9, - } - - def __add_real_block(self, theta: paddle.Tensor, position: List[int]) -> None: - assert len(theta) == 4, 'the length of theta is not right' - - position[0] = self.qubits_idx[position[0]] - position[1] = self.qubits_idx[position[1]] - - if self.count_history: - gate_history = [] - gate_history.append({'gate': 'ry', 'which_qubits': position[0], 'theta': theta[0]}) - gate_history.append({'gate': 'ry', 'which_qubits': position[1], 'theta': theta[1]}) - - gate_history.append({'gate': 'cnot', 'which_qubits': [position[0], position[1]], 'theta': None}) - - gate_history.append({'gate': 'ry', 'which_qubits': position[0], 'theta': theta[2]}) - gate_history.append({'gate': 'ry', 'which_qubits': position[1], 'theta': theta[3]}) - self.gate_history.extend(gate_history) - else: - state = functional.ry(self.state, theta[0], position[0], self.dtype, self.backend) - state = functional.ry(state, theta[1], position[1], self.dtype, self.backend) - - state = functional.cnot(state, [position[0], position[1]], self.dtype, self.backend) - - state = functional.ry(state, theta[2], position[0], self.dtype, self.backend) - state = functional.ry(state, theta[3], position[1], self.dtype, self.backend) - - self.state = state - - def __add_real_layer(self, theta: paddle.Tensor, position: List) -> None: - assert theta.shape[1] == 4 and theta.shape[0] == (position[1] - position[0] + 1) / 2, \ - 'the shape of theta is not right' - - for i in range(position[0], position[1], 2): - self.__add_real_block(theta[int((i - position[0]) / 2)], [i, i + 1]) - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - self.state = state - n = len(self.qubits_idx) - - if n % 2 == 0: - for depth_idx in range(self.depth): - self.__add_real_layer(self.theta[depth_idx, :int(n / 2)], [0, n - 1]) - self.__add_real_layer(self.theta[depth_idx, int(n / 2):], [1, n - 2]) if n > 2 else None - else: - for depth_idx in range(self.depth): - self.__add_real_layer(self.theta[depth_idx, :int((n - 1) / 2)], [0, n - 2]) - self.__add_real_layer(self.theta[depth_idx, int((n - 1) / 2):], [1, n - 1]) - - return self.state - - def gate_history_generation(self): - self.gate_history = [] - self.count_history = True - n = len(self.qubits_idx) - - if n % 2 == 0: - for depth_idx in range(self.depth): - self.__add_real_layer(self.theta[depth_idx, :int(n / 2)], [0, n - 1]) - self.__add_real_layer(self.theta[depth_idx, int(n / 2):], [1, n - 2]) if n > 2 else None - else: - for depth_idx in range(self.depth): - self.__add_real_layer(self.theta[depth_idx, :int((n - 1) / 2)], [0, n - 2]) - self.__add_real_layer(self.theta[depth_idx, int((n - 1) / 2):], [1, n - 1]) - self.count_history = False - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _cr_block_layer_display(self, ax, x) - - -class ComplexBlockLayer(Gate): - r"""Weakly entangled layers consisting of single-qubit rotation gates and CNOT gates. - - Note: - The mathematical representation of this layer of quantum gates is a complex unitary matrix. - - Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'full'``. - num_qubits: Total number of qubits. Defaults to ``None``. - depth: Number of layers. Defaults to ``1``. - """ - def __init__(self, qubits_idx: Union[Iterable[int], str] = 'full', num_qubits: int = None, depth: int = 1): - super().__init__(depth) - self.qubits_idx = qubits_idx_filter(qubits_idx, num_qubits) - assert len(self.qubits_idx) > 1, 'you need at least 2 qubits' - - float_dtype = _get_float_dtype(self.dtype) - # TODO: currently do not support multiple dimensions of qubits_idx - param_shape = [self.depth] + [len(self.qubits_idx) - 1] + [12] - initializer = paddle.nn.initializer.Uniform(low=0, high=2 * math.pi) - theta = self.create_parameter( - shape=param_shape, - dtype=float_dtype, - default_initializer=initializer - ) - self.add_parameter('theta', theta) - self.gate_info = { - 'gatename': 'CBLayer', - 'texname': r'$CBLayer$', - 'plot_width': 1.65, - } - - def __add_complex_block(self, theta: paddle.Tensor, position: List[int]) -> None: - assert len(theta) == 12, 'the length of theta is not right' - - position[0] = self.qubits_idx[position[0]] - position[1] = self.qubits_idx[position[1]] - - - if self.count_history: - gate_history = [] - gate_history.append({'gate': 'u', 'which_qubits': position[0], 'theta': theta[0:3]}) - gate_history.append({'gate': 'u', 'which_qubits': position[1], 'theta': theta[3:6]}) - - gate_history.append({'gate': 'cnot', 'which_qubits': [position[0], position[1]], 'theta': None}) - - gate_history.append({'gate': 'u', 'which_qubits': position[0], 'theta': theta[6:9]}) - gate_history.append({'gate': 'u', 'which_qubits': position[1], 'theta': theta[9:12]}) - self.gate_history.extend(gate_history) - else: - - state = functional.u3(self.state, theta[0:3], position[0], self.dtype, self.backend) - state = functional.u3(state, theta[3:6], position[1], self.dtype, self.backend) - - state = functional.cnot(state, [position[0], position[1]], self.dtype, self.backend) - - state = functional.u3(state, theta[6:9], position[0], self.dtype, self.backend) - state = functional.u3(state, theta[9:12], position[1], self.dtype, self.backend) - - self.state = state - - def __add_complex_layer(self, theta: paddle.Tensor, position: List[int]) -> None: - assert theta.shape[1] == 12 and theta.shape[0] == (position[1] - position[0] + 1) / 2, \ - 'the shape of theta is not right' - for i in range(position[0], position[1], 2): - self.__add_complex_block(theta[int((i - position[0]) / 2)], [i, i + 1]) - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - self.state = state - - num_acted_qubits = len(self.qubits_idx) - - if num_acted_qubits % 2 == 0: - for depth_idx in range(self.depth): - self.__add_complex_layer(self.theta[depth_idx, :num_acted_qubits // 2], [0, num_acted_qubits - 1]) - if num_acted_qubits > 2: - self.__add_complex_layer(self.theta[depth_idx, num_acted_qubits // 2:], [1, num_acted_qubits - 2]) - else: - for depth_idx in range(0, self.depth): - self.__add_complex_layer(self.theta[depth_idx, :(num_acted_qubits - 1) // 2], [0, num_acted_qubits - 2]) - self.__add_complex_layer(self.theta[depth_idx, (num_acted_qubits - 1) // 2:], [1, num_acted_qubits - 1]) - - return self.state - - def gate_history_generation(self): - self.gate_history = [] - self.count_history = True - n = len(self.qubits_idx) - - if n % 2 == 0: - for depth_idx in range(self.depth): - self.__add_complex_layer(self.theta[depth_idx, :int(n / 2)], [0, n - 1]) - self.__add_complex_layer(self.theta[depth_idx, int(n / 2):], [1, n - 2]) if n > 2 else None - else: - for depth_idx in range(self.depth): - self.__add_complex_layer(self.theta[depth_idx, :int((n - 1) / 2)], [0, n - 2]) - self.__add_complex_layer(self.theta[depth_idx, int((n - 1) / 2):], [1, n - 1]) - self.count_history = False - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _cr_block_layer_display(self, ax, x) - - -class QAOALayer(Gate): - r""" QAOA driving layers - - Note: - this layer only works for MAXCUT problem - - Args: - edges: edges of the graph - nodes: nodes of the graph - depth: depth of layer - - """ - # TODO: only maxcut now - def __init__( - self, edges: Iterable, nodes: Iterable, depth: int = 1 - ): - super().__init__(depth) - float_dtype = _get_float_dtype(self.dtype) - self.edges = edges - self.nodes = nodes - - theta = self.create_parameter( - shape=[self.depth * 2], - dtype=float_dtype, - default_initializer=paddle.nn.initializer.Uniform(low=0, high=2 * math.pi) - ) - self.add_parameter('theta', theta) - self.gate_info = { - 'gatename': 'QAOALayer', - 'texname': r'$QAOALayer$', - 'plot_width': 0.9, - } - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - gamma = self.theta[:self.depth] - beta = self.theta[self.depth:] - for depth_idx in range(0, self.depth): - for node0, node1 in self.edges: - state = functional.cnot(state, [node0, node1], self.dtype, self.backend) - state = functional.rz(state, gamma[depth_idx], node1, self.dtype, self.backend) - state = functional.cnot(state, [node0, node1], self.dtype, self.backend) - for node in self.nodes: - state = functional.rx(state, beta[depth_idx], node, self.dtype, self.backend) - return state - - def gate_history_generation(self): - gate_history = [] - gamma = self.theta[:self.depth] - beta = self.theta[self.depth:] - for depth_idx in range(0, self.depth): - for node0, node1 in self.edges: - gate_history.append({'gate': 'cnot', 'which_qubits': [node0, node1], 'theta': None}) - gate_history.append({'gate': 'rz', 'which_qubits': node1, 'theta': gamma[depth_idx]}) - gate_history.append({'gate': 'cnot', 'which_qubits': [node0, node1], 'theta': None}) - for node in self.nodes: - gate_history.append({'gate': 'rx', 'which_qubits': node, 'theta': beta[depth_idx]}) - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _qaoa_layer_display(self, ax, x) - -class QAOALayerWeighted(Gate): - r""" QAOA driving layers with weights - - Args: - edges: edges of the graph with weights - nodes: nodes of the graph with weights - depth: depth of layer - - """ - def __init__( - self, edges: Dict[Tuple[int, int], float], nodes: Dict[int, float], depth: int = 1 - ) -> None: - super().__init__(depth) - float_dtype = _get_float_dtype(self.dtype) - self.edges = edges.keys() - self.nodes = nodes.keys() - self.edges_full = edges - self.nodes_full = nodes - - theta = self.create_parameter( - shape=[self.depth * 2], - dtype=float_dtype, - default_initializer=paddle.nn.initializer.Uniform(low=0, high=2 * math.pi) - ) - self.add_parameter('theta', theta) - self.gate_history_generation() - self.gate_info = { - 'gatename': 'WQAOALayer', - 'texname': r'$WQAOALayer$', - 'plot_width': 0.9, - } - - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - gamma = self.theta[:self.depth] - beta = self.theta[self.depth:] - for depth_idx in range(0, self.depth): - for node0, node1 in self.edges: - state = functional.cnot(state, [node0, node1], self.dtype, self.backend) - state = functional.rz(state, gamma[depth_idx] * self.edges_full[(node0, node1)], node1, self.dtype, self.backend) - state = functional.cnot(state, [node0, node1], self.dtype, self.backend) - for node in self.nodes: - state = functional.rz(state, gamma[depth_idx] * self.nodes_full[node], node, self.dtype, self.backend) - state = functional.rx(state, beta[depth_idx], node, self.dtype, self.backend) - return state - - def gate_history_generation(self): - gate_history = [] - gamma = self.theta[:self.depth] - beta = self.theta[self.depth:] - for depth_idx in range(0, self.depth): - for node0, node1 in self.edges: - gate_history.append({'gate': 'cnot', 'which_qubits': [node0, node1], 'theta': None}) - gate_history.append({'gate': 'rz', 'which_qubits': node1, 'theta': gamma[depth_idx]}) - gate_history.append({'gate': 'cnot', 'which_qubits': [node0, node1], 'theta': None}) - for node in self.nodes: - gate_history.append({'gate': 'rx', 'which_qubits': node, 'theta': beta[depth_idx]}) - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _qaoa_layer_display(self, ax, x) - - - - - diff --git a/paddle_quantum/gate/matrix.py b/paddle_quantum/gate/matrix.py new file mode 100644 index 0000000..101208b --- /dev/null +++ b/paddle_quantum/gate/matrix.py @@ -0,0 +1,1018 @@ +# !/usr/bin/env python3 +# Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +r""" +The library of gate matrices. +""" + +import math +import paddle +from typing import Optional + +from ..base import get_dtype +from ..backend.unitary_matrix import unitary_transformation +from ..intrinsic import _zero, _one + + +def __get_complex_dtype(dtype: paddle.dtype) -> str: + if dtype == paddle.float32: + complex_dtype = 'complex64' + elif dtype == paddle.float64: + complex_dtype = 'complex128' + else: + raise ValueError( + f"The dtype should be paddle.float32 or paddle.float64: received {dtype}") + return complex_dtype + + +# ------------------------------------------------- Split line ------------------------------------------------- +r""" + Belows are single-qubit matrices. +""" + + +def h_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + H = \frac{1}{\sqrt{2}} + \begin{bmatrix} + 1&1\\ + 1&-1 + \end{bmatrix} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of H gate. + + """ + dtype = get_dtype() if dtype is None else dtype + element = math.sqrt(2) / 2 + gate_matrix = [ + [element, element], + [element, -element], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def s_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + S = + \begin{bmatrix} + 1&0\\ + 0&i + \end{bmatrix} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of S gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0], + [0, 1j], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def sdg_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + S^\dagger = + \begin{bmatrix} + 1&0\\ + 0&-i + \end{bmatrix} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of Sdg gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0], + [0, -1j], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def t_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + T = \begin{bmatrix} + 1&0\\ + 0&e^\frac{i\pi}{4} + \end{bmatrix} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of T gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0], + [0, math.sqrt(2) / 2 + math.sqrt(2) / 2 * 1j], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def tdg_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + T^\dagger = + \begin{bmatrix} + 1&0\\ + 0&e^{-\frac{i\pi}{4}} + \end{bmatrix} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of Sdg gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0], + [0, math.sqrt(2) / 2 - math.sqrt(2) / 2 * 1j], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def x_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + X = \begin{bmatrix} + 0 & 1 \\ + 1 & 0 + \end{bmatrix} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of X gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [0, 1], + [1, 0], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def y_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + Y = \begin{bmatrix} + 0 & -i \\ + i & 0 + \end{bmatrix} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of Y gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [0, -1j], + [1j, 0], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def z_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + Z = \begin{bmatrix} + 1 & 0 \\ + 0 & -1 + \end{bmatrix} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of Z gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0], + [0, -1], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def p_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + P(\theta) = \begin{bmatrix} + 1 & 0 \\ + 0 & e^{i\theta} + \end{bmatrix} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of P gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + gate_matrix = [ + _one(dtype), _zero(dtype), + _zero(dtype), paddle.cos(theta).cast(dtype) + 1j * paddle.sin(theta).cast(dtype), + ] + return paddle.reshape(paddle.concat(gate_matrix), [2, 2]) + + +def rx_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + R_X(\theta) = \begin{bmatrix} + \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ + -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of R_X gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + gate_matrix = [ + paddle.cos(theta / 2).cast(dtype), -1j * paddle.sin(theta / 2).cast(dtype), + -1j * paddle.sin(theta / 2).cast(dtype), paddle.cos(theta / 2).cast(dtype), + ] + return paddle.reshape(paddle.concat(gate_matrix), [2, 2]) + + +def ry_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + R_Y(\theta) = \begin{bmatrix} + \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ + \sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of R_Y gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + gate_matrix = [ + paddle.cos(theta / 2).cast(dtype), (-paddle.sin(theta / 2)).cast(dtype), + paddle.sin(theta / 2).cast(dtype), paddle.cos(theta / 2).cast(dtype), + ] + return paddle.reshape(paddle.concat(gate_matrix), [2, 2]) + + +def rz_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + R_Z(\theta) = \begin{bmatrix} + e^{-i\frac{\theta}{2}} & 0 \\ + 0 & e^{i\frac{\theta}{2}} + \end{bmatrix} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of R_Z gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + gate_matrix = [ + paddle.cos(theta / 2).cast(dtype) - 1j * paddle.sin(theta / 2).cast(dtype), _zero(dtype), + _zero(dtype), paddle.cos(theta / 2).cast(dtype) + 1j * paddle.sin(theta / 2).cast(dtype), + ] + return paddle.reshape(paddle.concat(gate_matrix), [2, 2]) + + +def u3_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + U_3(\theta, \phi, \lambda) = + \begin{bmatrix} + \cos\frac\theta2&-e^{i\lambda}\sin\frac\theta2\\ + e^{i\phi}\sin\frac\theta2&e^{i(\phi+\lambda)}\cos\frac\theta2 + \end{bmatrix} + \end{align} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of U_3 gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + gate_real = [ + paddle.cos(theta[0] / 2), + -paddle.cos(theta[2]) * paddle.sin(theta[0] / 2), + paddle.cos(theta[1]) * paddle.sin(theta[0] / 2), + paddle.cos(theta[1] + theta[2]) * paddle.cos(theta[0] / 2), + ] + gate_real = paddle.reshape(paddle.concat(gate_real), [2, 2]) + + gate_imag = [ + paddle.to_tensor(0, dtype=theta.dtype), + -paddle.sin(theta[2]) * paddle.sin(theta[0] / 2), + paddle.sin(theta[1]) * paddle.sin(theta[0] / 2), + paddle.sin(theta[1] + theta[2]) * paddle.cos(theta[0] / 2), + ] + gate_imag = paddle.reshape(paddle.concat(gate_imag), [2, 2]) + + return gate_real + 1j * gate_imag + + +# ------------------------------------------------- Split line ------------------------------------------------- +r""" + Belows are multi-qubit matrices. +""" + + +def cnot_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{CNOT} &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes X\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 \\ + 0 & 0 & 1 & 0 + \end{bmatrix} + \end{align} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of CNOT gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 0, 1], + [0, 0, 1, 0], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def cy_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{CY} &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Y\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & -i \\ + 0 & 0 & i & 0 + \end{bmatrix} + \end{align} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of CY gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 0, -1j], + [0, 0, 1j, 0], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def cz_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{CZ} &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Z\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & -1 + \end{bmatrix} + \end{align} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of CZ gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0, 0, 0], + [0, 1, 0, 0], + [0, 0, 1, 0], + [0, 0, 0, -1], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def swap_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{SWAP} = + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 1 + \end{bmatrix} + \end{align} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of SWAP gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0, 0, 0], + [0, 0, 1, 0], + [0, 1, 0, 0], + [0, 0, 0, 1], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def cp_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{CP}(\theta) = + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & e^{i\theta} + \end{bmatrix} + \end{align} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of CP gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + gate_matrix = [ + _one(dtype), _zero(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), _one(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), _zero(dtype), _one(dtype), _zero(dtype), + _zero(dtype), _zero(dtype), _zero(dtype), paddle.cos(theta).cast(dtype) + 1j * paddle.sin(theta).cast(dtype), + ] + return paddle.reshape(paddle.concat(gate_matrix), [4, 4]) + + +def crx_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{CR_X} &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes R_X\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ + 0 & 0 & -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of CR_X gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + gate_matrix = [ + _one(dtype), _zero(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), _one(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), _zero(dtype), paddle.cos(theta / 2).cast(dtype), -1j * paddle.sin(theta / 2).cast(dtype), + _zero(dtype), _zero(dtype), -1j * paddle.sin(theta / 2).cast(dtype), paddle.cos(theta / 2).cast(dtype), + ] + return paddle.reshape(paddle.concat(gate_matrix), [4, 4]) + + +def cry_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{CR_Y} &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes R_Y\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ + 0 & 0 & \sin\frac{\theta}{2} & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of CR_Y gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + gate_matrix = [ + _one(dtype), _zero(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), _one(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), _zero(dtype), paddle.cos(theta / 2).cast(dtype), (-paddle.sin(theta / 2)).cast(dtype), + _zero(dtype), _zero(dtype), paddle.sin(theta / 2).cast(dtype), paddle.cos(theta / 2).cast(dtype), + ] + return paddle.reshape(paddle.concat(gate_matrix), [4, 4]) + + +def crz_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{CR_Z} &= |0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes R_Z\\ + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & e^{-i\frac{\theta}{2}} & 0 \\ + 0 & 0 & 0 & e^{i\frac{\theta}{2}} + \end{bmatrix} + \end{align} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of CR_Z gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + param1 = paddle.cos(theta / 2).cast(dtype) - 1j * paddle.sin(theta / 2).cast(dtype) + param2 = paddle.cos(theta / 2).cast(dtype) + 1j * paddle.sin(theta / 2).cast(dtype) + gate_matrix = [ + _one(dtype), _zero(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), _one(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), _zero(dtype), param1, _zero(dtype), + _zero(dtype), _zero(dtype), _zero(dtype), param2, + ] + return paddle.reshape(paddle.concat(gate_matrix), [4, 4]) + + +def cu_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{CU} + &= + \begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & \cos\frac\theta2 &-e^{i\lambda}\sin\frac\theta2 \\ + 0 & 0 & e^{i\phi}\sin\frac\theta2&e^{i(\phi+\lambda)}\cos\frac\theta2 + \end{bmatrix} + \end{align} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of CU gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + param1 = paddle.cos(theta[0] / 2).cast(dtype) + param2 = (paddle.cos(theta[2]).cast(dtype) + 1j * paddle.sin(theta[2]).cast(dtype)) * \ + (-paddle.sin(theta[0] / 2)).cast(dtype) + param3 = (paddle.cos(theta[1]).cast(dtype) + 1j * paddle.sin(theta[1]).cast(dtype)) * \ + paddle.sin(theta[0] / 2).cast(dtype) + param4 = (paddle.cos(theta[1] + theta[2]).cast(dtype) + 1j * paddle.sin(theta[1] + theta[2]).cast(dtype)) * \ + paddle.cos(theta[0] / 2).cast(dtype) + gate_matrix = [ + _one(dtype), _zero(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), _one(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), _zero(dtype), param1, param2, + _zero(dtype), _zero(dtype), param3, param4, + ] + return paddle.reshape(paddle.concat(gate_matrix), [4, 4]) + +def rxx_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{R_{XX}}(\theta) = + \begin{bmatrix} + \cos\frac{\theta}{2} & 0 & 0 & -i\sin\frac{\theta}{2} \\ + 0 & \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} & 0 \\ + 0 & -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} & 0 \\ + -i\sin\frac{\theta}{2} & 0 & 0 & \cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of RXX gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + param1 = paddle.cos(theta / 2).cast(dtype) + param2 = -1j * paddle.sin(theta / 2).cast(dtype) + gate_matrix = [ + param1, _zero(dtype), _zero(dtype), param2, + _zero(dtype), param1, param2, _zero(dtype), + _zero(dtype), param2, param1, _zero(dtype), + param2, _zero(dtype), _zero(dtype), param1, + ] + return paddle.reshape(paddle.concat(gate_matrix), [4, 4]) + + +def ryy_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{R_{YY}}(\theta) = + \begin{bmatrix} + \cos\frac{\theta}{2} & 0 & 0 & i\sin\frac{\theta}{2} \\ + 0 & \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} & 0 \\ + 0 & -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} & 0 \\ + i\sin\frac{\theta}{2} & 0 & 0 & cos\frac{\theta}{2} + \end{bmatrix} + \end{align} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of RYY gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + param1 = paddle.cos(theta / 2).cast(dtype) + param2 = -1j * paddle.sin(theta / 2).cast(dtype) + param3 = 1j * paddle.sin(theta / 2).cast(dtype) + gate_matrix = [ + param1, _zero(dtype), _zero(dtype), param3, + _zero(dtype), param1, param2, _zero(dtype), + _zero(dtype), param2, param1, _zero(dtype), + param3, _zero(dtype), _zero(dtype), param1, + ] + return paddle.reshape(paddle.concat(gate_matrix), [4, 4]) + + +def rzz_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{R_{ZZ}}(\theta) = + \begin{bmatrix} + e^{-i\frac{\theta}{2}} & 0 & 0 & 0 \\ + 0 & e^{i\frac{\theta}{2}} & 0 & 0 \\ + 0 & 0 & e^{i\frac{\theta}{2}} & 0 \\ + 0 & 0 & 0 & e^{-i\frac{\theta}{2}} + \end{bmatrix} + \end{align} + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of RZZ gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + param1 = paddle.cos(theta / 2).cast(dtype) - 1j * paddle.sin(theta / 2).cast(dtype) + param2 = paddle.cos(theta / 2).cast(dtype) + 1j * paddle.sin(theta / 2).cast(dtype) + gate_matrix = [ + param1, _zero(dtype), _zero(dtype), _zero(dtype), + _zero(dtype), param2, _zero(dtype), _zero(dtype), + _zero(dtype), _zero(dtype), param2, _zero(dtype), + _zero(dtype), _zero(dtype), _zero(dtype), param1, + ] + return paddle.reshape(paddle.concat(gate_matrix), [4, 4]) + + +def ms_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{MS} = \mathit{R_{XX}}(-\frac{\pi}{2}) = \frac{1}{\sqrt{2}} + \begin{bmatrix} + 1 & 0 & 0 & i \\ + 0 & 1 & i & 0 \\ + 0 & i & 1 & 0 \\ + i & 0 & 0 & 1 + \end{bmatrix} + \end{align} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of MS gate. + + """ + dtype = get_dtype() if dtype is None else dtype + val1 = math.sqrt(2) / 2 + val2 = 1j / math.sqrt(2) + gate_matrix = [ + [val1, 0, 0, val2], + [0, val1, val2, 0], + [0, val2, val1, 0], + [val2, 0, 0, val1], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def cswap_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{CSWAP} = + \begin{bmatrix} + 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 + \end{bmatrix} + \end{align} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of CSWAP gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0, 0, 0], + [0, 0, 1, 0, 0, 0, 0, 0], + [0, 0, 0, 1, 0, 0, 0, 0], + [0, 0, 0, 0, 1, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 1, 0], + [0, 0, 0, 0, 0, 1, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 1], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def toffoli_gate(dtype: Optional[str] = None) -> paddle.Tensor: + r"""Generate the matrix + + .. math:: + + \begin{align} + \mathit{CSWAP} = + \begin{bmatrix} + 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\ + 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 + \end{bmatrix} + \end{align} + + Args: + dtype: the dtype of this matrix. Defaults to ``None``. + + Returns: + the matrix of Toffoli gate. + + """ + dtype = get_dtype() if dtype is None else dtype + gate_matrix = [ + [1, 0, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0, 0, 0], + [0, 0, 1, 0, 0, 0, 0, 0], + [0, 0, 0, 1, 0, 0, 0, 0], + [0, 0, 0, 0, 1, 0, 0, 0], + [0, 0, 0, 0, 0, 1, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 1], + [0, 0, 0, 0, 0, 0, 1, 0], + ] + return paddle.to_tensor(gate_matrix, dtype=dtype) + + +def universal2_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of universal two qubits gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + unitary = paddle.eye(2 ** 2).cast(dtype) + _cnot_gate = cnot_gate(dtype) + + unitary = unitary_transformation(unitary, u3_gate(theta[[0, 1, 2]]), qubit_idx=0, num_qubits=2) + unitary = unitary_transformation(unitary, u3_gate(theta[[3, 4, 5]]), qubit_idx=1, num_qubits=2) + unitary = unitary_transformation(unitary, _cnot_gate, qubit_idx=[1, 0], num_qubits=2) + + unitary = unitary_transformation(unitary, rz_gate(theta[[6]]), qubit_idx=0, num_qubits=2) + unitary = unitary_transformation(unitary, ry_gate(theta[[7]]), qubit_idx=1, num_qubits=2) + unitary = unitary_transformation(unitary, _cnot_gate, qubit_idx=[0, 1], num_qubits=2) + + unitary = unitary_transformation(unitary, ry_gate(theta[[8]]), qubit_idx=1, num_qubits=2) + unitary = unitary_transformation(unitary, _cnot_gate, qubit_idx=[1, 0], num_qubits=2) + + unitary = unitary_transformation(unitary, u3_gate(theta[[9, 10, 11]]), qubit_idx=0, num_qubits=2) + unitary = unitary_transformation(unitary, u3_gate(theta[[12, 13, 14]]), qubit_idx=1, num_qubits=2) + + return unitary + + +def universal3_gate(theta: paddle.Tensor) -> paddle.Tensor: + r"""Generate the matrix + + Args: + theta: the parameter of this matrix. + + Returns: + the matrix of universal three qubits gate. + + """ + dtype = __get_complex_dtype(theta.dtype) + unitary = paddle.eye(2 ** 3).cast(dtype) + _h_gate, _s_gate, _cnot_gate = h_gate(dtype), s_gate(dtype), cnot_gate(dtype) + + psi = paddle.reshape(theta[:60], shape=[4, 15]) + phi = paddle.reshape(theta[60:], shape=[7, 3]) + + def __block_u(_unitary, _theta): + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[1, 2], num_qubits=3) + _unitary = unitary_transformation(_unitary, ry_gate(_theta[0]), qubit_idx=1, num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[0, 1], num_qubits=3) + _unitary = unitary_transformation(_unitary, ry_gate(_theta[1]), qubit_idx=1, num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[0, 1], num_qubits=3) + + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[1, 2], num_qubits=3) + _unitary = unitary_transformation(_unitary, _h_gate, qubit_idx=2, num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[1, 0], num_qubits=3) + + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[0, 2], num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[1, 2], num_qubits=3) + _unitary = unitary_transformation(_unitary, rz_gate(_theta[2]), qubit_idx=2, num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[1, 2], num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[0, 2], num_qubits=3) + return _unitary + + def __block_v(_unitary, _theta): + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[2, 0], num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[1, 2], num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[2, 1], num_qubits=3) + + _unitary = unitary_transformation(_unitary, ry_gate(_theta[0]), qubit_idx=2, num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[1, 2], num_qubits=3) + _unitary = unitary_transformation(_unitary, ry_gate(_theta[1]), qubit_idx=2, num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[1, 2], num_qubits=3) + + _unitary = unitary_transformation(_unitary, _s_gate, qubit_idx=2, num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[2, 0], num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[0, 1], num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[1, 0], num_qubits=3) + + _unitary = unitary_transformation(_unitary, _h_gate, qubit_idx=2, num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[0, 2], num_qubits=3) + _unitary = unitary_transformation(_unitary, rz_gate(_theta[2]), qubit_idx=2, num_qubits=3) + _unitary = unitary_transformation(_unitary, _cnot_gate, qubit_idx=[0, 2], num_qubits=3) + return _unitary + + unitary = unitary_transformation(unitary, universal2_gate(psi[0]), qubit_idx=[0, 1], num_qubits=3) + unitary = unitary_transformation(unitary, u3_gate(phi[0, 0:3]), qubit_idx=2, num_qubits=3) + unitary = __block_u(unitary, phi[1]) + + unitary = unitary_transformation(unitary, universal2_gate(psi[1]), qubit_idx=[0, 1], num_qubits=3) + unitary = unitary_transformation(unitary, u3_gate(phi[2, 0:3]), qubit_idx=2, num_qubits=3) + unitary = __block_v(unitary, phi[3]) + + unitary = unitary_transformation(unitary, universal2_gate(psi[2]), qubit_idx=[0, 1], num_qubits=3) + unitary = unitary_transformation(unitary, u3_gate(phi[4, 0:3]), qubit_idx=2, num_qubits=3) + unitary = __block_u(unitary, phi[5]) + + unitary = unitary_transformation(unitary, universal2_gate(psi[3]), qubit_idx=[0, 1], num_qubits=3) + unitary = unitary_transformation(unitary, u3_gate(phi[6, 0:3]), qubit_idx=2, num_qubits=3) + return unitary diff --git a/paddle_quantum/gate/multi_qubit_gate.py b/paddle_quantum/gate/multi_qubit_gate.py index 22b7bde..5ea314a 100644 --- a/paddle_quantum/gate/multi_qubit_gate.py +++ b/paddle_quantum/gate/multi_qubit_gate.py @@ -17,18 +17,40 @@ r""" The source file of the classes for multi-qubit gates. """ -import copy +import matplotlib +from typing import Optional, Union, Iterable, List, Tuple + +import numpy as np import math +import paddle_quantum as pq import paddle -import paddle_quantum -from . import functional from .base import Gate, ParamGate +from .functional.visual import ( + _cnot_display, _cswap_display, _tofolli_display, _swap_display, + _cx_like_display, _crx_like_display, _oracle_like_display, _rxx_like_display +) +from .matrix import ( + cnot_gate, + cy_gate, + cz_gate, + swap_gate, + cp_gate, + crx_gate, + cry_gate, + crz_gate, + cu_gate, + rxx_gate, + ryy_gate, + rzz_gate, + ms_gate, + cswap_gate, + toffoli_gate, + universal2_gate, + universal3_gate +) from ..backend import Backend -from ..intrinsic import _format_qubits_idx, _get_float_dtype -from typing import Optional, Union, Iterable -from .functional.visual import (_cnot_display, _cswap_display, _tofolli_display, _swap_display, - _cx_like_display, _crx_like_display, _oracle_like_display, _rxx_like_display) -import matplotlib +from ..intrinsic import _cnot_idx_fetch, _inverse_gather_for_dm, _paddle_gather + class CNOT(Gate): r"""A collection of CNOT gates. @@ -52,69 +74,78 @@ class CNOT(Gate): qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'cycle'``. num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. + cnot_idx: CNOT gate index. Defaults to ``None``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.gate_info = { + + __matrix = cnot_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, + cnot_idx: Optional[List[int]] = None + ): + gate_info = { 'gatename': 'cnot', 'texname': r'$CNOT$', 'plot_width': 0.2, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=2) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'cnot', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubits_idx in self.qubits_idx: - state = functional.cnot(state, qubits_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _cnot_display(self, ax, x,) - + self.cnot_idx = cnot_idx + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return CNOT.__matrix.cast('complex64') + return CNOT.__matrix -class CX(Gate): - r"""Same as CNOT. + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: + return _cnot_display(self, ax, x, ) - Args: - qubits_idx: Indices of the qubits on which the gates are applied. Defaults to ``'cycle'``. - num_qubits: Total number of qubits. Defaults to ``None``. - depth: Number of layers. Defaults to ``1``. - """ - def __init__(self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', - num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.gate_info = { - 'gatename': 'cnot', - 'texname': r'$CNOT$', - 'plot_width': 0.2, - } + def forward(self, state: pq.State) -> pq.State: + if state.backend == Backend.QuLeaf or state.backend == Backend.UnitaryMatrix: + return super().forward(state=state) + + if self.cnot_idx is None: + self.cnot_idx = _cnot_idx_fetch(num_qubits=state.num_qubits, qubits_idx=self.qubits_idx) + + if state.is_swap_back: + state = state.clone() + + state.reset_sequence() + data = state.data + + num_qubits = int(math.log2(data.shape[-1])) + + if state.backend == Backend.StateVector: + for _ in range(self.depth): + # whether to use batch in state_vector backend. len(state.shape) equals 1 means not using batch + if len(data.shape) == 1: + data = _paddle_gather(data, index=paddle.to_tensor(self.cnot_idx)) + else: + data = paddle.reshape(data, [-1, 2 ** num_qubits]).T + data = _paddle_gather(data, index=paddle.to_tensor(self.cnot_idx)).T - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'cx', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubits_idx in self.qubits_idx: - state = functional.cx(state, qubits_idx, self.dtype, self.backend) + elif state.backend == Backend.DensityMatrix: + for _ in range(self.depth): + # left swap + # whether to use batch in density_matrix backend. len(state.shape) is greater than 2 means using batch + if len(data.shape) > 2: + data = paddle.reshape(data, [-1, 2 ** num_qubits, 2 ** num_qubits]) + data = paddle.transpose(data, perm=[1, 2, 0]) + + data = _paddle_gather(data, index=paddle.to_tensor(self.cnot_idx)) + + # right swap + data = _inverse_gather_for_dm(data, base_idx=paddle.to_tensor(self.cnot_idx)) + + state.data = data return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _cnot_display(self, ax, x,) +CX = CNOT + class CY(Gate): r"""A collection of controlled Y gates. @@ -139,31 +170,29 @@ class CY(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', - num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.gate_info = { + + __matrix = cy_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'cy', 'texname': r'$Y$', 'plot_width': 0.4, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=2) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'cy', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubits_idx in self.qubits_idx: - state = functional.cy(state, qubits_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _cx_like_display(self, ax, x,) + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return CY.__matrix.cast('complex64') + return CY.__matrix + + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: + return _cx_like_display(self, ax, x, ) class CZ(Gate): @@ -189,30 +218,28 @@ class CZ(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', - num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.gate_info = { + + __matrix = cz_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'cz', 'texname': r'$Z$', 'plot_width': 0.4, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=2) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'cz', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubits_idx in self.qubits_idx: - state = functional.cz(state, qubits_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return CZ.__matrix.cast('complex64') + return CZ.__matrix + + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _cx_like_display(self, ax, x) @@ -238,32 +265,30 @@ class SWAP(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', - num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.gate_info = { + + __matrix = swap_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'swap', 'texname': r'$SWAP$', 'plot_width': 0.2, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=2) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'swap', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubits_idx in self.qubits_idx: - state = functional.swap(state, qubits_idx, self.dtype, self.backend) - return state + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return SWAP.__matrix.cast('complex64') + return SWAP.__matrix + + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: + return _swap_display(self, ax, x, ) - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _swap_display(self, ax, x,) - class CP(ParamGate): r"""A collection of controlled P gates. @@ -289,36 +314,22 @@ class CP(ParamGate): Raises: ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ + def __init__( - self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'cp', 'texname': r'$P$', 'plot_width': 0.9, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.cp(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.cp( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state + super().__init__( + cp_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=2) - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _crx_like_display(self, ax, x) @@ -350,52 +361,22 @@ class CRX(ParamGate): Raises: ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ + def __init__( - self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'crx', 'texname': r'$R_{x}$', 'plot_width': 0.9, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.param_list.extend(self.theta) - if self.param_sharing: - param_idx_list = [[state.num_param]] - state.num_param += 1 - else: - param_idx_list = [] - for _ in range(0, self.depth): - param_idx_list.append(list(range(state.num_param, state.num_param + len(self.qubits_idx)))) - state.num_param += self.theta.size - state.gate_history.append({ - 'gate_name': 'crx', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - 'param': param_idx_list, - 'param_sharing': self.param_sharing, - }) - return state - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.crx(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.crx( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state + super().__init__( + crx_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=2) - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _crx_like_display(self, ax, x) @@ -427,53 +408,23 @@ class CRY(ParamGate): Raises: ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ + def __init__( - self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'cry', 'texname': r'$R_{y}$', 'plot_width': 0.9, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.param_list.extend(self.theta) - if self.param_sharing: - param_idx_list = [[state.num_param]] - state.num_param += 1 - else: - param_idx_list = [] - for _ in range(0, self.depth): - param_idx_list.append(list(range(state.num_param, state.num_param + len(self.qubits_idx)))) - state.num_param += self.theta.size - state.gate_history.append({ - 'gate_name': 'cry', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - 'param': param_idx_list, - 'param_sharing': self.param_sharing, - }) - return state - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.cry(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.cry( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _crx_like_display(self, ax, x,) + super().__init__( + cry_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=2) + + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: + return _crx_like_display(self, ax, x, ) class CRZ(ParamGate): @@ -504,52 +455,22 @@ class CRZ(ParamGate): Raises: ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ + def __init__( - self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'crz', 'texname': r'$R_{z}$', 'plot_width': 0.9, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.param_list.extend(self.theta) - if self.param_sharing: - param_idx_list = [[state.num_param]] - state.num_param += 1 - else: - param_idx_list = [] - for _ in range(0, self.depth): - param_idx_list.append(list(range(state.num_param, state.num_param + len(self.qubits_idx)))) - state.num_param += self.theta.size - state.gate_history.append({ - 'gate_name': 'crz', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - 'param': param_idx_list, - 'param_sharing': self.param_sharing, - }) - return state - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.crz(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.crz( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + super().__init__( + crz_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=2) + + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _crx_like_display(self, ax, x) @@ -581,55 +502,21 @@ class CU(ParamGate): Raises: ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ + def __init__( - self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.param_sharing = param_sharing - - if param_sharing: - param_shape = [depth, 3] - else: - param_shape = [depth, len(self.qubits_idx), 3] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'cu', 'texname': r'$U$', 'plot_width': 1.65, } + super().__init__( + cu_gate, param, depth, 3, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=2) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.param_list.extend(self.theta) - if self.param_sharing: - param_idx_list = [range(state.num_param, state.num_param + 3)] - state.num_param += 3 - else: - param_idx_list = [] - for _ in range(0, self.depth): - param_idx_list.append(list(range(state.num_param, state.num_param + len(self.qubits_idx)))) - state.num_param += self.theta.size - state.gate_history.append({ - 'gate_name': 'cu', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - 'param': param_idx_list, - 'param_sharing': self.param_sharing, - }) - return state - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.cu(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.cu( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _crx_like_display(self, ax, x) @@ -660,36 +547,21 @@ class RXX(ParamGate): Raises: ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ + def __init__( - self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'rxx', 'texname': r'$R_{xx}$', 'plot_width': 1.0, } + super().__init__( + rxx_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=2) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.rxx(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.rxx( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _rxx_like_display(self, ax, x) @@ -720,38 +592,25 @@ class RYY(ParamGate): Raises: ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ + def __init__( - self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'ryy', 'texname': r'$R_{yy}$', 'plot_width': 1.0, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.ryy(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.ryy( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + super().__init__( + ryy_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=2) + + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _rxx_like_display(self, ax, x) + class RZZ(ParamGate): r"""A collection of RZZ gates. @@ -779,38 +638,24 @@ class RZZ(ParamGate): Raises: ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ + def __init__( - self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'rzz', 'texname': r'$R_{zz}$', 'plot_width': 1.0, } + super().__init__( + rzz_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=2) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.rzz(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.rzz( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _rxx_like_display(self, ax, x) + class MS(Gate): r"""A collection of Mølmer-Sørensen (MS) gates for trapped ion devices. @@ -833,26 +678,31 @@ class MS(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.gate_info = { + + __matrix = ms_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'ms', 'texname': r'$MS$', 'plot_width': 0.6, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=2) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for _ in range(0, self.depth): - for qubits_idx in self.qubits_idx: - state = functional.ms(state, qubits_idx, self.dtype, self.backend) - return state + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return MS.__matrix.cast('complex64') + return MS.__matrix - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _oracle_like_display(self, ax, x) + class CSWAP(Gate): r"""A collection of CSWAP (Fredkin) gates. @@ -879,34 +729,32 @@ class CSWAP(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=3) - self.gate_info = { + __matrix = cswap_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'cswap', 'texname': r'$CSWAP$', 'plot_width': 0.2, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=3) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'cswap', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubits_idx in self.qubits_idx: - state = functional.cswap(state, qubits_idx, self.dtype, self.backend) - return state + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return CSWAP.__matrix.cast('complex64') + return CSWAP.__matrix - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _cswap_display(self, ax, x) - -class Toffoli(Gate): - r"""A collection of Toffoli gates. + +class CCX(Gate): + r"""A collection of CCX (Toffoli) gates. The matrix form of such a gate is: @@ -930,31 +778,33 @@ class Toffoli(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=3) - self.gate_info = { + __matrix = toffoli_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'ccx', 'texname': r'$Toffoli$', 'plot_width': 0.2, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'toffoli', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubits_idx in self.qubits_idx: - state = functional.toffoli(state, qubits_idx, self.dtype, self.backend) - return state + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=3) + + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return CCX.__matrix.cast('complex64') + return CCX.__matrix + + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: + return _tofolli_display(self, ax, x, ) + + +Toffoli = CCX - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: - return _tofolli_display(self, ax, x,) - class UniversalTwoQubits(ParamGate): r"""A collection of universal two-qubit gates. One of such a gate requires 15 parameters. @@ -969,40 +819,22 @@ class UniversalTwoQubits(ParamGate): Raises: ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ + def __init__( - self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=2) - self.param_sharing = param_sharing - - if param_sharing: - param_shape = [depth, 15] - else: - param_shape = [depth, len(self.qubits_idx), 15] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'uni2', 'texname': r'$U$', 'plot_width': 0.6, } + super().__init__( + universal2_gate, param, depth, 15, param_sharing, qubits_idx, gate_info, num_qubits, False, + num_acted_qubits=2) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.universal_two_qubits( - state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.universal_two_qubits( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _oracle_like_display(self, ax, x) @@ -1019,38 +851,20 @@ class UniversalThreeQubits(ParamGate): Raises: ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ + def __init__( - self, qubits_idx: Optional[Union[Iterable, str]] = 'cycle', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits, num_acted_qubits=3) - self.param_sharing = param_sharing - - if param_sharing: - param_shape = [depth, 81] - else: - param_shape = [depth, len(self.qubits_idx), 81] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'uni3', 'texname': r'$U$', 'plot_width': 0.6, } + super().__init__( + universal3_gate, param, depth, 81, param_sharing, qubits_idx, gate_info, num_qubits, False, + num_acted_qubits=3) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.universal_three_qubits( - state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.universal_three_qubits( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - - def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float,) -> float: + def display_in_circuit(self, ax: matplotlib.axes.Axes, x: float, ) -> float: return _oracle_like_display(self, ax, x) diff --git a/paddle_quantum/gate/single_qubit_gate.py b/paddle_quantum/gate/single_qubit_gate.py index c50986f..53e2b4c 100644 --- a/paddle_quantum/gate/single_qubit_gate.py +++ b/paddle_quantum/gate/single_qubit_gate.py @@ -17,16 +17,18 @@ r""" The source file of the classes for single-qubit gates. """ -import copy -import math -import numpy as np -import paddle.nn -import paddle_quantum -from . import functional +from typing import Optional, Union, Iterable + +import paddle from .base import Gate, ParamGate +from .matrix import ( + h_gate, s_gate, sdg_gate, t_gate, tdg_gate, + x_gate, y_gate, z_gate, p_gate, + rx_gate, ry_gate, rz_gate, u3_gate, +) from ..backend import Backend -from paddle_quantum.intrinsic import _format_qubits_idx, _get_float_dtype -from typing import Optional, List, Union, Iterable +from ..intrinsic import _format_qubits_idx, _get_float_dtype + class H(Gate): r"""A collection of single-qubit Hadamard gates. @@ -46,27 +48,25 @@ class H(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.gate_info = { + __matrix = h_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'h', - 'texname': '$H$', + 'texname': r'$H$', 'plot_width': 0.4, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=1) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'h', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - state = functional.h(state, qubit_idx, self.dtype, self.backend) - return state + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return H.__matrix.cast('complex64') + return H.__matrix class S(Gate): @@ -87,27 +87,26 @@ class S(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.gate_info = { + __matrix = s_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 's', - 'texname': '$S$', + 'texname': r'$S$', 'plot_width': 0.4, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=1) + + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return S.__matrix.cast('complex64') + return S.__matrix - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 's', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - state = functional.s(state, qubit_idx, self.dtype, self.backend) - return state class Sdg(Gate): r"""A collection of single-qubit S dagger (S inverse) gates. @@ -127,27 +126,26 @@ class Sdg(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.gate_info = { + __matrix = sdg_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'sdg', 'texname': r'$S^\dagger$', 'plot_width': 0.4, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=1) + + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return Sdg.__matrix.cast('complex64') + return Sdg.__matrix - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.Quleaf: - state.gate_history.append({ - 'gate_name': 'sdg', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - state = functional.sdg(state, qubit_idx, self.dtype, self.backend) - return state class T(Gate): r"""A collection of single-qubit T gates. @@ -167,27 +165,26 @@ class T(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.gate_info = { + __matrix = t_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 't', - 'texname': '$T$', + 'texname': r'$T$', 'plot_width': 0.4, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=1) + + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return T.__matrix.cast('complex64') + return T.__matrix - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 't', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - state = functional.t(state, qubit_idx, self.dtype, self.backend) - return state class Tdg(Gate): r"""A collection of single-qubit T dagger (T inverse) gates. @@ -207,26 +204,27 @@ class Tdg(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.gate_info = { + __matrix = tdg_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'tdg', 'texname': r'$T^\dagger$', 'plot_width': 0.4, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.Quleaf: - state.gate_history.append({ - 'gate_name': 'tdg', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - state = functional.tdg(state, qubit_idx, self.dtype, self.backend) - return state + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=1) + + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return Tdg.__matrix.cast('complex64') + return Tdg.__matrix + + class X(Gate): r"""A collection of single-qubit X gates. @@ -244,28 +242,26 @@ class X(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.gate_info = { + + __matrix = x_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'x', - 'texname': '$X$', + 'texname': r'$X$', 'plot_width': 0.4, } - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'x', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - state = functional.x(state, qubit_idx, self.dtype, self.backend) - return state - + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=1) + + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return X.__matrix.cast('complex64') + return X.__matrix class Y(Gate): @@ -285,28 +281,25 @@ class Y(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.gate_info = { + __matrix = y_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'y', - 'texname': '$Y$', + 'texname': r'$Y$', 'plot_width': 0.4, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=1) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'y', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - state = functional.y(state, qubit_idx, self.dtype, self.backend) - return state - + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return Y.__matrix.cast('complex64') + return Y.__matrix class Z(Gate): @@ -326,27 +319,25 @@ class Z(Gate): num_qubits: Total number of qubits. Defaults to ``None``. depth: Number of layers. Defaults to ``1``. """ - def __init__(self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.gate_info = { + __matrix = z_gate('complex128') + + def __init__( + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1 + ): + gate_info = { 'gatename': 'z', - 'texname': '$Z$', + 'texname': r'$Z$', 'plot_width': 0.4, } + super().__init__( + None, qubits_idx, depth, gate_info, num_qubits, check_legality=False, num_acted_qubits=1) - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.gate_history.append({ - 'gate_name': 'z', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - }) - return state - for _ in range(0, self.depth): - for qubit_idx in self.qubits_idx: - state = functional.z(state, qubit_idx, self.dtype, self.backend) - return state + @property + def matrix(self) -> paddle.Tensor: + if self.dtype == 'complex64': + return Z.__matrix.cast('complex64') + return Z.__matrix class P(ParamGate): @@ -372,34 +363,18 @@ class P(ParamGate): ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ def __init__( - self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'p', - 'texname': '$P$', + 'texname': r'$P$', 'plot_width': 0.9, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - raise NotImplementedError - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.p(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.p( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - + super().__init__( + p_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=1) class RX(ParamGate): @@ -425,50 +400,18 @@ class RX(ParamGate): ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ def __init__( - self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'rx', 'texname': r'$R_{x}$', 'plot_width': 0.9, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.param_list.extend(self.theta) - if self.param_sharing: - param_idx_list = [[state.num_param]] - state.num_param += 1 - else: - param_idx_list = [] - for _ in range(0, self.depth): - param_idx_list.append(list(range(state.num_param, state.num_param + len(self.qubits_idx)))) - state.num_param += self.theta.size - state.gate_history.append({ - 'gate_name': 'rx', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - 'param': param_idx_list, - 'param_sharing': self.param_sharing, - }) - return state - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.rx(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.rx( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - + super().__init__( + rx_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=1) class RY(ParamGate): @@ -494,51 +437,17 @@ class RY(ParamGate): ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ def __init__( - self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'ry', 'texname': r'$R_{y}$', 'plot_width': 0.9, } - - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.param_list.extend(self.theta) - if self.param_sharing: - param_idx_list = [[state.num_param]] - state.num_param += 1 - else: - param_idx_list = [] - for _ in range(0, self.depth): - param_idx_list.append(list(range(state.num_param, state.num_param + len(self.qubits_idx)))) - state.num_param += len(self.qubits_idx) - state.gate_history.append({ - 'gate_name': 'ry', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - 'param': param_idx_list, - 'param_sharing': self.param_sharing, - }) - return state - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.ry(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.ry( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - - + super().__init__( + ry_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=1) class RZ(ParamGate): @@ -564,50 +473,18 @@ class RZ(ParamGate): ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ def __init__( - self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, float]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.param_sharing = param_sharing - - param_shape = [depth, 1 if param_sharing else len(self.qubits_idx)] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'rz', 'texname': r'$R_{z}$', 'plot_width': 0.9, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.param_list.extend(self.theta) - if self.param_sharing: - param_idx_list = [[state.num_param]] - state.num_param += 1 - else: - param_idx_list = [] - for _ in range(0, self.depth): - param_idx_list.append(list(range(state.num_param, state.num_param + len(self.qubits_idx)))) - state.num_param += self.theta.size - state.gate_history.append({ - 'gate_name': 'rz', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - 'param': param_idx_list, - 'param_sharing': self.param_sharing, - }) - return state - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.rz(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.rz( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - + super().__init__( + rz_gate, param, depth, 1, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=1) class U3(ParamGate): @@ -636,51 +513,15 @@ class U3(ParamGate): ValueError: The ``param`` must be ``paddle.Tensor`` or ``float``. """ def __init__( - self, qubits_idx: Optional[Union[Iterable, int, str]] = 'full', num_qubits: Optional[int] = None, depth: Optional[int] = 1, + self, qubits_idx: Optional[Union[Iterable, int, str]] = None, + num_qubits: Optional[int] = None, depth: Optional[int] = 1, param: Optional[Union[paddle.Tensor, Iterable[float]]] = None, param_sharing: Optional[bool] = False ): - super().__init__(depth) - self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) - self.param_sharing = param_sharing - - if param_sharing: - param_shape = [depth, 3] - else: - param_shape = [depth, len(self.qubits_idx), 3] - self.theta_generation(param, param_shape) - self.gate_info = { + gate_info = { 'gatename': 'u', 'texname': r'$U$', 'plot_width': 1.65, } - def forward(self, state: paddle_quantum.State) -> paddle_quantum.State: - if self.backend == Backend.QuLeaf and state.backend == Backend.QuLeaf: - state.param_list.extend(self.theta) - if self.param_sharing: - param_idx_list = [range(state.num_param, state.num_param + 3)] - state.num_param += 3 - else: - param_idx_list = [] - for _ in range(0, self.depth): - param_idx_list.append(list(range(state.num_param, state.num_param + len(self.qubits_idx)))) - state.num_param += self.theta.size - state.gate_history.append({ - 'gate_name': 'u3', - 'qubits_idx': copy.deepcopy(self.qubits_idx), - 'depth': self.depth, - 'param': param_idx_list, - 'param_sharing': self.param_sharing, - }) - return state - for depth_idx in range(0, self.depth): - if self.param_sharing: - for qubit_idx in self.qubits_idx: - state = functional.u3(state, self.theta[depth_idx], qubit_idx, self.dtype, self.backend) - else: - for param_idx, qubit_idx in enumerate(self.qubits_idx): - state = functional.u3( - state, self.theta[depth_idx, param_idx], qubit_idx, self.dtype, self.backend) - return state - - \ No newline at end of file + super().__init__( + u3_gate, param, depth, 3, param_sharing, qubits_idx, gate_info, num_qubits, False, num_acted_qubits=1) diff --git a/paddle_quantum/hamiltonian.py b/paddle_quantum/hamiltonian.py index 931d8b8..cb3ef7c 100644 --- a/paddle_quantum/hamiltonian.py +++ b/paddle_quantum/hamiltonian.py @@ -25,6 +25,7 @@ from scipy import sparse import paddle import paddle_quantum import openfermion +import math class Hamiltonian: @@ -301,7 +302,7 @@ class Hamiltonian: r"""Construct a matrix form of the Hamiltonian in Z-basis. Args: - qubit_num: The number of qubits. Defaults to ``1``. + qubit_num: The number of qubits. Defaults to ``None``. Returns: The matrix form of the Hamiltonian in Z-basis. @@ -333,6 +334,11 @@ class Hamiltonian: def from_qubit_operator(cls, qubitOp: openfermion.QubitOperator): pauli_strs = [] for xyz_tuple, coef in qubitOp.terms.items(): + if isinstance(coef, complex): + if not math.isclose(coef.imag, 0.0): + raise ValueError("Coefficients in qubit Hamiltonian must be real since Hamiltonian is Hermitian.") + else: + coef = coef.real if len(xyz_tuple) == 0: pauli_strs.append((coef, "I")) else: diff --git a/paddle_quantum/intrinsic.py b/paddle_quantum/intrinsic.py index a21442a..adf9c52 100644 --- a/paddle_quantum/intrinsic.py +++ b/paddle_quantum/intrinsic.py @@ -19,17 +19,19 @@ The intrinsic function of the paddle quantum. import numpy as np import paddle -from typing import Union, Iterable, List +from typing import Union, Iterable, List, Tuple +import paddle_quantum as pq from .base import get_dtype +from .backend import Backend -def _zero(dtype = None): +def _zero(dtype=None): dtype = get_dtype() if dtype is None else dtype return paddle.to_tensor(0, dtype=dtype) -def _one(dtype = None): +def _one(dtype=None): dtype = get_dtype() if dtype is None else dtype return paddle.to_tensor(1, dtype=dtype) @@ -38,6 +40,18 @@ def _format_qubits_idx( qubits_idx: Union[Iterable[Iterable[int]], Iterable[int], int, str], num_qubits: int, num_acted_qubits: int = 1 ) -> Union[List[List[int]], List[int]]: + r"""Formatting the qubit indices that operations acts on + + Args: + qubits_idx: input qubit indices, could be a string + num_qubits: total number of qubits + + Note: + The shape of output qubit indices are formatted as follows: + - If num_acted_qubits is 1, the output shape is [# of qubits that one operation acts on]; + - otherwise, the output shape is [# of vertical gates, # of qubits that one operation acts on]. + + """ assert not (isinstance(qubits_idx, str) and num_qubits is None), \ f"Cannot specify the qubit indices when num_qubits is None: received qubit_idx {qubits_idx} and num_qubits {num_qubits}" if num_acted_qubits == 1: @@ -49,20 +63,24 @@ def _format_qubits_idx( qubits_idx = list(range(1, num_qubits, 2)) elif isinstance(qubits_idx, Iterable): qubits_idx = list(qubits_idx) + assert len(qubits_idx) == len(set(qubits_idx)), \ + f"Single-qubit operators do not allow repeated indices: received {qubits_idx}" else: qubits_idx = [qubits_idx] else: if qubits_idx == 'cycle': qubits_idx = [] for idx in range(0, num_qubits - num_acted_qubits): - qubits_idx.append([i for i in range(idx, idx + num_acted_qubits)]) + qubits_idx.append( + [i for i in range(idx, idx + num_acted_qubits)]) for idx in range(num_qubits - num_acted_qubits, num_qubits): - qubits_idx.append([i for i in range(idx, num_qubits)] + + qubits_idx.append([i for i in range(idx, num_qubits)] + [i for i in range(idx + num_acted_qubits - num_qubits)]) elif qubits_idx == 'linear': qubits_idx = [] - for idx in range(0, num_qubits - num_acted_qubits): - qubits_idx.append([i for i in range(idx, idx + num_acted_qubits)]) + for idx in range(0, num_qubits - num_acted_qubits + 1): + qubits_idx.append( + [i for i in range(idx, idx + num_acted_qubits)]) elif len(np.shape(qubits_idx)) == 1 and len(qubits_idx) == num_acted_qubits: qubits_idx = [list(qubits_idx)] elif len(np.shape(qubits_idx)) == 2 and all((len(indices) == num_acted_qubits for indices in qubits_idx)): @@ -76,11 +94,353 @@ def _format_qubits_idx( return qubits_idx +def _format_param_shape(depth: int, qubits_idx: Union[List[List[int]], List[int]], + num_acted_param: int, param_sharing: bool) -> List[int]: + r"""Formatting the shape of parameters + + Args: + depth: depth of the layer + qubits_idx: list of input qubit indices + num_acted_param: the number of parameters required for a single operation + param_sharing: whether all operations are shared by the same parameter set + + Note: + The input ``qubits_idx`` must be formatted by ``_format_qubits_idx`` first. + The shape of parameters are formatted as follows: + - If param_sharing is True, the shape is [depth, num_acted_param]; + - otherwise, the shape is [depth, len(qubits_idx), num_acted_param]. + + """ + if param_sharing: + return [depth, num_acted_param] + return [depth, len(qubits_idx), num_acted_param] + + def _get_float_dtype(complex_dtype: str) -> str: if complex_dtype == 'complex64': float_dtype = 'float32' elif complex_dtype == 'complex128': float_dtype = 'float64' else: - raise ValueError("The dtype should be complex64 or complex128.") + raise ValueError( + f"The dtype should be 'complex64' or 'complex128': received {complex_dtype}") return float_dtype + + +def _type_fetch(data: Union[np.ndarray, paddle.Tensor, pq.State]) -> str: + r""" fetch the type of ``data`` + + Args: + data: the input data, and datatype of which should be either ``numpy.ndarray``, + ''paddle.Tensor'' or ``paddle_quantum.State`` + + Returns: + string of datatype of ``data``, can be either ``"numpy"``, ``"tensor"``, + ``"state_vector"`` or ``"density_matrix"`` + + Raises: + ValueError: does not support the current backend of input state. + TypeError: cannot recognize the current type of input data. + + """ + if isinstance(data, np.ndarray): + return "numpy" + + if isinstance(data, paddle.Tensor): + return "tensor" + + if isinstance(data, pq.State): + if data.backend == Backend.StateVector: + return "state_vector" + if data.backend == Backend.DensityMatrix: + return "density_matrix" + raise ValueError( + f"does not support the current backend {data.backend} of input state.") + + raise TypeError( + f"cannot recognize the current type {type(data)} of input data.") + + +def __density_to_vector(rho: Union[np.ndarray, paddle.Tensor]) -> Union[np.ndarray, paddle.Tensor]: + r""" transform a density matrix to a state vector + + Args: + rho: a density matrix (pure state) + + Returns: + a state vector + + Raises: + ValueError: the output state may not be a pure state + + """ + type_str = _type_fetch(rho) + rho = paddle.to_tensor(rho) + eigval, eigvec = paddle.linalg.eigh(rho) + + max_eigval = paddle.max(eigval).item() + err = np.abs(max_eigval - 1) + if err > 1e-6: + raise ValueError( + f"the output state may not be a pure state, maximum distance: {err}") + + state = eigvec[:, paddle.argmax(eigval)] + + return state.numpy() if type_str == "numpy" else state + + +def _type_transform(data: Union[np.ndarray, paddle.Tensor, pq.State], + output_type: str) -> Union[np.ndarray, paddle.Tensor, pq.State]: + r""" transform the datatype of ``input`` to ``output_type`` + + Args: + data: data to be transformed + output_type: datatype of the output data, type is either ``"numpy"``, ``"tensor"``, + ``"state_vector"`` or ``"density_matrix"`` + + Returns: + the output data with expected type + + Raises: + ValueError: does not support transformation to type. + + """ + current_type = _type_fetch(data) + + support_type = {"numpy", "tensor", "state_vector", "density_matrix"} + if output_type not in support_type: + raise ValueError( + f"does not support transformation to type {output_type}") + + if current_type == output_type: + return data + + if current_type == "numpy": + if output_type == "tensor": + return paddle.to_tensor(data) + + data = np.squeeze(data) + # state_vector case + if output_type == "state_vector": + if len(data.shape) == 2: + data = __density_to_vector(data) + return pq.State(data, backend=Backend.StateVector) + # density_matrix case + if len(data.shape) == 1: + data = data.reshape([len(data), 1]) + data = data @ np.conj(data.T) + return pq.State(data, backend=Backend.DensityMatrix) + + if current_type == "tensor": + if output_type == "numpy": + return data.numpy() + + data = paddle.squeeze(data) + # state_vector case + if output_type == "state_vector": + if len(data.shape) == 2: + data = __density_to_vector(data) + return pq.State(data, backend=Backend.StateVector) + + # density_matrix case + if len(data.shape) == 1: + data = data.reshape([len(data), 1]) + data = data @ paddle.conj(data.T) + return pq.State(data, backend=Backend.DensityMatrix) + + if current_type == "state_vector": + if output_type == "density_matrix": + return pq.State(data.ket @ data.bra, backend=Backend.DensityMatrix, num_qubits=data.num_qubits, override=True) + return data.ket.numpy() if output_type == "numpy" else data.ket + + # density_matrix data + if output_type == "state_vector": + return pq.State(__density_to_vector(data.data), backend=Backend.StateVector, num_qubits=data.num_qubits, override=True) + return data.numpy() if output_type == "numpy" else data.data + + +def _perm_to_swaps(perm: List[int]) -> List[Tuple[int]]: + r"""This function takes a permutation as a list of integers and returns its + decomposition into a list of tuples representing the two-permutation (two conjugated 2-cycles). + + Args: + perm: the target permutation + + Returns: + the decomposition of the permutation. + """ + n = len(perm) + swapped = [False] * n + swap_ops = [] + + for idx in range(0, n): + if not swapped[idx]: + next_idx = idx + swapped[next_idx] = True + while not swapped[perm[next_idx]]: + swapped[perm[next_idx]] = True + if next_idx < perm[next_idx]: + swap_ops.append((next_idx, perm[next_idx])) + else: + swap_ops.append((perm[next_idx], next_idx)) + next_idx = perm[next_idx] + + return swap_ops + + +def _trans_ops(state: paddle.Tensor, swap_ops: List[Tuple[int]], higher_dims: List[int], num_qubits: int, + extra_dims: int = 1) -> paddle.Tensor: + r"""Transpose the state tensor given a list of swap operations. + + Args: + swap_ops: given list of swap operations + higher_dims: intrinsic dimension of the state tensor + num_qubits: the number of qubits in the system + extra_dims: labeling the dimension of state, 1 for statevector; 2 for density operator + + Returns: + paddle.Tensor: transposed state tensor given the swap list + """ + num_higher_dims = len(higher_dims) + for swap_op in swap_ops: + shape = higher_dims.copy() + shape.extend([2**(swap_op[0]), 2, 2**(swap_op[1] - swap_op[0] - 1), + 2, 2**(extra_dims * num_qubits - swap_op[1] - 1)]) + state = paddle.reshape(state, shape) + state = paddle.transpose( + state, list(range(0, num_higher_dims)) + + [item + num_higher_dims for item in [0, 3, 2, 1, 4]] + ) + return state + + +def _perm_of_list(orig_list: List[int], targ_list: List[int]) -> List[int]: + r"""Find the permutation mapping the original list to the target list + """ + perm_map = {val: index for index, val in enumerate(orig_list)} + return [perm_map[val] for val in targ_list] + + +def __gate_tensor(gate: List[paddle.Tensor]) -> paddle.Tensor: + gate_tensor = gate[0] + for i in range(1, len(gate)): + gate_tensor = paddle.kron(gate_tensor, gate[i]) + return gate_tensor + + +def _gate_tensor(gate: List[paddle.Tensor]) -> paddle.Tensor: + + # TODO extend to multi-qubit cases + # tensor product of single-qubit gates + if len(gate) > 1: + gate_half1 = __gate_tensor(gate[: len(gate) // 2]) + gate_half2 = __gate_tensor(gate[len(gate) // 2:]) + gate = paddle.kron(gate_half1, gate_half2) + else: + gate = gate[0] + return gate + + +def _paddle_gather(data: paddle.Tensor, index: paddle.Tensor) -> paddle.Tensor: + return paddle.gather(paddle.real(data), index=index) + \ + paddle.gather(paddle.imag(data), index=index) * 1.j + + +def _base_transpose(state: paddle.Tensor, perm: Union[List, Tuple]) -> paddle.Tensor: + r"""speed-up logic using using np.transpose + paddle.gather. + + Args: + state: input state data. + perm: permutation of qubit sequence. + + Returns: + paddle.Tensor: permuted state. + """ + num_qubits = len(perm) + # Using the logic changing the order of each component in a 2**n array + base_idx = np.arange(2 ** num_qubits).reshape([2] * num_qubits) + base_idx = np.transpose(base_idx, axes=perm).reshape([-1]) + + # whether to use batch in state_vector backend. len(state.shape) equals 1 means not using batch + if len(state.shape) == 1: + return _paddle_gather(state, index=paddle.to_tensor(base_idx)) + + state = paddle.reshape(state, [-1, 2 ** num_qubits]).T + state = _paddle_gather(state, index=paddle.to_tensor(base_idx)) + return state.T + + +def _inverse_gather_for_dm(state: paddle.Tensor, base_idx: paddle.Tensor) -> paddle.Tensor: + r"""replacement of the usage of paddle.gather(axis=1) + """ + # TODO When the `axis` bug is fixed, please use the `axis` argument instead of using transpose. + + # whether to use batch in density_matrix backend. len(state.shape) equals 2 means not using batch + if len(state.shape) == 2: + state = state.T + state = _paddle_gather(state, index=base_idx) + return state.T + + state = paddle.transpose(state, perm=[1, 0, 2]) + state = _paddle_gather(state, index=base_idx) + return paddle.transpose(state, perm=[2, 1, 0]) + + +def _base_transpose_for_dm(state: paddle.Tensor, perm: Union[List, Tuple]) -> paddle.Tensor: + r"""speed-up logic using using np.transpose + paddle.gather. + + Args: + state: input state data. + perm: permutation of qubit sequence. + + Returns: + paddle.Tensor: permuted state. + """ + num_qubits = len(perm) + # Using the logic changing the order of each component in a 2**n array + base_idx = np.arange(2 ** num_qubits).reshape([2] * num_qubits) + base_idx = paddle.to_tensor(np.transpose(base_idx, axes=perm).reshape([-1])) + + # left swap + # whether to use batch in density_matrix backend. len(state.shape) is greater than 2 means using batch + if len(state.shape) > 2: + state = paddle.reshape(state, [-1, 2 ** num_qubits, 2 ** num_qubits]) + state = paddle.transpose(state, perm=[1, 2, 0]) + + state = _paddle_gather(state, index=base_idx) + + # right swap + state = _inverse_gather_for_dm(state, base_idx) + + return state + + +def _cnot_idx_fetch(num_qubits: int, qubits_idx: List[Tuple[int, int]]) -> List[int]: + r""" + Compute the CNOT index obtained by applying the CNOT gate without using matrix multiplication. + + Args: + num_qubits: The total number of qubits in the system. + qubits_idx: A list of tuples, where each tuple contains the indices of the two qubits + involved in the CNOT gate. + + Returns: + List: A list of integers representing the decimal values of all binary strings + obtained by applying the CNOT gate. + """ + assert len(np.shape(qubits_idx)) == 2, \ + "The CNOT qubits_idx should be list of tuple of integers, e.g., [[0, 1], [1, 2]]." + binary_list = [bin(i)[2:].zfill(num_qubits) for i in range(2 ** num_qubits)] + qubits_idx_length = len(qubits_idx) + for item in range(len(binary_list)): + for bin_idx in range(qubits_idx_length): + id1 = qubits_idx[qubits_idx_length - bin_idx - 1][0] + id2 = qubits_idx[qubits_idx_length - bin_idx - 1][1] + if binary_list[item][id1] == "1": + if binary_list[item][id2] == '0': + binary_list[item] = binary_list[item][:id2] + '1' + binary_list[item][id2 + 1:] + else: + binary_list[item] = binary_list[item][:id2] + '0' + binary_list[item][id2 + 1:] + + decimal_list = [int(binary, 2) for binary in binary_list] + return decimal_list diff --git a/paddle_quantum/linalg.py b/paddle_quantum/linalg.py index d46cbbe..ce99cc5 100644 --- a/paddle_quantum/linalg.py +++ b/paddle_quantum/linalg.py @@ -24,14 +24,13 @@ import scipy import itertools from scipy.stats import unitary_group from functools import reduce -from typing import Optional, Union, Callable, List +from typing import Optional, Union, Callable, List, Tuple import paddle_quantum as pq -from .intrinsic import _get_float_dtype -from .state import State, _type_fetch, _type_transform +from .intrinsic import get_dtype, _get_float_dtype, _type_fetch, _type_transform -def abs_norm(mat: Union[np.ndarray, paddle.Tensor, State]) -> float: +def abs_norm(mat: Union[np.ndarray, paddle.Tensor, pq.State]) -> float: r""" tool for calculation of matrix norm Args: @@ -42,7 +41,7 @@ def abs_norm(mat: Union[np.ndarray, paddle.Tensor, State]) -> float: """ mat = _type_transform(mat, "tensor") - mat = mat.cast(pq.get_dtype()) + mat = mat.cast(get_dtype()) return paddle.norm(paddle.abs(mat)).item() @@ -94,6 +93,82 @@ def is_positive(mat: Union[np.ndarray, paddle.Tensor], eps: Optional[float] = 1e return (min(paddle.linalg.eigvalsh(mat)) >= -eps).item() return False + +def is_state_vector(vec: Union[np.ndarray, paddle.Tensor], eps: Optional[float] = None) -> Tuple[bool, int]: + r""" verify whether ``vec`` is a legal quantum state vector + + Args: + vec: state vector candidate :math:`x` + eps: tolerance of error, default to be `None` i.e. no testing for data correctness + + Returns: + determine whether :math:`x^\dagger x = 1`, and return the number of qubits or an error message + + Note: + error message is: + * ``-1`` if the above equation does not hold + * ``-2`` if the dimension of ``vec`` is not a power of 2 + * ``-3`` if ``vec`` is not a vector + + """ + vec = _type_transform(vec, "tensor") + vec = paddle.squeeze(vec) + + dimension = vec.shape[0] + if len(vec.shape) != 1: + return False, -3 + + num_qubits = int(math.log2(dimension)) + if 2 ** num_qubits != dimension: + return False, -2 + + if eps is None: + return True, num_qubits + + vec = vec.reshape([dimension, 1]) + vec_bra = paddle.conj(vec.T) + eps = min(eps * dimension, 1e-2) + return {False, -1} if paddle.abs(vec_bra @ vec - (1 + 0j)) > eps else {True, num_qubits} + + +def is_density_matrix(rho: Union[np.ndarray, paddle.Tensor], eps: Optional[float] = None) -> Tuple[bool, int]: + r""" verify whether ``rho`` is a legal quantum density matrix + + Args: + rho: density matrix candidate + eps: tolerance of error, default to be `None` i.e. no testing for data correctness + + Returns: + determine whether ``rho`` is a PSD matrix with trace 1 and return the number of qubits or an error message. + + Note: + error message is: + * ``-1`` if ``rho`` is not PSD + * ``-2`` if the trace of ``rho`` is not 1 + * ``-3`` if the dimension of ``rho`` is not a power of 2 + * ``-4`` if ``rho`` is not a square matrix + + """ + rho = _type_transform(rho, "tensor") + + dimension = rho.shape[0] + if len(rho.shape) != 2 or dimension != rho.shape[1]: + return False, -4 + + num_qubits = int(math.log2(dimension)) + if 2 ** num_qubits != dimension: + return False, -3 + + if eps is None: + return True, num_qubits + + eps = min(eps * dimension, 1e-2) + if paddle.abs(paddle.trace(rho) - (1 + 0j)).item() > eps: + return False, -2 + + return {False, -1} if not is_positive(rho, eps) else {True, num_qubits} + + def is_projector(mat: Union[np.ndarray, paddle.Tensor], eps: Optional[float] = 1e-6) -> bool: r""" verify whether ``mat`` is a projector @@ -154,7 +229,7 @@ def hermitian_random(num_qubits: int) -> paddle.Tensor: eigval= np.linalg.eigvalsh(mat) max_eigval = np.max(np.abs(eigval)) - return paddle.to_tensor(mat / max_eigval, dtype=pq.get_dtype()) + return paddle.to_tensor(mat / max_eigval, dtype=get_dtype()) def orthogonal_projection_random(num_qubits: int) -> paddle.Tensor: @@ -168,7 +243,7 @@ def orthogonal_projection_random(num_qubits: int) -> paddle.Tensor: """ assert num_qubits > 0 n = 2 ** num_qubits - float_dtype = _get_float_dtype(pq.get_dtype()) + float_dtype = _get_float_dtype(get_dtype()) vec = paddle.randn([n, 1], dtype=float_dtype) + 1j * paddle.randn([n, 1], dtype=float_dtype) mat = vec @ dagger(vec) return mat / paddle.trace(mat) @@ -184,12 +259,7 @@ def density_matrix_random(num_qubits: int) -> paddle.Tensor: a :math:`2^n \times 2^n` density matrix """ - float_dtype = _get_float_dtype(pq.get_dtype()) - real = paddle.rand([2 ** num_qubits, 2 ** num_qubits], dtype=float_dtype) - imag = paddle.rand([2 ** num_qubits, 2 ** num_qubits], dtype=float_dtype) - M = real + 1j * imag - M = M @ dagger(M) - return M / paddle.trace(M) + return haar_density_operator(num_qubits, rank=np.random.randint(1,2**num_qubits)) def unitary_random(num_qubits: int) -> paddle.Tensor: @@ -202,7 +272,7 @@ def unitary_random(num_qubits: int) -> paddle.Tensor: a :math:`2^n \times 2^n` unitary matrix """ - return paddle.to_tensor(unitary_group.rvs(2 ** num_qubits), dtype=pq.get_dtype()) + return paddle.to_tensor(unitary_group.rvs(2 ** num_qubits), dtype=get_dtype()) def unitary_hermitian_random(num_qubits: int) -> paddle.Tensor: @@ -242,7 +312,7 @@ def unitary_random_with_hermitian_block(num_qubits: int, is_unitary: bool = Fals mat = np.block([[mat0, mat1], [mat1, mat0]]) - return paddle.to_tensor(mat, dtype=pq.get_dtype()) + return paddle.to_tensor(mat, dtype=get_dtype()) def block_enc_herm(mat: Union[np.ndarray, paddle.Tensor], @@ -294,7 +364,7 @@ def haar_orthogonal(num_qubits: int) -> paddle.Tensor: # Step 3: make the decomposition unique mat_lambda = np.diag(mat_r) / abs(np.diag(mat_r)) mat_u = mat_q @ np.diag(mat_lambda) - return paddle.to_tensor(mat_u, dtype=pq.get_dtype()) + return paddle.to_tensor(mat_u, dtype=get_dtype()) def haar_unitary(num_qubits: int) -> paddle.Tensor: @@ -316,7 +386,7 @@ def haar_unitary(num_qubits: int) -> paddle.Tensor: # Step 3: make the decomposition unique mat_lambda = np.diag(mat_r) / np.abs(np.diag(mat_r)) mat_u = mat_q @ np.diag(mat_lambda) - return paddle.to_tensor(mat_u, dtype=pq.get_dtype()) + return paddle.to_tensor(mat_u, dtype=get_dtype()) def haar_state_vector(num_qubits: int, is_real: Optional[bool] = False) -> paddle.Tensor: @@ -343,7 +413,7 @@ def haar_state_vector(num_qubits: int, is_real: Optional[bool] = False) -> paddl # Perform u onto |0>, i.e., the first column of u phi = unitary[:, 0] - return paddle.to_tensor(phi, dtype=pq.get_dtype()) + return paddle.to_tensor(phi, dtype=get_dtype()) def haar_density_operator(num_qubits: int, rank: Optional[int] = None, is_real: Optional[bool] = False) -> paddle.Tensor: @@ -351,7 +421,7 @@ def haar_density_operator(num_qubits: int, rank: Optional[int] = None, is_real: Args: num_qubits: number of qubits :math:`n` - rank: rank of density matrix, default to be False refering to full ranks + rank: rank of density matrix, default to be ``None`` refering to full ranks is_real: whether the density matrix is real, default to be False Returns: @@ -367,7 +437,7 @@ def haar_density_operator(num_qubits: int, rank: Optional[int] = None, is_real: ginibre_matrix = np.random.randn(dim, rank) + 1j * np.random.randn(dim, rank) rho = ginibre_matrix @ ginibre_matrix.conj().T rho = rho / np.trace(rho) - return paddle.to_tensor(rho / np.trace(rho), dtype=pq.get_dtype()) + return paddle.to_tensor(rho, dtype=get_dtype()) def direct_sum(A: Union[np.ndarray, paddle.Tensor], @@ -411,8 +481,8 @@ def NKron( .. code-block:: python - from pq.state import density_op_random - from pq.linalg import NKron + from paddle_quantum.state import density_op_random + from paddle_quantum.linalg import NKron A = density_op_random(2) B = density_op_random(2) C = density_op_random(2) @@ -430,7 +500,7 @@ def NKron( return reduce(lambda result, index: np.kron(result, index), args, np.kron(matrix_A, matrix_B), ) -def herm_transform(fcn: Callable[[float], float], mat: Union[paddle.Tensor, np.ndarray, State], +def herm_transform(fcn: Callable[[float], float], mat: Union[paddle.Tensor, np.ndarray, pq.State], ignore_zero: Optional[bool] = False) -> paddle.Tensor: r""" function transformation for Hermitian matrix @@ -476,7 +546,7 @@ def pauli_basis_generation(num_qubits: int) -> List[paddle.Tensor]: def __single_pauli_basis() -> List[paddle.Tensor]: r"""The Pauli basis in single-qubit case. """ - complex_dtype = pq.get_dtype() + complex_dtype = get_dtype() I = paddle.to_tensor([[0.5, 0], [0, 0.5]], dtype=complex_dtype) X = paddle.to_tensor([[0, 0.5], diff --git a/paddle_quantum/locc/locc_ansatz.py b/paddle_quantum/locc/locc_ansatz.py index 89197f8..dd1d3c3 100644 --- a/paddle_quantum/locc/locc_ansatz.py +++ b/paddle_quantum/locc/locc_ansatz.py @@ -23,7 +23,7 @@ import paddle_quantum from ..gate import H, S, T, X, Y, Z, P, RX, RY, RZ, U3 from ..gate import CNOT, CX, CY, CZ, SWAP from ..gate import CP, CRX, CRY, CRZ, CU, RXX, RYY, RZZ -from ..gate import MS, CSWAP, Toffoli +from ..gate import MS, CSWAP, CCX from ..gate import UniversalTwoQubits, UniversalThreeQubits from ..gate import Oracle, ControlOracle from .locc_party import LoccParty @@ -685,7 +685,7 @@ class LoccAnsatz(paddle_quantum.ansatz.Circuit): self.append(oper) if num_qubits is None: num_qubits = self.num_local_qubits - oper = Toffoli(qubits_idx, num_qubits, depth) + oper = CCX(qubits_idx, num_qubits, depth) self.append(oper) def universal_two_qubits( diff --git a/paddle_quantum/locc/locc_state.py b/paddle_quantum/locc/locc_state.py index e4a2723..f026d68 100644 --- a/paddle_quantum/locc/locc_state.py +++ b/paddle_quantum/locc/locc_state.py @@ -69,6 +69,21 @@ class LoccState(paddle_quantum.State): assert backend == paddle_quantum.Backend.DensityMatrix self.backend = backend self.dtype = dtype if dtype is not None else paddle_quantum.get_dtype() + + @property + def is_swap_back(self) -> bool: + return True + + @is_swap_back.setter + def is_swap_back(self, value: bool) -> None: + # Currently is_swap_back for LOCC state is banned. + # TODO: add optimization logic for LOCC module + pass + + def reset_sequence(self) -> None: + # Currently reset_sequence for LOCC state is banned. + # TODO: add optimization logic for LOCC module + pass def clone(self) -> "LoccState": r"""Create a copy of the current object. diff --git a/paddle_quantum/loss/measure.py b/paddle_quantum/loss/measure.py index acb40e9..82678a7 100644 --- a/paddle_quantum/loss/measure.py +++ b/paddle_quantum/loss/measure.py @@ -20,9 +20,9 @@ The source file of the class for the measurement. import paddle import paddle_quantum from ..backend import quleaf -from ..backend import Backend -from ..intrinsic import _get_float_dtype -from typing import Optional, Union, Iterable +from ..backend import Backend, state_vector +from ..intrinsic import _get_float_dtype, _perm_of_list, _base_transpose, _base_transpose_for_dm +from typing import Optional, Union, Iterable, List class ExpecVal(paddle_quantum.Operator): @@ -34,6 +34,7 @@ class ExpecVal(paddle_quantum.Operator): hamiltonian: The input observable. shots: The number of measurement shots. Defaults to ``0``. Now it just need to be input when the backend is QuLeaf. """ + def __init__(self, hamiltonian: paddle_quantum.Hamiltonian, shots: Optional[int] = 0): super().__init__() self.hamiltonian = hamiltonian @@ -43,46 +44,15 @@ class ExpecVal(paddle_quantum.Operator): self.sites = self.hamiltonian.sites self.matrices = self.hamiltonian.pauli_words_matrix - def __state_qubits_swap(self, pauli_site, state_data, num_qubits): - # generate swap_list - origin_seq = list(range(0, num_qubits)) - target_seq = pauli_site + [x for x in origin_seq if x not in pauli_site] - swapped = [False] * num_qubits - swap_list = [] - for idx in range(0, num_qubits): - if not swapped[idx]: - next_idx = idx - swapped[next_idx] = True - while not swapped[target_seq[next_idx]]: - swapped[target_seq[next_idx]] = True - if next_idx < target_seq[next_idx]: - swap_list.append((next_idx, target_seq[next_idx])) - else: - swap_list.append((target_seq[next_idx], next_idx)) - next_idx = target_seq[next_idx] - - # function for swapping ath and bth qubit in state - def swap_a_and_b(target_state, size, pos_a, pos_b): - target_state = target_state.reshape([2 ** pos_a, 2, 2 ** (pos_b - pos_a - 1), 2, 2 ** (size - pos_b - 1)]) - return paddle.transpose(target_state, [0, 3, 2, 1, 4]) - - # begin swap - if self.backend == paddle_quantum.Backend.DensityMatrix: - for a, b in swap_list: - state_data = swap_a_and_b(state_data, 2 * num_qubits, a, b) - state_data = swap_a_and_b(state_data, 2 * num_qubits, a + num_qubits, b + num_qubits) - else: - for a, b in swap_list: - state_data = swap_a_and_b(state_data, num_qubits, a, b) - return state_data - - def forward(self, state: paddle_quantum.State) -> paddle.Tensor: + def forward(self, state: paddle_quantum.State, decompose: Optional[bool] = False) -> Union[ + paddle.Tensor, List[paddle.Tensor]]: r"""Compute the expectation value of the observable with respect to the input state. The value computed by this function can be used as a loss function to optimize. Args: state: The input state which will be used to compute the expectation value. + decompose: Defaults to ``False``. If decompose is ``True``, it will return the expectation value of each term. Raises: NotImplementedError: The backend is wrong or not supported. @@ -91,45 +61,63 @@ class ExpecVal(paddle_quantum.Operator): The expectation value. If the backend is QuLeaf, it is computed by sampling. """ if self.backend == Backend.QuLeaf: - if len(state.param_list) > 0: - param = paddle.concat(state.param_list) - else: - param = paddle.to_tensor(state.param_list) + param_list = [history['param'] for history in filter(lambda x: 'param' in x, state.oper_history)] expec_val = quleaf.ExpecValOp.apply( - param, - state, self.hamiltonian, self.shots + state, + self.hamiltonian, + paddle.to_tensor([self.shots], dtype=paddle.get_default_dtype()), + *param_list ) return expec_val num_qubits = state.num_qubits float_dtype = _get_float_dtype(paddle_quantum.get_dtype()) - expec_val = paddle.zeros([1], dtype=float_dtype) + origin_seq = list(range(num_qubits)) state_data = state.data - for i in range(0, self.num_terms): + if self.backend == Backend.StateVector: + expec_val = paddle.zeros([state_data.reshape([-1, 2 ** num_qubits]).shape[0]], dtype=float_dtype) + elif self.backend == Backend.DensityMatrix: + expec_val = paddle.zeros([state_data.reshape([-1, 2 ** num_qubits, 2 ** num_qubits]).shape[0]], + dtype=float_dtype) + else: + raise NotImplementedError + expec_val_each_term = [] + for i in range(self.num_terms): pauli_site = self.sites[i] if pauli_site == ['']: expec_val += self.coeffs[i] + expec_val_each_term.append(self.coeffs[i]) continue num_applied_qubits = len(pauli_site) matrix = self.matrices[i] - # extract current state and do swap operation - if num_qubits != 1: - _state_data = self.__state_qubits_swap(pauli_site, state_data, num_qubits) - else: - _state_data = state_data - # use einstein sum notation to shrink the size of operation of matrix multiplication + if self.backend == Backend.StateVector: - _state_data = _state_data.reshape([2 ** num_applied_qubits, 2 ** (num_qubits - num_applied_qubits)]) - output_state = paddle.einsum('ia, ab->ib', matrix, _state_data).reshape([2 ** num_qubits]) - _state_data = paddle.conj(_state_data.reshape([2 ** num_qubits])) - expec_val += paddle.real(paddle.matmul(_state_data, output_state)) * self.coeffs[i] + output_state, seq_for_acted = state_vector.unitary_transformation_without_swapback( + state_data, [matrix], pauli_site, num_qubits, origin_seq) + perm_map = _perm_of_list(seq_for_acted, origin_seq) + output_state = _base_transpose(output_state, perm_map).reshape([-1, 2 ** num_qubits, 1]) + state_data_bra = paddle.conj(state_data.reshape([-1, 1, 2 ** num_qubits])) + batch_values = paddle.squeeze(paddle.real(paddle.matmul(state_data_bra, output_state)), axis=[-2, -1]) * \ + self.coeffs[i] + expec_val_each_term.append(batch_values) + expec_val += batch_values + elif self.backend == Backend.DensityMatrix: - _state_data = _state_data.reshape([2 ** num_applied_qubits, 2 ** (2 * num_qubits - num_applied_qubits)]) - output_state = paddle.einsum('ia, ab->ib', matrix, _state_data) - output_state = output_state.reshape([2 ** num_qubits, 2 ** num_qubits]) - expec_val += paddle.real(paddle.trace(output_state)) * self.coeffs[i] + seq_for_acted = pauli_site + [x for x in origin_seq if x not in pauli_site] + perm_map = _perm_of_list(origin_seq, seq_for_acted) + output_state = _base_transpose_for_dm(state_data, perm=perm_map).reshape( + [-1, 2 ** num_applied_qubits, 2 ** (2 * num_qubits - num_applied_qubits)]) + output_state = paddle.matmul(matrix, output_state).reshape( + [-1, 2 ** num_qubits, 2 ** num_qubits]) + batch_values = paddle.real(paddle.trace(output_state, axis1=-2, axis2=-1)) * self.coeffs[i] + expec_val_each_term.append(batch_values) + expec_val += batch_values + else: raise NotImplementedError + + if decompose: + return expec_val_each_term return expec_val @@ -142,6 +130,7 @@ class Measure(paddle_quantum.Operator): Raises: NotImplementedError: Currently we just support the z basis. """ + def __init__(self, measure_basis: Optional[Union[Iterable[paddle.Tensor], str]] = 'z'): super().__init__() if measure_basis == 'z' or measure_basis == 'computational_basis': @@ -164,7 +153,7 @@ class Measure(paddle_quantum.Operator): NotImplementedError: The backend is wrong or not supported. NotImplementedError: The qubit index is wrong or not supported. NotImplementedError: Currently we just support the z basis. - + Returns: The probability of the measurement. """ @@ -198,7 +187,7 @@ class Measure(paddle_quantum.Operator): else: raise NotImplementedError("The qubit index is wrong or not supported.") - prob_array = prob_array / paddle.sum(prob_array) # normalize calculation error + prob_array = prob_array / paddle.sum(prob_array) # normalize calculation error if desired_result is None: return prob_array if isinstance(desired_result, str): diff --git a/paddle_quantum/mbqc/gates/mcalculus_tests/cnot_test.py b/paddle_quantum/mbqc/gates/mcalculus_tests/cnot_test.py index a46f2f4..a2535c9 100644 --- a/paddle_quantum/mbqc/gates/mcalculus_tests/cnot_test.py +++ b/paddle_quantum/mbqc/gates/mcalculus_tests/cnot_test.py @@ -16,11 +16,12 @@ CNOT test """ +import paddle +import paddle_quantum from paddle_quantum.mbqc.utils import random_state_vector, compare_by_vector, compare_by_density from paddle_quantum.mbqc.simulator import MBQC from paddle_quantum.mbqc.qobject import Circuit, State from paddle_quantum.mbqc.mcalculus import MCalculus -from paddle_quantum.circuit import UAnsatz n = 2 # Set the circuit width # Generate a random state vector @@ -56,9 +57,10 @@ mbqc.run_pattern() state_out = mbqc.get_quantum_output() # Find the standard result -cir_std = UAnsatz(n) +cir_std = paddle_quantum.Circuit(n) cir_std.cnot([0, 1]) -vec_std = cir_std.run_state_vector(input_psi.astype("complex128")) +vec_std = cir_std(paddle_quantum.state.to_state(paddle.flatten(input_psi))) +vec_std = vec_std.data system_std = state_out.system state_std = State(vec_std, system_std) # Compare with the standard result in UAnsatz diff --git a/paddle_quantum/mbqc/gates/mcalculus_tests/random_test.py b/paddle_quantum/mbqc/gates/mcalculus_tests/random_test.py index dee0fbb..7141103 100644 --- a/paddle_quantum/mbqc/gates/mcalculus_tests/random_test.py +++ b/paddle_quantum/mbqc/gates/mcalculus_tests/random_test.py @@ -14,7 +14,8 @@ from numpy import random, pi from paddle import to_tensor -from paddle_quantum.circuit import UAnsatz +import paddle +import paddle_quantum from paddle_quantum.mbqc.simulator import MBQC from paddle_quantum.mbqc.transpiler import transpile from paddle_quantum.mbqc.qobject import Circuit, State @@ -26,18 +27,24 @@ theta = to_tensor(random.rand(n) * 2 * pi, dtype='float64') # Generate random a # Instantiate a Circuit class cir_mbqc = Circuit(n) # Instantiate a UAnsatz class -cir_ansatz = UAnsatz(n) +cir_ansatz = paddle_quantum.Circuit(n) # Construct a circuit -for cir in [cir_mbqc, cir_ansatz]: - for i in range(n): - cir.h(i) - cir.rx(theta[i], i) - cir.cnot([0, 1]) - for i in range(n): - cir.ry(theta[i], i) - cir.rz(theta[i], i) - +# for cir in [cir_mbqc, cir_ansatz]: +for i in range(n): + cir_mbqc.h(i) + cir_mbqc.rx(theta[i], i) +cir_mbqc.cnot([0, 1]) +for i in range(n): + cir_mbqc.ry(theta[i], i) + cir_mbqc.rz(theta[i], i) +for i in range(n): + cir_ansatz.h(i) + cir_ansatz.rx(i, param=theta[i]) +cir_ansatz.cnot([0, 1]) +for i in range(n): + cir_ansatz.ry(i, param=theta[i]) + cir_ansatz.rz(i, param=theta[i]) # Generate a random state vector input_psi = random_state_vector(n, is_real=False) # Transpile circuit to measurement pattern @@ -50,7 +57,8 @@ mbqc.run_pattern() state_out = mbqc.get_quantum_output() # Find the standard result -vec_ansatz = cir_ansatz.run_state_vector(input_psi.astype("complex128")) +vec_ansatz = cir_ansatz(paddle_quantum.state.to_state(paddle.flatten(input_psi))) +vec_ansatz = vec_ansatz.data system_ansatz = state_out.system state_ansatz = State(vec_ansatz, system_ansatz) compare_by_vector(state_out, state_ansatz) diff --git a/paddle_quantum/mbqc/mcalculus.py b/paddle_quantum/mbqc/mcalculus.py index 2e06043..a3ccb52 100644 --- a/paddle_quantum/mbqc/mcalculus.py +++ b/paddle_quantum/mbqc/mcalculus.py @@ -12,8 +12,8 @@ # See the License for the specific language governing permissions and # limitations under the License. -""" -此模块包含处理 MBQC 测量模式的相关操作。 +r""" +This module contains the related operations for the MBQC measurement patterns. """ from numpy import pi @@ -27,13 +27,14 @@ __all__ = [ class MCalculus: - r"""定义测量模式类。 + r"""Define the class MCalculus. - 跟据文献 [The measurement calculus, arXiv: 0704.1263] 的测量语言,该类提供处理测量模式的各种基本操作。 + According to the paper's [The measurement calculus, arXiv: 0704.1263] measurement language, + this class provides series of basic operations dealing with measurement patterns. """ def __init__(self): - r"""``MCalculus`` 的构造函数,用于实例化一个 ``MCalculus`` 对象。 + r""" The constructors of ``MCalculus`` which is used for initialize a ``MCalculus`` object. """ self.__circuit_slice = [] # Restore the information of sliced circuit self.__wild_pattern = [] # Record the background pattern @@ -44,19 +45,19 @@ class MCalculus: self.__track = False # Switch of progress bar def track_progress(self, track=True): - r"""显示测量模式处理过程的进度条开关。 + r"""The button for revealing the progress bar during dealing with the measurement pattern. Args: - track (bool, optional): ``True`` 为打开进度条显示,``False`` 为关闭进度条显示,默认为 ``True`` + track (bool, optional): ``True`` open the progress bar, ``False`` close the progress bar, the default is ``True`` """ assert isinstance(track, bool), "parameter 'track' must be a bool." self.__track = track def set_circuit(self, circuit): - r"""对 ``MCalculus`` 类设置量子电路。 + r"""Set the quantum circuit for the ``MCalculus`` class. Args: - circuit (Circuit): 量子电路 + circuit (Circuit): quantum circuit """ assert isinstance(circuit, Circuit), "please input a parameter of type 'Circuit'." assert circuit.is_valid(), "the circuit is not valid as at least one qubit is not performed any gate yet." @@ -67,15 +68,16 @@ class MCalculus: self.__join_patterns() def __slice_circuit(self, circuit): - r"""对电路进行切片操作,标记每个量子门和量子测量的输入比特和输出比特。 + r"""Cut the circuit into slices, label the input and output qubit of each quantum gate. Note: - 这是内部方法,用户不需要直接调用到该方法。 - 在此,我们使用 ``str`` 类型的变量作为节点的标签。为了不丢失原先节点的坐标信息,便于后续的画图操作, - 我们使用形如 ``("1/1", "2/1")`` 类型作为所有节点的标签。 + This is an internal method which the users don't need to use directly. + Here we use``str`` type variables as the label of the nodes. In order to avoid losing the + coordinates of the previous nodes and benefit for the plotting operation, we label + all the nodes by the type looks like ``("1/1","2/1")``. Args: - circuit (list): 电路列表,列表中每个元素代表一个量子门或测量 + circuit (list): a list of circuits, each element represents a quantum gate or measurement. """ # Slice the circuit to mark the input_/output_ labels for measurement pattern counter = [] @@ -132,20 +134,22 @@ class MCalculus: @staticmethod def __set_ancilla_label(input_, output_, ancilla_num_list=None): - r"""插入辅助比特。 + r"""Insert the auxiliary qubit - 在输入比特和输出比特中间插入辅助比特,辅助比特节点的坐标根据数目而均分,其标签类型与输入和输出比特的标签类型相同。 + Insert auxiliary qubit between the input and output qubit. The coordinates of the auxiliary qubits are + assigned according to the qubit number, and the labels of them are the same as the input/output qubits. Note: - 这是内部方法,用户不需要直接调用到该方法。 + + This is an internal method which the users don't need to use directly. Args: - input_ (list): 测量模式的输入节点 - output_ (list): 测量模式的输出节点 - ancilla_num_list (list): 需要插入的辅助节点个数列表 + input_ (list): The input node of the measurement pattern. + output_ (list): The output node of the measurement pattern. + ancilla_num_list (list): The list of the auxiliary qubits required to be inserted to the system. Returns: - list: 辅助节点标签列表 + list: The list containing the labels of the auxiliary qubits. """ assert len(input_) == len(output_), "input and output must have same length." assert len(input_) in [1, 2], str(len(input_)) + "-qubit gate is not supported in this version." @@ -175,17 +179,20 @@ class MCalculus: return ancilla_labels def __to_pattern(self, gate): - r"""将量子电路中的门和测量翻译为等价的测量模式。 + r""" Translate the quantum gates and quantum measurements to their equivalent measurement patterns in MBQC. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. Warning: - 当前版本支持的量子门为 ``[H, X, Y, Z, S, T, Rx, Ry, Rz, Rz_5, U, CNOT, CNOT_15, CZ]`` 和单比特测量。 - 注意量子门和测量对应的测量模式不唯一,本方法目前仅选取常用的一种或者两种测量模式进行翻译。 + The current version supports ``[H, X, Y, Z, S, T, Rx, Ry, Rz, Rz_5, U, CNOT, CNOT_15, CZ]`` quantum gates + and single qubit measurement. + By the way, there are no one-to-one correspondence between the quantum circuits and measurement patterns. + Here, we adopt the most common onr or two measurement patterns. Args: - gate (list): 待翻译的量子门或量子测量,列表中存储的是原始量子门(其中包含量子门名称、作用比特、参数)、输入比特、输出比特 + gate (list): The quantum gates or quantum measurements to be translated. The elements in the list + contains the original quantum gates(the name of gate, acting qubits, parameters),input/output qubits. """ original_gate, input_, output_ = gate name, which_qubit, param = original_gate @@ -397,16 +404,18 @@ class MCalculus: input_, output_, commands)) def __list_to_net(self, bit_lst): - r"""把一个包含比特标签的一维列表处理为二维网状结构的列表,与电路图的网状结构相对应。 + r""" Change a 1-dimensional list containing the labels of qubits to a 2-dimensional list corresponding + to the circuit diagram. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. Args: - bit_lst (list): 输入或输出节点标签的列表 + bit_lst (list): the list containing the labels of the input/output nodes Returns: - list: 网状结构的二维列表,每行记录的是输入或输出节点所在的列数 + list: a 2-dimensional list with circuit structure, each line contains the column coordinates + of the input/output nodes. """ bit_net = [[] for _ in range(self.__circuit_width)] for qubit in bit_lst: @@ -414,16 +423,16 @@ class MCalculus: return bit_net def __get_input(self, bit_lst): - r"""获得列表中的输入比特节点标签。 + r"""Get the labels of the input qubits in the list. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. Args: - bit_lst (list): 节点标签的列表 + bit_lst (list): the list containing the labels of the nodes Returns: - list: 输入比特的节点标签列表 + list: the list containing node labels of the input qubits """ bit_net = self.__list_to_net(bit_lst) input_ = [] @@ -432,16 +441,16 @@ class MCalculus: return input_ def __get_output(self, bit_lst): - r"""获得列表中的输出比特节点标签。 + r""" Get the labels of the output qubits in the list. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. Args: - bit_lst (list): 节点标签的列表 + bit_lst (list): the list containing the labels of the nodes Returns: - list: 输出比特的节点标签列表 + list: the list containing node labels of the output qubits """ bit_net = self.__list_to_net(bit_lst) # Need to separate the classical output and quantum output @@ -456,10 +465,10 @@ class MCalculus: return output_ def __join_patterns(self): - r"""将逐个翻译好的量子门和测量的测量模式拼接到一起。 + r"""Connect the translated measurement patterns of the quantum gates and quantum measurements. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. """ names = "" input_list = [] @@ -479,24 +488,26 @@ class MCalculus: @staticmethod def __propagate(which_cmds): - r"""交换两个命令。 + r"""Swap two commands - 任意两个命令交换遵从对应算符的交换关系,详细的交换关系请参见 [arXiv:0704.1263]。 + The swap of any two commands obeys the commutation relation of the operators, see + more details in [arXiv:0704.1263]. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. Hint: - 我们默认算符由左至右的顺序运算,例如 ``"E"`` 要在所有运算之前,因此 ``"E"`` 要在命令列表中的最左侧,其他命令以此类推。 + We default to the left-to-right order of operators, such as "E" before all + operations, so "E" should be at the leftmost in the list of commands, and so on. Warning: - 该方法中只对 ``"E"``, ``"M"``, ``"X"``, ``"Z"``, ``"S"`` 五类命令中的任意两个进行交换。 + This method exchange any two of the five commands `"E"``, ``"M"``, ``"X"``, ``"Z"``, ``"S"``. Args: - which_cmds (list): 待交换的命令列表 + which_cmds (list): 待交换的命令列表 The list of commands to be exchanged. Returns: - list: 交换后的新命令列表 + list: The list of the commands after exchanged. """ cmd1 = which_cmds[0] cmd2 = which_cmds[1] @@ -613,20 +624,23 @@ class MCalculus: return which_cmds def __propagate_by_type(self, cmd_type, cmds): - r"""把列表中某指定类型的所有命令向前交换。 + r""" Move forward the commands of a specific type. - 向前交换不是指将其交换至整个命令列表的最左端,而是交换至规则允许范围内的最前方。 - 例如:对同一比特的测量操作必须在纠缠操作的后面,所以当调用该方法交换测量算符时,测量算符被交换到了它前面的纠缠算符之后。 + The "move forward" should obeys the commutation rules. For example, + the measurement operations should behind the entanglement operations + acting on the same qubits as the measurements. When we use his method to move + the measurement commands, the commands should be move forward until the first + entanglement operation in front of them. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. Args: - cmd_type (str): 待交换的命令类型,为 ``"E"``, ``"M"``, ``"X"``, ``"Z"`` 或 ``"S"`` - cmds (list): 待处理的命令列表 + cmd_type (str): the type of the command to be exchanged, 为 ``"E"``, ``"M"``, ``"X"``, ``"Z"`` 或 ``"S"`` + cmds (list): the list of commands to be dealt with. Returns: - list: 交换后的新命令列表 + list: 交换后的新命令列表the new command list after exchange. """ assert cmd_type in ["E", "M", "X", "Z", "S"], "command's name must be 'E', 'M', 'X', 'Z' or 'S'." @@ -646,18 +660,20 @@ class MCalculus: @staticmethod def __reorder_labels_by_row(labels): - r"""将标签按照行数从小到大进行排序。 + r""" Sort the labels by the number of rows form small to large. - 该方法是为了调整输入节点和输出节点的顺序,从而与电路图的顺序相一致,便于后续运行和使用。 + The purpose of this method is to adjust the order of input/output nodes, + so as to be consistent with the order of the circuit diagram and facilitate + subsequent operations. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. Args: - labels (list): 待改写的标签列表 + labels (list): the list of labels to be dealt with. Returns: - list: 改写后的标签列表,按照行数从小到大顺序排列 + list: the list of labels sorted by the number of rows form small to large. """ row = [] row_and_col = {} @@ -673,20 +689,20 @@ class MCalculus: @staticmethod def __commands_to_numbers(cmds): - r"""将命令列表映射成数字列表。 + r""" Map the list of commands to the list of numbers. - 映射规则为 CommandE -> 1, CommandM -> 2, CommandX -> 3, CommandZ -> 4, CommandS -> 5。 + The rule is CommandE -> 1, CommandM -> 2, CommandX -> 3, CommandZ -> 4, CommandS -> 5. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. Args: - cmds (list): 待处理的命令列表 + cmds (list): The list of commands to be dealt with. Returns: - list: 记录每种命令的个数 - list: 映射后的列表 - list: 映射后的列表进行从小到大排序得到的标准列表 + list: contains the number of each type of command + list: the list of numbers after the map + list: the sorted standard number list after the map """ cmd_map = {"E": 1, "M": 2, "X": 3, "Z": 4, "S": 5} cmd_num_wild = [cmd_map[cmd.name] for cmd in cmds] @@ -697,30 +713,31 @@ class MCalculus: return cmds_count, cmd_num_wild, cmd_num_standard def __distance_to_standard(self, cmds): - r"""采用 Hamming 距离定义当前命令列表的顺序和标准顺序的距离函数。 + r""" Use Hamming distance to measure the difference between the order of the current list + and the standard list. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. Args: - cmds (list): 当前命令列表 + cmds (list): the current command list """ _, cmd_wild, cmd_std = self.__commands_to_numbers(cmds[:]) return sum([cmd_wild[i] == cmd_std[i] for i in range(len(cmd_wild))]) / len(cmd_wild) def __is_standard(self, cmd_type, cmds): - r"""判断命令列表中指定的命令类型是否为标准顺序。 + r""" This method judges whether the given type of command is in the standard order. Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method which the users don't need to use directly. Args: - cmd_type (str): 待判断的命令名称,为 ``E``, ``M``, ``X``, ``Z`` 或 ``S`` - cmds (list): 待判断的命令列表 + cmd_type (str): The command to be judged, including ``E``, ``M``, ``X``, ``Z`` 或 ``S`` + cmds (list): the list of commands to be judged Returns: - bool: 列表是否为标准列表的布尔值 + bool: the bool value of whether the list is in the standard order. """ assert cmd_type in ["E", "M", "X", "Z", "S"], "command's name must be 'E', 'M', 'X', 'Z', or 'S'." @@ -735,10 +752,11 @@ class MCalculus: return cmd_num_wild[:pointer_map[cmd_type]] == cmd_num_standard[:pointer_map[cmd_type]] def __simplify_pauli_measurements(self): - r"""对节点依赖性进行简化。 + r""" This method simplifies the dependence relation between different nodes. - 在某些特殊情形下,测量节点对其他节点的依赖性可以被简化。 - 设 \alpha 为不考虑依赖关系的测量角度,则测量角度实际上只有四种可能性,分别为: + In some special cases, the dependence of the measurement nodes to other nodes can be simplified. + Assume that \alpha is a measurement angle without considering the dependence relation, there are four + possible measurement angles as: .. math:: @@ -750,12 +768,13 @@ class MCalculus: \theta_{\text{ad}} = - \alpha + \pi - \text{当 } \alpha \text{ 为 } 0, \pi / 2, \pi, 3 \times \pi / 2 \text{ 时,该依赖关系可以简化。} + \text{when } \alpha \text{ is } 0, \pi / 2, \pi, 3 \times \pi / 2 \text{ the dependence relation can be simplified.} - \text{例如 } \alpha = \pi \text{ 时,}\pm \alpha + t \times \pi \text{导致的测量效果一样,与 domain\_s 无关,因此 domain\_s 可以移除。其他情形同理。} + \text{For example, when } \alpha = \pi \text{, }\pm \alpha + t \times \pi \text{ lead to the same measurement result, + independent of domain\_s. As a result, domain\_s can be removed.} Note: - 这是内部方法,用户不需要直接调用到该方法。 + In some special cases, the dependence of the measurement nodes to other nodes can be simplified. """ for cmd in self.__pattern.commands: if cmd.name == 'M': # Find CommandM @@ -767,10 +786,11 @@ class MCalculus: cmd.domain_s = [] def standardize(self): - r"""对测量模式进行标准化。 + r"""Standardize the measurement pattern. - 该方法对测量模式进行标准化操作,转化成等价的 EMC 模型。即将所有的 ``CommandE`` 交换到最前面,其次是 ``CommandM``, - ``CommandX`` 和 ``CommandZ``。为了简化测量模式,该方法在标准化各类命令之后还对 ``CommandM`` 进行 Pauli 简化。 + This method standardize the measurement pattern to the equivalent EMC model. The method exchange all + the "Command E" to the first, followed by "Command M", "Command X" and "Command Z". To simplify the + measurement pattern, this method applies Pauli simplification to "Command M" after the standardization. """ cmds = self.__pattern.commands @@ -784,20 +804,22 @@ class MCalculus: @staticmethod def __pull_out_domain_t(cmds): - r"""在命令列表中把信号转移算符从测量算符中提取出来。 + r""" Extract the signal shifting operators from the measurement operators in the command list. Note: - 信号转移是一种特殊的操作,通过与其他命令算符的交换,解除测量命令的域 t 列表中节点的依赖性, - 从而在某些情况下简化测量模式,详情请参见 [arXiv:0704.1263]。 + Signal shifting is a special operation. By switching with other command operators, this method + remove the dependency among nodes in domain t in order to simplify the measurement patterns on some + conditions, see more details in [arXiv:0704.1263]. Warning: - 我们只提取 XY 平面测量算符的域 t 列表中节点的依赖性作为信号转移算符。对于 YZ 平面测量算符,我们并未采取此操作。 + We only extract the node dependence of the nodes in domain t of measurement operators in XY plane, and + we don't apply this operation to the measurement operator in YZ plane. Args: - cmds (list): 命令列表 + cmds (list): command list Returns: - list: 提取信号转移算符后的命令列表 + list: 提取信号转移算符后的命令列表 command list after extracting the signal shifting operators """ cmds_len = len(cmds) for i in range(cmds_len - 1, -1, -1): @@ -809,10 +831,10 @@ class MCalculus: return cmds def shift_signals(self): - r"""信号转移操作。 + r"""Signal shifting operation Note: - 这是用户选择性调用的方法之一。 + This is one of the choices of the users. """ cmds = self.__pattern.commands cmds = self.__pull_out_domain_t(cmds) @@ -827,27 +849,31 @@ class MCalculus: self.__pattern.commands = cmds def get_pattern(self): - r"""返回测量模式。 + r"""Return the measurement pattern Returns: - Pattern: 处理后的测量模式 + Pattern: the measurement pattern after processing. """ return self.__pattern @staticmethod def __default_order_by_row(labels): - r"""按照行的顺序对节点标签列表进行排序并返回。 + r""" Sort the nodes' labels by the number of rows. + + + sorting rules: If the number of rows of the labels are different, + smaller first; If the number of rows of the labels are the same, the labels + with smaller number of columns first. - 排序规则:不同行数,行数小的优先。相同行数,列数小的优先。 Note: - 这是内部方法,用户不需要直接调用到该方法。 + This is an internal method and users don't use it directly. Args: - labels (list): 待处理的节点标签列表 + labels (list): the list of the nodes' labels to be processed. Returns: - list: 排序后的节点标签列表 + list: the list of nodes' labels after sorting. """ # Construct a dict by string labels and their float values labels_dict = {label: (div_str_to_float(label[0]), div_str_to_float(label[1])) for label in labels} @@ -859,11 +885,14 @@ class MCalculus: return labels_sorted def optimize_by_row(self): - r"""按照行序优先的原则对测量模式中的测量顺序进行优化。 + r""" Optimize the measurement order in the measurement pattern according + to row major order. Warning: - 这是一种启发式的优化算法,对于特定的测量模式可以起到优化测量顺序的作用,不排除存在更优的测量顺序。例如,对于浅层量子电路, - 按照行序优先原则,测量完同一量子位上的量子门、测量对应的节点后,该量子位不再起作用,进而减少后续计算时可能涉及到的节点数目。 + This is a heuristic optimization algorithm works for specific measurement patterns. + It's also possible to find better measurement order. For example, for a shallow quantum + circuit, a specific qubit is no more needed after the quantum measurements according to the + row major order such that the computational cost in the follow-up process is simplified. """ cmds = self.__pattern.commands diff --git a/paddle_quantum/mbqc/qobject.py b/paddle_quantum/mbqc/qobject.py index 64097d7..d115c3c 100644 --- a/paddle_quantum/mbqc/qobject.py +++ b/paddle_quantum/mbqc/qobject.py @@ -12,8 +12,9 @@ # See the License for the specific language governing permissions and # limitations under the License. -""" -此模块包含量子信息处理的常用对象,如量子态、量子电路、测量模式等。 +r""" +This module contains the commonly used class in quantum information, e.g. quantum state, quantum circuit and measurement +patterns. """ from numpy import log2, sqrt @@ -27,19 +28,19 @@ __all__ = [ class State: - r"""定义量子态。 + r"""Define the quantum state. Attributes: - vector (Tensor): 量子态的列向量 - system (list): 量子态的系统标签列表 + vector (Tensor): the column vector of the quantum state. + system (list): the list of system labels of the quantum state. """ def __init__(self, vector=None, system=None): - r"""构造函数,用于实例化一个 ``"State"`` 量子态对象。 + r""" the constructor for initialize an object of the class `` "State`` . Args: - vector (Tensor, optional): 量子态的列向量 - system (list, optional): 量子态的系统标签列表 + vector (Tensor, optional): the column vector of the quantum state. + system (list, optional): the list of system labels of the quantum state. """ if vector is None and system is None: self.vector = to_tensor([1], dtype='float64') # A trivial state @@ -62,7 +63,7 @@ class State: self.norm = sqrt(matmul(t(conj(self.vector)), self.vector).numpy()) def __str__(self): - r"""打印该 ``State`` 类的信息,便于用户查看。 + r"""print the information of this class """ class_type_str = "State" vector_str = str(self.vector.numpy()) @@ -78,23 +79,25 @@ class State: class Circuit: - r"""定义量子电路。 + r"""Define the quantum circuit. Note: - 该类与 ``UAnsatz`` 类似,用户可以仿照 ``UAnsatz`` 电路的调用方式对此类进行实例化,完成电路图的构建。 + This class is similar to ``UAnsatz``, one can imitate the use of ``UAnsatz`` to instantiate this class and + construct the circuit diagram. Warning: - 当前版本仅支持 ``H, X, Y, Z, S, T, Rx, Ry, Rz, Rz_5, U, CNOT, CNOT_15, CZ`` 中的量子门以及测量操作。 + The current version supports the quantum operations(gates and measurement) in ``H, X, Y, Z, S, T, Rx, Ry, + Rz, Rz_5, U, CNOT, CNOT_15, CZ``. Attributes: - width (int): 电路的宽度(比特数) + width (int): The width of the circuit(number of qubits). """ def __init__(self, width): - r"""``Circuit`` 的构造函数,用于实例化一个 ``Circuit`` 对象。 + r""" The constructor of the class ``Circuit`` used of instantiate an object. Args: - width (int): 电路的宽度(比特数) + width (int): The width of the circuit(number of qubits). """ assert isinstance(width, int), "circuit 'width' must be a int." self.__history = [] # A list to record the circuit information @@ -102,18 +105,18 @@ class Circuit: self.__width = width # The width of circuit def h(self, which_qubit): - r"""添加 ``Hadamard`` 门。 + r"""Add a ``Hadamard`` gate. - 其矩阵形式为: + The matrix form: .. math:: \frac{1}{\sqrt{2}}\begin{bmatrix} 1&1\\1&-1 \end{bmatrix} Args: - which_qubit (int): 作用量子门的量子位编号 + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -134,18 +137,18 @@ class Circuit: self.__history.append(['h', [which_qubit], None]) def x(self, which_qubit): - r"""添加 ``Pauli X`` 门。 + r"""Add a ``Pauli X`` gate. - 其矩阵形式为: + The matrix form: .. math:: \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} Args: - which_qubit (int): 作用量子门的量子位编号 + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -166,18 +169,18 @@ class Circuit: self.__history.append(['x', [which_qubit], None]) def y(self, which_qubit): - r"""添加 ``Pauli Y`` 门。 + r"""Add a ``Pauli Y`` gate. - 其矩阵形式为: + The matrix form: .. math:: \begin{bmatrix} 0 & -i \\ i & 0 \end{bmatrix} Args: - which_qubit (int): 作用量子门的量子位编号 + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -198,18 +201,18 @@ class Circuit: self.__history.append(['y', [which_qubit], None]) def z(self, which_qubit): - r"""添加 ``Pauli Z`` 门。 + r"""Add a ``Pauli Z`` gate. - 其矩阵形式为: + The matrix form: .. math:: \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix} Args: - which_qubit (int): 作用量子门的量子位编号 + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -230,18 +233,18 @@ class Circuit: self.__history.append(['z', [which_qubit], None]) def s(self, which_qubit): - r"""添加 ``S`` 门。 + r"""Add a ``S`` gate. - 其矩阵形式为: + The matrix form: .. math:: \begin{bmatrix} 1&0\\0& i \end{bmatrix} Args: - which_qubit (int): 作用量子门的量子位编号 + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -262,18 +265,18 @@ class Circuit: self.__history.append(['s', [which_qubit], None]) def t(self, which_qubit): - r"""添加 ``T`` 门。 + r"""Add ``T`` gate. - 其矩阵形式为: + The matrix form: .. math:: \begin{bmatrix} 1&0\\0& e^{i\pi/ 4} \end{bmatrix} Args: - which_qubit (int): 作用量子门的量子位编号 + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -294,19 +297,19 @@ class Circuit: self.__history.append(['t', [which_qubit], None]) def rx(self, theta, which_qubit): - r"""添加关于 x 轴的旋转门。 + r"""Add a rotation gate in x direction. - 其矩阵形式为: + The matrix form: .. math:: \begin{bmatrix} \cos\frac{\theta}{2} & -i\sin\frac{\theta}{2} \\ -i\sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{bmatrix} Args: - theta (Tensor): 旋转角度 - which_qubit (int): 作用量子门的量子位编号 + theta (Tensor): rotation angle + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -330,19 +333,19 @@ class Circuit: self.__history.append(['rx', [which_qubit], theta]) def ry(self, theta, which_qubit): - r"""添加关于 y 轴的旋转门。 + r"""Add a rotation gate in y direction. - 其矩阵形式为: + The matrix form: .. math:: \begin{bmatrix} \cos\frac{\theta}{2} & -\sin\frac{\theta}{2} \\ \sin\frac{\theta}{2} & \cos\frac{\theta}{2} \end{bmatrix} Args: - theta (Tensor): 旋转角度 - which_qubit (int): 作用量子门的量子位编号 + theta (Tensor): rotation angle + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -366,19 +369,19 @@ class Circuit: self.__history.append(['ry', [which_qubit], theta]) def rz(self, theta, which_qubit): - r"""添加关于 z 轴的旋转门。 + r"""Add a rotation gate in z direction. - 其矩阵形式为: + The matrix form: .. math:: \begin{bmatrix} 1 & 0 \\ 0 & e^{i\theta} \end{bmatrix} Args: - theta (Tensor): 旋转角度 - which_qubit (int): 作用量子门的量子位编号 + theta (Tensor): rotation angle + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -402,19 +405,20 @@ class Circuit: self.__history.append(['rz', [which_qubit], theta]) def rz_5(self, theta, which_qubit): - r"""添加关于 z 轴的旋转门(该旋转门对应的测量模式由五个量子比特构成)。 + r"""Add a rotation gate in the z direction(the measurement pattern corresponding to this gate + is composed of five qubits). - 其矩阵形式为: + The matrix form: .. math:: \begin{bmatrix} 1 & 0 \\ 0 & e^{i\theta} \end{bmatrix} Args: - theta (Tensor): 旋转角度 - which_qubit (int): 作用量子门的量子位编号 + theta (Tensor): rotation angle + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -438,22 +442,23 @@ class Circuit: self.__history.append(['rz_5', [which_qubit], theta]) def u(self, params, which_qubit): - r"""添加单量子比特的任意酉门。 + r"""Add a general single qubit gate. Warning: - 与 ``UAnsatz`` 类中的 U3 的三个参数不同,这里的酉门采用 ``Rz Rx Rz`` 分解, + Different from the 3 parameters of the U3 gate in ``UAnsatz`` class, + the unitary here adopts a ``Rz Rx Rz`` decomposition. - 其分解形式为: + The decomposition takes the form: .. math:: U(\alpha, \beta, \gamma) = Rz(\gamma) Rx(\beta) Rz(\alpha) Args: - params (list): 单比特酉门的三个旋转角度 - which_qubit (int): 作用量子门的量子位编号 + params (list): three rotation angles of the unitary gate + which_qubit (int): The number(No.) of the qubit that the gate applies to. - 代码示例: + Code example: .. code-block:: python @@ -485,18 +490,19 @@ class Circuit: self.__history.append(['u', [which_qubit], params]) def cnot(self, which_qubits): - r"""添加控制非门。 + r"""Add a CNOT gate. - 当 ``which_qubits`` 为 ``[0, 1]`` 时,其矩阵形式为: + When ``which_qubits`` is ``[0, 1]`` ,the matrix form is: .. math:: \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix} Args: - which_qubits (list): 作用量子门的量子位,其中列表第一个元素为控制位,第二个元素为受控位 + which_qubits (list): A two element list contains the qubits that the CNOT gate applies to, the first + element is the control qubit, the second is the target qubit. - 代码示例: + Code example: .. code-block:: python @@ -522,18 +528,19 @@ class Circuit: self.__history.append(['cnot', which_qubits, None]) def cnot_15(self, which_qubits): - r"""添加控制非门 (该门对应的测量模式由十五个量子比特构成)。 + r"""Add a CNOT gate(the measurement pattern corresponding to this gate is composed of 15 qubits). - 当 ``which_qubits`` 为 ``[0, 1]`` 时,其矩阵形式为: + When ``which_qubits`` is ``[0, 1]`` ,the matrix form is: .. math:: \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix} Args: - which_qubits (list): 作用量子门的量子位,其中列表第一个元素为控制位,第二个元素为受控位 + which_qubits (list): A two element list contains the qubits that the CNOT gate applies to, the first + element is the control qubit, the second is the target qubit. - 代码示例: + Code example: .. code-block:: python @@ -559,18 +566,19 @@ class Circuit: self.__history.append(['cnot_15', which_qubits, None]) def cz(self, which_qubits): - r"""添加控制 Z 门。 + r"""Add a controlled-Z gate. - 当 ``which_qubits`` 为 ``[0, 1]`` 时,其矩阵形式为: + When ``which_qubits`` is ``[0, 1]`` ,the matrix form is: .. math:: \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix} Args: - which_qubits (list): 作用量子门的量子位,其中列表第一个元素为控制位,第二个元素为受控位 + which_qubits (list): A two element list contains the qubits that the CZ gate applies to, the first + element is the control qubit, the second is the target qubit. - 代码示例: + Code example: .. code-block:: python @@ -596,22 +604,25 @@ class Circuit: self.__history.append(['cz', which_qubits, None]) def measure(self, which_qubit=None, basis_list=None): - r"""对量子电路输出的量子态进行测量。 + r"""Measure the output state of the quantum circuit. Note: - 与 ``UAnsatz`` 类中的测量不同,除默认的 Z 测量外,此处的测量方式可以由用户自定义,但需要将测量方式与测量比特相对应。 + Unlike the measurement operations in the ``UAnsatz`` class, besides the default measurement in Z basis, + the users can define the measurement ways themselves by providing the measurement basis and the qubits + to be measured. Warning: - 此方法只接受三种输入方式: - 1. 不输入任何参数,表示对所有的量子位进行 Z 测量; - 2. 输入量子位,但不输入测量基,表示对输入的量子位进行 Z 测量; - 3. 输入量子位和对应测量基,表示对输入量子位进行指定的测量。 - 如果用户希望自定义测量基参数,需要注意输入格式为 ``[angle, plane, domain_s, domain_t]``, - 且当前版本的测量平面 ``plane`` 只能支持 ``XY`` 或 ``YZ``。 + There are three kinds of inputs: + 1. which_qubit=None,basis_list=None(default): measure all the qubits in Z basis. + 2. which_qubit=input, basis_list=None: measure the input qubit in Z basis. + 3. which_qubit=input1, basis_list=input2: measure the input1 qubit by the basis in input2. + If the users want to define the measurement basis themselves, the input format looks like: + ``[angle,plane,domain_s,domain_t]``. By the way,in the current version paddle_quantum, the + ``plane`` parameter can only take ``XY`` or ``YZ``. Args: - which_qubit (int, optional): 被测量的量子位 - basis_list (list, optional): 测量方式 + which_qubit (int, optional): the qubit to be measured + basis_list (list, optional): measurement basis """ # Measure all the qubits by Z measurement if which_qubit is None and basis_list is None: @@ -645,12 +656,12 @@ class Circuit: raise ValueError("such a combination of input parameters is not supported. Please see our API for details.") def is_valid(self): - r"""检查输入的量子电路是否符合规定。 + r"""Check that if the circuit is valid. - 我们规定输入的量子电路中,每一个量子位上至少作用一个量子门。 + We require that for each qubit in the quantum circuit, at least one quantum gate should be applied to it. Returns: - bool: 量子电路是否符合规定的布尔值 + bool: the boolean values of whether the quantum circuit is valid. """ all_qubits = [] for gate in self.__history: @@ -661,36 +672,36 @@ class Circuit: return self.__width == len(effective_qubits) def get_width(self): - r"""返回量子电路的宽度。 + r"""Return the width of the quantum circuit. Returns: - int: 量子电路的宽度 + int: the width of the quantum circuit. """ return self.__width def get_circuit(self): - r"""返回量子电路列表。 + r"""Return the list of quantum circuits. Returns: - list: 量子电路列表 + list: the list of quantum circuits """ return self.__history def get_measured_qubits(self): - r"""返回量子电路中测量的比特位。 + r"""Return the list of measured qubits in the quantum circuit. Returns: - list: 量子电路中测量的比特位列表 + list: the list of measured qubits in the quantum circuit. """ return self.__measured_qubits def print_circuit_list(self): - r"""打印电路图的列表。 + r"""Print the list of the circuit. Returns: - string: 用来打印的字符串 + string: the strings to be printed - 代码示例: + Code example: .. code-block:: python @@ -742,27 +753,27 @@ class Circuit: class Pattern: - r"""定义测量模式。 + r"""Define the measurement pattern. - 该测量模式的结构依据文献 [The measurement calculus, arXiv: 0704.1263]。 + see more details of the measurement pattern in [The measurement calculus, arXiv: 0704.1263]. Attributes: - name (str): 测量模式的名称 - space (list): 测量模式所有节点列表 - input_ (list): 测量模式的输入节点列表 - output_ (list): 测量模式的输出节点列表 - commands (list): 测量模式的命令列表 + name (str): the name of the measurement pattern. + space (list): the list contains all the nodes of the measurement pattern. + input_ (list): the list contains the input nodes of the measurement pattern. + output_ (list): the list contains the output nodes of the measurement pattern. + commands (list): the list contains the commands of the measurement pattern. """ def __init__(self, name, space, input_, output_, commands): - r"""构造函数,用于实例化一个 ``Pattern`` 对象。 + r"""Constructor of the class ``Pattern`` used for instantiated an object. Args: - name (str): 测量模式的名称 - space (list): 测量模式所有节点列表 - input_ (list): 测量模式的输入节点列表 - output_ (list): 测量模式的输出节点列表 - commands (list): 测量模式的命令列表 + name (str): the name of the measurement pattern. + space (list): the list contains all the nodes of the measurement pattern. + input_ (list): the list contains the input nodes of the measurement pattern. + output_ (list): the list contains the output nodes of the measurement pattern. + commands (list): the list contains the commands of the measurement pattern. """ self.name = name self.space = space @@ -771,59 +782,67 @@ class Pattern: self.commands = commands class CommandE: - r"""定义纠缠命令类。 + r"""Define the class ``CommandE`` corresponding to some entanglement commands. Note: - 此处纠缠命令对应作用控制 Z 门。 + The entanglement command here corresponds to the controlled-Z gate. Attributes: - which_qubits (list): 作用纠缠命令的两个节点标签构成的列表 + which_qubits (list): A two-element list contains the labels of the node + that the entanglement command applies to. """ def __init__(self, which_qubits): - r"""纠缠命令类构造函数,用于实例化一个 ``CommandE`` 对象。 + r""" Constructor of the ``CommandE`` class used for instantiate an object. Args: - which_qubits (list): 作用纠缠命令的两个节点标签构成的列表 + which_qubits (list): A two-element list contains the labels of the node + that the entanglement command applies to. """ self.name = "E" self.which_qubits = which_qubits class CommandM: - r"""定义测量命令类。 + r"""Define the ``CommandM`` class corresponding to the measurement commands. - 测量命令有五个属性,分别为测量比特的标签 ``which_qubit``,原始的测量角度 ``angle``, - 测量平面 ``plane``,域 s 对应的节点标签列表 ``domain_s``,域 t 对应的节点标签列表 ``domain_t``。 - 设原始角度为 :math:`\alpha`,则考虑域中节点依赖关系后的测量角度 :math:`\theta` 为: + ``CommandM`` has 5 attributes, including: + 1.which_qubit: the qubit to be measured. + 2.angle: the original measurement angle. + 3.plane: the measurement plane. + 4.domain_s: the node list corresponding to domain s. + 5.domain_t: the node list corresponding to domain t. + The original angle :math:`\alpha` is transformed into :math:`\theta` as: .. math:: \theta = (-1)^s \times \alpha + t \times \pi + after considering the node dependence in the domain. Note: - 域 s 和域 t 是 MBQC 模型中的概念,分别记录了 Pauli X 算符和 Pauli Z 算符对测量角度产生的影响, - 二者共同记录了该测量节点对其他节点的测量结果的依赖关系。 + Domain s(domain t) is the concept in MBQC containing the influence on the measurement angles induced + by Pauli X(Pauli Z) operator. Both of them record the dependence of the measurement node on the + measurement results of other nodes. Warning: - 该命令当前只支持 XY 和 YZ 平面的测量。 + Only measurements in "XY" and "YZ" planes are allowed in this version. Attributes: - which_qubit (any): 作用测量命令的节点标签 - angle (Tensor): 原始的测量角度 - plane (str): 测量平面 - domain_s (list): 域 s 对应的节点标签列表 - domain_t (list): 域 t 对应的节点标签列表 + which_qubit (any): the qubit to be measured. + angle (Tensor): the original measurement angle. + plane (str): the measurement plane. + domain_s (list): the node list corresponding to domain s. + domain_t (list): the node list corresponding to domain t. """ def __init__(self, which_qubit, angle, plane, domain_s, domain_t): - r"""构造函数,用于实例化一个 ``CommandM`` 对象。 + r"""The constructor of the ``CommandM`` class used for instantiated an object. Args: - which_qubit (any): 作用测量命令的节点标签 - angle (Tensor): 原始的测量角度 - plane (str): 测量平面 - domain_s (list): 域 s 对应的节点标签列表 - domain_t (list): 域 t 对应的节点标签列表 + which_qubit (any): the qubit to be measured. + angle (Tensor): the original measurement angle. + plane (str): the measurement plane. + domain_s (list): the node list corresponding to domain s. + domain_t (list): the node list corresponding to domain t. """ self.name = "M" self.which_qubit = which_qubit @@ -833,69 +852,70 @@ class Pattern: self.domain_t = domain_t class CommandX: - r"""定义 Pauli X 副产品修正命令类。 + r"""Define the ``CommandX`` class used for correcting the byproduct induced by Pauli X. Attributes: - which_qubit (any): 作用修正算符的节点标签 - domain (list): 依赖关系列表 + which_qubit (any): the label of the qubit that the correcting operator applies to. + domain (list): the list contains the dependence relation. """ def __init__(self, which_qubit, domain): - r"""构造函数,用于实例化一个 ``CommandX`` 对象。 + r"""The constructor of the ``CommandX`` class used for instantiated an object. Args: - which_qubit (any): 作用修正算符的节点标签 - domain (list): 依赖关系列表 + which_qubit (any): the label of the qubit that the correcting operator applies to. + domain (list): the list contains the dependence relation. """ self.name = "X" self.which_qubit = which_qubit self.domain = domain class CommandZ: - r"""定义 Pauli Z 副产品修正命令。 + r"""Define the ``CommandZ`` class used for correcting the byproduct induced by Pauli Z. Attributes: - which_qubit (any): 作用修正命令的节点标签 - domain (list): 依赖关系列表 + which_qubit (any): the label of the qubit that the correcting operator applies to. + domain (list): the list contains the dependence relation. """ def __init__(self, which_qubit, domain): - r"""构造函数,用于实例化一个 ``CommandZ`` 对象。 + r"""The constructor of the ``CommandZ`` class used for instantiated an object. Args: - which_qubit (any): 作用修正命令的节点标签 - domain (list): 依赖关系列表 + which_qubit (any): the label of the qubit that the correcting operator applies to. + domain (list): the list contains the dependence relation. """ self.name = "Z" self.which_qubit = which_qubit self.domain = domain class CommandS: - r"""定义 "信号转移" 命令类。 + r"""Define the ``CommandS`` class used for signal shifting. Note: - "信号转移" 是一类特殊的操作,用于消除测量命令对域 t 中节点的依赖关系,在某些情况下对测量模式进行简化。 + Signal shifting is a class of special operations used for eliminating the measurement operations' dependence + on the nodes in domain t and simplify the measurement patterns on some conditions. Attributes: - which_qubit (any): 消除依赖关系的测量命令作用的节点标签 - domain (list): 依赖关系列表 + which_qubit (any): the labels of the nodes applied by the signal shifting operations. + domain (list): the list contains the dependence relation. """ def __init__(self, which_qubit, domain): - r"""构造函数,用于实例化一个 ``CommandS`` 对象。 + r"""The constructor of the ``CommandS`` class used for instantiated an object. Args: - which_qubit (any): 消除依赖关系的测量命令作用的节点标签 - domain (list): 依赖关系列表 + which_qubit (any): the labels of the nodes applied by the signal shifting operations. + domain (list): the list contains the dependence relation. """ self.name = "S" self.which_qubit = which_qubit self.domain = domain def print_command_list(self): - r"""打印该 ``Pattern`` 类中的命令的信息,便于用户查看。 + r"""Print the information of commands in the ``Pattern`` class. - 代码示例: + Code example: .. code-block:: python diff --git a/paddle_quantum/mbqc/simulator.py b/paddle_quantum/mbqc/simulator.py index 1e6d859..5fdef80 100644 --- a/paddle_quantum/mbqc/simulator.py +++ b/paddle_quantum/mbqc/simulator.py @@ -12,8 +12,8 @@ # See the License for the specific language governing permissions and # limitations under the License. -""" -此模块包含构造 MBQC 模型的常用类和配套的运算模拟工具。 +r""" +This module contains the commonly used class and simulation tools in MBQC. """ from numpy import random, pi @@ -33,14 +33,11 @@ __all__ = [ class MBQC: - r"""定义基于测量的量子计算模型 ``MBQC`` 类。 + r""" Define a ``MBQC`` class used for measurement based quantum computation. - 用户可以通过实例化该类来定义自己的 MBQC 模型。 + The users can define their MBQC models by instantiate the objects of this class. """ - def __init__(self): - r"""MBQC 类的构造函数,用于实例化一个 ``MBQC`` 对象。 - """ self.__graph = None # Graph in a MBQC model self.__pattern = None # Measurement pattern in a MBQC model @@ -58,41 +55,36 @@ class MBQC: self.__pos = None # Position for drawing class Vertex: - r"""定义维护点列表,用于实例化一个 ``Vertex`` 对象。 + r"""Define the list of maintenance point used for instantiate a ``Vertex`` object. - 将 MBQC 算法中图的节点分为三类,并进行动态维护。 + Device the nodes in MBQC to three classes and maintain them dynamically. Note: - 这是内部类,用户不需要直接调用到该类。 + This is an internal class and the users don't need to use it directly. - Attributes: - total (list): MBQC 算法中图上的全部节点,不随运算而改变 - pending (list): 待激活的节点,随着运算的执行而逐渐减少 - active (list): 激活的节点,与当前测量步骤直接相关的节点 - measured (list): 已被测量过的节点,随着运算的执行而逐渐增加 + Args: + total (list): a list contains all the nodes in MBQC diagram, irrespective of the computation process. + pending (list): a list contains the nodes to be activated. The number of nodes decreases as the operations + are performed. + active (list): a list contains the active nodes directly related to the current measurement operations. + measured (list): a list contains the nodes which have been measured. The number of nodes decreases as the + operations are performed. + + :meta private: """ - def __init__(self, total=None, pending=None, active=None, measured=None): - r"""``Vertex`` 类的构造函数,用于实例化一个 ``Vertex`` 对象。 - - Args: - total (list): MBQC 算法中图上的全部节点,不随运算而改变 - pending (list): 待激活的节点,随着运算的执行而逐渐减少 - active (list): 激活的节点,与当前测量步骤直接相关的节点 - measured (list): 已被测量过的节点,随着运算的执行而逐渐增加 - """ self.total = [] if total is None else total self.pending = [] if pending is None else pending self.active = [] if active is None else active self.measured = [] if measured is None else measured def set_graph(self, graph): - r"""设置 MBQC 模型中的图。 + r"""Set the graphs in MBQC model. - 该函数用于将用户自己构造的图传递给 ``MBQC`` 实例。 + The users can use this function to transport their own graphs to the ``MBQC`` object. Args: - graph (list): MBQC 模型中的图,由列表 ``[V, E]`` 给出, 其中 ``V`` 为节点列表,``E`` 为边列表 + graph: The graphs in MBQC model. The list takes the form ``[V, E]``, where ``V`` are nodes, and ``E`` are edges. """ vertices, edges = graph @@ -106,23 +98,24 @@ class MBQC: self.vertex = self.Vertex(total=vertices, pending=vertices, active=[], measured=[]) def get_graph(self): - r"""获取图的信息。 + r"""Get the information of graphs. Returns: - nx.Graph: 图 + nx.Graph: graph """ return self.__graph def set_pattern(self, pattern): - r"""设置 MBQC 模型的测量模式。 + r"""Set the measurement patterns of the MBQC model. - 该函数用于将用户由电路图翻译得到或自己构造的测量模式传递给 ``MBQC`` 实例。 + This function is used for transport the measurement patterns to ``MBQC`` object. The measurement patterns + are acquired by either translation from the quantum circuit or the construction of users. Warning: - 输入的 pattern 参数是 ``Pattern`` 类型,其中命令列表为标准 ``EMC`` 命令。 + The input pattern parameter is of type ``Pattern``, in which the command list contains ``EMC`` commands. Args: - pattern (Pattern): MBQC 算法对应的测量模式 + pattern (Pattern): The measurement patterns corresponding to the MBQC algorithms. """ assert isinstance(pattern, Pattern), "please input a pattern of type 'Pattern'." @@ -143,22 +136,24 @@ class MBQC: self.set_graph(graph) def get_pattern(self): - r"""获取测量模式的信息。 + r"""Get the information of the measurement patterns. Returns: - Pattern: 测量模式 + Pattern: measurement pattern """ return self.__pattern def set_input_state(self, state=None): - r"""设置需要替换的输入量子态。 + r"""Set the input state to be replaced. Warning: - 与电路模型不同,MBQC 模型通常默认初始态为加态。如果用户不调用此方法设置初始量子态,则默认为加态。 - 如果用户以测量模式运行 MBQC,则此处输入量子态的系统标签会被限制为从零开始的自然数,类型为整型。 + Unlike the circuit model, the initial state of MBQC model is |+> state. If the users don't use + this method to initialize the quantum state, the initial state will be |+> state. + If the users run the MBQC model in measurement mode, the system labels of the input state here + will be restricted to natural number(start from 0) of ``int`` type. Args: - state (State): 需要替换的量子态,默认为加态 + state: the input state to be replaced, the default is |+> state. """ assert self.__graph is not None, "please set 'graph' or 'pattern' before calling 'set_input_state'." assert isinstance(state, State) or state is None, "please input a state of type 'State'." @@ -189,14 +184,15 @@ class MBQC: self.max_active = len(self.vertex.active) def __set_position(self, pos): - r"""设置动态过程图绘制时节点的位置坐标。 + r"""Set the coordinates of the nodes during the dynamical plotting process. Note: - 这是内部方法,用户并不需要直接调用到该方法。 + This is an internal method and the users don't need to use it directly. Args: - pos (dict or bool, optional): 节点坐标的字典数据或者内置的坐标选择, - 内置的坐标选择有:``True`` 为测量模式自带的坐标,``False`` 为 ``spring_layout`` 坐标 + pos (dict or bool, optional): the dict of the nodes' labels or built-in choice of coordinates. + The built-in choice of coordinates are: ``True`` is the coordinates of the measurement patterns, + ``False`` is the ``spring_layout`` coordinates. """ assert isinstance(pos, bool) or isinstance(pos, dict), "'pos' should be either bool or dict." if isinstance(pos, dict): @@ -208,14 +204,16 @@ class MBQC: self.__pos = spring_layout(self.__graph) # Use 'spring_layout' otherwise def __draw_process(self, which_process, which_qubit): - r"""根据当前节点状态绘图,用以实时展示 MBQC 模型的模拟计算过程。 + r""" Draw pictures according to the status of the nodes. This method is used for showing the + computation process of the MBQC model. Note: - 这是内部方法,用户并不需要直接调用到该方法。 + This is an internal method and the users don't need to use directly. Args: - which_process (str): MBQC 执行的阶段,"measuring", "active" 或者 "measured" - which_qubit (any): 当前关注的节点,可以是 ``str``, ``tuple`` 等任意数据类型,但需要和图的标签类型匹配 + which_process (str): The status of MBQC model, "measuring", "active" or "measured" + which_qubit (any): the current focal node. Any type(e.g. ``str``, ``tuple``) can be input, but should + match the type of the labels of the graph. """ if self.__draw: assert which_process in ["measuring", "active", "measured"] @@ -269,13 +267,14 @@ class MBQC: plt.pause(self.__pause_time) def draw_process(self, draw=True, pos=False, pause_time=0.5): - r"""动态过程图绘制,用以实时展示 MBQC 模型的模拟计算过程。 + r"""Dynamically plot the computation process of the MBQC model. Args: - draw (bool, optional): 是否绘制动态过程图的布尔开关 - pos (bool or dict, optional): 节点坐标的字典数据或者内置的坐标选择,内置的坐标选择有: - ``True`` 为测量模式自带的坐标,``False`` 为 `spring_layout` 坐标 - pause_time (float, optional): 绘制动态过程图时每次更新的停顿时间 + draw (bool, optional): The boolean switch of whether plot the computation process. + pos (bool or dict, optional): the dict of the nodes' labels or built-in choice of coordinates. + The built-in choice of coordinates are: ``True`` is the coordinates of the measurement patterns, + ``False`` is the ``spring_layout`` coordinates. + pause_time (float, optional): The time step for updating the picture. """ assert self.__graph is not None, "please set 'graph' or 'pattern' before calling 'draw_process'." assert isinstance(draw, bool), "'draw' must be bool." @@ -291,25 +290,26 @@ class MBQC: self.__set_position(pos) def track_progress(self, track=True): - r""" 显示 MBQC 模型运行进度的开关。 + r""" A switch for whether showing the progress bar of MBQC computation process. Args: - track (bool, optional): ``True`` 打开进度条显示功能, ``False`` 关闭进度条显示功能 + track (bool, optional): ``True`` open the progress bar, ``False`` close the progress bar. """ assert isinstance(track, bool), "the parameter 'track' must be bool." self.__track = track def __apply_cz(self, which_qubits_list): - r"""对给定的两个比特作用控制 Z 门。 + r"""Apply a controlled-Z gate to given two qubits. Note: - 这是内部方法,用户并不需要直接调用到该方法。 + This is an internal method and the users don't use it directly. Warning: - 作用控制 Z 门的两个比特一定是被激活的。 + The two qubits that the CZ gate applies to must be active. Args: - which_qubits_list (list): 作用控制 Z 门的比特对标签列表,例如 ``[(1, 2), (3, 4),...]`` + which_qubits_list (list): A list contains the qubits that the CZ gate applies to. + e.g.``[(1, 2), (3, 4),...]`` """ for which_qubits in which_qubits_list: assert set(which_qubits).issubset(self.vertex.active), \ @@ -333,15 +333,16 @@ class MBQC: self.__bg_state = State(new_state.vector, new_state.system) def __apply_pauli_gate(self, gate, which_qubit): - r"""对给定的单比特作用 Pauli 门。 + r"""Apply a Pauli gate to the given single qubit. Note: - 这是内部方法,用户并不需要直接调用到该方法。 + This is an internal method and the users don't use it directly. Args: - gate (str): Pauli 门的索引字符,"I", "X", "Y", "Z" 分别表示对应的门,在副产品处理时用 "X" 和 "Z" 门 - which_qubit (any): 作用 Pauli 门的系统标签, - 可以是 ``str``, ``tuple`` 等任意数据类型,但需要和 MBQC 模型中节点的标签类型匹配 + gate (str): Pauli gate, "I", "X", "Y", "Z". Use "X" and "Z" gate when correcting the byproduct. + which_qubit (any): The label of the system that the Pauli gate applies to. Any type + (e.g. ``str``, ``tuple`` ) can be used, as long as the type matches the type of labels of the + nodes in MBQC model. """ new_state = permute_to_front(self.__bg_state, which_qubit) new_state_len = new_state.length @@ -354,14 +355,15 @@ class MBQC: self.__bg_state = State(new_state.vector, new_state.system) def __create_graph_state(self, which_qubit): - r"""以待测量的比特为输入参数,生成测量当前节点所需要的最小的量子图态。 + r""" Generate the minimal graph state for measuring the current node. Note: - 这是内部方法,用户并不需要直接调用到该方法。 + This is an internal method and the users don't use it directly. Args: - which_qubit (any): 待测量比特的系统标签。 - 可以是 ``str``, ``tuple`` 等任意数据类型,但需要和 MBQC 模型中节点的标签类型匹配 + which_qubit (any): The system labels of the qubit to be measured. Any type + (e.g. ``str``, ``tuple`` ) can be used, as long as the type matches the type of labels of the + nodes in MBQC model. """ # Find the neighbors of 'which_qubit' which_qubit_neighbors = set(self.__graph.neighbors(which_qubit)) @@ -384,28 +386,32 @@ class MBQC: self.__draw_process("active", which_qubit) def __update(self): - r"""更新历史列表和量子态信息。 + r"""Update the history and the quantum states' information. """ self.__history.append(self.__bg_state) self.__status = self.__history[-1] def measure(self, which_qubit, basis_list): - r"""以待测量的比特和测量基为输入参数,对该比特进行测量。 + r"""Measure given qubits with given measurement basis. Note: - 这是用户在实例化 MBQC 类之后最常调用的方法之一,此处我们对单比特测量模拟进行了最大程度的优化, - 随着用户对该函数的调用,MBQC 类将自动完成激活相关节点、生成所需的图态以及对特定比特进行测量的全过程, - 并记录测量结果和对应测量后的量子态。用户每调用一次该函数,就完成一次对单比特的测量操作。 + This is one of the most common methods we use after instantiating an MBQC object. + Here we optimize the single bit measurement simulation to the maximum extent. + Once use this method, the MBQC class will automatically activate the related nodes, generate + the corresponding graph state, measure specific qubits and store the results of the numerical + simulations. Warning: - 当且仅当用户调用 ``measure`` 类方法时,MBQC 模型才真正进行运算。 + If and only if the users use this method, the MBQC model carries out the computation. Args: - which_qubit (any): 待测量量子比特的系统标签, - 可以是 ``str``, ``tuple`` 等任意数据类型,但需要和 MBQC 模型的图上标签匹配 - basis_list (list): 测量基向量构成的列表,列表元素为 ``Tensor`` 类型的列向量 + which_qubit (any): The system labels of the qubit to be measured. Any type + (e.g. ``str``, ``tuple`` ) can be used, as long as the type matches the type of labels + of the nodes in MBQC model. + basis_list (list): a list composed of measurement basis, the elements are column vectors + of type ``Tensor``. - 代码示例: + Code example: .. code-block:: python @@ -474,19 +480,22 @@ class MBQC: self.__draw_process("measured", which_qubit) def sum_outcomes(self, which_qubits, start=0): - r"""根据输入的量子系统标签,在存储测量结果的字典中找到对应的测量结果,并进行求和。 + r"""Based on the input system labels, find the corresponding measurement results in the dict and sum over. - Note: - 在进行副产品纠正操作和定义适应性测量角度时,用户可以调用该方法对特定比特的测量结果求和。 + Note: + When correcting the byproduct or defining the angle of adaptive measurement, one + can use this method to sum over the measurement results of given qubits. + Args: - which_qubits (list): 需要查找测量结果并求和的比特的系统标签列表 - start (int): 对结果进行求和后需要额外相加的整数 + which_qubits (list):the list contains the system labels of the nodes whose measurement + results should be find out and summed over. + start (int): an extra integer added to the results. Returns: - int: 指定比特的测量结果的和 + int: The sum of the measurement results of given qubit. - 代码示例: + Code example: .. code-block:: python @@ -517,19 +526,20 @@ class MBQC: return sum([self.__outcome[label] for label in which_qubits], start) def correct_byproduct(self, gate, which_qubit, power): - r"""对测量后的量子态进行副产品纠正。 + r"""Correct the byproduct of the measured quantum state. Note: - 这是用户在实例化 MBQC 类并完成测量后,经常需要调用的一个方法。 + This is a commonly used method after the measurement process of the MBQC model. Args: - gate (str): ``'X'`` 或者 ``'Z'``,分别表示 Pauli X 或 Z 门修正 - which_qubit (any): 待操作的量子比特的系统标签,可以是 ``str``, ``tuple`` 等任意数据类型,但需要和 MBQC 中图的标签类型匹配 - power (int): 副产品纠正算符的指数 - - 代码示例: + gate (str): ``'X'`` or ``'Z'``, representing Pauli X or Pauli Z correction respectively. + which_qubit (any): The system labels of the qubit to be processed. Any type + (e.g. ``str``, ``tuple`` ) can be used, as long as the type matches the type of labels of the + nodes in MBQC model. + power (int): the index of the byproduct correcting. - 此处展示的是 MBQC 模型下实现隐形传态的一个例子。 + Code example: + Here is an example of quantum teleportation in MBQC framework. .. code-block:: python @@ -565,10 +575,11 @@ class MBQC: self.__update() def __run_cmd(self, cmd): - r"""执行测量或副产品处理命令。 + r"""Carry out the command of measurement or byproduct correction. Args: - cmd (Pattern.CommandM / Pattern.CommandX / Pattern.CommandZ): 测量或副产品处理命令 + cmd (Pattern.CommandM / Pattern.CommandX / Pattern.CommandZ): the command of measurement + or byproduct correction. """ assert cmd.name in ["M", "X", "Z"], "the input 'cmd' must be CommandM, CommandX or CommandZ." if cmd.name == "M": # Execute measurement commands @@ -583,12 +594,12 @@ class MBQC: self.correct_byproduct(cmd.name, cmd.which_qubit, power) def __run_cmd_lst(self, cmd_lst, bar_start, bar_end): - r"""对列表执行测量或副产品处理命令。 + r"""Carry out a list of commands, including measurement and byproduct correction. Args: - cmd_lst (list): 命令列表,包含测量或副产品处理命令 - bar_start (int): 进度条的开始点 - bar_end (int): 进度条的结束点 + cmd_lst (list): the list of commands, including measurement and byproduct correction. + bar_start (int): the starting point of the progress bar. + bar_end (int): the end point of the progress bar. """ for i in range(len(cmd_lst)): cmd = cmd_lst[i] @@ -596,10 +607,12 @@ class MBQC: print_progress((bar_start + i + 1) / bar_end, "Pattern Running Progress", self.__track) def __kron_unmeasured_qubits(self): - r"""该方法将没有被作用 CZ 纠缠的节点初始化为 |+> 态,并与当前的量子态做张量积。 + r"""This method initialize the nodes without being applied by CZ gate to |+> state, and take the tensor + product between these nodes and the current quantum state. Warning: - 该方法仅在用户输入测量模式时调用,当用户输入图时,如果节点没有被激活,我们默认用户没有对该节点进行任何操作。 + This method is used when the users input the measurement patterns. When the users input a graph, + if the nodes are not activated, we deem the users do nothing to the node by default. """ # Turn off the plot switch self.__draw = False @@ -618,10 +631,10 @@ class MBQC: self.vertex.measured = measured_qubits def run_pattern(self): - r"""按照设置的测量模式对 MBQC 模型进行模拟。 + r"""Run the MBQC model by the measurement patterns set before. Warning: - 该方法必须在 ``set_pattern`` 调用后调用。 + This method must be used after ``set_pattern``. """ assert self.__pattern is not None, "please use this method after calling 'set_pattern'!" @@ -643,18 +656,20 @@ class MBQC: @staticmethod def __map_qubit_to_row(out_lst): - r"""将输出比特的标签与行数对应起来,便于查找其对应关系。 + r"""Construct a map between the labels of output qubits and the number of rows. Returns: - dict: 返回字典,代表行数与标签的对应关系 + dict: return a dict representing the correspondence between labels and number of rows. """ return {int(div_str_to_float(qubit[0])): qubit for qubit in out_lst} def get_classical_output(self): - r"""获取 MBQC 模型运行后的经典输出结果。 + r"""Get the classical output of the MBQC model. Returns: - str or dict: 如果用户输入是测量模式,则返回测量输出节点得到的比特串,与原电路的测量结果相一致,没有被测量的比特位填充 "?",如果用户输入是图,则返回所有节点的测量结果 + str or dict: if the users input the measurement patterns, the method returns the bit strings of the + measurement results of the output qubits which is the same as the results of the circuit based model. The + qubits haven't been measured fills "?". If the input is graph, return the measurement results of all nodes. """ # If the input is pattern, return the equivalent result as the circuit model if self.__pattern is not None: @@ -678,40 +693,41 @@ class MBQC: return self.__outcome def get_history(self): - r"""获取 MBQC 计算模拟时的中间步骤信息。 + r"""Get the information during the MBQC computation process. Returns: - list: 生成图态、进行测量、纠正副产品后运算结果构成的列表 + list: the list of the results, including generate graph state, measurement and byproduct correction. """ return self.__history def get_quantum_output(self): - r"""获取 MBQC 模型运行后的量子态输出结果。 + r"""Get the quantum state output of the MBQC model. Returns: - State: MBQC 模型运行后的量子态 + State: the quantum state output of the MBQC model. """ return self.__status def simulate_by_mbqc(circuit, input_state=None): - r"""使用等价的 MBQC 模型模拟量子电路。 + r"""Simulate the quantum circuit by equivalent MBQC model. - 该函数通过将量子电路转化为等价的 MBQC 模型并运行,从而获得等价于原始量子电路的输出结果。 + This function transform the quantum circuit to equivalent MBQC models and acquire output equivalent to the circuit + based model. Warning: - 与 ``UAnsatz`` 不同,此处输入的 ``circuit`` 参数包含了测量操作。 - 另,MBQC 模型默认初始态为加态,因此,如果用户不输入参数 ``input_state`` 设置初始量子态,则默认为加态。 + Unlike the ``UAnsatz``, the input ``circuit`` here contains the measurement operations. + By the way, if the users set ``input_state=None``, the initial state of the MBQC is |+> state. Args: - circuit (Circuit): 量子电路图 - input_state (State, optional): 量子电路的初始量子态,默认为 :math:`|+\rangle` 态 + circuit (Circuit): quantum circuit + input_state (State, optional): the initial state of quantum circuit, default to :math:`|+\rangle`. Returns: - tuple: 包含如下两个元素: + tuple: contains two elements: - - str: 经典输出 - - State: 量子输出 + - str: classical output + - State: quantum output """ if input_state is not None: assert isinstance(input_state, State), "the 'input_state' must be of type 'State'." @@ -729,15 +745,16 @@ def simulate_by_mbqc(circuit, input_state=None): def __get_sample_dict(bit_num, mea_bits, samples): - r"""根据比特数和测量比特索引的列表,统计采样结果。 + r"""Make statistics of the sampling results based on the number of qubits and the list of the + index of the measured qubits. Args: - bit_num (int): 比特数 - mea_bits (list): 测量的比特列表 - samples (list): 采样结果 + bit_num (int): number of qubits. + mea_bits (list): the list of the measured qubits. + samples (list): the list of the measurement results. Returns: - dict: 统计得到的采样结果 + dict: the statistical results """ sample_dict = {} for i in range(2 ** len(mea_bits)): @@ -760,22 +777,24 @@ def __get_sample_dict(bit_num, mea_bits, samples): def sample_by_mbqc(circuit, input_state=None, plot=False, shots=1024, print_or_not=True): - r"""将 MBQC 模型重复运行多次,获得经典结果的统计分布。 + r""" Repeatedly run the MBQC model and acquire the distributions of the results. Warning: - 与 ``UAnsatz`` 不同,此处输入的 circuit 参数包含了测量操作。 - 另,MBQC 模型默认初始态为加态,因此,如果用户不输入参数 `input_state` 设置初始量子态,则默认为加态。 + Unlike the ``UAnsatz``, the input ``circuit`` here contains the measurement operations. + By the way, if the users set ``input_state=None``, the initial state of the MBQC is |+> state. Args: - circuit (Circuit): 量子电路图 - input_state (State, optional): 量子电路的初始量子态,默认为加态 - plot (bool, optional): 绘制经典采样结果的柱状图开关,默认为关闭状态 - shots (int, optional): 采样次数,默认为 1024 次 - print_or_not (bool, optional): 是否打印采样结果和绘制采样进度,默认为开启状态 + circuit (Circuit): quantum circuit + input_state (State, optional): the initial state of quantum circuit, default to |+> + plot (bool, optional): the boolean switch of whether plotting the histogram of the sampling results, + default to ``False``. + shots (int, optional): the number of samples, default to 1024. + print_or_not (bool, optional): boolean switch of whether print the sampling results and the progress bar, + default to open. Returns: - dict: 经典结果构成的频率字典 - list: 经典测量结果和所有采样结果(包括经典输出和量子输出)的列表 + dict: the frequency dict composed of the classical results. + list: the list contains all the sampling results(both quantum and classical). """ # Initialize if shots == 1: diff --git a/paddle_quantum/mbqc/transpiler.py b/paddle_quantum/mbqc/transpiler.py index 79e2f90..14ba170 100644 --- a/paddle_quantum/mbqc/transpiler.py +++ b/paddle_quantum/mbqc/transpiler.py @@ -12,8 +12,8 @@ # See the License for the specific language governing permissions and # limitations under the License. -""" -此模块包含电路模型和 MBQC 测量模式的转义工具。 +r""" +This module contains the transpile of the circuit models and MBQC measurement patterns. """ from paddle_quantum.mbqc.qobject import Circuit @@ -25,14 +25,14 @@ __all__ = [ def transpile(circuit, track=False): - r"""将输入的量子电路翻译为等价的测量模式。 + r"""Translate the input circuit model to equivalent measurement patterns. Args: - circuit (Circuit): 量子电路,包含可能的测量部分 - track (bool): 是否显示翻译进度条的开关 + circuit (Circuit): quantum circuit, possibly contains measurement. + track (bool): The boolean switch of whether showing the progress bar. Returns: - pattern (Pattern): 等价的测量模式 + pattern (Pattern): equivalent measurement pattern """ assert isinstance(circuit, Circuit), "'circuit' must be of type 'Circuit'." assert isinstance(track, bool), "'track' must be a 'bool'." diff --git a/paddle_quantum/mbqc/utils.py b/paddle_quantum/mbqc/utils.py index 48074c7..0809039 100644 --- a/paddle_quantum/mbqc/utils.py +++ b/paddle_quantum/mbqc/utils.py @@ -12,8 +12,8 @@ # See the License for the specific language governing permissions and # limitations under the License. -""" -此模块包含计算所需的各种常用类和函数。 +r""" +This module contains various common classes and functions used for computation. """ from numpy import array, exp, pi, linalg @@ -58,18 +58,18 @@ __all__ = ["plus_state", def plus_state(): - r"""定义加态。 + r"""Define plus state. - 其矩阵形式为: + The matrix form is: .. math:: \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ 1 \end{bmatrix} Returns: - Tensor: 加态对应的 ``Tensor`` 形式 + Tensor: The ``Tensor`` form of plus state. - 代码示例: + Code example: .. code-block:: python @@ -86,18 +86,18 @@ def plus_state(): def minus_state(): - r"""定义减态。 + r"""Define minus state. - 其矩阵形式为: + The matrix form is: .. math:: \frac{1}{\sqrt{2}} \begin{bmatrix} 1 \\ -1 \end{bmatrix} Returns: - Tensor: 减态对应的 ``Tensor`` 形式 + Tensor: The ``Tensor`` form of minus state. - 代码示例: + Code example: .. code-block:: python @@ -114,18 +114,18 @@ def minus_state(): def zero_state(): - r"""定义零态。 + r"""Define zero state. - 其矩阵形式为: + The matrix form is: .. math:: \begin{bmatrix} 1 \\ 0 \end{bmatrix} Returns: - Tensor: 零态对应的 ``Tensor`` 形式 + Tensor: The ``Tensor`` form of zero state. - 代码示例: + Code example: .. code-block:: python @@ -142,18 +142,18 @@ def zero_state(): def one_state(): - r"""定义一态。 + r"""Define one state. - 其矩阵形式为: + The matrix form is: .. math:: \begin{bmatrix} 0 \\ 1 \end{bmatrix} Returns: - Tensor: 一态对应的 ``Tensor`` 形式 + Tensor: The ``Tensor`` form of one state. - 代码示例: + Code example: .. code-block:: python @@ -170,18 +170,18 @@ def one_state(): def h_gate(): - r"""定义 ``Hadamard`` 门。 + r"""Define ``Hadamard`` gate. - 其矩阵形式为: + The matrix form is: .. math:: \frac{1}{\sqrt{2}} \begin{bmatrix} 1 & 1 \\ 1 & -1 \end{bmatrix} Returns: - Tensor: ``Hadamard`` 门对应矩阵的 ``Tensor`` 形式 + Tensor: The ``Tensor`` form of ``Hadamard`` gate. - 代码示例: + Code example: .. code-block:: python @@ -198,9 +198,9 @@ def h_gate(): def s_gate(): - r"""定义 ``S`` 门。 + r"""Define ``S`` gate. - 其矩阵形式为: + The matrix form is: .. math:: @@ -209,7 +209,7 @@ def s_gate(): Returns: Tensor: ``S`` 门矩阵对应的 ``Tensor`` 形式 - 代码示例: + Code example: .. code-block:: python @@ -226,18 +226,18 @@ def s_gate(): def t_gate(): - r"""定义 ``T`` 门。 + r"""Define ``T`` gate. - 其矩阵形式为: + The matrix form is: .. math:: \begin{bmatrix} 1 & 0 \\ 0 & e^{i \pi / 4} \end{bmatrix} Returns: - Tensor: ``T`` 门矩阵对应的 ``Tensor`` 形式 + Tensor: The ``Tensor`` form of ``T`` gate. - 代码示例: + Code example: .. code-block:: python @@ -254,18 +254,18 @@ def t_gate(): def cz_gate(): - r"""定义 ``Controlled-Z`` 门。 + r"""Define ``Controlled-Z`` gate. - 其矩阵形式为: + The matrix form is: .. math:: \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & -1 \end{bmatrix} Returns: - Tensor: ``Controlled-Z`` 门矩阵对应的 ``Tensor`` 形式 + Tensor: The ``Tensor`` form of ``Controlled-Z`` gate. - 代码示例: + Code example: .. code-block:: python @@ -287,18 +287,18 @@ def cz_gate(): def cnot_gate(): - r"""定义 ``Controlled-NOT (CNOT)`` 门。 + r"""Define ``Controlled-NOT (CNOT)`` gate. - 其矩阵形式为: + The matrix form is: .. math:: \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \\ 0 & 0 & 1 & 0 \end{bmatrix} Returns: - Tensor: ``Controlled-NOT (CNOT)`` 门矩阵对应的 ``Tensor`` 形式 + Tensor: The ``Tensor`` form of ``Controlled-NOT (CNOT)`` gate. - 代码示例: + Code example: .. code-block:: python @@ -320,18 +320,18 @@ def cnot_gate(): def swap_gate(): - r"""定义 ``SWAP`` 门。 + r"""Define ``SWAP`` gate. - 其矩阵形式为: + The matrix form is: .. math:: \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} Returns: - Tensor: ``SWAP`` 门矩阵对应的 ``Tensor`` 形式 + Tensor: The ``Tensor`` form of ``SWAP`` gate. - 代码示例: + Code example: .. code-block:: python @@ -353,39 +353,39 @@ def swap_gate(): def pauli_gate(gate): - r"""定义 ``Pauli`` 门。 + r"""Define ``Pauli`` gate. - 单位阵 ``I`` 的矩阵形式为: + The matrix form of Identity gate ``I`` is: .. math:: \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} - ``Pauli X`` 门的矩阵形式为: + The matrix form of Pauli gate ``X`` is: .. math:: \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} - ``Pauli Y`` 门的矩阵形式为: + The matrix form of Pauli gate ``Y`` is: .. math:: \begin{bmatrix} 0 & - i \\ i & 0 \end{bmatrix} - ``Pauli Z`` 门的矩阵形式为: + The matrix form of Pauli gate ``Z`` is: .. math:: \begin{bmatrix} 1 & 0 \\ 0 & - 1 \end{bmatrix} Args: - gate (str): Pauli 门的索引字符,"I", "X", "Y", "Z" 分别表示对应的门 + gate (str): Index of Pauli gate. “I”, “X”, “Y”, or “Z” denotes the corresponding gate. Returns: - Tensor: Pauli 门对应的矩阵 + Tensor: The matrix form of the Pauli gate. - 代码示例: + Code example: .. code-block:: python @@ -428,7 +428,7 @@ def pauli_gate(gate): def rotation_gate(axis, theta): - r"""定义旋转门矩阵。 + r"""Define Rotation gate. .. math:: @@ -439,13 +439,13 @@ def rotation_gate(axis, theta): R_{z}(\theta) = \cos(\theta / 2) I - i\sin(\theta / 2) Z Args: - axis (str): 旋转轴,绕 ``X`` 轴旋转输入 'x',绕 ``Y`` 轴旋转输入 'y',绕 ``Z`` 轴旋转输入 'z' - theta (Tensor): 旋转的角度 + axis (str): Rotation axis. 'x', 'y' or 'z' denotes the corresponding axis. + theta (Tensor): Rotation angle. Returns: - Tensor: 旋转门对应的矩阵 + Tensor: The matrix form of Rotation gate. - 代码示例: + Code example: .. code-block:: python @@ -495,19 +495,19 @@ def rotation_gate(axis, theta): def to_projector(vector): - r"""把列向量转化为密度矩阵(或测量基对应的投影算符)。 + r"""Transform a vector into its density matrix (or measurement projector). .. math:: |\psi\rangle \to |\psi\rangle\langle\psi| Args: - vector (Tensor): 量子态列向量(或投影测量中的测量基向量) + vector (Tensor): Vector of a quantum state or a measurement basis Returns: - Tensor: 密度矩阵(或测量基对应的投影算符) + Tensor: Density matrix (or measurement projector) - 代码示例: + Code example: .. code-block:: python @@ -534,10 +534,10 @@ def to_projector(vector): def basis(label, theta=to_tensor([0], dtype='float64')): - r"""测量基。 + r"""Measurement basis. Note: - 常用的测量方式有 XY-平面测量,YZ-平面测量,X 测量,Y 测量,Z 测量。 + Commonly used measurements are measurements in the XY and YZ planes, and Pauli X, Y, Z measurements. .. math:: \begin{align*} @@ -549,13 +549,15 @@ def basis(label, theta=to_tensor([0], dtype='float64')): \end{align*} Args: - label (str): 测量基索引字符,"XY" 表示 XY-平面测量,"YZ" 表示 YZ-平面测量,"X" 表示 X 测量,"Y" 表示 Y 测量,"Z" 表示 Z 测量 - theta (Tensor, optional): 测量角度,这里只有 XY-平面测量和 YZ-平面测量时需要 + label (str): the labels of the measurement basis, "XY" denotes XY plane, "YZ" denotes YZ plane, + "X" denotes X measurement, "Y" denotes Y measurement, "Z" denotes Z measurement. + theta (Tensor, optional): measurement angle, the parameter is needed when the measurement is in + XY plane or YZ plane. Returns: - list: 测量基向量构成的列表,列表元素为 ``Tensor`` 类型 + list: the list composed of measurement basis, the elements are of type ``Tensor``. - 代码示例: + Code example: .. code-block:: python @@ -634,19 +636,20 @@ def basis(label, theta=to_tensor([0], dtype='float64')): def kron(tensor_list): - r"""把列表中的所有元素做张量积。 + r"""Take the tensor product of all the elements in the list. .. math:: [A, B, C, \cdots] \to A \otimes B \otimes C \otimes \cdots Args: - tensor_list (list): 需要做张量积的元素组成的列表 + tensor_list (list): a list contains the element to taking tensor product. Returns: - Tensor: 所有元素做张量积运算得到的 ``Tensor``,当列表中只有一个 ``Tensor`` 时,返回该 ``Tensor`` 本身 + Tensor: the results of the tensor product are of type ``Tensor``. If there is only + one ``Tensor`` in the list, return the ``Tensor``. - 代码示例 1: + Code example 1: .. code-block:: python @@ -671,7 +674,7 @@ def kron(tensor_list): [0. 0. 0. 0. 1. 2. 1. 2.] [0. 0. 0. 0. 3. 4. 3. 4.]] - 代码示例 2: + Code example 2: .. code-block:: python @@ -698,35 +701,35 @@ def kron(tensor_list): def permute_to_front(state, which_system): - r"""将一个量子态中某个子系统的顺序变换到最前面。 + r"""Move a subsystem of a system to the first. - 假设当前系统的量子态列向量 :math:`\psi\rangle` 可以分解成多个子系统列向量的 tensor product 形式: + Assume that a quantum state :math:`\psi\rangle` can be decomposed to tensor product form: .. math:: |\psi\rangle = |\psi_1\rangle \otimes |\psi_2\rangle \otimes |\psi_3\rangle \otimes \cdots - 每个 :math:`|\psi_i\rangle` 的系统标签为 :math:`i` ,则当前总系统的标签为: + the labels of each :math:`|\psi_i\rangle` is :math:`i` , so the total labels of the current system are: .. math:: \text{label} = \{1, 2, 3, \cdots \} - 假设需要操作的子系统的标签为:i + Assume that the label of the subsystem to be moved is: i - 输出新系统量子态的列向量为: + The output new quantum state is: .. math:: |\psi_i\rangle \otimes |\psi_1\rangle \otimes \cdots |\psi_{i-1}\rangle \otimes |\psi_{i+1}\rangle \otimes \cdots Args: - state (State): 需要操作的量子态 - which_system (str): 要变换到最前面的子系统标签 + state (State): the quantum state to be processed + which_system (str): the labels of the subsystem to be moved. Returns: - State: 系统顺序变换后的量子态 + State: the final state after the move operation. """ assert which_system in state.system, 'the system to permute must be in the state systems.' system_idx = state.system.index(which_system) @@ -746,38 +749,38 @@ def permute_to_front(state, which_system): def permute_systems(state, new_system): - r"""变换量子态的系统到指定顺序。 + r""" Permute the quantum system to given order - 假设当前系统的量子态列向量 :math:`|\psi\rangle` 可以分解成多个子系统列向量的 tensor product 形式: + Assume that a quantum state :math:`\psi\rangle` can be decomposed to tensor product form: .. math:: |\psi\rangle = |\psi_1\rangle \otimes |\psi_2\rangle \otimes |\psi_3\rangle \otimes \cdots - 每个 :math:`\psi_i\rangle` 的系统标签为 :math:`i` ,则当前总系统的标签为: + the labels of each :math:`|\psi_i\rangle` is :math:`i` , so the total labels of the current system are: .. math:: \text{label} = \{1, 2, 3, \cdots \} - 给定新系统的标签顺序为: + the order of labels of the given new system is: .. math:: \{i_1, i_2, i_3, \cdots \} - 输出新系统量子态的列向量为: + The output new quantum state is: .. math:: |\psi_{i_1}\rangle \otimes |\psi_{i_2}\rangle \otimes |\psi_{i_3}\rangle \otimes \cdots Args: - state (State): 需要操作的量子态 - new_system (list): 目标系统顺序 + state (State): the quantum state to be processed + new_system (list): target order of the system Returns: - State: 系统顺序变换后的量子态 + State: the quantum state after permutation. """ for label in reversed(new_system): state = permute_to_front(state, label) @@ -785,11 +788,11 @@ def permute_systems(state, new_system): def compare_by_density(state1, state2): - r"""通过密度矩阵形式比较两个量子态是否相同。 + r"""Compare whether two quantum states are the same by their density operators. Args: - state1 (State): 第一个量子态 - state2 (State): 第二个量子态 + state1 (State): the first quantum state + state2 (State): the second quantum state """ assert state1.size == state2.size, "two state vectors compared are not of the same length." @@ -812,11 +815,11 @@ def compare_by_density(state1, state2): def compare_by_vector(state1, state2): - r"""通过列向量形式比较两个量子态是否相同。 + r"""Compare whether two quantum states are the same by their column vector form. Args: - state1 (State): 第一个量子态 - state2 (State): 第二个量子态 + state1 (State): the first quantum state + state2 (State): the second quantum state """ assert state1.size == state2.size, "two state vectors compared are not of the same length." # Check if they are normalized quantum states @@ -847,16 +850,17 @@ def compare_by_vector(state1, state2): def random_state_vector(n, is_real=False): - r"""随机生成一个量子态列向量。 + r"""Generate a state vector randomly. Args: - n (int): 随机生成的量子态的比特数 - is_real (int, optional): ``True`` 表示实数量子态,``False`` 表示复数量子态,默认为 ``False`` + n (int): the number of qubits of the random state. + is_real (int, optional): ``True`` denotes a state vector with real values, ``False`` denotes a quantum + state with complex values, default to ``False`` Returns: - Tensor: 随机生成量子态的列向量 + Tensor: the column vector of the random quantum state. - 代码示例: + Code example: .. code-block:: python @@ -890,17 +894,17 @@ def random_state_vector(n, is_real=False): def div_str_to_float(div_str): - r"""将除式字符串转化为对应的浮点数。 + r"""Converts the division string to the corresponding floating point number. - 例如将字符串 '3/2' 转化为 1.5。 + For example, the string '3/2' to the float number 1.5. Args: - div_str (str): 除式字符串 + div_str (str): division string Returns: - float: 除式对应的浮点数结果 + float: the float number - 代码示例: + Code example: .. code-block:: python @@ -918,16 +922,16 @@ def div_str_to_float(div_str): def int_to_div_str(idx1, idx2=1): - r"""将两个整数转化为除式字符串。 + r"""Transform two integers to a division string. Args: - idx1 (int): 第一个整数 - idx2 (int): 第二个整数 + idx1 (int): the first integer + idx2 (int): the second integer Returns: - str: 对应的除式字符串 + str: the division string - 代码示例: + Code example: .. code-block:: python @@ -946,14 +950,14 @@ def int_to_div_str(idx1, idx2=1): def print_progress(current_progress, progress_name, track=True): - r"""画出当前步骤的进度条。 + r"""Plot the progress bar. Args: - current_progress (float / int): 当前的进度百分比 - progress_name (str): 当前步骤的名称 - track (bool): 是否绘图的布尔开关 + current_progress (float / int): the percentage of the current progress. + progress_name (str): the name of the current progress. + track (bool): the boolean switch of whether plot. - 代码示例: + Code example: .. code-block:: python @@ -978,18 +982,19 @@ def print_progress(current_progress, progress_name, track=True): def plot_results(dict_lst, bar_label, title, xlabel, ylabel, xticklabels=None): - r"""根据字典的键值对,以键为横坐标,对应的值为纵坐标,画出柱状图。 + r"""Plot the histogram based on the key-value pair of the dict. + The key is the abscissa, and the corresponding value is the ordinate Note: - 该函数主要调用来画出采样分布或时间比较的柱状图。 + The function is mainly used for plotting the sampling statistics or histogram. Args: - dict_lst (list): 待画图的字典列表 - bar_label (list): 每种柱状图对应的名称 - title (str): 整个图的标题 - xlabel (str): 横坐标的名称 - ylabel (str): 纵坐标的名称 - xticklabels (list, optional): 柱状图中每个横坐标的名称 + dict_lst (list): a list contains the data to be plotted + bar_label (list): the name of different bars in the histogram + title (str): the title of the figure + xlabel (str): the label of the x axis. + ylabel (str): the label of the y axis. + xticklabels (list, optional): the label of each ticks of the x-axis. """ assert isinstance(dict_lst, list), "please input a list with dictionaries." assert isinstance(bar_label, list), "please input a list with bar_labels." @@ -1023,23 +1028,25 @@ def plot_results(dict_lst, bar_label, title, xlabel, ylabel, xticklabels=None): def write_running_data(textfile, eg, width, mbqc_time, reference_time): - r"""写入电路模拟运行的时间。 + r"""Write the running times of the quantum circuit. - 由于在许多电路模型模拟案例中,需要比较我们的 ``MBQC`` 模拟思路与 ``Qiskit`` 或量桨平台的 ``UAnsatz`` 电路模型模拟思路的运行时间。 - 因而单独定义了写入文件函数。 + In many cases of circuit models, we need to compare the simulation time of our MBQC model with other methods + such as qiskit or ``UAnsatz`` circuit model in paddle_quantum. So we define this function. Hint: - 该函数与 ``read_running_data`` 函数配套使用。 + this function is used with the ``read_running_data`` function. Warning: - 在调用该函数之前,需要调用 ``open`` 打开 ``textfile``;在写入结束之后,需要调用 ``close`` 关闭 ``textfile``。 + Before using this function, we need to open a textfile. After using this function, + we need to close the textfile. Args: - textfile (TextIOWrapper): 待写入的文件 - eg (str): 当前案例的名称 - width (float): 电路宽度(比特数) - mbqc_time (float): ``MBQC`` 模拟电路运行时间 - reference_time (float): ``Qiskit`` 或量桨平台的 ``UAnsatz`` 电路模型运行时间 + textfile (TextIOWrapper): the file to be written in. + eg (str): the name of the current case + width (float): the width of the circuit(number of qubits) + mbqc_time (float): `the simulation time of the ``MBQC`` model. + reference_time (float): the simulation time of the circuit + based model in qiskit or ``UAnsatz`` in paddle_quantum. """ textfile.write("The current example is: " + eg + "\n") textfile.write("The qubit number is: " + str(width) + "\n") @@ -1048,20 +1055,21 @@ def write_running_data(textfile, eg, width, mbqc_time, reference_time): def read_running_data(file_name): - r"""读取电路模拟运行的时间。 + r"""Read the running time of the quantum circuit. - 由于在许多电路模型模拟案例中,需要比较我们的 ``MBQC`` 模拟思路与 ``Qiskit`` 或量桨平台的 ``UAnsatz`` 电路模型模拟思路的运行时间。 - 因而单独定义了读取文件函数读取运行时间,将其处理为一个列表, - 列表中的两个元素分别为 ``Qiskit`` 或 ``UAnsatz`` 电路模型模拟思路运行时间的字典和 ``MBQC`` 模拟思路运行时间的字典。 + In many cases of circuit models, we need to compare the simulation time of our MBQC model with other methods + such as qiskit or ``UAnsatz`` circuit model in paddle_quantum. So we define this function and save the running + time to a list. There are two dicts in the list, the first dict contains the running time of qiskit or ``UAnsatz``, + the second contains the simulation time of our MBQC model. Hint: - 该函数与 ``write_running_data`` 函数配套使用。 + This function is used with the ``write_running_data`` function. Args: - file_name (str): 待读取的文件名 + file_name (str): the name of the file to be read. Returns: - list: 运行时间列表 + list: The list of running time. """ bit_num_lst = [] mbqc_list = [] diff --git a/paddle_quantum/operator/operator.py b/paddle_quantum/operator/operator.py index fc6553e..af538ac 100644 --- a/paddle_quantum/operator/operator.py +++ b/paddle_quantum/operator/operator.py @@ -84,7 +84,12 @@ class Collapse(Operator): self.measure_basis = [] # the qubit indices must be sorted - self.qubits_idx = sorted(_format_qubits_idx(qubits_idx, num_qubits)) + self.qubits_idx = _format_qubits_idx(qubits_idx, num_qubits) + idx_shape = np.array(self.qubits_idx).shape + assert len(idx_shape) < 2, \ + f"The input qubit indices for Collapse must be a flattened list or a integer: received {idx_shape}" + assert sorted(self.qubits_idx) == self.qubits_idx, \ + f"The input qubit indices for Collapse must be sorted: received {self.qubits_idx}" self.desired_result = desired_result self.if_print = if_print diff --git a/paddle_quantum/qchem/algorithm.py b/paddle_quantum/qchem/algorithm.py index 8eb9dc3..48a697b 100644 --- a/paddle_quantum/qchem/algorithm.py +++ b/paddle_quantum/qchem/algorithm.py @@ -23,6 +23,7 @@ import numpy as np import paddle from paddle.optimizer import Optimizer from paddle_quantum.loss import ExpecVal +from paddle_quantum import Hamiltonian from ..ansatz import Circuit from ..state import State from .molecule import Molecule @@ -77,31 +78,46 @@ class GroundStateSolver(VQESolver): def solve( self, - mol: Molecule, ansatz: Circuit, + mol: Optional[Molecule] = None, + ham: Optional[Hamiltonian] = None, init_state: Optional[State] = None, **optimizer_kwargs ) -> Tuple[float, paddle.Tensor]: r"""Run VQE to calculate the ground state energy for a given molecule. Args: - mol: the molecule object. - ansatz : the quantum circuit represents the wfn transformation. - init_state: default is None, the initial state passed to the ansatz. - **optimizer_kwargs: The other args. + ansatz (Circuit): the quantum circuit represents the wfn transformation. + mol (Molecule): default is None, the molecule object. + ham (Hamiltonian): default is None, the Hamiltonian on which to calculate the ground state energy. + init_state (State): default is None, the initial state passed to the ansatz. + optimizer_kwargs. Returns: The estimated ground state energy and the ground state wave function. """ + if mol is None: + if ham is None: + raise ValueError("`mol` and `ham` can't be None simultaneously.") + elif isinstance(ham, Hamiltonian): + num_qubits = ham.n_qubits + h = ham + else: + raise ValueError("`ham` must be an instance of `paddle_quantum.Hamiltonian`.") + elif isinstance(mol, Molecule): + num_qubits = mol.num_qubits + h = mol.get_molecular_hamiltonian() + else: + raise ValueError("`mol` must be an instance of `paddle_quantum.qchem.Molecule`") + logging.info("\n#######################################\nVQE (Ground State)\n#######################################") - logging.info(f"Number of qubits: {mol.num_qubits:d}") + logging.info(f"Number of qubits: {num_qubits:d}") logging.info(f"Ansatz: {ansatz.__class__.__name__:s}") logging.info(f"Optimizer: {self.optimizer.__name__:s}") optimizer = self.optimizer(parameters=ansatz.parameters(), **optimizer_kwargs) logging.info(f"\tlearning_rate: {optimizer.get_lr()}") - h = mol.get_molecular_hamiltonian() energy_fn = ExpecVal(h) logging.info("\nOptimization:") diff --git a/paddle_quantum/qinfo.py b/paddle_quantum/qinfo.py index 842fd7e..46eeae0 100644 --- a/paddle_quantum/qinfo.py +++ b/paddle_quantum/qinfo.py @@ -26,23 +26,20 @@ from scipy.stats import unitary_group import cvxpy import matplotlib.image from itertools import product +from typing import Optional, Tuple, List, Union import paddle import paddle_quantum as pq -from .state import State, _type_fetch, _type_transform from .base import get_dtype -from .linalg import abs_norm, dagger, NKron, unitary_random, is_positive -from .channel.custom import ChoiRepr, KrausRepr, StinespringRepr -from .channel.custom import ( - _choi_to_kraus, _choi_to_stinespring, - _kraus_to_choi, _kraus_to_stinespring, - _stinespring_to_choi, _stinespring_to_kraus -) -from typing import Optional, Tuple, List, Union +from .intrinsic import _type_fetch, _type_transform +from .linalg import dagger, NKron, unitary_random, is_positive +from .channel import Channel +from .hamiltonian import Hamiltonian +from .shadow import shadow_sample -def partial_trace(state: Union[np.ndarray, paddle.Tensor, State], - dim1: int, dim2: int, A_or_B: int) -> Union[np.ndarray, paddle.Tensor, State]: +def partial_trace(state: Union[np.ndarray, paddle.Tensor, pq.State], + dim1: int, dim2: int, A_or_B: int) -> Union[np.ndarray, paddle.Tensor, pq.State]: r"""Calculate the partial trace of the quantum state. Args: @@ -71,8 +68,8 @@ def partial_trace(state: Union[np.ndarray, paddle.Tensor, State], return _type_transform(new_state, type_str) -def partial_trace_discontiguous(state: Union[np.ndarray, paddle.Tensor, State], - preserve_qubits: list=None) -> Union[np.ndarray, paddle.Tensor, State]: +def partial_trace_discontiguous(state: Union[np.ndarray, paddle.Tensor, pq.State], + preserve_qubits: list=None) -> Union[np.ndarray, paddle.Tensor, pq.State]: r"""Calculate the partial trace of the quantum state with arbitrarily selected subsystem Args: @@ -110,8 +107,8 @@ def partial_trace_discontiguous(state: Union[np.ndarray, paddle.Tensor, State], return _type_transform(rho, type_str) -def trace_distance(rho: Union[np.ndarray, paddle.Tensor, State], - sigma: Union[np.ndarray, paddle.Tensor, State]) -> Union[np.ndarray, paddle.Tensor]: +def trace_distance(rho: Union[np.ndarray, paddle.Tensor, pq.State], + sigma: Union[np.ndarray, paddle.Tensor, pq.State]) -> Union[np.ndarray, paddle.Tensor]: r"""Calculate the trace distance of two quantum states. .. math:: @@ -135,8 +132,8 @@ def trace_distance(rho: Union[np.ndarray, paddle.Tensor, State], return dist.item() if type_rho == "numpy" and type_sigma == "numpy" else dist -def state_fidelity(rho: Union[np.ndarray, paddle.Tensor, State], - sigma: Union[np.ndarray, paddle.Tensor, State]) -> Union[np.ndarray, paddle.Tensor]: +def state_fidelity(rho: Union[np.ndarray, paddle.Tensor, pq.State], + sigma: Union[np.ndarray, paddle.Tensor, pq.State]) -> Union[np.ndarray, paddle.Tensor]: r"""Calculate the fidelity of two quantum states. .. math:: @@ -154,8 +151,7 @@ def state_fidelity(rho: Union[np.ndarray, paddle.Tensor, State], sigma = _type_transform(sigma, "density_matrix").numpy() assert rho.shape == sigma.shape, 'The shape of two quantum states are different' - fidelity = np.trace(sqrtm(sqrtm(rho) @ sigma @ sqrtm(rho))).real - + fidelity = np.trace(sqrtm(sqrtm(rho) @ sigma @ sqrtm(rho)).astype(rho.dtype)).real if type_rho == "numpy" and type_sigma == "numpy": return fidelity return paddle.to_tensor(fidelity) @@ -189,7 +185,7 @@ def gate_fidelity(U: Union[np.ndarray, paddle.Tensor], return fidelity.item() if type_u == "numpy" or type_v == "numpy" else fidelity -def purity(rho: Union[np.ndarray, paddle.Tensor, State]) -> Union[np.ndarray, paddle.Tensor]: +def purity(rho: Union[np.ndarray, paddle.Tensor, pq.State]) -> Union[np.ndarray, paddle.Tensor]: r"""Calculate the purity of a quantum state. .. math:: @@ -209,7 +205,7 @@ def purity(rho: Union[np.ndarray, paddle.Tensor, State]) -> Union[np.ndarray, pa return gamma.item() if type_rho == "numpy" else gamma -def von_neumann_entropy(rho: Union[np.ndarray, paddle.Tensor, State], base: Optional[int] = 2) -> Union[np.ndarray, paddle.Tensor]: +def von_neumann_entropy(rho: Union[np.ndarray, paddle.Tensor, pq.State], base: Optional[int] = 2) -> Union[np.ndarray, paddle.Tensor]: r"""Calculate the von Neumann entropy of a quantum state. .. math:: @@ -231,8 +227,8 @@ def von_neumann_entropy(rho: Union[np.ndarray, paddle.Tensor, State], base: Opti return entropy.item() if type_rho == "numpy" else entropy -def relative_entropy(rho: Union[np.ndarray, paddle.Tensor, State], - sig: Union[np.ndarray, paddle.Tensor, State], base: Optional[int] = 2) -> Union[np.ndarray, paddle.Tensor]: +def relative_entropy(rho: Union[np.ndarray, paddle.Tensor, pq.State], + sig: Union[np.ndarray, paddle.Tensor, pq.State], base: Optional[int] = 2) -> Union[np.ndarray, paddle.Tensor]: r"""Calculate the relative entropy of two quantum states. .. math:: @@ -258,7 +254,7 @@ def relative_entropy(rho: Union[np.ndarray, paddle.Tensor, State], return paddle.to_tensor(entropy) -def random_pauli_str_generator(n: int, terms: Optional[int] = 3) -> List: +def random_pauli_str_generator(num_qubits: int, terms: Optional[int] = 3) -> List: r"""Generate a random observable in list form. An observable :math:`O=0.3X\otimes I\otimes I+0.5Y\otimes I\otimes Z`'s list form is @@ -266,23 +262,56 @@ def random_pauli_str_generator(n: int, terms: Optional[int] = 3) -> List: ``random_pauli_str_generator(3, terms=2)`` Args: - n: Number of qubits. + num_qubits: Number of qubits. terms: Number of terms in the observable. Defaults to 3. Returns: - The randomly generated observable's list form. + The Hamiltonian of randomly generated observable. """ pauli_str = [] - for sublen in np.random.randint(1, high=n + 1, size=terms): + for sublen in np.random.randint(1, high=num_qubits + 1, size=terms): # Tips: -1 <= coeff < 1 coeff = np.random.rand() * 2 - 1 ops = np.random.choice(['x', 'y', 'z'], size=sublen) - pos = np.random.choice(range(n), size=sublen, replace=False) + pos = np.random.choice(range(num_qubits), size=sublen, replace=False) op_list = [ops[i] + str(pos[i]) for i in range(sublen)] + op_list.sort(key=lambda x: int(x[1:])) pauli_str.append([coeff, ','.join(op_list)]) return pauli_str +def pauli_str_convertor(observable: List) -> List: + r"""Concatenate the input observable with coefficient 1. + + For example, if the input ``observable`` is ``[['z0,x1'], ['z1']]``, + then this function returns the observable ``[[1, 'z0,x1'], [1, 'z1']]``. + + Args: + observable: The observable to be concatenated with coefficient 1. + + Returns: + The observable with coefficient 1 + """ + + for i in range(len(observable)): + assert len(observable[i]) == 1, 'Each term should only contain one string' + + return [[1, term] for term in observable] + + +def random_hamiltonian_generator(num_qubits: int, terms: Optional[int] = 3) -> List: + r"""Generate a random Hamiltonian. + + Args: + num_qubits: Number of qubits. + terms: Number of terms in the Hamiltonian. Defaults to 3. + + Returns: + The randomly generated Hamiltonian. + """ + return Hamiltonian(random_pauli_str_generator(num_qubits, terms)) + + def pauli_str_to_matrix(pauli_str: list, n: int) -> paddle.Tensor: r"""Convert the input list form of an observable to its matrix form. @@ -332,7 +361,7 @@ def pauli_str_to_matrix(pauli_str: list, n: int) -> paddle.Tensor: return paddle.to_tensor(sum(matrices), dtype=get_dtype()) -def partial_transpose_2(density_op: Union[np.ndarray, paddle.Tensor, State], +def partial_transpose_2(density_op: Union[np.ndarray, paddle.Tensor, pq.State], sub_system: int = None) -> Union[np.ndarray, paddle.Tensor]: r"""Calculate the partial transpose :math:`\rho^{T_A}` of the input quantum state. @@ -381,7 +410,7 @@ def partial_transpose_2(density_op: Union[np.ndarray, paddle.Tensor, State], return paddle.to_tensor(transposed_density_op) -def partial_transpose(density_op: Union[np.ndarray, paddle.Tensor, State], +def partial_transpose(density_op: Union[np.ndarray, paddle.Tensor, pq.State], n: int) -> Union[np.ndarray, paddle.Tensor]: r"""Calculate the partial transpose :math:`\rho^{T_A}` of the input quantum state. @@ -405,8 +434,8 @@ def partial_transpose(density_op: Union[np.ndarray, paddle.Tensor, State], return density_op.numpy() if type_str == "numpy" else density_op -def permute_systems(mat: Union[np.ndarray, paddle.Tensor, State], - perm_list: List[int], dim_list: List[int]) -> Union[np.ndarray, paddle.Tensor, State]: +def permute_systems(mat: Union[np.ndarray, paddle.Tensor, pq.State], + perm_list: List[int], dim_list: List[int]) -> Union[np.ndarray, paddle.Tensor, pq.State]: r"""Permute quantum system based on a permute list Args: @@ -438,7 +467,7 @@ def permute_systems(mat: Union[np.ndarray, paddle.Tensor, State], return _type_transform(perm_mat, mat_type) -def negativity(density_op: Union[np.ndarray, paddle.Tensor, State]) -> Union[np.ndarray, paddle.Tensor]: +def negativity(density_op: Union[np.ndarray, paddle.Tensor, pq.State]) -> Union[np.ndarray, paddle.Tensor]: r"""Compute the Negativity :math:`N = ||\frac{\rho^{T_A}-1}{2}||` of the input quantum state. Args: @@ -462,7 +491,7 @@ def negativity(density_op: Union[np.ndarray, paddle.Tensor, State]) -> Union[np. return n if type_str == "numpy" else paddle.to_tensor(n) -def logarithmic_negativity(density_op: Union[np.ndarray, paddle.Tensor, State]) -> Union[np.ndarray, paddle.Tensor]: +def logarithmic_negativity(density_op: Union[np.ndarray, paddle.Tensor, pq.State]) -> Union[np.ndarray, paddle.Tensor]: r"""Calculate the Logarithmic Negativity :math:`E_N = ||\rho^{T_A}||` of the input quantum state. Args: @@ -477,7 +506,7 @@ def logarithmic_negativity(density_op: Union[np.ndarray, paddle.Tensor, State]) return paddle.log2(2 * n + 1) -def is_ppt(density_op: Union[np.ndarray, paddle.Tensor, State]) -> bool: +def is_ppt(density_op: Union[np.ndarray, paddle.Tensor, pq.State]) -> bool: r"""Check if the input quantum state is PPT. Args: @@ -514,7 +543,7 @@ def is_choi(op: Union[np.ndarray, paddle.Tensor]) -> bool: return is_positive(paddle.eye(sys_dim) - op_partial) return False -def schmidt_decompose(psi: Union[np.ndarray, paddle.Tensor, State], +def schmidt_decompose(psi: Union[np.ndarray, paddle.Tensor, pq.State], sys_A: List[int]=None) -> Union[Tuple[paddle.Tensor, paddle.Tensor, paddle.Tensor], Tuple[np.ndarray, np.ndarray, np.ndarray]]: r"""Calculate the Schmidt decomposition of a quantum state :math:`\lvert\psi\rangle=\sum_ic_i\lvert i_A\rangle\otimes\lvert i_B \rangle`. @@ -557,7 +586,7 @@ def schmidt_decompose(psi: Union[np.ndarray, paddle.Tensor, State], return paddle.to_tensor(c), paddle.to_tensor(u), paddle.to_tensor(v) -def image_to_density_matrix(image_filepath: str) -> State: +def image_to_density_matrix(image_filepath: str) -> pq.State: r"""Encode image to density matrix Args: @@ -577,10 +606,10 @@ def image_to_density_matrix(image_filepath: str) -> State: # Density matrix whose trace is 1 rho = image_matrix@image_matrix.T rho = rho/np.trace(rho) - return State(rho, backend=pq.Backend.DensityMatrix) + return _type_transform(rho, "density_matrix") -def shadow_trace(state: 'State', hamiltonian: pq.Hamiltonian, +def shadow_trace(state: pq.State, hamiltonian: Hamiltonian, sample_shots: int, method: Optional[str] = 'CS') -> float: r"""Estimate the expectation value :math:`\text{trace}(H\rho)` of an observable :math:`H`. @@ -601,9 +630,9 @@ def shadow_trace(state: 'State', hamiltonian: pq.Hamiltonian, num_qubits = state.num_qubits mode = state.backend if method == "LBCS": - result, beta = pq.shadow.shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian, method) + result, beta = shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian, method) else: - result = pq.shadow.shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian, method) + result = shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian, method) def prepare_hamiltonian(hamiltonian, num_qubits): new_hamiltonian = [] @@ -723,7 +752,7 @@ def shadow_trace(state: 'State', hamiltonian: pq.Hamiltonian, return trace_estimation -def tensor_state(state_a: State, state_b: State, *args: State) -> State: +def tensor_state(state_a: pq.State, state_b: pq.State, *args: pq.State) -> pq.State: r"""calculate tensor product (kronecker product) between at least two state. This function automatically returns State instance Args: @@ -740,20 +769,20 @@ def tensor_state(state_a: State, state_b: State, *args: State) -> State: """ state_a, state_b = _type_transform(state_a, "tensor"), _type_transform(state_b, "tensor") - return State(NKron(state_a, state_b, [_type_transform(st, "tensor") for st in args])) + return pq.State(NKron(state_a, state_b, [_type_transform(st, "tensor") for st in args])) -def diamond_norm(channel_repr: Union[ChoiRepr, KrausRepr, StinespringRepr, paddle.Tensor], +def diamond_norm(channel_repr: Union[Channel, paddle.Tensor], dim_io: Union[int, Tuple[int, int]] = None, **kwargs) -> float: r'''Calculate the diamond norm of input. Args: - channel_repr: A ``ChoiRepr`` or ``KrausRepr`` or ``StinespringRepr`` instance or a ``paddle.Tensor`` instance. + channel_repr: A ``Channel`` or a ``paddle.Tensor`` instance. dim_io: The input and output dimensions. **kwargs: Parameters to set cvx. Raises: - RuntimeError: `channel_repr` must be `ChoiRepr`or `KrausRepr` or `StinespringRepr` or `paddle.Tensor`. + RuntimeError: `channel_repr` must be `Channel` or `paddle.Tensor`. TypeError: "dim_io" should be "int" or "tuple". Warning: @@ -768,16 +797,12 @@ def diamond_norm(channel_repr: Union[ChoiRepr, KrausRepr, StinespringRepr, paddl Watrous, J. . "Semidefinite Programs for Completely Bounded Norms." Theory of Computing 5.1(2009):217-238. ''' - if isinstance(channel_repr, ChoiRepr): + if isinstance(channel_repr, Channel): choi_matrix = channel_repr.choi_repr elif isinstance(channel_repr, paddle.Tensor): choi_matrix = channel_repr - elif isinstance(channel_repr, (KrausRepr, StinespringRepr)): - warnings.warn('`channel_repr` is not in Choi representaiton, and is converted into `ChoiRepr`') - choi_matrix = channel_repr.to_choi().choi_repr - else: raise RuntimeError('`channel_repr` must be `ChoiRepr`or `KrausRepr` or `StinespringRepr` or `paddle.Tensor`.') @@ -847,35 +872,38 @@ def channel_repr_convert(representation: Union[paddle.Tensor, np.ndarray, List[p return representation if source not in ['Choi', 'Kraus', 'Stinespring']: raise ValueError(f"Unsupported channel representation: require Choi, Kraus or Stinespring, not {source}") - is_ndarray = False - if isinstance(representation, np.ndarray): - is_ndarray = True - representation = paddle.to_tensor(representation) - elif isinstance(representation, List) and isinstance(representation[0], np.ndarray): - is_ndarray = True - representation = [paddle.to_tensor(representation[i]) for i in range(len(representation))] + + if isinstance(representation, List): + assert source == 'Kraus', \ + f"Unsupported data input: expected Kraus representation, received {source}" + type_str = _type_fetch(representation[0]) + representation = [_type_transform(repr, 'tensor') for repr in representation] + else: + type_str = _type_fetch(representation) + representation = _type_transform(repr, 'tensor') + + oper = Channel(source, representation) if source == 'Choi': if target == 'Kraus': - representation = _choi_to_kraus(representation, tol) - return [representation[i].numpy() for i in range(len(representation))] if is_ndarray else representation + representation = oper.kraus_repr + return [_type_transform(repr, type_str) for repr in representation] # stinespring repr - representation = _choi_to_stinespring(representation, tol) + representation = oper.stinespring_repr elif source == 'Kraus': - representation = representation if isinstance(representation, List) else [representation] - representation = _kraus_to_choi(representation) if target == 'Choi' else _kraus_to_stinespring(representation) + representation = oper.choi_repr if target == 'Choi' else oper.stinespring_repr else: # if source == 'Stinespring' if target == 'Kraus': - representation = _stinespring_to_kraus(representation) - return [representation[i].numpy() for i in range(len(representation))] if is_ndarray else representation + representation = oper.kraus_repr + return [_type_transform(repr, type_str) for repr in representation] # choi repr - representation = _stinespring_to_choi(representation) + representation = oper.choi_repr - return representation.numpy() if is_ndarray else representation + return _type_transform(representation, type_str) def random_channel(num_qubits: int, rank: int = None, target: str = 'Kraus') -> Union[paddle.Tensor, List[paddle.Tensor]]: @@ -898,7 +926,7 @@ def random_channel(num_qubits: int, rank: int = None, target: str = 'Kraus') -> # rank = 1 unitary = unitary_group.rvs(rank * dim) - stinespring_mat = paddle.to_tensor(unitary[:, :dim], dtype=pq.get_dtype()).reshape([rank, dim, dim]) + stinespring_mat = paddle.to_tensor(unitary[:, :dim], dtype=get_dtype()).reshape([rank, dim, dim]) list_kraus = [stinespring_mat[j] for j in list(range(rank))] if target == 'Choi': diff --git a/paddle_quantum/qml/bert_qtc.py b/paddle_quantum/qml/bert_qtc.py new file mode 100644 index 0000000..0ff8daa --- /dev/null +++ b/paddle_quantum/qml/bert_qtc.py @@ -0,0 +1,440 @@ +# !/usr/bin/env python3 +# Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +r""" +The BERT-QTC(Quantum Temporal Convolution) model. +""" + +import logging +import paddle +import paddle.nn +import paddle_quantum as pq +import paddlenlp as ppnlp +import paddle.nn.functional as F +from functools import partial +from tqdm import tqdm +from paddle.io import Dataset, DataLoader +from paddlenlp.transformers import BertModel, BertTokenizer +from typing import List, Tuple, Callable + +ppnlp.utils.log.logger.disable() + + +class QuantumTemporalConvolution(paddle.nn.Layer): + r""" + The class of the quantum temporal convolution layer. + + Args: + num_filter: The number of the qubits which the quantum circuit contains. + kernel_size: The size of the kernel, which means the number of the qubits. + circuit_depth: The depth of the quantum circuit, which means the number of repetitions of the circuit template. + padding: The padding size. It will pad in the left and the right sides with elements of the same length if the input type is int. + If the input type is list, it should be [pad_left, pad_right]. + """ + def __init__(self, num_filter: int, kernel_size: int, circuit_depth: int, padding: int): + super().__init__() + # Define the variational quantum circuit. + self.kernel_size = kernel_size + self.num_filter = num_filter + self.pad = paddle.nn.Pad1D(padding=padding) + if isinstance(padding, list): + self.num_pad = padding[0] + padding[1] + elif isinstance(padding, int): + self.num_pad = padding * 2 + vqc_list = [ + pq.ansatz.layer.ComplexEntangledLayer(num_qubits=kernel_size, depth=circuit_depth) for _ in range(num_filter)] + self.vqc = paddle.nn.LayerList(vqc_list) + self.hamiltonian_list = [pq.Hamiltonian([[1, f'Z{idx:d}']]) for idx in range(kernel_size)] + + def forward(self, hidden_state: paddle.Tensor) -> paddle.Tensor: + r"""The forward function to execute the model. + + Args: + hidden_state: The feature obtained by the BERT model. + + Returns: + The feature extracted by the quantum temporal convolution layer. + """ + # The shape of the hidden_state should be [batch_size, hidden_size]. + batch_size, hidden_size = hidden_state.shape + _hidden_size = hidden_size + self.num_pad - self.kernel_size - 1 + # Make the shape to [1, batch_size, hidden_size]. + hidden_state = paddle.unsqueeze(hidden_state, axis=0) + hidden_state = self.pad(hidden_state) + # Make the shape to [batch_size, hidden_size]. + hidden_state = paddle.squeeze(hidden_state, axis=0) + init_state = pq.state.zero_state(num_qubits=self.kernel_size) + batch_feature = [] + for batch_idx in range(batch_size): + filter_feature = [] + for filter_idx in range(self.num_filter): + for hidden_idx in range(_hidden_size): + _state = init_state + for qubit_idx in range(self.kernel_size): + _state = pq.gate.RX(qubits_idx=qubit_idx, + param=hidden_state[batch_idx][hidden_idx + qubit_idx])(_state) + _state = self.vqc[filter_idx](_state) + circuit_output = [pq.loss.ExpecVal(hamiltonian)(_state) for hamiltonian in self.hamiltonian_list] + circuit_output = paddle.concat(circuit_output) + filter_feature.append(circuit_output) + batch_feature.append(paddle.stack(filter_feature, axis=0)) + # The shape of the return tensor is (batch_size, num_filter * _hidden_size, kernel_size) + return paddle.stack(batch_feature, axis=0) + + +class Decoder(paddle.nn.Layer): + r""" + The decoder module of the BERT-QTC model. It contains quantum temporal convolution layer, + global max pooling layer, and the linear layer. + + Args: + num_filter: The number of the quantum temporal convolution filters. + kernel_size: The size of the kernel, which means the number of the qubits. + circuit_depth: The depth of the quantum circuit, which means the number of repetitions of the circuit template. + padding: The padding size. It will pad in the left and the right sides with elements of the same length + if the input type is int. If the input type is list, it should be [pad_left, pad_right]. + num_classes: The number of the classes which the model will classify. + hidden_size: The size of the hidden state obtained through the BERT model. + """ + def __init__( + self, num_filter: int, kernel_size: int, circuit_depth: int, padding: int, + num_classes: int, hidden_size: int + ): + super().__init__() + # The quantum temporal convolution layer. + self.qtc = QuantumTemporalConvolution(num_filter, kernel_size, circuit_depth, padding) + if isinstance(padding, list): + _hidden_size = hidden_size + padding[0] + padding[1] - kernel_size - 1 + elif isinstance(padding, int): + _hidden_size = hidden_size + padding * 2 - kernel_size - 1 + # The global max pooling layer + self.gmp = paddle.nn.MaxPool1D(kernel_size=[kernel_size]) + self.linear = paddle.nn.Linear(in_features=num_filter * _hidden_size, out_features=num_classes) + + def forward(self, bert_feature: paddle.Tensor) -> paddle.Tensor: + r"""The forward function to execute the model. + + Args: + bert_feature: The feature obtained by the BERT model. + + Returns: + The logits of each class obtained by prediction. + """ + # The shape of qtc_output is (batch_size, num_filter * _hidden_size, kernel_size). + qtc_output = self.qtc(bert_feature) + # The shape of gmp_output is (batch_size, num_filter * _hidden_size). + gmp_output = paddle.squeeze(self.gmp(qtc_output), axis=2) + # The shape of predict_logits is (batch_size, num_classes). + predict_logits = self.linear(gmp_output) + return predict_logits + + +class BERTQTC(paddle.nn.Layer): + r"""The BERT-QTC model. + + The details can be referred to https://arxiv.org/abs/2203.03550 . + + Args: + bert_model: The name of the pretrained BERT model. + decoder: The decoder network. + """ + def __init__(self, bert_model: str, decoder: paddle.nn.Layer): + super().__init__() + self.tokenizer = BertTokenizer.from_pretrained(bert_model) + self.token_pad = ppnlp.data.Pad() + self.bert_model = BertModel.from_pretrained(bert_model) + self.decoder = decoder + + def forward(self, token_ids: paddle.Tensor) -> paddle.Tensor: + r"""The forward function to execute the BERT-QTC model. + + Args: + token_ids: The id of the token converted by the sentences. + + Returns: + The probability of each class obtained by prediction. + """ + with paddle.no_grad(): + # The shape of bert_feature is (batch_size, hidden_state_size). + bert_feature = self.bert_model(token_ids)[0][:, 0, :] + bert_feature.stop_gradient = True + predict_logits = self.decoder(bert_feature) + # The shape of predict_logits is (batch_size, num_classes). + return predict_logits + + +class TextDataset(Dataset): + r""" + The class to implement the text dataset. + + Args: + file_path: The dataset file. + bert_model: The name of the pretrained BERT model. + """ + def __init__(self, file_path: str, bert_model: str): + super().__init__() + self.contents = [] + self.pad_func = ppnlp.data.Pad() + tokenizer = BertTokenizer.from_pretrained(bert_model) + with open(file_path, 'r', encoding='utf-8') as file: + lines = file.readlines() + for line in lines: + text, label = line.strip().split('\t') + token_ids = tokenizer(text)['input_ids'] + self.contents.append((token_ids, int(label))) + self.len_data = len(self.contents) + + def __getitem__(self, idx: int): + return self.contents[idx] + + def __len__(self): + return self.len_data + + +def train( + num_filter: int, kernel_size: int, circuit_depth: int, padding: int, num_classes: int, + model_name: str, dataset: str, batch_size: int, num_epochs: int, + bert_model: str = 'bert-base-chinese', hidden_size: int = 768, + learning_rate: float = 0.01, + saved_dir: str = '', using_validation: bool = False, + early_stopping: int = 1000, +) -> None: + r""" + The function of training the BERT-QTC model. + + Args: + num_filter: The number of the qubits which the quantum circuit contains. + kernel_size: The size of the kernel, which means the number of the qubits. + circuit_depth: The depth of the quantum circuit, which means the number of repetitions of the circuit template. + padding: The padding size. It will pad in the left and the right sides with elements of the same length + if the input type is int. If the input type is list, it should be [pad_left, pad_right]. + num_classes: The number of the classes which the model will classify. + model_name: The name of the model. It is the filename of the saved model. + dataset: The dataset used to train the model, which should be a directory. + batch_size: The size of the batch samplers. + num_epochs: The number of the epochs to train the model. + bert_model: The name of the pretrained BERT model. Defaults to ``bert-base-chinese`` . + hidden_size: The size of the hidden state obtained through the BERT model. Defaults to ``768`` . + learning_rate: The learning rate used to update the parameters. Defaults to ``0.01`` . + saved_dir: The directory to saved the trained model and the training log. Defaults to use the current path. + using_validation: If the datasets contains the validation dataset. + Defaults to ``False`` , which means the validation dataset is not included. + early_stopping: Number of iterations with no improvement after which training will be stopped. + Defaults to ``1000`` . + """ + if not saved_dir: + saved_dir = './' + elif saved_dir[-1] != '/': + saved_dir += '/' + if dataset[-1] != '/': + dataset += '/' + logging.basicConfig( + filename=f'{saved_dir}{model_name}.log', + filemode='w', + format='%(asctime)s %(levelname)s %(message)s', + level=logging.INFO, + ) + + def collate_fn(batch_data: List[tuple], pad_func: Callable): + batch_token_ids = [text for text, _ in batch_data] + batch_labels = [label for _, label in batch_data] + return paddle.to_tensor(pad_func(batch_token_ids)), paddle.to_tensor(batch_labels) + + train_dataset = TextDataset(file_path=f'{dataset}train.txt', bert_model=bert_model) + if using_validation: + dev_dataset = TextDataset(file_path=f'{dataset}dev.txt', bert_model=bert_model) + test_dataset = TextDataset(file_path=f'{dataset}test.txt', bert_model=bert_model) + + train_loader = DataLoader( + dataset=train_dataset, batch_size=batch_size, shuffle=True, + collate_fn=partial(collate_fn, pad_func=train_dataset.pad_func), + num_workers=4, use_buffer_reader=True) + if using_validation: + dev_loader = DataLoader( + dataset=dev_dataset, batch_size=batch_size, shuffle=True, + collate_fn=partial(collate_fn, pad_func=dev_dataset.pad_func), + num_workers=4, use_buffer_reader=True) + test_loader = DataLoader( + dataset=test_dataset, batch_size=batch_size, shuffle=True, + collate_fn=partial(collate_fn, pad_func=test_dataset.pad_func), + num_workers=4, use_buffer_reader=True) + + decoder = Decoder( + num_filter=num_filter, kernel_size=kernel_size, circuit_depth=circuit_depth, padding=padding, + num_classes=num_classes, hidden_size=hidden_size) + model = BERTQTC(bert_model=bert_model, decoder=decoder) + model.train() + opt = paddle.optimizer.Adam(learning_rate=learning_rate, parameters=model.decoder.parameters()) + total_batch = 0 + dev_best_loss = float('inf') + last_improve = 0 + stopping_flag = False + for epoch in range(num_epochs): + p_bar = tqdm( + total=len(train_loader), + desc=f'Epoch[{epoch: 3d}]', + ascii=True, + dynamic_ncols=True, + ) + for token_ids, labels in train_loader: + p_bar.update(1) + model.clear_gradients() + logits = model(token_ids) + # The shape of logits is (batch_size, num_classes). + loss = F.cross_entropy(logits, labels) + loss.backward() + opt.minimize( + loss, parameters=model.decoder.parameters(), + no_grad_set=model.bert_model.parameters()) + opt.clear_grad() + if total_batch % 10 == 0 and total_batch > 0: + predictions = paddle.argmax(logits, axis=1).tolist() + labels = labels.tolist() + train_acc = sum(labels[idx] == predictions[idx] for idx in range(len(labels))) / len(labels) + if using_validation: + with paddle.no_grad(): + dev_loss, dev_acc = evaluate(model, dev_loader) + if dev_loss < dev_best_loss: + paddle.save(decoder.state_dict(), f'{saved_dir}/{model_name}.pdparams') + improve = '*' + last_improve = total_batch + dev_best_loss = dev_loss + else: + improve = ' ' + msg = ( + f"Iter:{total_batch: 5d}, Train loss:{loss.item(): 3.5f}, acc:{train_acc: 3.2%}; " + f"Val loss:{dev_loss: 3.5f}, acc:{dev_acc: 3.2%}{improve}" + ) + else: + with paddle.no_grad(): + test_loss, test_acc = evaluate(model, test_loader) + paddle.save(decoder.state_dict(), f'{saved_dir}{model_name}.pdparams') + msg = ( + f"Iter:{total_batch: 5d}, Train loss:{loss.item(): 3.5f}, acc:{train_acc: 3.2%}; " + f"Test loss:{test_loss: 3.5f}, acc:{test_acc: 3.2%}" + ) + model.train() + p_bar.set_postfix_str(msg) + logging.info(msg) + total_batch += 1 + if using_validation and total_batch - last_improve >= early_stopping: + stopping_flag = True + break + p_bar.close() + if stopping_flag: + break + if stopping_flag: + msg = "No optimization for a long time, auto-stopping..." + else: + msg = "The training of the model has been finished." + logging.info(msg) + print(msg) + if using_validation: + test(model, f'{saved_dir}/{model_name}.pdparams', test_loader) + else: + paddle.save(decoder.state_dict(), f'{saved_dir}/{model_name}.pdparams') + with paddle.no_grad(): + test_loss, test_acc = evaluate(model, test_loader) + msg = f"Test loss: {test_loss:3.5f}, acc: {test_acc:3.2%}" + logging.info(msg) + print(msg) + + +def evaluate(model: paddle.nn.Layer, data_loader: DataLoader) -> Tuple[float, float]: + r""" + Evaluate the model. + + Args: + model: The trained model to be evaluated. + data_loader: The dataloader of the data used to evaluate the model. + + Returns: + Return the average loss and accuracy in the data of the input dataloader. + """ + dev_loss = 0 + model.eval() + labels_all = [] + predicts_all = [] + with paddle.no_grad(): + for token_ids, labels in tqdm(data_loader): + logits = model(token_ids) + loss = paddle.nn.functional.cross_entropy(logits, labels, reduction='sum') + labels = labels.tolist() + dev_loss += loss.item() + labels_all.extend(labels) + predict = paddle.argmax(logits, axis=1) + predicts_all.extend(predict.tolist()) + dev_acc = sum(labels_all[idx] == predicts_all[idx] for idx in range(len(labels_all))) + return dev_loss / len(labels_all), dev_acc / len(labels_all) + + +def test(model: paddle.nn.Layer, model_path: str, test_loader: DataLoader) -> None: + r""" + Use the test dataset to test the model. + + Args: + model: The model to be tested. + model_path: The file path of the models' file. + test_loader: The dataloader of the test dataset. + """ + model.decoder.set_state_dict(paddle.load(model_path)) + test_loss, test_acc = evaluate(model, test_loader) + msg = f"Test loss: {test_loss:3.5f}, acc: {test_acc:3.2%}" + logging.info(msg) + print(msg) + + +def inference( + text: str, model_path: str, classes: List[str], + num_filter: int, kernel_size: int, circuit_depth: int, padding: int, + bert_model: str = 'bert-base-chinese', hidden_size: int = 768 +) -> str: + r""" + The inference function. Using the trained model to predict new data. + + Args: + text: The path of the image to be predicted. + model_path: The path of the model file. + classes: The classes of all the labels. + num_filter: The number of the qubits which the quantum circuit contains. + kernel_size: The size of the kernel, which means the number of the qubits. + circuit_depth: The depth of the quantum circuit, which means the number of repetitions of the circuit template. + padding: The padding size. It will pad in the left and the right sides with elements of the same length + if the input type is int. If the input type is list, it should be [pad_left, pad_right]. + model_name: The name of the model. It is the filename of the saved model. + dataset: The dataset used to train the model, which should be a directory. + bert_model: The name of the pretrained BERT model. Defaults to ``bert-base-chinese`` . + hidden_size: The size of the hidden state obtained through the BERT model. Defaults to ``768`` . + + Returns: + Return the class which the model predicted. + """ + num_classes = len(classes) + decoder = Decoder( + num_filter=num_filter, kernel_size=kernel_size, circuit_depth=circuit_depth, padding=padding, + num_classes=num_classes, hidden_size=hidden_size + ) + model = BERTQTC(bert_model=bert_model, decoder=decoder) + model.decoder.set_state_dict(paddle.load(model_path)) + model.eval() + tokenizer = BertTokenizer.from_pretrained(bert_model) + token_ids = tokenizer(text)['input_ids'] + logits = model(paddle.to_tensor([token_ids])) + prediction = paddle.argmax(logits[0], axis=0) + return classes[prediction] + + +if __name__ == '__main__': + exit(0) diff --git a/paddle_quantum/qml/qcaan.py b/paddle_quantum/qml/qcaan.py new file mode 100644 index 0000000..ecc7614 --- /dev/null +++ b/paddle_quantum/qml/qcaan.py @@ -0,0 +1,532 @@ +# !/usr/bin/env python3 +# Copyright (c) 2023 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. +# +# Licensed under the Apache License, Version 2.0 (the "License"); +# you may not use this file except in compliance with the License. +# You may obtain a copy of the License at +# +# http://www.apache.org/licenses/LICENSE-2.0 +# +# Unless required by applicable law or agreed to in writing, software +# distributed under the License is distributed on an "AS IS" BASIS, +# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +# See the License for the specific language governing permissions and +# limitations under the License. + +r""" +Quantum-circuit associative adversarial network (QCAAN) model +""" + +import paddle +import paddle.nn as nn +import paddle.optimizer as optim +import paddle.io as data +from paddle.vision.transforms import Compose, Normalize, ToTensor +from paddle.vision.datasets import MNIST +from tqdm import tqdm +from paddle_quantum.ansatz import Circuit +import paddle_quantum +from paddle_quantum.loss import ExpecVal +from typing import List, Tuple +import numpy as np +import matplotlib.pyplot as plt +import warnings +import os +import logging + +warnings.filterwarnings("ignore", category=Warning) +os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python' + + +def Data_Load() -> paddle.vision.datasets.MNIST: + r""" + Load the MNIST dataset + + Returns: + MNIST dataset + + """ + transform = Compose([ToTensor(), Normalize(mean=[127.5], std=[127.5])]) + dataset = MNIST(mode="train", transform=transform, backend="cv2") + return dataset + + +class ConvBlock(nn.Layer): + r""" + Convolution block for building neural networks. + + Each ConvBlock consists of several convolution, Silu and layer normalization layers. + And ConvBlock keeps the spatial dimensions unchanged, i.e., height and weight. + + Args: + shape: The required shape for layer normalization. + in_channels: The number of input channels in the input. + out_channels: The number of output channels produced by the convolution. + kernel_size: The size of the convolution kernel. + stride: The stride size. + padding: The padding size. + activation: Activation function. + normalize: A symbol indicating whether layer normalization is needed. + """ + + def __init__(self, shape: List[int], in_channels: int, out_channels: int, + kernel_size: int = 3, stride: int = 1, padding: int = 1, + activation: nn.Layer = None, normalize: bool = True) -> None: + super(ConvBlock, self).__init__() + self.layer_norm = nn.LayerNorm(shape) + self.conv1 = nn.Conv2D(in_channels, out_channels, + kernel_size, stride, padding) + self.conv2 = nn.Conv2D(out_channels, out_channels, + kernel_size, stride, padding) + self.conv3 = nn.Conv2D(out_channels, out_channels, + kernel_size, stride, padding) + self.conv4 = nn.Conv2D(out_channels, out_channels, + kernel_size, stride, padding) + self.activation = nn.Silu() if activation is None else activation + self.normalize = normalize + + def forward(self, x: paddle.Tensor) -> paddle.Tensor: + r""" + The ConvBlock's forward function + + Args: + x: The input tensor + + Returns: + The output tensor + + """ + x = self.layer_norm(x) if self.normalize else x + x = self.conv1(x) + x = self.activation(x) + # x = self.conv2(x) + # x = self.activation(x) + # x = self.conv3(x) + # x = self.activation(x) + # x = self.conv4(x) + # x = self.activation(x) + return x + + +class Generator(nn.Layer): + r""" + The Generator network + + Args: + latent_dim: Latent feature numbers which represents the input dimension of the Generator. + """ + + def __init__(self, latent_dim: int = 16): + super(Generator, self).__init__() + + self.channels = 128 + self.d2 = self.channels // 2 + self.d4 = self.channels // 4 + self.d8 = self.channels // 8 + + self.fc = nn.Sequential( + nn.Linear(latent_dim, self.channels * 3 * 3), # [-1, 128 * 3 * 3] + nn.Silu(), + nn.Linear(self.channels * 3 * 3, self.channels * 3 * 3) # [-1, 128 * 3 * 3] + ) + + self.conv = nn.Sequential( + ConvBlock([self.channels, 3, 3], self.channels, self.d2), # [-1, 64, 3, 3] + nn.Conv2DTranspose(self.d2, self.d2, 3, 2, 0), # [-1, 64, 7, 7] + + ConvBlock([self.d2, 7, 7], self.d2, self.d4), # [-1, 32, 7, 7] + nn.Conv2DTranspose(self.d4, self.d4, 4, 2, 1), # [-1, 32, 14, 14] + + ConvBlock([self.d4, 14, 14], self.d4, self.d8), # [-1, 16, 14, 14] + nn.Conv2DTranspose(self.d8, self.d8, 4, 2, 1), # [-1, 16, 28, 28] + + ConvBlock([self.d8, 28, 28], self.d8, 1, + activation=nn.Tanh(), normalize=False), # [-1, 1, 28, 28] + ) + + def forward(self, x: paddle.Tensor) -> paddle.Tensor: + r""" + The Generator's forward function + + Args: + x: The input tensor + + Returns: + The output tensor + + """ + x = self.fc(x) + x = self.conv(paddle.reshape(x, [-1, self.channels, 3, 3])) + return x + + +class Discriminator(nn.Layer): + r""" + The Discriminator network + + Args: + latent_dim: Latent feature numbers which represents the input dimension of the Generator. + """ + + def __init__(self, latent_dim: int = 16): + super(Discriminator, self).__init__() + + self.channels = 128 + self.d2 = self.channels // 2 + self.d4 = self.channels // 4 + self.d8 = self.channels // 8 + + self.conv = nn.Sequential( + ConvBlock([1, 28, 28], 1, self.d8, normalize=False), # [-1, 16, 28, 28] + + nn.Conv2D(self.d8, self.d8, 4, 2, 1), # [-1, 16, 14, 14] + ConvBlock([self.d8, 14, 14], self.d8, self.d4), # [-1, 32, 14, 14] + + nn.Conv2D(self.d4, self.d4, 4, 2, 1), # [-1, 32, 7, 7] + ConvBlock([self.d4, 7, 7], self.d4, self.d2), # [-1, 64, 7, 7] + + nn.Conv2D(self.d2, self.d2, 3, 2, 0), # [-1, 64, 3, 3] + ConvBlock([self.d2, 3, 3], self.d2, self.channels), # [-1, 128, 3, 3] + ) + + self.fc = nn.Sequential( + nn.Linear(self.channels * 3 * 3, self.channels * 3 * 3), # [-1, 128 * 3] + nn.Silu(), + nn.Linear(self.channels * 3 * 3, latent_dim), # [-1, 16] + nn.Tanh(), + ) + + self.output = nn.Sequential( + nn.Linear(latent_dim, self.channels), # [-1, 128] + nn.Silu(), + nn.Linear(self.channels, 1), # [-1, 1] + nn.Sigmoid() + ) + + def forward(self, x: paddle.Tensor) -> Tuple[paddle.Tensor, paddle.Tensor]: + r""" + The Discriminator's forward function + + Args: + x: The input tensor + + Returns: + The output tensor + + """ + x = self.conv(x) + x_tanh = self.fc(paddle.reshape(x, [-1, self.channels * 3 * 3])) + x = self.output(x_tanh) + return x, x_tanh + + +def generate_pauli_string_list(num_qubits: int, num_terms: int) -> List[list]: + r""" + Generate the Pauli string list. + Args: + num_qubits: The number of the qubits. + num_terms: The number of the generated observables. + Returns: + Return the generated Pauli string list. + """ + ob = [[[1.0, f'z{idx:d}']] for idx in range(num_qubits)] + ob.extend([[1.0, f'x{idx:d}']] for idx in range(num_qubits)) + ob.extend([[1.0, f'y{idx:d}']] for idx in range(num_qubits)) + if len(ob) >= num_terms: + ob = ob[:num_terms] + else: + ob.extend(ob * (num_terms // len(ob) - 1)) + ob.extend(ob[:num_terms % len(ob)]) + return ob + + +class QCBM(nn.Layer): + r""" + Quantum Circuit Boltzmann Machine, which is exactly a quantum neural network here. + + Args: + num_qubits: The number of qubits which the quantum circuit contains. + num_depths: The number of depths of complex entangled layers which the quantum circuit contains. + latent_dim: Latent feature numbers which represents the input dimension of the generator. + """ + + def __init__(self, num_qubits: int, num_depths: int, latent_dim: int = 16): + super(QCBM, self).__init__() + + self.num_qubits = num_qubits + self.latent_dim = latent_dim + + # 定义量子电路 + self.cir = Circuit(num_qubits=num_qubits) + self.cir.complex_entangled_layer(depth=num_depths) + self.cir.rz(qubits_idx="full") + self.cir.ry(qubits_idx="full") + self.cir.rz(qubits_idx="full") + + def forward(self) -> paddle.Tensor: + r""" + The forward function of QCBM + + Returns: + A series of expectation values on Z0, Z1, ..., X0, X1, ..., Y0, Y1, ... + + """ + final_state = self.cir() + + # 定义一系列观测量 + pauli_list = generate_pauli_string_list(num_qubits=self.num_qubits, num_terms=self.latent_dim) + obs = [paddle_quantum.Hamiltonian(pauli) for pauli in pauli_list] + + # 计算一系列观测量的平均值 + expec_obs = [ExpecVal(ob)(final_state) for ob in obs] + expec_obs = paddle.concat(expec_obs) + return expec_obs + + +def prior_sampling(expec_obs: paddle.Tensor, batch_size: int) -> paddle.Tensor: + r""" + Simulate the sampling process of the prior distribution, from QCBM. + + Args: + expec_obs: The vector of expectation values whose length is the same as 'latent_dim'. + batch_size: The number of samples in a batch. + + Returns: + The sampling results, values in {-1, 1}. + + """ + prior_samples = paddle.rand([batch_size, len(expec_obs)]) + expec_obs_probs = (expec_obs + 1) / 2. + prior_samples = paddle.cast(expec_obs_probs - prior_samples >= 0, dtype="float32") + prior_samples = prior_samples * 2 - 1 + return prior_samples + + +def train( + # Define the hyperparameters + num_qubits: int = 8, + num_depths: int = 4, + lr_qnn: paddle.float32 = 0.005, + batch_size: int = 128, + latent_dim: int = 16, + epochs: int = 21, + lr_g: paddle.float32 = 0.0002, + lr_d: paddle.float32 = 0.0002, + beta1: paddle.float32 = 0.5, + beta2: paddle.float32 = 0.9, + manual_seed: int = 888, +) -> None: + r""" + The training function of QCAAN model + + Args: + num_qubits: The number of qubits which the quantum circuit contains. + num_depths: The number of depths of complex entangled layers which the quantum circuit contains. + lr_qnn: The learning rate used to update the QNN parameters, default to 0.005. + batch_size: The batch size in each iteration. + latent_dim: Latent feature numbers which represents the input dimension of the generator. + epochs: The number of epochs to train the model. + lr_g: The learning rate used to update the generator parameters, default to 0.0002. + lr_d: The learning rate used to update the discriminator parameters, default to 0.0002. + beta1: The beta1 used in Adam optimizer of generator and discriminator, default to 0.5. + beta2: The beta2 used in Adam optimizer of generator and discriminator, default to 0.9. + manual_seed: The manual seed for reproducibility. + + Returns: + The parameters of QNN, Generator and Discriminator are saved. + + """ + # Set random seed for reproducibility + paddle.seed(manual_seed) + np.random.seed(manual_seed) + + paddle.set_device(paddle.device.get_device()) # Run on GPU if available + print(f"\nThis program is running on your {paddle.device.get_device()}!\n") + + # Define the data loader + dataset = Data_Load() + loader = data.DataLoader(dataset, batch_size=batch_size, shuffle=True) + + # Define the G and D networks and quantum circuit for sampling + generator = Generator(latent_dim=latent_dim) + discriminator = Discriminator(latent_dim=latent_dim) + cir = QCBM(num_qubits=num_qubits, num_depths=num_depths, latent_dim=latent_dim) + + # Define the loss functions and optimizers + bce_loss = nn.BCELoss() + mse_loss = nn.loss.MSELoss() + + opt_g = optim.Adam(parameters=generator.parameters(), + learning_rate=lr_g, beta1=beta1, beta2=beta2) + opt_d = optim.Adam(parameters=discriminator.parameters(), + learning_rate=lr_d, beta1=beta1, beta2=beta2) + opt_qnn = optim.Adam(parameters=cir.parameters(), + learning_rate=lr_qnn) + + # Train the GAN + for epoch in tqdm(range(epochs), ncols=80): + qnn_update_interval = paddle.randint(50, 100).numpy()[0] + print("QNN update interval in this epoch:", qnn_update_interval) + for i, (real_data, _) in enumerate(tqdm(loader, ncols=80)): + # Define the labels for real and fake data + real_labels = paddle.ones((len(real_data), 1)) + fake_labels = paddle.zeros((len(real_data), 1)) + + # Train the qnn + if i % qnn_update_interval == 0: + opt_qnn.clear_grad() + expec_obs = cir() + _, real_tanh = discriminator(real_data) + qnn_loss = mse_loss(expec_obs, paddle.mean(real_tanh.detach(), axis=0)) + qnn_loss.backward() + opt_qnn.step() + + # Train the discriminator + opt_d.clear_grad() + # Generate fake data and compute the discriminator + prior_samples = prior_sampling(expec_obs.detach(), batch_size=len(real_data)) + fake_data = generator(prior_samples) + fake_scores, _ = discriminator(fake_data.detach()) + real_scores, _ = discriminator(real_data) + d_loss = bce_loss(fake_scores, fake_labels) + bce_loss(real_scores, real_labels) + d_loss.backward() + opt_d.step() + + # Train the generator + opt_g.clear_grad() + fake_scores, _ = discriminator(fake_data) + g_loss = bce_loss(fake_scores, real_labels) + g_loss.backward() + opt_g.step() + + # # Print the losses every 100 steps + # if i % 100 == 0: + print("\nEpoch [%d/%d]," % (epoch, epochs), + "Discriminator Loss: :%.4f, Generator Loss: %.4f, " % (d_loss.numpy(), g_loss.numpy()), + "QCBM Loss: %.4f" % qnn_loss.numpy()) + if epoch == epochs - 1: + if not os.path.exists("params"): + os.makedirs("params") + paddle.save(cir.state_dict(), "params/params_qnn_epoch%d.pdparams" % epoch) + paddle.save(generator.state_dict(), "params/params_G_epoch%d.pdparams" % epoch) + # paddle.save(discriminator.state_dict(), "params/params_D_epoch%d.pdparams" % epoch) + + +# 加载保存的模型参数,并生成一些图片,最后将这些图片保存。 +def model_test( + model_name: str = 'qcaan-model', + latent_dim: int = 16, + params_path: str = 'params', + num_qubits: int = 8, + num_depths: int = 4, + manual_seed: int = 20230313, +) -> None: + r""" + Load the saved model parameters, and generate some pictures. Finally save these pictures. + + Args: + model_name: The name of the model, which is used to save the model. + latent_dim: Latent feature numbers which represents the input dimension of the generator. + params_path: The path to load the parameters of the trained model. Both relative and absolute paths are allowed. + num_qubits: The number of qubits which the quantum circuit contains. + num_depths: The number of depths of complex entangled layers which the quantum circuit contains. + manual_seed: The manual seed for reproducibility. + + Returns: + The generated pictures are saved to a .png file. + + """ + + logging.basicConfig( + filename='./qcaan_inference.log', + filemode='w', + format='%(asctime)s %(levelname)s %(message)s', + level=logging.INFO + ) + logging.info( + f"\nThe full config for inferring the QC-AAN model.\n" + f"The mode of this config. Available values: 'train' | 'inference'.\n" + f" mode = 'inference'\n" + f"The name of the model, which is used to save the model.\n" + f" model_name = '{model_name}'\n" + f"The path to load the parameters of the trained model. Both relative and absolute paths are allowed.\n" + f" params_path = '{params_path}'\n" + f"The number of qubits which the quantum circuit contains.\n" + f" num_qubits = {num_depths}\n" + f"The number of depths of complex entangled layers which the quantum circuit contains.\n" + f" num_depths = {num_qubits}\n" + f"Latent feature numbers which represents the input dimension of the generator.\n" + f" latent_dim = {latent_dim}\n" + f"The manual seed for reproducibility.\n" + f" manual_seed = {manual_seed}\n" + ) + + # Set random seed for reproducibility + paddle.seed(manual_seed) + np.random.seed(manual_seed) + + paddle.set_device(paddle.device.get_device()) # Run on GPU if available + print(f"\nThis program is running on your {paddle.device.get_device()}!\n") + + # load models + gen = Generator(latent_dim=latent_dim) + cir = QCBM(num_qubits=num_qubits, num_depths=num_depths, latent_dim=latent_dim) + # load weights + load_epoch = 20 + gen.set_state_dict(paddle.load(f"{params_path}/params_G_epoch{load_epoch}.pdparams")) + gen.eval() + cir.set_state_dict(paddle.load(f"{params_path}/params_qnn_epoch{load_epoch}.pdparams")) + cir.eval() + print("Model loaded, generating new images...") + + # 定义总生成图片数量 + num_shows_rows, num_shows_cols = 6, 10 + # 总共展示 11x10 张图片。上半部分是生成的,下面 40 张是原图。 + fig, axs = plt.subplots(num_shows_rows + 5, num_shows_cols) + # plt.rcParams["figure.figsize"] = [28, 30] + plt.gray() + + # generating pics using trained Generator + expec_obs = cir() + prior_samples = prior_sampling(expec_obs.detach(), batch_size=num_shows_rows * num_shows_cols) + print("The first 10 QNN samples are listed below:\n", prior_samples.numpy()[0:10]) + + with paddle.no_grad(): + gen_pics = gen(prior_samples).numpy() + + for r in range(num_shows_rows): + for c in range(num_shows_cols): + axs[r, c].imshow(gen_pics[r * num_shows_cols + c].reshape(28, 28)) + axs[r, c].axis("off") + + for c in range(num_shows_cols): + axs[num_shows_rows, c].axis("off") + + # 获取一些初始图片并展示,作为对比 + # Define the data loader + dataset = Data_Load() + loader = data.DataLoader(dataset, batch_size=40, shuffle=True) + rand_i = np.random.randint(low=1, high=10, size=1) + for i, (real_data, _) in enumerate(loader): + if i == rand_i: + original_pics = real_data.numpy() + break + + for r in range(4): + for c in range(num_shows_cols): + axs[r + num_shows_rows + 1, c].imshow(original_pics[r * num_shows_cols + c].reshape(28, 28)) + axs[r + num_shows_rows + 1, c].axis("off") + + axs[0, 4].set_title("Generated pictures by QCAAN") + axs[7, 4].set_title("Original pictures from MNIST") + + if not os.path.exists("gen_pics"): + os.makedirs("gen_pics") + plt.savefig(f"gen_pics/qcaan_generated_vs_original_{manual_seed}.png") + print(f"\nThe generated pictures are saved to the file " + f"named 'gen_pics/qcaan_generated_vs_original_{manual_seed}.png'.\n") + plt.show() + + +if __name__ == "__main__": + exit(0) diff --git a/paddle_quantum/qml/qnnmic.py b/paddle_quantum/qml/qnnmic.py index 5409002..207b196 100644 --- a/paddle_quantum/qml/qnnmic.py +++ b/paddle_quantum/qml/qnnmic.py @@ -138,7 +138,7 @@ def _filter_circuit(num_qubits: int, depth:int) -> pq.ansatz.Circuit: """ cir = Circuit(num_qubits) - cir.complex_entangled_layer(qubits_idx='full', depth=depth) + cir.complex_entangled_layer(depth=depth) return cir diff --git a/paddle_quantum/qml/qnnqd.py b/paddle_quantum/qml/qnnqd.py index 3007ceb..0abe158 100644 --- a/paddle_quantum/qml/qnnqd.py +++ b/paddle_quantum/qml/qnnqd.py @@ -118,7 +118,7 @@ def _filter_circuit(num_qubits: int, depth:int) -> pq.ansatz.Circuit: """ cir = Circuit(num_qubits) - cir.complex_entangled_layer(qubits_idx='full', depth=depth) + cir.complex_entangled_layer(depth=depth) return cir diff --git a/paddle_quantum/qml/qsann.py b/paddle_quantum/qml/qsann.py index 4d90712..3374708 100644 --- a/paddle_quantum/qml/qsann.py +++ b/paddle_quantum/qml/qsann.py @@ -119,52 +119,34 @@ class QSANN(paddle.nn.Layer): embedding_state = pq.state.zero_state(num_qubits) for d in range(depth): for idx in range(num_qubits): + qubits_idx = [idx, (idx + 1) % num_qubits] param_idx = 2 * num_qubits * d + 2 * idx - embedding_state = functional.rx( - state=embedding_state, qubit_idx=idx, - theta=params[param_idx][0], - dtype=embedding_state.dtype, backend=embedding_state.backend - ) - embedding_state = functional.ry( - state=embedding_state, qubit_idx=idx, - theta=params[param_idx][1], - dtype=embedding_state.dtype, backend=embedding_state.backend - ) - embedding_state = functional.rx( - state=embedding_state, qubit_idx=(idx + 1) % num_qubits, - theta=params[param_idx + 1][0], - dtype=embedding_state.dtype, backend=embedding_state.backend - ) - embedding_state = functional.ry( - state=embedding_state, qubit_idx=(idx + 1) % num_qubits, - theta=params[param_idx + 1][1], - dtype=embedding_state.dtype, backend=embedding_state.backend - ) - embedding_state = functional.cnot( - state=embedding_state, qubit_idx=[idx, (idx + 1) % num_qubits], - dtype=embedding_state.dtype, backend=embedding_state.backend - ) + + cir = pq.Circuit(embedding_state.num_qubits) + cir.rx(qubits_idx, param=params[param_idx:param_idx+2][0]) + cir.ry(qubits_idx, param=params[param_idx:param_idx+2][1]) + cir.cnot(qubits_idx) + embedding_state = cir(embedding_state) + for idx in range(num_qubits): param_idx = 2 * num_qubits * depth + idx - embedding_state = functional.rx( - state=embedding_state, qubit_idx=idx, theta=params[param_idx][0], - dtype=embedding_state.dtype, backend=embedding_state.backend - ) - embedding_state = functional.ry( - state=embedding_state, qubit_idx=idx, theta=params[param_idx][1], - dtype=embedding_state.dtype, backend=embedding_state.backend - ) + + cir = pq.Circuit(embedding_state.num_qubits) + cir.rx(idx, param=params[param_idx][0]) + cir.ry(idx, param=params[param_idx][1]) + embedding_state = cir(embedding_state) + return embedding_state def forward(self, batch_text: List[List[int]]) -> List[paddle.Tensor]: r""" - The forward function to excute the model. + The forward function to execute the model. Args: batch_text: The batch of input texts. Each of them is a list of int. Returns: - Retrun a list which contains the predictions of the input texts. + Return a list which contains the predictions of the input texts. """ predictions = [] for text in batch_text: @@ -477,7 +459,7 @@ def test(model: paddle.nn.Layer, model_path: str, test_loader: list) -> None: def inference( text: str, model_path: str, vocab_path: str, classes: List[str], num_qubits: int, num_layers: int, depth_ebd: int, - depth_query: int, depth_key: int, depth_value: int, + depth_query: int, depth_key: int, depth_value: int ) -> str: r""" The inference function. Using the trained model to predict new data. diff --git a/paddle_quantum/qpp/utils.py b/paddle_quantum/qpp/utils.py index 720c7d7..d54e579 100644 --- a/paddle_quantum/qpp/utils.py +++ b/paddle_quantum/qpp/utils.py @@ -25,12 +25,12 @@ from ..ansatz import Circuit from ..backend import Backend from ..base import get_dtype from ..gate import X -from ..intrinsic import _get_float_dtype +from ..intrinsic import _get_float_dtype, _type_transform from ..linalg import unitary_random, is_unitary from ..loss import Measure from ..operator import Collapse from ..qinfo import dagger, partial_trace -from ..state import State, _type_transform, zero_state +from ..state import State, zero_state r""" diff --git a/paddle_quantum/shadow.py b/paddle_quantum/shadow.py index f00f422..b6622f1 100644 --- a/paddle_quantum/shadow.py +++ b/paddle_quantum/shadow.py @@ -21,7 +21,7 @@ import math import numpy as np import paddle import re -import paddle_quantum +import paddle_quantum as pq from paddle_quantum import Hamiltonian from typing import List, Optional @@ -31,8 +31,8 @@ __all__ = [ def shadow_sample( - state: 'paddle_quantum.State', num_qubits: int, sample_shots: int, mode: paddle_quantum.Backend, - hamiltonian: Optional[paddle_quantum.Hamiltonian] = None, method: str = 'CS' + state: 'pq.State', num_qubits: int, sample_shots: int, mode: pq.Backend, + hamiltonian: Optional[pq.Hamiltonian] = None, method: str = 'CS' ) -> list: r"""Measure a given quantum state with random Pauli operators and return the measurement results. @@ -96,15 +96,15 @@ def shadow_sample( # Convert to tensor form for qubit in range(num_qubits): if pauli_str[qubit] == 'x': - input_state = paddle_quantum.gate.functional.h(input_state, qubit, input_state.dtype, input_state.backend) + input_state = pq.gate.H(qubits_idx=qubit)(input_state) elif pauli_str[qubit] == 'y': - input_state = paddle_quantum.gate.functional.s(input_state, qubit, input_state.dtype, input_state.backend) - input_state = paddle_quantum.gate.functional.z(input_state, qubit, input_state.dtype, input_state.backend) - input_state = paddle_quantum.gate.functional.h(input_state, qubit, input_state.dtype, input_state.backend) - if input_state.backend == paddle_quantum.Backend.StateVector: + input_state = pq.gate.S(qubits_idx=qubit)(input_state) + input_state = pq.gate.Z(qubits_idx=qubit)(input_state) + input_state = pq.gate.H(qubits_idx=qubit)(input_state) + if input_state.backend == pq.Backend.StateVector: data = input_state.data.numpy() prob_array = np.real(np.multiply(data, np.conj(data))) - elif input_state.backend == paddle_quantum.Backend.DensityMatrix: + elif input_state.backend == pq.Backend.DensityMatrix: data = input_state.data.numpy() prob_array = np.real(np.diag(data)) else: diff --git a/paddle_quantum/state/__init__.py b/paddle_quantum/state/__init__.py index 4bf7a72..86a7900 100644 --- a/paddle_quantum/state/__init__.py +++ b/paddle_quantum/state/__init__.py @@ -17,8 +17,7 @@ r""" The module of the quantum state. """ -from .state import State, is_state_vector, is_density_matrix -from .state import _type_fetch, _type_transform +from .state import State from .common import zero_state from .common import computational_basis from .common import bell_state diff --git a/paddle_quantum/state/common.py b/paddle_quantum/state/common.py index 19f1044..d301ac4 100644 --- a/paddle_quantum/state/common.py +++ b/paddle_quantum/state/common.py @@ -19,17 +19,17 @@ The common function of the quantum state. import numpy as np import paddle -import paddle_quantum +import paddle_quantum as pq import QCompute -from ..backend import Backend -from ..backend import quleaf +from ..base import get_backend, get_dtype +from ..backend import Backend, quleaf from .state import State from typing import Union, Optional, List def to_state( data: Union[paddle.Tensor, np.ndarray, QCompute.QEnv], num_qubits: Optional[int] = None, - backend: Optional[paddle_quantum.Backend] = None, dtype: Optional[str] = None + backend: Optional[Backend] = None, dtype: Optional[str] = None ) -> State: r"""The function to generate a specified state instance. @@ -48,7 +48,7 @@ def to_state( def zero_state( - num_qubits: int, backend: Optional[paddle_quantum.Backend] = None, dtype: Optional[str] = None + num_qubits: int, backend: Optional[Backend] = None, dtype: Optional[str] = None ) -> State: r"""The function to generate a zero state. @@ -63,12 +63,12 @@ def zero_state( Returns: The generated quantum state. """ - dtype = paddle_quantum.get_dtype() if dtype is None else dtype + dtype = get_dtype() if dtype is None else dtype np_dtype = np.complex64 if dtype == 'complex64' else np.complex128 data = np.zeros((2 ** num_qubits,), dtype=np_dtype) data[0] = 1 data = paddle.to_tensor(data) - backend = paddle_quantum.get_backend() if backend is None else backend + backend = get_backend() if backend is None else backend if backend == Backend.StateVector: state = State(data, num_qubits, backend=backend, dtype=dtype) elif backend == Backend.DensityMatrix: @@ -86,7 +86,7 @@ def zero_state( def computational_basis( - num_qubits: int, index: int, backend: Optional[paddle_quantum.Backend] = None, dtype: Optional[str] = None + num_qubits: int, index: int, backend: Optional[Backend] = None, dtype: Optional[str] = None ) -> State: r"""Generate a computational basis state :math:`|e_{i}\rangle` , whose i-th element is 1 and all the other elements are 0. @@ -102,12 +102,12 @@ def computational_basis( Returns: The generated quantum state. """ - dtype = paddle_quantum.get_dtype() if dtype is None else dtype + dtype = get_dtype() if dtype is None else dtype np_dtype = np.complex64 if dtype == 'complex64' else np.complex128 data = np.zeros((2 ** num_qubits,), dtype=np_dtype) data[index] = 1 data = paddle.to_tensor(data) - backend = paddle_quantum.get_backend() if backend is None else backend + backend = get_backend() if backend is None else backend if backend == Backend.StateVector: state = State(data, num_qubits, backend=backend) elif backend == Backend.DensityMatrix: @@ -119,7 +119,7 @@ def computational_basis( return state -def bell_state(num_qubits: int, backend: Optional[paddle_quantum.Backend] = None) -> State: +def bell_state(num_qubits: int, backend: Optional[Backend] = None) -> State: r"""Generate a bell state. Its matrix form is: @@ -138,7 +138,7 @@ def bell_state(num_qubits: int, backend: Optional[paddle_quantum.Backend] = None Returns: The generated quantum state. """ - np_dtype = np.complex64 if paddle_quantum.get_dtype() == 'complex64' else np.complex128 + np_dtype = np.complex64 if get_dtype() == 'complex64' else np.complex128 dim = 2 ** num_qubits local_dim = 2 ** int(num_qubits / 2) coeff = 1 / local_dim @@ -146,7 +146,7 @@ def bell_state(num_qubits: int, backend: Optional[paddle_quantum.Backend] = None for i in range(0, dim, local_dim + 1): for j in range(0, dim, local_dim + 1): data[i, j] = coeff - backend = paddle_quantum.get_backend() if backend is None else backend + backend = get_backend() if backend is None else backend if backend == Backend.StateVector: eigenvalue, eigenvector = paddle.linalg.eig(paddle.to_tensor(data)) data = eigenvector[:, paddle.argmax(paddle.real(eigenvalue))] @@ -182,7 +182,7 @@ def bell_diagonal_state(prob: List[float]) -> State: assert 0 <= p1 <= 1 and 0 <= p2 <= 1 and 0 <= p3 <= 1 and 0 <= p4 <= 1, "Each probability must be in [0, 1]." assert abs(p1 + p2 + p3 + p4 - 1) < 1e-6, "The sum of probabilities should be 1." - np_dtype = np.complex64 if paddle_quantum.get_dtype() == 'complex64' else np.complex128 + np_dtype = np.complex64 if get_dtype() == 'complex64' else np.complex128 coeff = np.sqrt(0.5) phi_p_vec = np.array([[coeff, 0, 0, coeff]], dtype=np_dtype) phi_p_mat = np.matmul(phi_p_vec.T, phi_p_vec) @@ -195,7 +195,7 @@ def bell_diagonal_state(prob: List[float]) -> State: state = p1 * phi_p_mat + p2 * psi_p_mat + p3 * phi_m_mat + p4 * psi_m_mat - backend = paddle_quantum.get_backend() + backend = get_backend() if backend == Backend.StateVector: trace_rho = paddle.trace(paddle.to_tensor(state) @ paddle.to_tensor(state)) if trace_rho.numpy()[0] == 1: @@ -225,32 +225,14 @@ def random_state(num_qubits: int, is_real: Optional[bool] = False, rank: Optiona Returns: The generated quantum state. """ - float_dtype = 'float32' if paddle_quantum.get_dtype() == 'complex64' else 'float64' - backend = paddle_quantum.get_backend() + backend = get_backend() if backend == Backend.StateVector: - if is_real: - data = paddle.rand((2 ** num_qubits,), dtype=float_dtype) - else: - data_real = paddle.rand((2 ** num_qubits,), dtype=float_dtype) - data_imag = paddle.rand((2 ** num_qubits,), dtype=float_dtype) - data = data_real + 1j * data_imag - norm = np.linalg.norm(data.numpy()) - data = data / paddle.to_tensor(norm) - state = State(data, num_qubits, backend=backend) + data = pq.linalg.haar_state_vector(num_qubits, is_real) elif backend == Backend.DensityMatrix: - rank = 2 ** num_qubits if rank is None else rank - if is_real: - data = paddle.rand((2 ** num_qubits, rank), dtype=float_dtype) - else: - data_real = paddle.rand((2 ** num_qubits, rank), dtype=float_dtype) - data_imag = paddle.rand((2 ** num_qubits, rank), dtype=float_dtype) - data = data_real + 1j * data_imag - data = paddle.matmul(data, paddle.conj(paddle.t(data))) - data = data / paddle.trace(data) - state = State(data, num_qubits, backend=backend) + data = pq.linalg.haar_density_operator(num_qubits, rank, is_real) else: raise NotImplementedError - return state + return State(data, num_qubits, backend=backend) def w_state(num_qubits: int) -> 'State': @@ -265,11 +247,11 @@ def w_state(num_qubits: int) -> 'State': Returns: The generated quantum state. """ - np_dtype = np.complex64 if paddle_quantum.get_dtype() == 'complex64' else np.complex128 - coeff = np.ones((1, 2 ** num_qubits)) / np.sqrt(num_qubits) - backend = paddle_quantum.get_backend() + np_dtype = np.complex64 if get_dtype() == 'complex64' else np.complex128 + coeff = np.ones(2 ** num_qubits) / np.sqrt(num_qubits) + backend = get_backend() if backend == Backend.StateVector: - state = np.zeros((1, 2 ** num_qubits), dtype=np_dtype) + state = np.zeros(2 ** num_qubits, dtype=np_dtype) for i in range(num_qubits): state[0][2 ** i] = coeff[0][num_qubits - i - 1] state = State(paddle.to_tensor(state), num_qubits, backend=backend) @@ -298,12 +280,12 @@ def ghz_state(num_qubits: int) -> 'State': Returns: The generated quantum state. """ - np_dtype = np.complex64 if paddle_quantum.get_dtype() == 'complex64' else np.complex128 - backend = paddle_quantum.get_backend() + np_dtype = np.complex64 if get_dtype() == 'complex64' else np.complex128 + backend = get_backend() if backend == Backend.StateVector: - state = np.zeros((1, 2 ** num_qubits)) - state[0][0] = 1 / np.sqrt(2) - state[0][-1] = 1 / np.sqrt(2) + state = np.zeros(2 ** num_qubits, dtype=np_dtype) + state[0] = 1 / np.sqrt(2) + state[-1] = 1 / np.sqrt(2) state = State(paddle.to_tensor(state), num_qubits, backend=backend) elif backend == Backend.DensityMatrix: state = np.zeros(2 ** num_qubits, dtype=np_dtype) @@ -333,10 +315,10 @@ def completely_mixed_computational(num_qubits: int) -> State: """ assert num_qubits > 0, 'qubit number must be positive' - np_dtype = np.complex64 if paddle_quantum.get_dtype() == 'complex64' else np.complex128 + np_dtype = np.complex64 if get_dtype() == 'complex64' else np.complex128 state = np.eye(2 ** num_qubits) / (2 ** num_qubits) state = state.astype(np_dtype) - backend = paddle_quantum.get_backend() + backend = get_backend() if backend == Backend.StateVector: trace_rho = paddle.trace(paddle.to_tensor(state) @ paddle.to_tensor(state)) if trace_rho.numpy()[0] == 1: @@ -373,7 +355,7 @@ def r_state(prob: float) -> State: """ assert 0 <= prob <= 1, "Probability must be in [0, 1]" - np_dtype = np.complex64 if paddle_quantum.get_dtype() == 'complex64' else np.complex128 + np_dtype = np.complex64 if get_dtype() == 'complex64' else np.complex128 coeff = np.sqrt(0.5) psi_p_vec = np.array([[0, coeff, coeff, 0]]) psi_p_mat = np.matmul(psi_p_vec.T, psi_p_vec) @@ -381,7 +363,7 @@ def r_state(prob: float) -> State: state_11[3, 3] = 1 state = prob * psi_p_mat + (1 - prob) * state_11 state = state.astype(np_dtype) - backend = paddle_quantum.get_backend() + backend = get_backend() if backend == Backend.StateVector: trace_rho = paddle.trace(paddle.to_tensor(state) @ paddle.to_tensor(state)) if trace_rho.numpy()[0] == 1: @@ -418,14 +400,14 @@ def s_state(prob: float) -> State: """ assert 0 <= prob <= 1, "Probability must be in [0, 1]" - np_dtype = np.complex64 if paddle_quantum.get_dtype() == 'complex64' else np.complex128 + np_dtype = np.complex64 if get_dtype() == 'complex64' else np.complex128 phi_p = bell_state(2).data.numpy() psi0 = np.zeros_like(phi_p) psi0[0, 0] = 1 state = prob * phi_p + (1 - prob) * psi0 state = state.astype(np_dtype) - backend = paddle_quantum.get_backend() + backend = get_backend() if backend == Backend.StateVector: trace_rho = paddle.trace(paddle.to_tensor(state) @ paddle.to_tensor(state)) if trace_rho.numpy()[0] == 1: @@ -463,13 +445,13 @@ def isotropic_state(num_qubits: int, prob: float) -> State: """ assert 0 <= prob <= 1, "Probability must be in [0, 1]" - np_dtype = np.complex64 if paddle_quantum.get_dtype() == 'complex64' else np.complex128 + np_dtype = np.complex64 if get_dtype() == 'complex64' else np.complex128 dim = 2 ** num_qubits phi_b = bell_state(num_qubits).data.numpy() state = prob * phi_b + (1 - prob) * np.eye(dim) / dim state = state.astype(np_dtype) - backend = paddle_quantum.get_backend() + backend = get_backend() if backend == Backend.StateVector: trace_rho = paddle.trace(paddle.to_tensor(state) @ paddle.to_tensor(state)) if trace_rho.numpy()[0] == 1: diff --git a/paddle_quantum/state/state.py b/paddle_quantum/state/state.py index 8625721..7aa22ae 100644 --- a/paddle_quantum/state/state.py +++ b/paddle_quantum/state/state.py @@ -18,6 +18,7 @@ The basic class of the quantum state. """ import collections +import copy import math import matplotlib.pyplot as plt import numpy as np @@ -26,11 +27,10 @@ import random import paddle import QCompute -import paddle_quantum -from ..backend import Backend -from ..backend import state_vector, density_matrix, quleaf -from ..hamiltonian import Hamiltonian -from typing import Optional, Union, Iterable, Tuple +import paddle_quantum as pq +from ..backend import Backend, state_vector, density_matrix, quleaf +from ..base import get_backend, get_dtype +from typing import Optional, Union, Iterable, List, Dict class State(object): @@ -42,60 +42,65 @@ class State(object): backend: Used to specify the backend used. Defaults to ``None``, which means to use the default backend. dtype: Used to specify the data dtype of the data. Defaults to ``None``, which means to use the default data type. override: whether override the input test. ONLY for internal use. Defaults to ``False``. - + Raises: ValueError: Cannot recognize the backend. """ def __init__( self, data: Union[paddle.Tensor, np.ndarray, QCompute.QEnv], num_qubits: Optional[int] = None, - backend: Optional[paddle_quantum.Backend] = None, dtype: Optional[str] = None, override: Optional[bool] = False + backend: Optional[Backend] = None, dtype: Optional[str] = None, override: Optional[bool] = False ): # TODO: need to check whether it is a legal quantum state super().__init__() - self.backend = paddle_quantum.get_backend() if backend is None else backend - self.dtype = dtype if dtype is not None else paddle_quantum.get_dtype() - if self.backend != Backend.QuLeaf and not isinstance(data, paddle.Tensor): + self.backend = get_backend() if backend is None else backend + self.dtype = dtype if dtype is not None else get_dtype() + # TODO: If the dtype is right, don't do the cast operation. + if isinstance(data, paddle.Tensor): + self.data = paddle.cast(data, self.dtype) if data.dtype != self.dtype else data + elif self.backend != Backend.QuLeaf: data = paddle.to_tensor(data, dtype=self.dtype) - self.data = paddle.cast(data, self.dtype) if data.dtype != self.dtype else data - + self.data = paddle.cast(data, self.dtype) # data input test if self.backend == Backend.StateVector: if data.shape[-1] == 1: self.data = paddle.squeeze(data) - if not override: - is_vec, data_message = is_state_vector(data) - assert is_vec, \ - f"The input data is not a legal state vector: error message {data_message}" - assert num_qubits is None or num_qubits == data_message, \ - f"num_qubits does not agree: expected {num_qubits}, received {data_message}" + is_vec, data_message = pq.linalg.is_state_vector(data) + assert is_vec, f"The input data is not a legal state vector: error message {data_message}" + assert num_qubits is None or num_qubits == data_message, ( + f"num_qubits does not agree: expected {num_qubits}, received {data_message}") num_qubits = data_message - elif self.backend == Backend.DensityMatrix: - if not override: - is_den, data_message = is_density_matrix(data) - assert is_den, \ - f"The input data is not a legal density matrix: error message {data_message}" - assert num_qubits is None or num_qubits == data_message, \ - f"num_qubits does not agree: expected {num_qubits}, received {data_message}" + is_den, data_message = pq.linalg.is_density_matrix(data) + assert is_den, f"The input data is not a legal density matrix: error message {data_message}" + assert num_qubits is None or num_qubits == data_message, ( + f"num_qubits does not agree: expected {num_qubits}, received {data_message}") num_qubits = data_message - elif self.backend == Backend.UnitaryMatrix: # no need to check the state in unitary backend if num_qubits is None: num_qubits = int(math.log2(data.shape[0])) - elif self.backend == Backend.QuLeaf: + self.data = data if quleaf.get_quleaf_backend() != QCompute.BackendName.LocalBaiduSim2: assert quleaf.get_quleaf_token() is not None, "You must input token tu use cloud server." - self.gate_history = [] - self.param_list = [] - self.num_param = 0 else: raise ValueError( f"Cannot recognize the backend {self.backend}") self.num_qubits = num_qubits + + # initialize default qubit sequence + self.qubit_sequence = list(range(num_qubits)) + + # whether use the old doubly-swap logic to compute the matrix multiplication. Defaults to ``False``. + self.is_swap_back = True + + def __getitem__(self, key: Union[int, slice]) -> 'State': + r"""Indexing of the State class + """ + qubits = list(range(self.num_qubits))[key] + return pq.qinfo.partial_trace_discontiguous(self, qubits if isinstance(qubits, List) else [qubits]) @property def ket(self) -> paddle.Tensor: @@ -113,7 +118,7 @@ class State(object): f"the backend must be in StateVector: received {self.backend}") return self.data.reshape([2 ** self.num_qubits, 1]) - + @property def bra(self) -> paddle.Tensor: r"""Return the bra form in state_vector backend @@ -130,13 +135,12 @@ class State(object): f"the backend must be in StateVector: received {self.backend}") return paddle.conj(self.data.reshape([1, 2 ** self.num_qubits])) - + def normalize(self) -> None: r"""Normalize this state - + Raises: NotImplementedError: does not support normalization for the backend - """ data = self.data if self.backend == Backend.StateVector: @@ -147,28 +151,29 @@ class State(object): raise NotImplementedError( f"Does not support normalization for the backend {self.backend}") self.data = data - - def evolve(self, H: Union[np.ndarray, paddle.Tensor, Hamiltonian], t: float) -> None: + + def evolve(self, H: Union[np.ndarray, paddle.Tensor, 'pq.Hamiltonian'], t: float) -> None: r"""Evolve the state under the Hamiltonian `H` i.e. apply unitary operator :math:`e^{-itH}` - + Args: H: the Hamiltonian of the system t: the evolution time - + Raises: NotImplementedError: does not support evolution for the backend """ - if isinstance(H, Hamiltonian): + if isinstance(H, pq.Hamiltonian): num_qubits = max(self.num_qubits, H.n_qubits) H = H.construct_h_matrix(qubit_num=num_qubits) else: num_qubits = int(math.log2(H.shape[0])) - H = _type_transform(H, "numpy") - assert num_qubits == self.num_qubits, \ - f"the # of qubits of Hamiltonian and this state are not the same: received {num_qubits}, expect {self.num_qubits}" + H = pq.intrinsic._type_transform(H, "numpy") + assert num_qubits == self.num_qubits, ( + "the # of qubits of Hamiltonian and this state are not the same: " + f"received {num_qubits}, expect {self.num_qubits}") e_itH = paddle.to_tensor(expm(-1j * t * H), dtype=self.dtype) - + if self.backend == Backend.StateVector: self.data = paddle.squeeze(e_itH @ self.ket) elif self.backend == Backend.DensityMatrix: @@ -176,31 +181,29 @@ class State(object): else: raise NotImplementedError( f"Does not support evolution for the backend {self.backend}") - + def kron(self, other: 'State') -> 'State': r"""Kronecker product between states - + Args: other: a quantum state - + Returns: the tensor product of these two states - """ backend, dtype = self.backend, self.dtype assert backend == other.backend, \ f"backends between two States are not the same: received {backend} and {other.backend}" assert dtype == other.dtype, \ f"dtype between two States are not the same: received {dtype} and {other.dtype}" - if backend == Backend.StateVector: return State(paddle.kron(self.ket, other.ket), backend=backend) else: return State(paddle.kron(self.data, other.data), backend=backend, dtype=dtype) - + def __matmul__(self, other: 'State') -> paddle.Tensor: r"""Matrix product between states or between tensor and state - + Args: other: a quantum state @@ -218,10 +221,10 @@ class State(object): raise ValueError( "Cannot multiply two state vectors: check the backend") return self.data @ other.data - + def __rmatmul__(self, other: 'State') -> paddle.Tensor: r"""Matrix product between states or between state and tensor - + Args: other: a quantum state @@ -231,7 +234,6 @@ class State(object): Returns: the product of these two states - """ if not isinstance(other, State): raise NotImplementedError( @@ -240,7 +242,7 @@ class State(object): raise ValueError( "Cannot multiply two state vectors: check your backend") return other.data @ self.data - + def numpy(self) -> np.ndarray: r"""Get the data in numpy. @@ -257,22 +259,23 @@ class State(object): dtype: Specify the new data type of the state. device: Specify the new device of the state. blocking: Specify the new blocking of the state. - + Raises NotImplementedError: only support transformation between StateVector and DensityMatrix NotImplementedError: Transformation for device or blocking is not supported. - """ - if (backend not in {"state_vector", "density_matrix"} or - self.backend not in {Backend.StateVector, Backend.DensityMatrix}): + if ( + backend not in {"state_vector", "density_matrix"} or + self.backend not in {Backend.StateVector, Backend.DensityMatrix} + ): raise NotImplementedError( "Only support transformation between StateVector and DensityMatrix") - + if device is not None or blocking is not None: raise NotImplementedError( "Transformation for device or blocking is not supported") - - self.data = _type_transform(self, backend).data + + self.data = pq.intrinsic._type_transform(self, backend).data self.dtype = self.dtype if dtype is None else dtype def clone(self) -> 'State': @@ -281,12 +284,43 @@ class State(object): Returns: A new state which is identical to this state. """ - return State(self.data, self.num_qubits, self.backend, self.dtype, override=True) + new_state = State(paddle.clone(self.data), self.num_qubits, self.backend, self.dtype, override=True) + new_state.qubit_sequence = self.qubit_sequence + new_state.is_swap_back = self.is_swap_back + return new_state + + def __copy__(self) -> 'State': + return self.clone() def __str__(self): return str(self.data.numpy()) + + @property + def oper_history(self) -> List[Dict[str, Union[str, List[int], paddle.Tensor]]]: + r"""The operator history stored for the QPU backend + + Raises: + NotImplementedError: This property should be called for the backend ``quleaf`` only. + ValueError: This state does not have operator history: run the circuit first. + + """ + if self.backend != Backend.QuLeaf: + raise NotImplementedError( + "This property should be called for backend `quleaf only.") + + if not hasattr(self, '_State__oper_history'): + raise ValueError( + "This state does not have operator history: run the circuit first.") + return self.__oper_history + + @oper_history.setter + def oper_history(self, oper_history: List[Dict[str, Union[str, List[int], paddle.Tensor]]]) -> None: + if self.backend != Backend.QuLeaf: + raise NotImplementedError( + "This property should be changed for backend `quleaf only.") + self.__oper_history = oper_history - def expec_val(self, hamiltonian: Hamiltonian, shots: Optional[int] = 0) -> float: + def expec_val(self, hamiltonian: 'pq.Hamiltonian', shots: Optional[int] = 0) -> float: r"""The expectation value of the observable with respect to the quantum state. Args: @@ -300,7 +334,7 @@ class State(object): The expectation value of the input observable for the quantum state. """ if shots == 0: - func = paddle_quantum.loss.ExpecVal(hamiltonian) + func = pq.loss.ExpecVal(hamiltonian) result = func(self) return result.item() result = 0 @@ -337,9 +371,9 @@ class State(object): state_data = simulator( state_data, gate_for_y, idx, self.num_qubits ) - if self.backend == paddle_quantum.Backend.StateVector: + if self.backend == Backend.StateVector: prob_amplitude = paddle.multiply(paddle.conj(state_data), state_data).real() - elif self.backend == paddle_quantum.Backend.DensityMatrix: + elif self.backend == Backend.DensityMatrix: prob_amplitude = paddle.zeros([2 ** self.num_qubits]) for idx in range(2 ** self.num_qubits): prob_amplitude[idx] += state_data[idx, idx].real() @@ -354,8 +388,10 @@ class State(object): result += coeff * temp_res return result - def measure(self, shots: Optional[int] = 0, qubits_idx: Optional[Union[Iterable[int], int]] = None, - plot: Optional[bool] = False) -> dict: + def measure( + self, shots: Optional[int] = 0, qubits_idx: Optional[Union[Iterable[int], int]] = None, + plot: Optional[bool] = False, record: Optional[bool] = False + ) -> dict: r"""Measure the quantum state Args: @@ -363,270 +399,121 @@ class State(object): Default is ``0``, which means the exact probability distribution of measurement results are returned. qubits_idx: The index of the qubit to be measured. Defaults to ``None``, which means all qubits are measured. plot: Whether to draw the measurement result plot. Defaults to ``False`` which means no plot. + record: Whether to return the original measurement record. Defaults to ``False`` which means no record. Raises: - Exception: The number of shots should be greater than 0. + ValueError: The number of shots should be greater than 0. + NotImplementedError: When the backend is Quleaf, record is not supprted . NotImplementedError: If the backend is wrong or not implemented. NotImplementedError: The qubit index is wrong or not supported. + ValueError: Returning records requires the number of shots to be greater than 0. Returns: Measurement results """ - if self.backend == paddle_quantum.Backend.QuLeaf: + if self.backend == Backend.QuLeaf: if shots == 0: - raise Exception("The quleaf server requires the number of shots to be greater than 0.") - state_data = self.data - QCompute.MeasureZ(*state_data.Q.toListPair()) - result = state_data.commit(shots, fetchMeasure=True)['counts'] - result = {''.join(reversed(key)): value for key, value in result.items()} - elif self.backend == paddle_quantum.Backend.StateVector: - prob_amplitude = paddle.multiply(paddle.conj(self.data), self.data).real() - elif self.backend == paddle_quantum.Backend.DensityMatrix: - prob_amplitude = paddle.zeros([2 ** self.num_qubits]) - for idx in range(2 ** self.num_qubits): - prob_amplitude[idx] += self.data[idx, idx].real() - else: - raise NotImplementedError - if qubits_idx is None: - prob_array = prob_amplitude - num_measured = self.num_qubits - elif isinstance(qubits_idx, (Iterable, int)): - qubits_idx = [qubits_idx] if isinstance(qubits_idx, int) else list(qubits_idx) + raise ValueError("The quleaf server requires the number of shots to be greater than 0.") + if record == True: + raise NotImplementedError + state_data = copy.deepcopy(self.data) + if qubits_idx is None: + qubits_idx = list(range(self.num_qubits)) + elif isinstance(qubits_idx, int): + qubits_idx = [qubits_idx] num_measured = len(qubits_idx) - prob_array = paddle.zeros([2 ** num_measured]) - for idx in range(2 ** self.num_qubits): - binary = bin(idx)[2:].zfill(self.num_qubits) - target_qubits = ''.join(binary[qubit_idx] for qubit_idx in qubits_idx) - prob_array[int(target_qubits, base=2)] += prob_amplitude[idx] - else: - raise NotImplementedError - if shots == 0: - freq = prob_array.tolist() - result = {bin(idx)[2:].zfill(num_measured): val for idx, val in enumerate(freq)} + q_reg, _ = state_data.Q.toListPair() + q_reg = [q_reg[idx] for idx in qubits_idx] + c_reg = list(range(num_measured)) + state_data = quleaf._act_gates_to_state(self.oper_history, state_data) + QCompute.MeasureZ(q_reg, c_reg) + result = state_data.commit(shots, fetchMeasure=True)['counts'] + result = {key[::-1]: value for key, value in result.items()} + basis_list = [bin(idx)[2:].zfill(num_measured) for idx in range(2 ** num_measured)] + freq = [0 if basis not in result else result[basis] / shots for basis in basis_list] else: - samples = random.choices(range(0, 2 ** num_measured), weights=prob_array, k=shots) - freq = [0] * (2 ** num_measured) - for item in samples: - freq[item] += 1 - freq = [val / shots for val in freq] - result = {bin(idx)[2:].zfill(num_measured): val for idx, val in enumerate(freq)} + if self.backend == Backend.StateVector: + prob_amplitude = paddle.multiply(paddle.conj(self.data), self.data).real() + elif self.backend == Backend.DensityMatrix: + prob_amplitude = paddle.zeros([2 ** self.num_qubits]) + for idx in range(2 ** self.num_qubits): + prob_amplitude[idx] += self.data[idx, idx].real() + else: + raise NotImplementedError + if qubits_idx is None: + prob_array = prob_amplitude + num_measured = self.num_qubits + elif isinstance(qubits_idx, (Iterable, int)): + qubits_idx = [qubits_idx] if isinstance(qubits_idx, int) else list(qubits_idx) + num_measured = len(qubits_idx) + prob_array = paddle.zeros([2 ** num_measured]) + for idx in range(2 ** self.num_qubits): + binary = bin(idx)[2:].zfill(self.num_qubits) + target_qubits = ''.join(binary[qubit_idx] for qubit_idx in qubits_idx) + prob_array[int(target_qubits, base=2)] += prob_amplitude[idx] + else: + raise NotImplementedError + if shots == 0: + if record == True: + raise ValueError("Returning records requires the number of shots to be greater than 0.") + freq = prob_array.tolist() + else: + result_record = [] # record of original measurement results + samples = random.choices(range(2 ** num_measured), weights=prob_array, k=shots) + freq = [0] * (2 ** num_measured) + for item in samples: + freq[item] += 1 + result_record.append(bin(item)[2:].zfill(num_measured)) + freq = [val / shots for val in freq] + if record == False: + result = {bin(idx)[2:].zfill(num_measured): val for idx, val in enumerate(freq)} + else: + result = {"Measurement Record": result_record} if plot: assert num_measured < 6, "Too many qubits to plot" ylabel = "Measured Probabilities" if shots == 0 else "Probabilities" - state_list = [bin(idx)[2:].zfill(num_measured) for idx in range(0, 2 ** num_measured)] - plt.bar(range(2 ** num_measured), freq, tick_label=state_list) + basis_list = [bin(idx)[2:].zfill(num_measured) for idx in range(2 ** num_measured)] + plt.bar(range(2 ** num_measured), freq, tick_label=basis_list) plt.xticks(rotation=90) plt.xlabel("Qubit State") plt.ylabel(ylabel) plt.show() return result - - -def _type_fetch(data: Union[np.ndarray, paddle.Tensor, State]) -> str: - r""" fetch the type of ``data`` - - Args: - data: the input data, and datatype of which should be either ``numpy.ndarray``, - ''paddle.Tensor'' or ``paddle_quantum.State`` - - Returns: - string of datatype of ``data``, can be either ``"numpy"``, ``"tensor"``, - ``"state_vector"`` or ``"density_matrix"`` - Raises: - ValueError: does not support the current backend of input state. - TypeError: cannot recognize the current type of input data. - - """ - if isinstance(data, np.ndarray): - return "numpy" - - if isinstance(data, paddle.Tensor): - return "tensor" - - if isinstance(data, State): - if data.backend == Backend.StateVector: - return "state_vector" - if data.backend == Backend.DensityMatrix: - return "density_matrix" - raise ValueError( - f"does not support the current backend {data.backend} of input state.") - - raise TypeError( - f"cannot recognize the current type {type(data)} of input data.") + def __set_qubit_seq__(self, qubit_sequence: List[int]) -> None: + data = self.data + perm_map = pq.intrinsic._perm_of_list(self.qubit_sequence, qubit_sequence) + if self.backend == Backend.StateVector: + higher_dims = data.shape[:-1] + data = pq.intrinsic._base_transpose(data, perm_map) + data = paddle.reshape(data, higher_dims.copy() + [2 ** self.num_qubits]) -def _density_to_vector(rho: Union[np.ndarray, paddle.Tensor]) -> Union[np.ndarray, paddle.Tensor]: - r""" transform a density matrix to a state vector - - Args: - rho: a density matrix (pure state) - - Returns: - a state vector - - Raises: - ValueError: the output state may not be a pure state - - """ - type_str = _type_fetch(rho) - rho = paddle.to_tensor(rho) - eigval, eigvec = paddle.linalg.eigh(rho) - - max_eigval = paddle.max(eigval).item() - err = np.abs(max_eigval - 1) - if err > 1e-6: - raise ValueError( - f"the output state may not be a pure state, maximum distance: {err}") - - state = eigvec[:, paddle.argmax(eigval)] - - return state.numpy() if type_str == "numpy" else state - + elif self.backend == Backend.DensityMatrix: + higher_dims = data.shape[:-2] + data = pq.intrinsic._base_transpose_for_dm(data, perm_map) + data = paddle.reshape(data, higher_dims.copy() + [2 ** self.num_qubits] * 2) + else: + raise NotImplementedError -def _type_transform(data: Union[np.ndarray, paddle.Tensor, State], - output_type: str) -> Union[np.ndarray, paddle.Tensor, State]: - r""" transform the datatype of ``input`` to ``output_type`` - - Args: - data: data to be transformed - output_type: datatype of the output data, type is either ``"numpy"``, ``"tensor"``, - ``"state_vector"`` or ``"density_matrix"`` - - Returns: - the output data with expected type - - Raises: - ValueError: does not support transformation to type. - - """ - current_type = _type_fetch(data) - - support_type = {"numpy", "tensor", "state_vector", "density_matrix"} - if output_type not in support_type: - raise ValueError( - f"does not support transformation to type {output_type}") - - if current_type == output_type: - return data - - if current_type == "numpy": - if output_type == "tensor": - return paddle.to_tensor(data) - - data = np.squeeze(data) - # state_vector case - if output_type == "state_vector": - if len(data.shape) == 2: - data = _density_to_vector(data) - return State(data, backend=Backend.StateVector) - # density_matrix case - if len(data.shape) == 1: - data = data.reshape([len(data), 1]) - data = data @ np.conj(data.T) - return State(data, backend=Backend.DensityMatrix) - - if current_type == "tensor": - if output_type == "numpy": - return data.numpy() - - data = paddle.squeeze(data) - # state_vector case - if output_type == "state_vector": - if len(data.shape) == 2: - data = _density_to_vector(data) - return State(data, backend=Backend.StateVector) - - # density_matrix case - if len(data.shape) == 1: - data = data.reshape([len(data), 1]) - data = data @ paddle.conj(data.T) - return State(data, backend=Backend.DensityMatrix) - - if current_type == "state_vector": - if output_type == "density_matrix": - return State(data.ket @ data.bra, backend=Backend.DensityMatrix, num_qubits=data.num_qubits, override=True) - return data.ket.numpy() if output_type == "numpy" else data.ket - - # density_matrix data - if output_type == "state_vector": - return State(_density_to_vector(data.data), backend=Backend.StateVector, num_qubits=data.num_qubits, override=True) - return data.numpy() if output_type == "numpy" else data.data + self.data = data + self.qubit_sequence = qubit_sequence + def reset_sequence(self, target_sequence: Optional[List[int]] = None) -> None: + r"""reset the qubit order to a given sequence -def is_state_vector(vec: Union[np.ndarray, paddle.Tensor], - eps: Optional[float] = None) -> Tuple[bool, int]: - r""" verify whether ``vec`` is a legal quantum state vector - - Args: - vec: state vector candidate :math:`x` - eps: tolerance of error, default to be `None` i.e. no testing for data correctness - - Returns: - determine whether :math:`x^\dagger x = 1`, and return the number of qubits or an error message - - Note: - error message is: - * ``-1`` if the above equation does not hold - * ``-2`` if the dimension of ``vec`` is not a power of 2 - * ``-3`` if ``vec`` is not a vector - - """ - vec = _type_transform(vec, "tensor") - vec = paddle.squeeze(vec) - - dimension = vec.shape[0] - if len(vec.shape) != 1: - return False, -3 - - num_qubits = int(math.log2(dimension)) - if 2 ** num_qubits != dimension: - return False, -2 - - if eps is None: - return True, num_qubits - - vec = vec.reshape([dimension, 1]) - vec_bra = paddle.conj(vec.T) - eps = min(eps * dimension, 1e-2) - return {False, -1} if paddle.abs(vec_bra @ vec - (1 + 0j)) > eps else {True, num_qubits} + Args: + target_sequence: target sequence. Defaults to None. + Returns: + State: state with given qubit order + """ -def is_density_matrix(rho: Union[np.ndarray, paddle.Tensor], - eps: Optional[float] = None) -> Tuple[bool, int]: - r""" verify whether ``rho`` is a legal quantum density matrix - - Args: - rho: density matrix candidate - eps: tolerance of error, default to be `None` i.e. no testing for data correctness - - Returns: - determine whether ``rho`` is a PSD matrix with trace 1 and return the number of qubits or an error message. - - Note: - error message is: - * ``-1`` if ``rho`` is not PSD - * ``-2`` if the trace of ``rho`` is not 1 - * ``-3`` if the dimension of ``rho`` is not a power of 2 - * ``-4`` if ``rho`` is not a square matrix - - """ - rho = _type_transform(rho, "tensor") - - dimension = rho.shape[0] - if len(rho.shape) != 2 or dimension != rho.shape[1]: - return False, -4 - - num_qubits = int(math.log2(dimension)) - if 2 ** num_qubits != dimension: - return False, -3 - - if eps is None: - return True, num_qubits - - eps = min(eps * dimension, 1e-2) - if paddle.abs(paddle.trace(rho) - (1 + 0j)).item() > eps: - return False, -2 - - min_eigval = paddle.min(paddle.linalg.eigvalsh(rho)) - return {False, -1} if paddle.abs(min_eigval) > eps else {True, num_qubits} + if target_sequence is None: + self.__set_qubit_seq__(list(range(self.num_qubits))) + elif target_sequence == self.qubit_sequence: + pass + else: + if len(target_sequence) != self.num_qubits: + raise ValueError(f"The length of target sequence does not match! expected {self.num_qubits}, received {len(target_sequence)}") + self.__set_qubit_seq__(target_sequence) diff --git a/requirements.txt b/requirements.txt index f97f2fc..e708b17 100644 --- a/requirements.txt +++ b/requirements.txt @@ -7,6 +7,7 @@ scipy tqdm openfermion pyscf; platform_system == "Linux" or platform_system == "Darwin" +paddlenlp scikit-learn opencv-python cvxpy diff --git a/setup.py b/setup.py index 1d9d57e..2d2fdec 100644 --- a/setup.py +++ b/setup.py @@ -24,7 +24,7 @@ with open("README.md", "r", encoding="utf-8") as fh: setuptools.setup( name='paddle-quantum', - version='2.3.0', + version='2.4.0', author='Institute for Quantum Computing, Baidu INC.', author_email='qml@baidu.com', description='Paddle Quantum is a quantum machine learning (QML) toolkit developed based on Baidu PaddlePaddle.', @@ -94,6 +94,7 @@ setuptools.setup( 'tqdm', 'openfermion', 'pyscf; platform_system == "Linux" or platform_system == "Darwin"', + 'paddlenlp', 'opencv-python', 'scikit-learn', 'fastdtw', diff --git a/tutorials/combinatorial_optimization/MAXCUT_CN.ipynb b/tutorials/combinatorial_optimization/MAXCUT_CN.ipynb index d959ada..490e2a9 100644 --- a/tutorials/combinatorial_optimization/MAXCUT_CN.ipynb +++ b/tutorials/combinatorial_optimization/MAXCUT_CN.ipynb @@ -136,14 +136,27 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:08.078417Z", "start_time": "2021-04-30T09:11:04.569758Z" } }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "# 加载量桨、飞桨的相关模块\n", "import paddle\n", @@ -180,7 +193,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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    " ] @@ -206,13 +219,13 @@ " \"font_weight\": \"bold\",\n", " \"font_color\": \"white\",\n", " \"node_size\": 2000,\n", - " \"width\": 2\n", + " \"width\": 2,\n", "}\n", "nx.draw_networkx(G, pos, **options)\n", "ax = plt.gca()\n", "ax.margins(0.20)\n", "plt.axis(\"off\")\n", - "plt.show()" + "plt.show()\n" ] }, { @@ -328,13 +341,13 @@ "metadata": {}, "outputs": [], "source": [ - "def circuit_QAOA(p):\n", + "def circuit_QAOA(num_qubits, depth, edges, vertices):\n", " # 初始化 n 个量子比特的量子电路\n", - " cir = Circuit(n)\n", + " cir = Circuit(num_qubits)\n", " # 制备量子态 |s>\n", " cir.superposition_layer()\n", " # 搭建p层U_D电路\n", - " cir.qaoa_layer(E,V,p)\n", + " cir.qaoa_layer(edges, vertices, depth)\n", " \n", " return cir\n" ] @@ -391,9 +404,9 @@ }, "outputs": [], "source": [ - "p = 4 # 量子电路的层数\n", - "ITR = 120 # 训练迭代的次数\n", - "LR = 0.1 # 基于梯度下降的优化方法的学习率\n", + "depth = 4 # 量子电路的层数\n", + "ITR = 120 # 训练迭代的次数\n", + "LR = 0.1 # 基于梯度下降的优化方法的学习率\n", "SEED = 1024 #设置全局随机数种子" ] }, @@ -406,32 +419,32 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "iter: 10 loss: -1.8359\n", - "iter: 20 loss: -2.5392\n", - "iter: 30 loss: -2.7250\n", - "iter: 40 loss: -2.8061\n", - "iter: 50 loss: -2.8748\n", - "iter: 60 loss: -2.9134\n", - "iter: 70 loss: -2.9302\n", - "iter: 80 loss: -2.9321\n", - "iter: 90 loss: -2.9321\n", - "iter: 100 loss: -2.9325\n", - "iter: 110 loss: -2.9327\n", - "iter: 120 loss: -2.9328\n" + "iter: 10 loss: -2.5212\n", + "iter: 20 loss: -2.7688\n", + "iter: 30 loss: -2.9486\n", + "iter: 40 loss: -2.9832\n", + "iter: 50 loss: -2.9907\n", + "iter: 60 loss: -2.9969\n", + "iter: 70 loss: -2.9990\n", + "iter: 80 loss: -2.9997\n", + "iter: 90 loss: -2.9999\n", + "iter: 100 loss: -3.0000\n", + "iter: 110 loss: -3.0000\n", + "iter: 120 loss: -3.0000\n" ] } ], "source": [ "paddle.seed(SEED)\n", "\n", - "cir = circuit_QAOA(p)\n", + "cir = circuit_QAOA(n, depth, E, V)\n", "# 使用 Adam 优化器\n", "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=cir.parameters())\n", "\n", @@ -465,7 +478,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 10, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:55.548009Z", @@ -475,7 +488,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
    " ] @@ -506,7 +519,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:11:55.906817Z", @@ -518,12 +531,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "找到的割的比特串形式: 0101\n" + "找到的割的比特串形式: 1010\n" ] }, { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ "
    " ] @@ -542,24 +555,18 @@ "\n", "edge_cut = []\n", "for u in range(n):\n", - " for v in range(u+1,n):\n", + " for v in range(u + 1, n):\n", " if (u, v) in E or (v, u) in E:\n", " if cut_bitstring[u] == cut_bitstring[v]:\n", " edge_cut.append(\"solid\")\n", " else:\n", " edge_cut.append(\"dashed\")\n", "\n", - "nx.draw(\n", - " G,\n", - " pos,\n", - " node_color=node_cut,\n", - " style=edge_cut,\n", - " **options\n", - ")\n", + "nx.draw(G, pos, node_color=node_cut, style=edge_cut, **options)\n", "ax = plt.gca()\n", "ax.margins(0.20)\n", "plt.axis(\"off\")\n", - "plt.show()" + "plt.show()\n" ] }, { diff --git a/tutorials/combinatorial_optimization/MAXCUT_EN.ipynb b/tutorials/combinatorial_optimization/MAXCUT_EN.ipynb index aaed257..2cfd7c4 100644 --- a/tutorials/combinatorial_optimization/MAXCUT_EN.ipynb +++ b/tutorials/combinatorial_optimization/MAXCUT_EN.ipynb @@ -139,14 +139,27 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:07:40.001750Z", "start_time": "2021-04-30T09:07:36.983994Z" } }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "# Import related modules from Paddle Quantum and PaddlePaddle\n", "import paddle\n", @@ -184,7 +197,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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    " ] @@ -331,13 +344,13 @@ "metadata": {}, "outputs": [], "source": [ - "def circuit_QAOA(p):\n", + "def circuit_QAOA(num_qubits, depth, edges, vertices):\n", " # Initialize the quantum circuit of n qubits\n", - " cir = Circuit(n)\n", + " cir = Circuit(num_qubits)\n", " # Prepare quantum state |s>\n", " cir.superposition_layer()\n", " # Build a circuit with p layers of U_D\n", - " cir.qaoa_layer(E,V,p)\n", + " cir.qaoa_layer(edges, vertices, depth)\n", " \n", " return cir\n" ] @@ -400,7 +413,7 @@ }, "outputs": [], "source": [ - "p = 4 # Number of layers in the quantum circuit\n", + "depth = 4 # Number of layers in the quantum circuit\n", "ITR = 120 # Number of training iterations\n", "LR = 0.1 # Learning rate of the optimization method based on gradient descent\n", "SEED = 1024 # Set global RNG seed " @@ -422,25 +435,25 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 10 loss: -1.8359\n", - "iter: 20 loss: -2.5392\n", - "iter: 30 loss: -2.7250\n", - "iter: 40 loss: -2.8061\n", - "iter: 50 loss: -2.8748\n", - "iter: 60 loss: -2.9134\n", - "iter: 70 loss: -2.9302\n", - "iter: 80 loss: -2.9321\n", - "iter: 90 loss: -2.9321\n", - "iter: 100 loss: -2.9325\n", - "iter: 110 loss: -2.9327\n", - "iter: 120 loss: -2.9328\n" + "iter: 10 loss: -2.5212\n", + "iter: 20 loss: -2.7688\n", + "iter: 30 loss: -2.9486\n", + "iter: 40 loss: -2.9832\n", + "iter: 50 loss: -2.9907\n", + "iter: 60 loss: -2.9969\n", + "iter: 70 loss: -2.9990\n", + "iter: 80 loss: -2.9997\n", + "iter: 90 loss: -2.9999\n", + "iter: 100 loss: -3.0000\n", + "iter: 110 loss: -3.0000\n", + "iter: 120 loss: -3.0000\n" ] } ], "source": [ "paddle.seed(SEED)\n", "\n", - "cir = circuit_QAOA(p)\n", + "cir = circuit_QAOA(n, depth, E, V)\n", "# Use Adam optimizer\n", "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=cir.parameters())\n", "\n", @@ -485,7 +498,7 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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", + "image/png": 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", "text/plain": [ "
    " ] @@ -552,23 +565,17 @@ "\n", "edge_cut = []\n", "for u in range(n):\n", - " for v in range(u+1,n):\n", + " for v in range(u + 1, n):\n", " if (u, v) in E or (v, u) in E:\n", " if cut_bitstring[u] == cut_bitstring[v]:\n", " edge_cut.append(\"solid\")\n", " else:\n", " edge_cut.append(\"dashed\")\n", - "nx.draw(\n", - " G,\n", - " pos,\n", - " node_color=node_cut,\n", - " style=edge_cut,\n", - " **options\n", - ")\n", + "nx.draw(G, pos, node_color=node_cut, style=edge_cut, **options)\n", "ax = plt.gca()\n", "ax.margins(0.20)\n", "plt.axis(\"off\")\n", - "plt.show()" + "plt.show()\n" ] }, { diff --git a/tutorials/machine_learning/QClassifier_CN.ipynb b/tutorials/machine_learning/QClassifier_CN.ipynb index ff61cb6..7f97a3d 100644 --- a/tutorials/machine_learning/QClassifier_CN.ipynb +++ b/tutorials/machine_learning/QClassifier_CN.ipynb @@ -62,7 +62,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 145, "metadata": { "ExecuteTime": { "end_time": "2021-03-02T09:15:03.419838Z", @@ -78,6 +78,7 @@ "\n", "# 构建量子电路\n", "from paddle_quantum.ansatz import Circuit\n", + "from paddle_quantum.state import zero_state\n", "\n", "# 一些用到的函数\n", "from numpy import pi as PI\n", @@ -99,7 +100,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 146, "metadata": {}, "outputs": [], "source": [ @@ -141,7 +142,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 147, "metadata": { "ExecuteTime": { "end_time": "2021-03-02T09:15:04.631031Z", @@ -199,7 +200,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 148, "metadata": {}, "outputs": [], "source": [ @@ -229,7 +230,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 149, "metadata": { "ExecuteTime": { "end_time": "2021-03-02T09:15:06.422981Z", @@ -249,7 +250,7 @@ }, { "data": { - "image/png": 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\n", 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", 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\n", 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", 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    " ] @@ -423,7 +424,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 150, "metadata": { "ExecuteTime": { "end_time": "2021-03-02T09:15:06.589265Z", @@ -432,51 +433,32 @@ }, "outputs": [], "source": [ - "# 构建绕 Y 轴,绕 Z 轴旋转 theta 角度矩阵\n", - "def Ry(theta):\n", - " \"\"\"\n", - " :param theta: 参数\n", - " :return: Y 旋转矩阵\n", - " \"\"\"\n", - " return np.array([[np.cos(theta / 2), -np.sin(theta / 2)],\n", - " [np.sin(theta / 2), np.cos(theta / 2)]])\n", + "# 量子数据编码器电路\n", + "def encoding_circuit(data, n_qubits):\n", + " cir = Circuit(n_qubits)\n", + " for i in range(n_qubits):\n", + " param = data[0] if i % 2 == 0 else data[1]\n", + " cir.ry(qubits_idx=i, param=np.arcsin(param))\n", + " cir.rz(qubits_idx=i, param=np.arccos(param**2))\n", + " return cir\n", "\n", - "def Rz(theta):\n", - " \"\"\"\n", - " :param theta: 参数\n", - " :return: Z 旋转矩阵\n", - " \"\"\"\n", - " return np.array([[np.cos(theta / 2) - np.sin(theta / 2) * 1j, 0],\n", - " [0, np.cos(theta / 2) + np.sin(theta / 2) * 1j]])\n", "\n", - "# 经典 -> 量子数据编码器\n", + "# 经典数据编码成量子态\n", "def datapoints_transform_to_state(data, n_qubits):\n", " \"\"\"\n", - " :param data: 形状为 [-1, 2],numpy向量形式\n", + " :param data: 形状为 [BATCHSIZE, 2],numpy向量形式\n", " :param n_qubits: 数据转化后的量子比特数量\n", - " :return: 形状为 [-1, 1, 2 ^ n_qubits]\n", - " 形状中-1表示第一个参数为任意大小。在此教程实例分析中,对应于BATCH,用以得到Eq.(1)中平方误差的平均值\n", + " :return: 编码后的量子态,大小为 [BATCHSIZE, 1, 2 ^ n_qubits]\n", " \"\"\"\n", - " dim1, dim2 = data.shape\n", + "\n", + " batchsize, _ = data.shape\n", " res = []\n", - " for sam in range(dim1):\n", - " res_state = 1.\n", - " zero_state = np.array([[1, 0]])\n", - " # 角度编码\n", - " for i in range(n_qubits):\n", - " # 对偶数编号量子态作用 Rz(arccos(x0^2)) Ry(arcsin(x0))\n", - " if i % 2 == 0:\n", - " state_tmp=np.dot(zero_state, Ry(np.arcsin(data[sam][0])).T)\n", - " state_tmp=np.dot(state_tmp, Rz(np.arccos(data[sam][0] ** 2)).T)\n", - " res_state=np.kron(res_state, state_tmp)\n", - " # 对奇数编号量子态作用 Rz(arccos(x1^2)) Ry(arcsin(x1))\n", - " elif i % 2 == 1:\n", - " state_tmp=np.dot(zero_state, Ry(np.arcsin(data[sam][1])).T)\n", - " state_tmp=np.dot(state_tmp, Rz(np.arccos(data[sam][1] ** 2)).T)\n", - " res_state=np.kron(res_state, state_tmp)\n", - " res.append(res_state)\n", + " init_state = zero_state(n_qubits)\n", + " for i in range(batchsize):\n", + " cir = encoding_circuit(data[i], n_qubits)\n", + " out_state = cir(init_state)\n", + " res.append(out_state.numpy().reshape(1, -1))\n", " res = np.array(res, dtype=paddle_quantum.get_dtype())\n", - "\n", " return res" ] }, @@ -489,7 +471,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 151, "metadata": {}, "outputs": [ { @@ -499,7 +481,8 @@ "作为测试我们输入以上的经典信息:\n", "(x_0, x_1) = (1, 0)\n", "编码后输出的2比特量子态为:\n", - "[[[0.5-0.5j 0. +0.j 0.5-0.5j 0. +0.j ]]]\n" + "[[[0.49999997-0.49999997j 0. +0.j 0.49999997-0.49999997j\n", + " 0. +0.j ]]]\n" ] } ], @@ -655,7 +638,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 152, "metadata": { "ExecuteTime": { "end_time": "2021-03-02T09:15:07.667491Z", @@ -678,12 +661,12 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 153, "metadata": {}, "outputs": [], "source": [ "# 搭建整个优化流程图\n", - "class Opt_Classifier(paddle_quantum.gate.Gate):\n", + "class Opt_Classifier(paddle_quantum.Operator):\n", " \"\"\"\n", " 创建模型训练网络\n", " \"\"\"\n", @@ -692,6 +675,7 @@ " super(Opt_Classifier, self).__init__()\n", " self.n = n\n", " self.depth = depth\n", + " paddle.seed(seed_paras)\n", " # 初始化偏置 (bias)\n", " self.bias = self.create_parameter(\n", " shape=[1],\n", @@ -701,27 +685,22 @@ " \n", " self.circuit = Circuit(n)\n", " # 先搭建广义的旋转层\n", - " for i in range(n):\n", - " self.circuit.rz(qubits_idx=i)\n", - " self.circuit.ry(qubits_idx=i)\n", - " self.circuit.rz(qubits_idx=i)\n", + " self.circuit.rz()\n", + " self.circuit.ry()\n", + " self.circuit.rz()\n", "\n", - " # 默认深度为 depth = 1\n", " # 对每一层搭建电路\n", - " for d in range(3, depth + 3):\n", + " for _ in range(depth):\n", " # 搭建纠缠层\n", - " for i in range(n-1):\n", - " self.circuit.cnot(qubits_idx=[i, i + 1])\n", - " self.circuit.cnot(qubits_idx=[n-1, 0])\n", + " self.circuit.cnot()\n", " # 对每一个量子比特搭建Ry\n", - " for i in range(n):\n", - " self.circuit.ry(qubits_idx=i)\n", + " self.circuit.ry()\n", "\n", " # 定义前向传播机制、计算损失函数 和交叉验证正确率\n", " def forward(self, state_in, label):\n", " \"\"\"\n", - " 输入: state_in:输入量子态,shape: [-1, 1, 2^n] -- 此教程中为[BATCH, 1, 2^n]\n", - " label:输入量子态对应标签,shape: [-1, 1]\n", + " 输入: state_in:输入量子态,shape: [BATCH, 1, 2^n]\n", + " label:输入量子态对应标签,shape: [BATCH, 1]\n", " 计算损失函数:\n", " L = 1/BATCH * (( + 1)/2 + bias - label)^2\n", " \"\"\"\n", @@ -760,7 +739,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 154, "metadata": {}, "outputs": [], "source": [ @@ -805,7 +784,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 155, "metadata": {}, "outputs": [], "source": [ @@ -829,13 +808,12 @@ " # 读取训练集的维度\n", " N_train = train_x.shape[0]\n", "\n", - " paddle.seed(seed_paras)\n", - " # 初始化寄存器存储正确率 acc 等信息\n", + " # 存储正确率 acc 等信息\n", " summary_iter, summary_test_acc = [], []\n", "\n", " # 一般来说,我们利用Adam优化器来获得相对好的收敛\n", " # 当然你可以改成SGD或者是RMSprop\n", - " myLayer = Opt_Classifier(n=N, depth=DEPTH) # 得到初始化量子电路\n", + " myLayer = Opt_Classifier(n=N, depth=DEPTH, seed_paras=seed_paras) # 得到初始化量子电路\n", " opt = paddle.optimizer.Adam(learning_rate=LR, parameters=myLayer.parameters())\n", "\n", " # 优化循环\n", @@ -882,7 +860,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 156, "metadata": {}, "outputs": [ { @@ -892,27 +870,27 @@ "训练集的维度大小 x (200, 2) 和 y (200, 1)\n", "测试集的维度大小 x (100, 2) 和 y (100, 1) \n", "\n", - "epoch: 0 iter: 4 loss: 0.2750 train acc: 0.7000 test acc: 0.6700\n", - "epoch: 3 iter: 4 loss: 0.2471 train acc: 0.2500 test acc: 0.5500\n", - "epoch: 6 iter: 4 loss: 0.1976 train acc: 0.8000 test acc: 0.9200\n", - "epoch: 9 iter: 4 loss: 0.1639 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 12 iter: 4 loss: 0.1441 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 15 iter: 4 loss: 0.1337 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 18 iter: 4 loss: 0.1287 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 0 iter: 4 loss: 0.2157 train acc: 0.9000 test acc: 0.6900\n", + "epoch: 3 iter: 4 loss: 0.2033 train acc: 0.4000 test acc: 0.5500\n", + "epoch: 6 iter: 4 loss: 0.1467 train acc: 1.0000 test acc: 0.9700\n", + "epoch: 9 iter: 4 loss: 0.1287 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 12 iter: 4 loss: 0.1215 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 15 iter: 4 loss: 0.1202 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 18 iter: 4 loss: 0.1197 train acc: 1.0000 test acc: 1.0000\n", "训练后的电路:\n", - "--Rz(3.490)----Ry(5.436)----Rz(3.281)----*--------------x----Ry(0.098)--\n", + "--Rz(5.489)----Ry(4.294)----Rz(3.063)----*--------------x----Ry(2.788)--\n", " | | \n", - "--Rz(1.499)----Ry(2.579)----Rz(3.496)----x----*---------|----Ry(1.282)--\n", + "--Rz(2.359)----Ry(4.117)----Rz(2.727)----x----*---------|----Ry(1.439)--\n", " | | \n", - "--Rz(5.956)----Ry(3.158)----Rz(3.949)---------x----*----|----Ry(1.418)--\n", + "--Rz(2.349)----Ry(3.474)----Rz(5.971)---------x----*----|----Ry(1.512)--\n", " | | \n", - "--Rz(1.604)----Ry(0.722)----Rz(5.037)--------------x----*----Ry(2.437)--\n", + "--Rz(1.973)----Ry(-0.04)----Rz(-0.01)--------------x----*----Ry(2.075)--\n", " \n" ] }, { "data": { - "image/png": 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\n", 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x7ftT/Z8NfI+7t4F3gIMjbEtEZopDt1PulXt3YOTuLeDqwGi7XwGedvfzAO7+VtFKp9rayMweNbPjZnb87bNnp7krIlKG+7hOOcsMjH4M+DEz+30z+4P+tfvUKAntNHD7tu9v6/9s4HvMbA7YR+/mwA9w92fc/bC7Hz50UAM4keuBebfUC1i9OmDpvx4dclNzwJ3Ax4BHgC+b2f6iBYZ1DLjTzO6gl7geBj6x4z1HgF8Gvgn8IvCyrp+JVET5a2hn3P1wECszMDoFfMvdt4D/Z2bfppfgjkUbHDqhuXvbzB4DXqJXtvGcu79qZk8Bx939CPBbwG+b2UngHL2klzOD2uABo8018mWTeL0R/y/WF5pxrJkPXucW4vXWGvGyi0kJwEY3Lw9YTEoA8vKK+AAsmNxqYmUbzaTcPPsdZbFGwTYbybL1Rj2OJcdCvZn/CdWS4y89ri3e5nSHBj5MQsuUGRj9Lr2R2X8ws1V6p6CvZysdqQ7N3Y8CR3f87MltX28Af3OUdYvIDHPGktBKDoxeAv6amZ0AOsA/dff0YrueFBCRIcTz5w69puKBkQO/3n+VooQmIsMZzynnRCihiUh57tO+iJdSQhOR4WiEJiJVMY5HnyZFCU1EhjC2so2JmKGEZnht8O5YI64XA6g1F8JYfTFedi6pQ2su59tsLW/Fy+6J64uWtrKasHidPaM9qZbVfLW6o8+UlClq5TNqHdpyUou3L6klA5hfmY/3J/nMsmNhbjk+9iA/xiw5br0e70/RZ7IVfKZjufLlDt3x3OWchBlKaCIy6wydcopIlXSV0ESkElS2ISJVMaZHnyZFCU1EhuCYbgqISGVohFbMISzb8Ln4djuALS6HscZSfGu8uRIv17x4Jd3m/Hr8r1R3q7D98ED7C+LNzXibC0kZxEZSmjGLZRvZ/8ueubhsYzkpywCYX4lLKNKSjpXFOLY3PoYAaktLYSw7bn0u3tetgp5O7SA+lktf7mXaa0/NzCQ0Ebk+uO5yikg1aIQmIlXhKKGJSDW4O75V9Ije9CihicgQdMopIlXhjiuhFXOgFdxubszlHQ1qyythrL6yP4zN749LM9obm+k2vTPanR4LZraCfOYhgMbleKi/vBGXdGwlseKyjTQc2s2sT41kRq3mctyFIiu9AFhajcsvllbj8oqFg/HxNb9/T7rN+p79Yay2FK+33Yj3tegz22gPTjg+nn4bepZTRKpCIzQRqQrd5RSRytBdThGpDt3lFJGq0LOcIlIlepazBPf4dvTifN7RILs1Xt93MIwtbFyO92fEsgwASybyaCwmJQnJRB0ArUvxtYt2UprRacX/onYKOoP4iHUbVlC3kZWozCW/o7mkpKOobGPxQFwKsXjz/jC2dOhAGGveFC8HUEuOP1+ISz58Po5tXsw/s83g2C2o9ihJIzQRqQh3x9u6KSAiVaCyDRGpDp1yikhVOHhHCU1EKsH1LKeIVIhOOUWkEtzp6i5nsa7DRntwocxKM69D86V9Yax24FAYq7dbYWyxlrfyqTWzWqm4Hqq1N659m9+/kW6zfSWObyWzUGV1aKPOULVbtaQOLavVm1uIa/WaK3ELIMhb/SwcjI+hhUM3xftz8JZ0m/Uk3lmMt7nZjev4rmzlp3wXgprEzjgK0dx3VaM5aTOT0ERk9rnvruh80uKSdhGRH+J4t1vqVcTM7jOz18zspJk9PiD+STN728xe6b/+ftE6NUITkfLGNEIzszrwNHAvcAo4ZmZH3P3Ejrd+1d0fK7teJTQRKc3d6bTGclPgbuCku78OYGYvAA8COxPaUHTKKSJDGdMp563AG9u+P9X/2U4Pmdkfm9mLZnZ70UqV0ESkvP5dzjIvYNXMjm97PTrk1r4GfNDdPwz8d+D5ogVm5pSzi7PeHpzV2wv57Xhbitu71LtxOUO6zrlmHm/GM1E198b727oYzzS1dbmgbOPyehjrbCVlG+txeUrRv6TdEa+X1JIWSgC1RnzojVoSk/3eIS/rmNsfl2bUs9KfQ4MGFe/x5Xi93eS4vZSUZryzmR/Ta1cGnxKOpWyDoa6hnXH3w0HsNLB9xHVb/2fvbcf97LZvnwV+o2iDGqGJSGnuY7vLeQy408zuMLMm8DBwZPsbzGx7Ed8DwJ8UrXRmRmgicn0YddS+nbu3zewx4CWgDjzn7q+a2VPAcXc/AvwjM3sAaAPngE8WrVcJTUTK6zrd1miXcXZy96PA0R0/e3Lb108ATwyzTiU0ESnN0ZwCIlIVepZTRKpECa0ET7ptZLewAfYlt7/xeNlaLSsPyDt81PbuD2Pdi2thrL4ed9vIZqEC8FZc1tHZ2Iz3JzkAu0m5xyRlZRv1rKRjIS6XsYLyntryShzLZg47cHMYy8oyADp7VsPYOnHnkAtJacaZK3EZDsC5S4OPhc44ThUdujrlFJEqcHTKKSJV4U53Sw0eRaQKZrwfmhKaiAxBp5wiUhHu43lSYFKU0ERkCK7C2jLaXefc+uCLjcuN/Bn6RjKhydKeuFMC9bijhjUW021aMjFLI7nN303KNrKyDADfjLttzGUz8SQxL5qSbNQpywommbEsPheXM2RdTmqLeamNJaU4vhBPoNJd2JvE4uMAYKMeH0drG/HvNvpbADhbULbx1oXBZRtbnTF02+hCN5l0Z9pmJqGJyOxzXKecIlIRDj6mvmqToIQmIkPpjuPUdUKU0ESktFmfl1MJTUTKc8c1QhORSnDo6C6niFSBA13dFCjW6Trng9qbffOj7+ZWM65hW1yI2w41k9ojANuKa8a67biVj+2Jl7OslgywZAarLEYWS9orTZQltYVJWydPage9HtevAXQbcQ2bN+MatW4zbktU1Nrqwno8mjmb1JqdvhAfJ6fX8nrFcxcHH3/tcZwq6pRTRKpEdWgiUgm9u5waoYlIFSihiUhluNPZ0l1OEakAR08KiEhVaBq7ctpJ2cZSQfugrse38luduE3Nwlz8wczXLd1msx7fym8kbWrmavF66xQcKFnZRlZ+0bnOyjbqSdlGVtKRxABaychiI4mtX4l/f1cKyjbOr8fLvhnMzgRwKinb+LMz+exgl4NlxzVbk66hiUgl9DrWKqGJSBXopoCIVIbKNkSkKhy1DxKRqtA1NBGpDj2cXkq76+FsNkmlAwAb7XgIvLcZ/y8uNZLZopr5rEVzSdVBWpphSSyvTqFu8T7VkpgRd6GoJfsDUBAOecEx303e4EmVSXa2s5V1FSEv29hKWuJc3IzX+04Sg3yGpu8FXTEAXn/rUhh74+yVdJtXglmfxjGycs8/u2mbmYQmIrPPgZb6oYlIVXRmeIRWcJIjIvIeBzpe7lXEzO4zs9fM7KSZPZ687yEzczM7XLROjdBEpDT38YzQzKwOPA3cC5wCjpnZEXc/seN9e4F/DHyrzHo1QhORoYxphHY3cNLdX3f3FvAC8OCA9/1z4AtA3ne8TwlNREpznI6XexW4FXhj2/en+j97l5n9JeB2d/8vZfdvZk45290ubwVdAjoFd1WyjgdLjXgiioW5uNRhPqvLABpJaUYj6dTRqMXrzZaDvMQiKwdJNpkuN0nZAZ81hdhKgln5DsBmEt9I6kEu7aJs462ghALgzbX1MPadpDTjwpm8bOPS+cHdOLrt3T+D2bvLWfrtq2Z2fNv3z7j7M2UWNLMa8K+BTw6zfzOT0ERk9g15De2Mu0cX8k8Dt2/7/rb+z67aC/wU8A3r/aP7fuCImT3g7tuT5A9QQhORoYzpQYFjwJ1mdge9RPYw8ImrQXd/B1i9+r2ZfQP4TJbMQAlNRIbQK9sYxxMH3jazx4CXgDrwnLu/amZPAcfd/cgo61VCE5HSrtahjWVd7keBozt+9mTw3o+VWacSmoiU5q5Hn0SkQirz6JP1/Jv+owp/3K8TGfS+X+rHXzWzL4xnV0Vk2hzolnxNw7AjtPuBO/uvjwD/vv/fd5nZQeBfAj/r7m+b2fNmdo+7fz1bcbvjYc1Oq6C+aK0Z15otJm2AslqzZkEdWj2rQ0sKv7IWQUWtfNJas2TRbF+LtjkpWQuarO4wa/OzVXBxZyOpw1pvxbGLG3Gt2blk5iaAs5fi9kHnkvZBl9biwvgL5+P6NYD1898f+PNuNvtXaaWKZqdm2CcFHgS+4j1/AOw3s1t2vOfPAf/X3d/uf/8/gId2uZ8iMgPG+XD6JAw7QoseV3hz289OAj9uZh/sx/8GEE+cKSLXjXGVbUzK2G8KuPt5M/sHwFfpnUr/b+DPD3qvmT0KPAqwfPD9494VERmzWb/LWXjKaWafNrNXzOwVeiOx7HEFANz9a+7+EXf/OeA14NuD1u3uz7j7YXc/vLByYKT/ARG5tmb5lLMwobn70+7+0+7+08DvAn+3f7fzLwPvuPubO5cxs5v7/z0A/EPg2bHutYhMxdVTzjF025iIYU85jwJ/nd51sivA37saMLNX+kkP4Etm9hf7Xz/l7gNHaCJyfRnnkwKTYD4jF/jM7G3gz/rfrgJnprg7Mjx9ZrNp++fyAXc/tJuVmdl/ZdtD4wXOuPt9u9nesGYmoW1nZseTtiMyg/SZzaYb7XNRx1oRqQwlNBGpjFlNaKXa9MpM0Wc2m26oz2Umr6GJiIxiVkdoIiJDm2pCUzui60/RbNdmNm9mX+3Hv9V/plcmqMRn8gEz+3r/b+gbZnbbNPbzWpj2CG17O6JH6bUj+gHb2hHd4+4/CbzfzO65pnspwA/Mdn0/cBfwiJndteNtnwLOu/uHgC/SmyRWJqTkZ/Kb9LrkfBh4Cvjctd3La2faCU3tiK4vZWa7fhB4vv/1i8A9ZlNqunZjKPOZ3AW83P/69wbEK2PaCa1w9mS2tSMyszl67YhuR6ahzOf17nvcvQ28Axy8Jnt3YyrzmfwR8Av9rz8O7O2f+VTOtBNaIXc/D1xtR/S/gD8Fdj8FtMiN4zPAR83sD4GP0uuQU8m/oWs+SYqZfRr4lf63xyjZjgj4Wn/5R6noh3EdKJrtevt7TvVH1PuAs9dm925IhZ+Ju3+X/gjNzPYAD7n72rXawWvpmo/Q1I7ouvbubNdm1qQ32/XOCWGPAL/c//oXgZddxY6TVPiZmNmqmV39W38CeO4a7+M1M+1TzqPA6/Suk32ZXrICeu2Itr3vS2Z2Avh94PNqRzQd/WtiV2e7/hPgd67Odm1mD/Tf9lvAQTM7Cfw68ENlBDI+JT+TjwGvmdm3gfcB/2IqO3sN6EkBEamMaY/QRETGRglNRCpDCU1EKkMJTUQqQwlNRCpDCU1EKkMJTUQqQwlNRCrj/wPpPX8+eJdfQQAAAABJRU5ErkJggg==", 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    " ] @@ -926,7 +904,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "主程序段总共运行了 7.0908989906311035 秒\n" + "主程序段总共运行了 44.10896015167236 秒\n" ] } ], @@ -946,7 +924,7 @@ " EPOCH = int(200 * BATCH / Ntrain), \n", " # 训练 epoch 轮数,使得总迭代次数 EPOCH * (Ntrain / BATCH) 在200左右\n", " LR = 0.01, # 设置学习速率\n", - " seed_paras = 19, # 设置随机种子用以初始化各种参数\n", + " seed_paras = 10, # 设置随机种子用以初始化各种参数\n", " seed_data = 2, # 固定生成数据集所需要的随机种子\n", " )\n", " \n", @@ -975,7 +953,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 157, "metadata": {}, "outputs": [ { @@ -1008,7 +986,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 158, "metadata": {}, "outputs": [], "source": [ @@ -1028,8 +1006,6 @@ " BATCH # 一个批量的大小\n", " \"\"\"\n", " Ntrain = len(quantum_train_x)\n", - " \n", - " paddle.seed(1)\n", "\n", " net = Opt_Classifier(n=N, depth=DEPTH)\n", "\n", @@ -1075,7 +1051,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 159, "metadata": {}, "outputs": [ { @@ -1083,30 +1059,30 @@ "output_type": "stream", "text": [ "Encoding method: amplitude_encoding\n", - "epoch: 0 iter: 0 loss: 0.3005 train acc: 0.6000 test acc: 0.4600\n", - "epoch: 0 iter: 5 loss: 0.2908 train acc: 0.3000 test acc: 0.5000\n", - "epoch: 0 iter: 10 loss: 0.2313 train acc: 0.8000 test acc: 0.6200\n", - "epoch: 0 iter: 15 loss: 0.2181 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 0 loss: 0.2448 train acc: 0.7000 test acc: 0.5500\n", + "epoch: 0 iter: 5 loss: 0.4895 train acc: 0.3000 test acc: 0.6100\n", + "epoch: 0 iter: 10 loss: 0.1318 train acc: 0.8000 test acc: 0.5800\n", + "epoch: 0 iter: 15 loss: 0.2297 train acc: 0.6000 test acc: 0.6500\n", "Encoding method: angle_encoding\n", - "epoch: 0 iter: 0 loss: 0.4141 train acc: 0.4000 test acc: 0.3700\n", - "epoch: 0 iter: 5 loss: 0.2942 train acc: 0.6000 test acc: 0.6700\n", - "epoch: 0 iter: 10 loss: 0.1952 train acc: 0.6000 test acc: 0.6700\n", - "epoch: 0 iter: 15 loss: 0.2389 train acc: 0.6000 test acc: 0.6000\n", + "epoch: 0 iter: 0 loss: 0.2437 train acc: 0.6000 test acc: 0.3900\n", + "epoch: 0 iter: 5 loss: 0.1325 train acc: 0.8000 test acc: 0.7100\n", + "epoch: 0 iter: 10 loss: 0.1397 train acc: 0.8000 test acc: 0.6600\n", + "epoch: 0 iter: 15 loss: 0.1851 train acc: 0.6000 test acc: 0.6300\n", "Encoding method: pauli_rotation_encoding\n", - "epoch: 0 iter: 0 loss: 0.1985 train acc: 0.7000 test acc: 0.7400\n", - "epoch: 0 iter: 5 loss: 0.2303 train acc: 0.6000 test acc: 0.6900\n", - "epoch: 0 iter: 10 loss: 0.1970 train acc: 0.6000 test acc: 0.7200\n", - "epoch: 0 iter: 15 loss: 0.2120 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 0 loss: 0.3170 train acc: 0.6000 test acc: 0.7000\n", + "epoch: 0 iter: 5 loss: 0.2119 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.2736 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 15 loss: 0.2186 train acc: 0.7000 test acc: 0.7000\n", "Encoding method: IQP_encoding\n", - "epoch: 0 iter: 0 loss: 0.2962 train acc: 0.5000 test acc: 0.4500\n", - "epoch: 0 iter: 5 loss: 0.2074 train acc: 0.7000 test acc: 0.7000\n", - "epoch: 0 iter: 10 loss: 0.2463 train acc: 0.6000 test acc: 0.6500\n", - "epoch: 0 iter: 15 loss: 0.2090 train acc: 0.9000 test acc: 0.5800\n", + "epoch: 0 iter: 0 loss: 0.3279 train acc: 0.3000 test acc: 0.6200\n", + "epoch: 0 iter: 5 loss: 0.1772 train acc: 0.7000 test acc: 0.7200\n", + "epoch: 0 iter: 10 loss: 0.2051 train acc: 0.8000 test acc: 0.6500\n", + "epoch: 0 iter: 15 loss: 0.1951 train acc: 0.7000 test acc: 0.6700\n", "Encoding method: complex_entangled_encoding\n", - "epoch: 0 iter: 0 loss: 0.2500 train acc: 0.6000 test acc: 0.6800\n", - "epoch: 0 iter: 5 loss: 0.2571 train acc: 0.5000 test acc: 0.6800\n", - "epoch: 0 iter: 10 loss: 0.2661 train acc: 0.7000 test acc: 0.6700\n", - "epoch: 0 iter: 15 loss: 0.1916 train acc: 0.8000 test acc: 0.7200\n" + "epoch: 0 iter: 0 loss: 0.5466 train acc: 0.4000 test acc: 0.2900\n", + "epoch: 0 iter: 5 loss: 0.2075 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.2951 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 15 loss: 0.2614 train acc: 0.7000 test acc: 0.7000\n" ] } ], @@ -1142,12 +1118,12 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 160, "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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", 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    " ] @@ -1183,34 +1159,34 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 161, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "epoch: 0 iter: 0 loss: 0.3372 train acc: 0.5000 test acc: 0.5000\n", - "epoch: 0 iter: 5 loss: 0.2687 train acc: 0.2500 test acc: 0.5500\n", - "epoch: 0 iter: 10 loss: 0.0781 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 0 iter: 15 loss: 0.0786 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 1 iter: 0 loss: 0.0903 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 1 iter: 5 loss: 0.1020 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 1 iter: 10 loss: 0.0553 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 1 iter: 15 loss: 0.0559 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 2 iter: 0 loss: 0.0770 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 2 iter: 5 loss: 0.0879 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 2 iter: 10 loss: 0.0438 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 2 iter: 15 loss: 0.0538 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 3 iter: 0 loss: 0.0768 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 3 iter: 5 loss: 0.0887 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 3 iter: 10 loss: 0.0417 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 3 iter: 15 loss: 0.0511 train acc: 1.0000 test acc: 1.0000\n" + "epoch: 0 iter: 0 loss: 0.1864 train acc: 0.7500 test acc: 0.9000\n", + "epoch: 0 iter: 5 loss: 0.0841 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 0 iter: 10 loss: 0.0490 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 0 iter: 15 loss: 0.0562 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 0 loss: 0.0800 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 5 loss: 0.0554 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 10 loss: 0.0421 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 15 loss: 0.0454 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 0 loss: 0.0752 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 5 loss: 0.0569 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 10 loss: 0.0413 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 15 loss: 0.0436 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 0 loss: 0.0775 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 5 loss: 0.0597 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 10 loss: 0.0419 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 15 loss: 0.0425 train acc: 1.0000 test acc: 1.0000\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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siIgFM2fO3JJxr1dc18/ql9e5i6uZtZwJdTz3MmDnsuW5ed16EfF7cglC0lTgnRGxStIHgHsjYk3edgtwCPDTOsa7WboLpXkgXMVkZq2lniWI+4A9Je0maRJwAnBT+Q6SZkgqxXA2cFl+/DtSyWKCpImk0sVGVUzNYP0oalcxmVmLqVuCiIg+4AzgVtLF/dqIWCxpoaSj826HAY9JehyYDXwhr78OeBL4Famd4qGI+M96xToSHkVtZq2qnlVMRMTNwM0V684pe3wdKRlUHtcPfLCesY2W9QnCU42aWYtpdCP1mNfd08vkCeOYtlVdc62Z2RbnBDFCnatTF9cmHuhtZrZZnCBGqKtQdPWSmbUkJ4gR6u7p9V1czawlOUGMQETQubroHkxm1pKcIEagp7ePl9f1eyY5M2tJThAj4ImCzKyVOUGMQFe+zYarmMysFTlBjEDn6nybDScIM2tBThAj0NXjKiYza11OECPQXeilY8oEtp7kUdRm1nqcIEagq+AurmbWupwgRqCzUHT7g5m1rGEThKTxWyKQsai74FHUZta6ailBPCHpS5Lm1z2aMWRgIOjucRWTmbWuWhLEvsDjwHck3SvpdEnT6hxX01v50lrW9YermMysZQ2bICKiJyK+HRGvB/4O+CzwnKQrJO1R9wib1CszybmKycxaU01tEJKOlnQD8BXgy8Crgf+kYra4dtKdR1HPcgnCzFpULR34nwDuBL4UET8vW3+dpD+uT1jNz3NRm1mrqyVB7BMRa6ptiIiPjXI8Y0Zn6UZ9Ha5iMrPWVEsj9cWSti0tSNpO0mX1C2ls6Cr0MmPqJCaO91ASM2tNtVzd9omIVaWFiHgB2L9uEY0R3YUiszzVqJm1sFoSxDhJ25UWJG1PbVVTLa2zUGTOdCcIM2tdtVzovwzcI+nfAQF/AXyhrlGNAV2FXvaZO73RYZiZ1c2wCSIirpR0P/AnedVxEfFIfcNqbuv6B3j+xV5XMZlZS6upqigiFktaDkwBkLRLRPyurpE1sRVreolwF1cza221DJQ7WtITwG+BnwBPA7fUOa6mtn4muenu4mpmrauWRupzgYOBxyNiN+AtwL11jarJleaidhWTmbWyWhLEuoh4ntSbaVxE3AksqHNcTa27x6Oozaz11dIGsUrSVOBu4GpJ3cCL9Q2ruXWuLjJhnNhhm0mNDsXMrG5qKUEcA7wEfBL4EfAk8PZaTi7pCEmPSVoi6awq23eVdLukhyXdJWlu2bZdJP1Y0qOSHpE0r6ZXtAV0FXqZ1TGZcePU6FDMzOpmyASRZ5P7YUQMRERfRFwRERflKqch5WMvBo4E5gMnVpl06ELgyojYB1gInF+27UrSDQL/EDgI6K75VdVZd0/Rd3E1s5Y3ZIKIiH5gQNLmjAg7CFgSEU9FxFrgGlJppNx84I78+M7S9pxIJkTEbTmONRHx0mbEUBddhaLngTCzlldLFdMa4FeSLpV0UemnhuN2Ap4tW16a15V7CDguP34H0CFpB+A1pLaP6yX9Mk95utHc2Hl2u0WSFi1fvryGkEZH5+qiZ5Izs5ZXSyP19fmnHs4Evi7pNFIj+DKgP8f1JtJNAX8HfB84Dbi0/OCIuAS4BGDBggVRpxg38PLafgrFPlcxmVnLq+VWG1ds5rmXATuXLc/N68rP/XtyCSL3lHpnRKyStBR4MCKeyttuJI3F2CBBNIK7uJpZuxg2QUj6LbDRt/OIePUwh94H7ClpN1JiOAE4qeLcM4CVETEAnA1cVnbstpJmRsRy4M3AouFi3RJKo6jdBmFmra6WKqbyQXFTgOOB7Yc7KCL6JJ0B3AqMBy7L93RaCCyKiJuAw4DzJQWpiukj+dh+SWcCt0sScD/w7dpfVv109aRR1G6DMLNWV0sVU2WX1q/ku7ueU8OxNwM3V6w7p+zxdcB1gxx7G7DPcM+xpXWXphp1gjCzFldLFdMBZYvjSCWKtp0wqKtQZMrEcUyb0rZvgZm1iVonDCrpI93V9V31Caf5dRZ6mTNtCqnmy8ysddVSxfQnw+3TTroKHkVtZu2hlvkgzpO0bdnydpI+X9eomlh3oegurmbWFmoZSX1kRKwqLUTEC8Db6hZRE4sIOgtFZne4i6uZtb5aEsR4SeuviJK2AtryClko9lFcN8Cc6S5BmFnrq6WR+mrSeITv5uX3AZs7unpMcxdXM2sntTRS/5Okh4DD86pzI+LW+obVnEpTjbqKyczaQS3jIHYD7oqIH+XlrSTNi4in6x1cs+nMJQhXMZlZO6ilDeLfgYGy5f68ru10laqYOpwgzKz11ZIgJuQJfwDIj9tyMubuQpFpUyaw1aSNpqYwM2s5tSSI5ZKOLi1IOgZYUb+Qmlenx0CYWRuppRfTh4CrJX0dEGmWuPfWNaom1VXodfuDmbWNWnoxPQkcnCf0ISLW1D2qJtVdKLL7zBmNDsPMbIuo6Zakkv4c2AuYUrpJXUQsrGNcTWdgIOju6fVEQWbWNmq5F9M3gXcDHyVVMR0P7FrnuJrO8y+upW8gXMVkZm2jlkbq10fEe4EXIuIfgUOA19Q3rObjLq5m1m5qSRAv598vSdoRWAe8qn4hNafuHs9FbWbtpZY2iB/m231/CXgACJpkfugtqXN1vs2Gu7maWZuopRfTufnhDyT9EJgSEavrG1bz6SoUkWCm78NkZm1ikyZWjoheoLdOsTS17p4iO2wzmYnja6mVMzMb+3y1q1FXwV1czay9OEHUqHN1kTlufzCzNlLL7b4PqLJ6NfBMRPSNfkjNqbunyL47b9voMMzMtpha2iC+ARwAPEwaKLc3sBiYLunDEfHjOsbXFNb1D7BizVpXMZlZW6mliun3wP4RsSAi/gjYH3gK+FPgi/UMrlks73EXVzNrP7UkiNdExOLSQkQ8Arw2Ip6qX1jNZf1Mck4QZtZGaqliWizpX4Br8vK7gUckTSaNqm553aXbbLiKyczaSC0liNOAJcAn8s9Ted064E/qE1Zz6Sq4isnM2k8tI6lfBr6cfyq1xdwQnYUiE8eL7bduy5lWzaxN1dLN9Q3A50i3+F6/f0S8un5hNZeuQpFZHVMYN06NDsXMbIuppYrpUuCfgTcCB5b9DEvSEZIek7RE0llVtu8q6XZJD0u6S9Lciu3TJC3N0502THeh1+0PZtZ2akkQqyPilojojojnSz/DHSRpPHAxcCQwHzhR0vyK3S4EroyIfYCFwPkV288F7q4hxrrqKhSZ7XkgzKzN1JIg7pT0JUmHSDqg9FPDcQcBSyLiqYhYS+oFdUzFPvOBO0rPU75d0h8Bs4GGD8TrLBQ9k5yZtZ1aurm+Lv9eULYugDcPc9xOwLNly0vLzlXyEHAc8FXgHUCHpB2AF0iN4qcAhw/2BJJOB04H2GWXXYYJZ/O8tLaPnmKfq5jMrO3U0oupnl1ZzwS+Luk0UlXSMqAf+Gvg5ohYKg3eMBwRlwCXACxYsCDqEWB3qYurq5jMrM0MmiAknRIRV0n6VLXtEfHPw5x7GbBz2fLcvK78HL8nlSCQNBV4Z0SsknQI8CZJfw1MBSZJWhMRGzV011tpFLXHQJhZuxmqBLFN/t1RZVst39bvA/aUtBspMZwAnFS+g6QZwMqIGADOBi4DiIiTy/Y5DVjQiOQAqYEaYM50VzGZWXsZNEFExLfyw/+OiJ+Vb8tjI4YUEX2SzgBuBcYDl0XEYkkLgUURcRNwGHC+pCBVMX1k815G/ZSqmGa5BGFmbaaWRuqvkW73Pdy6jUTEzcDNFevOKXt8HXDdMOe4HLi8hjjroqtQZKuJ4+mYvEmzs5qZjXlDtUEcArwemFnRDjGNVCJoC6UurkM1lpuZtaKhvhZPIjUQT2DDdogC8Bf1DKqZdBd6mdXh9gczaz9DtUH8BPiJpMsj4hkASeOAqRFR2FIBNlpXT5F9527b6DDMzLa4WkZSn5/vibQN8GvSXBB/U+e4mkJE0Lm66KlGzawt1ZIg5ucSw7HALcBuwHvqGVSzKLzcR2/fgMdAmFlbqiVBTJQ0kZQgboqIddQ2DmLM6+rxIDkza1+1JIhvAU+TBs7dLWlXUkN1y+vyKGoza2O13IvpIuCislXPSGqLqUY7V+dR1E4QZtaGhi1BSJot6VJJt+Tl+cCpdY+sCXT3lEZRu5HazNpPLVVMl5Nul7FjXn4c+ESd4mkqXYUi07eayJSJbTMu0MxsvUEThKRS9dOMiLgWGIB0jyXSLblbnru4mlk7G6oE8Yv8+8U8iU8ASDoYWF3vwJpBV0+vG6jNrG0N1UhduvnQp4CbgN0l/QyYSZvcaqO7UGTPWTMaHYaZWUMMlSDKb9J3A+murAJ6SdOAPlzn2BpqYCDo7ul1FZOZta2hEsR40s36Km9junX9wmkeK17spX8g3MXVzNrWUAniuYhYuMUiaTKeKMjM2t1QjdRtPQGCR1GbWbsbKkG8ZYtF0YQ61ycIt0GYWXsaNEFExMotGUiz6Sr0IsHMqU4QZtaeahlJ3Za6C0VmTJ3MhPF+i8ysPfnqN4iugkdRm1l7c4IYRGehl9kdbqA2s/blBDGI7kKR2dOdIMysfTlBVLG2b4DnX1zrEoSZtTUniCq6e9zF1czMCaKKrjyK2lVMZtbOnCCq6C4NknMVk5m1MSeIKro8itrMzAmims5CLxPHi+22ntToUMzMGsYJooruQpFZHVMYN66t71doZm2urglC0hGSHpO0RNJZVbbvKul2SQ9LukvS3Lx+P0n3SFqct727nnFW6urxKGozs7olCEnjgYuBI4H5wImS5lfsdiFwZUTsAywEzs/rXwLeGxF7AUcAX5G0bb1irdS5uujbfJtZ26tnCeIgYElEPBURa4FrgGMq9pkP3JEf31naHhGPR8QT+fHvgW7SXNhbRHeh1wnCzNpePRPETsCzZctL87pyDwHH5cfvADok7VC+g6SDgEnAk5VPIOl0SYskLVq+fPmoBP1ibx89vX1OEGbW9hrdSH0mcKikXwKHAsuA/tJGSa8C/hV4X0QMVB4cEZdExIKIWDBz5ugUMLp78iA5t0GYWZsbak7qkVoG7Fy2PDevWy9XHx0HIGkq8M6IWJWXpwH/Bfx9RNxbxzg30LnaU42amUF9SxD3AXtK2k3SJOAE4KbyHSTNkFSK4Wzgsrx+EnADqQH7ujrGuJFX7sPkBGFm7a1uCSIi+oAzgFuBR4FrI2KxpIWSjs67HQY8JulxYDbwhbz+XcAfA6dJejD/7FevWMt5FLWZWVLPKiYi4mbg5op155Q9vg7YqIQQEVcBV9UztsF0FXrZetJ4pk6u61tjZtb0Gt1I3XQ6C0XmTJuC5FHUZtbenCAqdBeKzHL1kpmZE0SlLg+SMzMDnCA2EBF0FnybDTMzcILYwOqX17G2b8AJwswMJ4gNrJ9q1G0QZmZOEOVeGQPhEoSZmRNEmc6cIOY4QZiZOUGU684JYmaHq5jMzJwgynQVetl264lMmTi+0aGYmTWcE0SZzkKR2R2uXjIzAyeIDXQXisye7gRhZgZOEBvoKvQy2+0PZmaAE8R6/QPB8jW+zYaZWYkTRPb8ml76B8KD5MzMMieI7JVR1C5BmJmBE8R6HkVtZrYhJ4is0wnCzGwDThBZd6HIOMGMqZMaHYqZWVNwgsi6Cr3MmDqZCeP9lpiZgRPEel09nijIzKycE0TWubroLq5mZmWcILLuHg+SMzMr5wQB9Pb1s/LFtU4QZmZlnCCAbk81ama2EScIoLvHYyDMzCo5QeDbbJiZVeMEgW+zYWZWjRME6TYbk8aPY7utJzY6FDOzpuEEQWqknjVtMpIaHYqZWdNwgiBVMbl6ycxsQ3VNEJKOkPSYpCWSzqqyfVdJt0t6WNJdkuaWbTtV0hP559R6xtlZ8ChqM7NKdUsQksYDFwNHAvOBEyXNr9jtQuDKiNgHWAicn4/dHvgs8DrgIOCzkrarV6zdBY+iNjOrVM8SxEHAkoh4KiLWAtcAx1TsMx+4Iz++s2z7nwG3RcTKiHgBuA04oh5BruntY01vnxOEmVmFeiaInYBny5aX5nXlHgKOy4/fAXRI2qHGY5F0uqRFkhYtX758s4Jc2zfA2/fdkb12nLZZx5uZtapGN1KfCRwq6ZfAocAyoL/WgyPikohYEBELZs6cuVkBbL/NJL524v68ac/NO97MrFVNqOO5lwE7ly3PzevWi4jfk0sQkqYC74yIVZKWAYdVHHtXHWM1M7MK9SxB3AfsKWk3SZOAE4CbyneQNENSKYazgcvy41uBt0raLjdOvzWvMzOzLaRuCSIi+oAzSBf2R4FrI2KxpIWSjs67HQY8JulxYDbwhXzsSuBcUpK5D1iY15mZ2RaiiGh0DKNiwYIFsWjRokaHYWY2pki6PyIWVNvW6EZqMzNrUk4QZmZWlROEmZlV5QRhZmZVtUwjtaTlwDMjOMUMYMUohVMPzR4fNH+MzR4fOMbR0OzxQXPFuGtEVB0p3DIJYqQkLRqsJb8ZNHt80PwxNnt84BhHQ7PHB2MjRnAVk5mZDcIJwszMqnKCeMUljQ5gGM0eHzR/jM0eHzjG0dDs8cHYiNFtEGZmVp1LEGZmVpUThJmZVdX2CULSEZIek7RE0lmNjqeSpJ0l3SnpEUmLJX280TFVI2m8pF9K+mGjY6lG0raSrpP0G0mPSjqk0TGVk/TJ/Pf9taTvSWr4HLiSLpPULenXZeu2l3SbpCfy77rNFT+CGL+U/84PS7pB0rYNDLFqjGXbPi0pJM1oRGzDaesEIWk8cDFwJGl+7BMlzW9sVBvpAz4dEfOBg4GPNGGMAB8n3da9WX0V+FFEvBbYlyaKVdJOwMeABRGxNzCeNH9Ko13OxnPBnwXcHhF7Arfn5Ua6nI1jvA3YOyL2AR4nzTXTSJezcYxI2pk0183vtnRAtWrrBAEcBCyJiKciYi1wDXBMg2PaQEQ8FxEP5Mc9pAvbRvNzN5KkucCfA99pdCzVSJoO/DFwKUBErI2IVQ0NamMTgK0kTQC2Bn7f4HiIiLuBynlYjgGuyI+vAI7dkjFVqhZjRPw4z0cDcC9pRsqGGeR9BPj/wN8CTdtTqN0TxE7As2XLS2myi285SfOA/YH/bXAolb5C+qAPNDiOwewGLAe+m6vBviNpm0YHVRIRy4ALSd8knwNWR8SPGxvVoGZHxHP5cSdpoq9m9n7glkYHUUnSMcCyiHio0bEMpd0TxJiR5+z+AfCJiCg0Op4SSUcB3RFxf6NjGcIE4ADgXyJif+BFGl81sl6uxz+GlMh2BLaRdEpjoxpepD7yTfvtV9Lfk6por250LOUkbQ18Bjin0bEMp90TxDJg57LluXldU5E0kZQcro6I6xsdT4U3AEdLeppURfdmSVc1NqSNLAWWRkSp5HUdKWE0i8OB30bE8ohYB1wPvL7BMQ2mS9KrAPLv7gbHU5Wk04CjgJOj+QZ77U76MvBQ/r+ZCzwgaU5Do6qi3RPEfcCeknaTNInUMHhTg2PagCSR6s4fjYh/bnQ8lSLi7IiYGxHzSO/fHRHRVN9+I6ITeFbSH+RVbwEeaWBIlX4HHCxp6/z3fgtN1Ihe4Sbg1Pz4VOA/GhhLVZKOIFV5Hh0RLzU6nkoR8auImBUR8/L/zVLggPw5bSptnSByQ9YZwK2kf8hrI2JxY6PayBuA95C+mT+Yf97W6KDGoI8CV0t6GNgPOK+x4bwil2yuAx4AfkX6v2z4rRgkfQ+4B/gDSUsl/SVwAfCnkp4glXwuaMIYvw50ALfl/5dvNmGMY4JvtWFmZlW1dQnCzMwG5wRhZmZVOUGYmVlVThBmZlaVE4SZmVXlBGFWhaQ1+fc8SSeN8rk/U7H889E8v9locYIwG9o8YJMSRL7h3lA2SBAR0ayjpq3NOUGYDe0C4E15wNUn87wXX5J0X55v4IMAkg6T9FNJN5FHaUu6UdL9eZ6H0/O6C0h3bX1Q0tV5Xam0onzuX0v6laR3l537rrL5LK7OI67N6mq4bzpm7e4s4MyIOAogX+hXR8SBkiYDP5NUuvPqAaR5CH6bl98fESslbQXcJ+kHEXGWpDMiYr8qz3UcaZT3vsCMfMzdedv+wF6k24D/jDTC/n9G+8WalXMJwmzTvBV4r6QHSbdd3wHYM2/7RVlyAPiYpIdIcxLsXLbfYN4IfC8i+iOiC/gJcGDZuZdGxADwIKnqy6yuXIIw2zQCPhoRt26wUjqMdBvx8uXDgUMi4iVJdwEjmUa0t+xxP/7ftS3AJQizofWQbvxWcivw4XwLdiS9ZpDJh6YDL+Tk8FrSdLEl60rHV/gp8O7czjGTNAveL0blVZhtBn8LMRvaw0B/riq6nDS39TzS/ftFmqnu2CrH/Qj4kKRHgcdI1UwllwAPS3ogIk4uW38DcAjwEGkinr+NiM6cYMy2ON/N1czMqnIVk5mZVeUEYWZmVTlBmJlZVU4QZmZWlROEmZlV5QRhZmZVOUGYmVlV/wcZilWdaYkX2wAAAABJRU5ErkJggg==", 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    " ] @@ -1262,33 +1238,33 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 162, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "epoch: 0 iter: 0 loss: 0.2345 train acc: 0.5750 test acc: 0.5350\n", - "epoch: 0 iter: 5 loss: 0.2322 train acc: 0.6500 test acc: 0.5800\n", - "epoch: 0 iter: 10 loss: 0.2423 train acc: 0.6250 test acc: 0.5550\n", - "epoch: 1 iter: 0 loss: 0.1909 train acc: 0.8000 test acc: 0.6900\n", - "epoch: 1 iter: 5 loss: 0.1938 train acc: 0.7250 test acc: 0.6450\n", - "epoch: 1 iter: 10 loss: 0.2055 train acc: 0.6750 test acc: 0.7250\n", - "epoch: 2 iter: 0 loss: 0.1855 train acc: 0.8000 test acc: 0.7400\n", - "epoch: 2 iter: 5 loss: 0.1627 train acc: 0.8000 test acc: 0.7650\n", - "epoch: 2 iter: 10 loss: 0.1684 train acc: 0.8250 test acc: 0.7900\n", - "epoch: 3 iter: 0 loss: 0.1676 train acc: 0.8250 test acc: 0.7750\n", - "epoch: 3 iter: 5 loss: 0.1387 train acc: 0.8500 test acc: 0.7500\n", - "epoch: 3 iter: 10 loss: 0.1679 train acc: 0.8500 test acc: 0.7950\n", - "epoch: 4 iter: 0 loss: 0.1584 train acc: 0.7250 test acc: 0.8050\n", - "epoch: 4 iter: 5 loss: 0.1408 train acc: 0.8500 test acc: 0.8150\n", - "epoch: 4 iter: 10 loss: 0.1603 train acc: 0.8500 test acc: 0.8100\n" + "epoch: 0 iter: 0 loss: 0.3369 train acc: 0.4500 test acc: 0.4700\n", + "epoch: 0 iter: 5 loss: 0.2124 train acc: 0.6250 test acc: 0.5750\n", + "epoch: 0 iter: 10 loss: 0.2885 train acc: 0.4500 test acc: 0.5550\n", + "epoch: 1 iter: 0 loss: 0.2455 train acc: 0.4750 test acc: 0.6300\n", + "epoch: 1 iter: 5 loss: 0.1831 train acc: 0.7750 test acc: 0.7550\n", + "epoch: 1 iter: 10 loss: 0.1584 train acc: 0.8000 test acc: 0.8000\n", + "epoch: 2 iter: 0 loss: 0.2106 train acc: 0.7000 test acc: 0.7800\n", + "epoch: 2 iter: 5 loss: 0.1612 train acc: 0.8250 test acc: 0.7600\n", + "epoch: 2 iter: 10 loss: 0.1550 train acc: 0.8250 test acc: 0.8300\n", + "epoch: 3 iter: 0 loss: 0.1663 train acc: 0.8000 test acc: 0.8400\n", + "epoch: 3 iter: 5 loss: 0.1485 train acc: 0.8500 test acc: 0.8450\n", + "epoch: 3 iter: 10 loss: 0.1655 train acc: 0.8000 test acc: 0.8350\n", + "epoch: 4 iter: 0 loss: 0.1625 train acc: 0.8000 test acc: 0.8700\n", + "epoch: 4 iter: 5 loss: 0.1297 train acc: 0.8500 test acc: 0.8400\n", + "epoch: 4 iter: 10 loss: 0.1646 train acc: 0.7750 test acc: 0.8850\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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", 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    " ] diff --git a/tutorials/machine_learning/QClassifier_EN.ipynb b/tutorials/machine_learning/QClassifier_EN.ipynb index dd7f032..0af59f2 100644 --- a/tutorials/machine_learning/QClassifier_EN.ipynb +++ b/tutorials/machine_learning/QClassifier_EN.ipynb @@ -51,7 +51,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ @@ -62,6 +62,7 @@ "\n", "# To construct quantum circuit\n", "from paddle_quantum.ansatz import Circuit\n", + "from paddle_quantum.state import zero_state\n", "\n", "# Some functions\n", "from numpy import pi as PI\n", @@ -83,7 +84,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ @@ -125,7 +126,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 15, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T04:03:35.707224Z", @@ -184,7 +185,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 16, "metadata": {}, "outputs": [], "source": [ @@ -213,7 +214,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 17, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T04:03:37.244233Z", @@ -233,7 +234,7 @@ }, { "data": { - "image/png": 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\n", 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", 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\n", 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", 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    " ] @@ -409,7 +410,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 18, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T04:03:37.354267Z", @@ -418,52 +419,33 @@ }, "outputs": [], "source": [ - "# Gate: rotate around Y-axis, Z-axis with angle theta\n", - "def Ry(theta):\n", - " \"\"\"\n", - " :param theta: parameter\n", - " :return: Y rotation matrix\n", - " \"\"\"\n", - " return np.array([[np.cos(theta / 2), -np.sin(theta / 2)],\n", - " [np.sin(theta / 2), np.cos(theta / 2)]])\n", + "# Construct quantum circuit for data encoding\n", + "def encoding_circuit(data, n_qubits):\n", + " cir = Circuit(n_qubits)\n", + " for i in range(n_qubits):\n", + " param = data[0] if i % 2 == 0 else data[1]\n", + " cir.ry(qubits_idx=i, param=np.arcsin(param))\n", + " cir.rz(qubits_idx=i, param=np.arccos(param**2))\n", + " return cir\n", "\n", - "def Rz(theta):\n", - " \"\"\"\n", - " :param theta: parameter\n", - " :return: Z rotation matrix\n", - " \"\"\"\n", - " return np.array([[np.cos(theta / 2) - np.sin(theta / 2) * 1j, 0],\n", - " [0, np.cos(theta / 2) + np.sin(theta / 2) * 1j]])\n", "\n", - "# Classical -> Quantum Data Encoder\n", + "# Encode the data points to quantum states\n", "def datapoints_transform_to_state(data, n_qubits):\n", " \"\"\"\n", - " :param data: shape [-1, 2]\n", + " :param data: shape [BATCHSIZE, 2]\n", " :param n_qubits: the number of qubits to which\n", " the data transformed\n", - " :return: shape [-1, 1, 2 ^ n_qubits]\n", - " the first parameter -1 in this shape means can be arbitrary. In this tutorial, it equals to BATCH.\n", + " :return: shape [BATCHSIZE, 1, 2 ^ n_qubits]\n", " \"\"\"\n", - " dim1, dim2 = data.shape\n", + "\n", + " batchsize, _ = data.shape\n", " res = []\n", - " for sam in range(dim1):\n", - " res_state = 1.\n", - " zero_state = np.array([[1, 0]])\n", - " # Angle Encoding\n", - " for i in range(n_qubits):\n", - " # For even number qubits, perform Rz(arccos(x0^2)) Ry(arcsin(x0))\n", - " if i % 2 == 0:\n", - " state_tmp=np.dot(zero_state, Ry(np.arcsin(data[sam][0])).T)\n", - " state_tmp=np.dot(state_tmp, Rz(np.arccos(data[sam][0] ** 2)).T)\n", - " res_state=np.kron(res_state, state_tmp)\n", - " # For odd number qubits, perform Rz(arccos(x1^2)) Ry(arcsin(x1))\n", - " elif i% 2 == 1:\n", - " state_tmp=np.dot(zero_state, Ry(np.arcsin(data[sam][1])).T)\n", - " state_tmp=np.dot(state_tmp, Rz(np.arccos(data[sam][1] ** 2)).T)\n", - " res_state=np.kron(res_state, state_tmp)\n", - " res.append(res_state)\n", + " init_state = zero_state(n_qubits)\n", + " for i in range(batchsize):\n", + " cir = encoding_circuit(data[i], n_qubits)\n", + " out_state = cir(init_state)\n", + " res.append(out_state.numpy().reshape(1, -1))\n", " res = np.array(res, dtype=paddle_quantum.get_dtype())\n", - " \n", " return res" ] }, @@ -476,7 +458,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 19, "metadata": {}, "outputs": [ { @@ -486,7 +468,8 @@ "As a test, we enter the classical information:\n", "(x_0, x_1) = (1, 0)\n", "The 2-qubit quantum state output after encoding is:\n", - "[[[0.5-0.5j 0. +0.j 0.5-0.5j 0. +0.j ]]]\n" + "[[[0.49999997-0.49999997j 0. +0.j 0.49999997-0.49999997j\n", + " 0. +0.j ]]]\n" ] } ], @@ -648,7 +631,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 20, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T04:03:37.439183Z", @@ -671,7 +654,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 21, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T04:03:37.503213Z", @@ -681,7 +664,7 @@ "outputs": [], "source": [ "# Build the computational graph\n", - "class Opt_Classifier(paddle_quantum.gate.Gate):\n", + "class Opt_Classifier(paddle_quantum.Operator):\n", " \"\"\"\n", " Construct the model net\n", " \"\"\"\n", @@ -690,6 +673,7 @@ " super(Opt_Classifier, self).__init__()\n", " self.n = n\n", " self.depth = depth\n", + " paddle.seed(seed_paras)\n", " # Initialize bias\n", " self.bias = self.create_parameter(\n", " shape=[1],\n", @@ -699,28 +683,23 @@ " \n", " self.circuit = Circuit(n)\n", " # Build a generalized rotation layer\n", - " for i in range(n):\n", - " self.circuit.rz(qubits_idx=i)\n", - " self.circuit.ry(qubits_idx=i)\n", - " self.circuit.rz(qubits_idx=i)\n", - "\n", - " # The default depth is depth = 1\n", - " # Build the entangleed layer and Ry rotation layer\n", - " for d in range(3, depth + 3):\n", + " self.circuit.rz()\n", + " self.circuit.ry()\n", + " self.circuit.rz()\n", + "\n", + " # Build the entangled layer and Ry rotation layer\n", + " for _ in range(depth):\n", " # The entanglement layer\n", - " for i in range(n-1):\n", - " self.circuit.cnot(qubits_idx=[i, i + 1])\n", - " self.circuit.cnot(qubits_idx=[n-1, 0])\n", + " self.circuit.cnot()\n", " # Add Ry to each qubit\n", - " for i in range(n):\n", - " self.circuit.ry(qubits_idx=i)\n", + " self.circuit.ry()\n", "\n", " # Define forward propagation mechanism, and then calculate loss function and cross-validation accuracy\n", " def forward(self, state_in, label):\n", " \"\"\"\n", " Args:\n", - " state_in: The input quantum state, shape [-1, 1, 2^n] -- in this tutorial: [BATCH, 1, 2^n]\n", - " label: label for the input state, shape [-1, 1]\n", + " state_in: The input quantum state, shape [BATCH, 1, 2^n]\n", + " label: label for the input state, shape [BATCH, 1]\n", " Returns:\n", " The loss:\n", " L = 1/BATCH * (( + 1)/2 + bias - label)^2\n", @@ -760,7 +739,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 22, "metadata": {}, "outputs": [], "source": [ @@ -805,7 +784,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 23, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T04:03:38.325454Z", @@ -835,13 +814,12 @@ " # Read the dimension of the training set\n", " N_train = train_x.shape[0]\n", " \n", - " paddle.seed(seed_paras)\n", " # Initialize the registers to store the accuracy rate and other information\n", " summary_iter, summary_test_acc = [], []\n", "\n", " # Generally, we use Adam optimizer to get relatively good convergence\n", " # Of course, it can be changed to SGD or RMSprop\n", - " myLayer = Opt_Classifier(n=N, depth=DEPTH) # Initial PQC\n", + " myLayer = Opt_Classifier(n=N, depth=DEPTH, seed_paras=seed_paras) # Initial PQC\n", " opt = paddle.optimizer.Adam(learning_rate=LR, parameters=myLayer.parameters())\n", "\n", "\n", @@ -890,7 +868,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 24, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T04:04:19.852356Z", @@ -905,27 +883,27 @@ "The dimensions of the training set x (200, 2) and y (200, 1)\n", "The dimensions of the test set x (100, 2) and y (100, 1) \n", "\n", - "epoch: 0 iter: 4 loss: 0.2750 train acc: 0.7000 test acc: 0.6700\n", - "epoch: 3 iter: 4 loss: 0.2471 train acc: 0.2500 test acc: 0.5500\n", - "epoch: 6 iter: 4 loss: 0.1976 train acc: 0.8000 test acc: 0.9200\n", - "epoch: 9 iter: 4 loss: 0.1639 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 12 iter: 4 loss: 0.1441 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 15 iter: 4 loss: 0.1337 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 18 iter: 4 loss: 0.1287 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 0 iter: 4 loss: 0.2157 train acc: 0.9000 test acc: 0.6900\n", + "epoch: 3 iter: 4 loss: 0.2033 train acc: 0.4000 test acc: 0.5500\n", + "epoch: 6 iter: 4 loss: 0.1467 train acc: 1.0000 test acc: 0.9700\n", + "epoch: 9 iter: 4 loss: 0.1287 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 12 iter: 4 loss: 0.1215 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 15 iter: 4 loss: 0.1202 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 18 iter: 4 loss: 0.1197 train acc: 1.0000 test acc: 1.0000\n", "The trained circuit:\n", - "--Rz(3.490)----Ry(5.436)----Rz(3.281)----*--------------x----Ry(0.098)--\n", + "--Rz(5.489)----Ry(4.294)----Rz(3.063)----*--------------x----Ry(2.788)--\n", " | | \n", - "--Rz(1.499)----Ry(2.579)----Rz(3.496)----x----*---------|----Ry(1.282)--\n", + "--Rz(2.359)----Ry(4.117)----Rz(2.727)----x----*---------|----Ry(1.439)--\n", " | | \n", - "--Rz(5.956)----Ry(3.158)----Rz(3.949)---------x----*----|----Ry(1.418)--\n", + "--Rz(2.349)----Ry(3.474)----Rz(5.971)---------x----*----|----Ry(1.512)--\n", " | | \n", - "--Rz(1.604)----Ry(0.722)----Rz(5.037)--------------x----*----Ry(2.437)--\n", + "--Rz(1.973)----Ry(-0.04)----Rz(-0.01)--------------x----*----Ry(2.075)--\n", " \n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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x7ftT/Z8NfI+7t4F3gIMjbEtEZopDt1PulXt3YOTuLeDqwGi7XwGedvfzAO7+VtFKp9rayMweNbPjZnb87bNnp7krIlKG+7hOOcsMjH4M+DEz+30z+4P+tfvUKAntNHD7tu9v6/9s4HvMbA7YR+/mwA9w92fc/bC7Hz50UAM4keuBebfUC1i9OmDpvx4dclNzwJ3Ax4BHgC+b2f6iBYZ1DLjTzO6gl7geBj6x4z1HgF8Gvgn8IvCyrp+JVET5a2hn3P1wECszMDoFfMvdt4D/Z2bfppfgjkUbHDqhuXvbzB4DXqJXtvGcu79qZk8Bx939CPBbwG+b2UngHL2klzOD2uABo8018mWTeL0R/y/WF5pxrJkPXucW4vXWGvGyi0kJwEY3Lw9YTEoA8vKK+AAsmNxqYmUbzaTcPPsdZbFGwTYbybL1Rj2OJcdCvZn/CdWS4y89ri3e5nSHBj5MQsuUGRj9Lr2R2X8ws1V6p6CvZysdqQ7N3Y8CR3f87MltX28Af3OUdYvIDHPGktBKDoxeAv6amZ0AOsA/dff0YrueFBCRIcTz5w69puKBkQO/3n+VooQmIsMZzynnRCihiUh57tO+iJdSQhOR4WiEJiJVMY5HnyZFCU1EhjC2so2JmKGEZnht8O5YI64XA6g1F8JYfTFedi6pQ2su59tsLW/Fy+6J64uWtrKasHidPaM9qZbVfLW6o8+UlClq5TNqHdpyUou3L6klA5hfmY/3J/nMsmNhbjk+9iA/xiw5br0e70/RZ7IVfKZjufLlDt3x3OWchBlKaCIy6wydcopIlXSV0ESkElS2ISJVMaZHnyZFCU1EhuCYbgqISGVohFbMISzb8Ln4djuALS6HscZSfGu8uRIv17x4Jd3m/Hr8r1R3q7D98ED7C+LNzXibC0kZxEZSmjGLZRvZ/8ueubhsYzkpywCYX4lLKNKSjpXFOLY3PoYAaktLYSw7bn0u3tetgp5O7SA+lktf7mXaa0/NzCQ0Ebk+uO5yikg1aIQmIlXhKKGJSDW4O75V9Ije9CihicgQdMopIlXhjiuhFXOgFdxubszlHQ1qyythrL6yP4zN749LM9obm+k2vTPanR4LZraCfOYhgMbleKi/vBGXdGwlseKyjTQc2s2sT41kRq3mctyFIiu9AFhajcsvllbj8oqFg/HxNb9/T7rN+p79Yay2FK+33Yj3tegz22gPTjg+nn4bepZTRKpCIzQRqQrd5RSRytBdThGpDt3lFJGq0LOcIlIlepazBPf4dvTifN7RILs1Xt93MIwtbFyO92fEsgwASybyaCwmJQnJRB0ArUvxtYt2UprRacX/onYKOoP4iHUbVlC3kZWozCW/o7mkpKOobGPxQFwKsXjz/jC2dOhAGGveFC8HUEuOP1+ISz58Po5tXsw/s83g2C2o9ihJIzQRqQh3x9u6KSAiVaCyDRGpDp1yikhVOHhHCU1EKsH1LKeIVIhOOUWkEtzp6i5nsa7DRntwocxKM69D86V9Yax24FAYq7dbYWyxlrfyqTWzWqm4Hqq1N659m9+/kW6zfSWObyWzUGV1aKPOULVbtaQOLavVm1uIa/WaK3ELIMhb/SwcjI+hhUM3xftz8JZ0m/Uk3lmMt7nZjev4rmzlp3wXgprEzjgK0dx3VaM5aTOT0ERk9rnvruh80uKSdhGRH+J4t1vqVcTM7jOz18zspJk9PiD+STN728xe6b/+ftE6NUITkfLGNEIzszrwNHAvcAo4ZmZH3P3Ejrd+1d0fK7teJTQRKc3d6bTGclPgbuCku78OYGYvAA8COxPaUHTKKSJDGdMp563AG9u+P9X/2U4Pmdkfm9mLZnZ70UqV0ESkvP5dzjIvYNXMjm97PTrk1r4GfNDdPwz8d+D5ogVm5pSzi7PeHpzV2wv57Xhbitu71LtxOUO6zrlmHm/GM1E198b727oYzzS1dbmgbOPyehjrbCVlG+txeUrRv6TdEa+X1JIWSgC1RnzojVoSk/3eIS/rmNsfl2bUs9KfQ4MGFe/x5Xi93eS4vZSUZryzmR/Ta1cGnxKOpWyDoa6hnXH3w0HsNLB9xHVb/2fvbcf97LZvnwV+o2iDGqGJSGnuY7vLeQy408zuMLMm8DBwZPsbzGx7Ed8DwJ8UrXRmRmgicn0YddS+nbu3zewx4CWgDjzn7q+a2VPAcXc/AvwjM3sAaAPngE8WrVcJTUTK6zrd1miXcXZy96PA0R0/e3Lb108ATwyzTiU0ESnN0ZwCIlIVepZTRKpECa0ET7ptZLewAfYlt7/xeNlaLSsPyDt81PbuD2Pdi2thrL4ed9vIZqEC8FZc1tHZ2Iz3JzkAu0m5xyRlZRv1rKRjIS6XsYLyntryShzLZg47cHMYy8oyADp7VsPYOnHnkAtJacaZK3EZDsC5S4OPhc44ThUdujrlFJEqcHTKKSJV4U53Sw0eRaQKZrwfmhKaiAxBp5wiUhHu43lSYFKU0ERkCK7C2jLaXefc+uCLjcuN/Bn6RjKhydKeuFMC9bijhjUW021aMjFLI7nN303KNrKyDADfjLttzGUz8SQxL5qSbNQpywommbEsPheXM2RdTmqLeamNJaU4vhBPoNJd2JvE4uMAYKMeH0drG/HvNvpbADhbULbx1oXBZRtbnTF02+hCN5l0Z9pmJqGJyOxzXKecIlIRDj6mvmqToIQmIkPpjuPUdUKU0ESktFmfl1MJTUTKc8c1QhORSnDo6C6niFSBA13dFCjW6Trng9qbffOj7+ZWM65hW1yI2w41k9ojANuKa8a67biVj+2Jl7OslgywZAarLEYWS9orTZQltYVJWydPage9HtevAXQbcQ2bN+MatW4zbktU1Nrqwno8mjmb1JqdvhAfJ6fX8nrFcxcHH3/tcZwq6pRTRKpEdWgiUgm9u5waoYlIFSihiUhluNPZ0l1OEakAR08KiEhVaBq7ctpJ2cZSQfugrse38luduE3Nwlz8wczXLd1msx7fym8kbWrmavF66xQcKFnZRlZ+0bnOyjbqSdlGVtKRxABaychiI4mtX4l/f1cKyjbOr8fLvhnMzgRwKinb+LMz+exgl4NlxzVbk66hiUgl9DrWKqGJSBXopoCIVIbKNkSkKhy1DxKRqtA1NBGpDj2cXkq76+FsNkmlAwAb7XgIvLcZ/y8uNZLZopr5rEVzSdVBWpphSSyvTqFu8T7VkpgRd6GoJfsDUBAOecEx303e4EmVSXa2s5V1FSEv29hKWuJc3IzX+04Sg3yGpu8FXTEAXn/rUhh74+yVdJtXglmfxjGycs8/u2mbmYQmIrPPgZb6oYlIVXRmeIRWcJIjIvIeBzpe7lXEzO4zs9fM7KSZPZ687yEzczM7XLROjdBEpDT38YzQzKwOPA3cC5wCjpnZEXc/seN9e4F/DHyrzHo1QhORoYxphHY3cNLdX3f3FvAC8OCA9/1z4AtA3ne8TwlNREpznI6XexW4FXhj2/en+j97l5n9JeB2d/8vZfdvZk45290ubwVdAjoFd1WyjgdLjXgiioW5uNRhPqvLABpJaUYj6dTRqMXrzZaDvMQiKwdJNpkuN0nZAZ81hdhKgln5DsBmEt9I6kEu7aJs462ghALgzbX1MPadpDTjwpm8bOPS+cHdOLrt3T+D2bvLWfrtq2Z2fNv3z7j7M2UWNLMa8K+BTw6zfzOT0ERk9g15De2Mu0cX8k8Dt2/7/rb+z67aC/wU8A3r/aP7fuCImT3g7tuT5A9QQhORoYzpQYFjwJ1mdge9RPYw8ImrQXd/B1i9+r2ZfQP4TJbMQAlNRIbQK9sYxxMH3jazx4CXgDrwnLu/amZPAcfd/cgo61VCE5HSrtahjWVd7keBozt+9mTw3o+VWacSmoiU5q5Hn0SkQirz6JP1/Jv+owp/3K8TGfS+X+rHXzWzL4xnV0Vk2hzolnxNw7AjtPuBO/uvjwD/vv/fd5nZQeBfAj/r7m+b2fNmdo+7fz1bcbvjYc1Oq6C+aK0Z15otJm2AslqzZkEdWj2rQ0sKv7IWQUWtfNJas2TRbF+LtjkpWQuarO4wa/OzVXBxZyOpw1pvxbGLG3Gt2blk5iaAs5fi9kHnkvZBl9biwvgL5+P6NYD1898f+PNuNvtXaaWKZqdm2CcFHgS+4j1/AOw3s1t2vOfPAf/X3d/uf/8/gId2uZ8iMgPG+XD6JAw7QoseV3hz289OAj9uZh/sx/8GEE+cKSLXjXGVbUzK2G8KuPt5M/sHwFfpnUr/b+DPD3qvmT0KPAqwfPD9494VERmzWb/LWXjKaWafNrNXzOwVeiOx7HEFANz9a+7+EXf/OeA14NuD1u3uz7j7YXc/vLByYKT/ARG5tmb5lLMwobn70+7+0+7+08DvAn+3f7fzLwPvuPubO5cxs5v7/z0A/EPg2bHutYhMxdVTzjF025iIYU85jwJ/nd51sivA37saMLNX+kkP4Etm9hf7Xz/l7gNHaCJyfRnnkwKTYD4jF/jM7G3gz/rfrgJnprg7Mjx9ZrNp++fyAXc/tJuVmdl/ZdtD4wXOuPt9u9nesGYmoW1nZseTtiMyg/SZzaYb7XNRx1oRqQwlNBGpjFlNaKXa9MpM0Wc2m26oz2Umr6GJiIxiVkdoIiJDm2pCUzui60/RbNdmNm9mX+3Hv9V/plcmqMRn8gEz+3r/b+gbZnbbNPbzWpj2CG17O6JH6bUj+gHb2hHd4+4/CbzfzO65pnspwA/Mdn0/cBfwiJndteNtnwLOu/uHgC/SmyRWJqTkZ/Kb9LrkfBh4Cvjctd3La2faCU3tiK4vZWa7fhB4vv/1i8A9ZlNqunZjKPOZ3AW83P/69wbEK2PaCa1w9mS2tSMyszl67YhuR6ahzOf17nvcvQ28Axy8Jnt3YyrzmfwR8Av9rz8O7O2f+VTOtBNaIXc/D1xtR/S/gD8Fdj8FtMiN4zPAR83sD4GP0uuQU8m/oWs+SYqZfRr4lf63xyjZjgj4Wn/5R6noh3EdKJrtevt7TvVH1PuAs9dm925IhZ+Ju3+X/gjNzPYAD7n72rXawWvpmo/Q1I7ouvbubNdm1qQ32/XOCWGPAL/c//oXgZddxY6TVPiZmNmqmV39W38CeO4a7+M1M+1TzqPA6/Suk32ZXrICeu2Itr3vS2Z2Avh94PNqRzQd/WtiV2e7/hPgd67Odm1mD/Tf9lvAQTM7Cfw68ENlBDI+JT+TjwGvmdm3gfcB/2IqO3sN6EkBEamMaY/QRETGRglNRCpDCU1EKkMJTUQqQwlNRCpDCU1EKkMJTUQqQwlNRCrj/wPpPX8+eJdfQQAAAABJRU5ErkJggg==", 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    " ] @@ -939,7 +917,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The main program finished running in 7.628719806671143 seconds.\n" + "The main program finished running in 44.9472119808197 seconds.\n" ] } ], @@ -959,7 +937,7 @@ " EPOCH = int(200 * BATCH / Ntrain),\n", " # Number of training epochs, the total iteration number \"EPOCH * (Ntrain / BATCH)\" is chosen to be about 200\n", " LR = 0.01, # Set the learning rate\n", - " seed_paras = 19, # Set random seed to initialize various parameters\n", + " seed_paras = 10, # Set random seed to initialize various parameters\n", " seed_data = 2, # Fixed random seed required to generate the data set\n", " )\n", " \n", @@ -988,7 +966,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 25, "metadata": {}, "outputs": [ { @@ -1021,7 +999,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 26, "metadata": {}, "outputs": [], "source": [ @@ -1088,7 +1066,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 27, "metadata": {}, "outputs": [ { @@ -1096,30 +1074,30 @@ "output_type": "stream", "text": [ "Encoding method: amplitude_encoding\n", - "epoch: 0 iter: 0 loss: 0.3005 train acc: 0.6000 test acc: 0.4600\n", - "epoch: 0 iter: 5 loss: 0.2908 train acc: 0.3000 test acc: 0.5000\n", - "epoch: 0 iter: 10 loss: 0.2313 train acc: 0.8000 test acc: 0.6200\n", - "epoch: 0 iter: 15 loss: 0.2181 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 0 loss: 0.2448 train acc: 0.7000 test acc: 0.5500\n", + "epoch: 0 iter: 5 loss: 0.4895 train acc: 0.3000 test acc: 0.6100\n", + "epoch: 0 iter: 10 loss: 0.1318 train acc: 0.8000 test acc: 0.5800\n", + "epoch: 0 iter: 15 loss: 0.2297 train acc: 0.6000 test acc: 0.6500\n", "Encoding method: angle_encoding\n", - "epoch: 0 iter: 0 loss: 0.4141 train acc: 0.4000 test acc: 0.3700\n", - "epoch: 0 iter: 5 loss: 0.2942 train acc: 0.6000 test acc: 0.6700\n", - "epoch: 0 iter: 10 loss: 0.1952 train acc: 0.6000 test acc: 0.6700\n", - "epoch: 0 iter: 15 loss: 0.2389 train acc: 0.6000 test acc: 0.6000\n", + "epoch: 0 iter: 0 loss: 0.2437 train acc: 0.6000 test acc: 0.3900\n", + "epoch: 0 iter: 5 loss: 0.1325 train acc: 0.8000 test acc: 0.7100\n", + "epoch: 0 iter: 10 loss: 0.1397 train acc: 0.8000 test acc: 0.6600\n", + "epoch: 0 iter: 15 loss: 0.1851 train acc: 0.6000 test acc: 0.6300\n", "Encoding method: pauli_rotation_encoding\n", - "epoch: 0 iter: 0 loss: 0.1985 train acc: 0.7000 test acc: 0.7400\n", - "epoch: 0 iter: 5 loss: 0.2303 train acc: 0.6000 test acc: 0.6900\n", - "epoch: 0 iter: 10 loss: 0.1970 train acc: 0.6000 test acc: 0.7200\n", - "epoch: 0 iter: 15 loss: 0.2120 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 0 loss: 0.3170 train acc: 0.6000 test acc: 0.7000\n", + "epoch: 0 iter: 5 loss: 0.2119 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.2736 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 15 loss: 0.2186 train acc: 0.7000 test acc: 0.7000\n", "Encoding method: IQP_encoding\n", - "epoch: 0 iter: 0 loss: 0.2962 train acc: 0.5000 test acc: 0.4500\n", - "epoch: 0 iter: 5 loss: 0.2074 train acc: 0.7000 test acc: 0.7000\n", - "epoch: 0 iter: 10 loss: 0.2463 train acc: 0.6000 test acc: 0.6500\n", - "epoch: 0 iter: 15 loss: 0.2090 train acc: 0.9000 test acc: 0.5800\n", + "epoch: 0 iter: 0 loss: 0.3279 train acc: 0.3000 test acc: 0.6200\n", + "epoch: 0 iter: 5 loss: 0.1772 train acc: 0.7000 test acc: 0.7200\n", + "epoch: 0 iter: 10 loss: 0.2051 train acc: 0.8000 test acc: 0.6500\n", + "epoch: 0 iter: 15 loss: 0.1951 train acc: 0.7000 test acc: 0.6700\n", "Encoding method: complex_entangled_encoding\n", - "epoch: 0 iter: 0 loss: 0.2500 train acc: 0.6000 test acc: 0.6800\n", - "epoch: 0 iter: 5 loss: 0.2571 train acc: 0.5000 test acc: 0.6800\n", - "epoch: 0 iter: 10 loss: 0.2661 train acc: 0.7000 test acc: 0.6700\n", - "epoch: 0 iter: 15 loss: 0.1916 train acc: 0.8000 test acc: 0.7200\n" + "epoch: 0 iter: 0 loss: 0.5466 train acc: 0.4000 test acc: 0.2900\n", + "epoch: 0 iter: 5 loss: 0.2075 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 10 loss: 0.2951 train acc: 0.7000 test acc: 0.7000\n", + "epoch: 0 iter: 15 loss: 0.2614 train acc: 0.7000 test acc: 0.7000\n" ] } ], @@ -1155,12 +1133,12 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 28, "metadata": {}, "outputs": [ { "data": { - "image/png": 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uezl7Yci1prCQnPQCEo6lakrheBrZaQUAeNVzJbhdPQZMbIuDQ8XvqVIQdYQSh/eOxB3sPL+TI6lHlMNbYRFSSi7kXDA+/E1/p+SnGNs5OzgT4hNCc9/mhPmGGX+H+IRcNWuVUpJWkGZUFhdzL5r9nFGQcZU87k7uVymP0orkep+NFOTpOHdcUwYJR1NJu5ALgKunE0Ft/AlqW4+gtv74BrhXSdkqBVFHySjIYPeF3caQ2rjMOADqudWjZ+PLK7yDvIPsK6ii2igsLuRM5hnjwz82M5bT6aeJy4wjT5dnbOfj4mN8+JsqgqZeTXF0cLSqTPm6fJJzk0nKSzKrQNRsRENXVMyF05kkHE0l4XgaSXGZSAlOzg40aeVHUFt/gtvWo0GQF6ISM4WyUAriOuFCzgVthbdhhlHa4R3ZJJKeTXpSz62enSVVVJXMwkxtFpB+mtjMWGLTNWWQkJVAsSw2tgv0DDQqAVNlUM+tXo16qNpiNmK6rybORvR6yaWzWQY/QiqJpzIoLtIjHASNQr2NM4TGYb44OtvOIqAUxHWIlJLYjFh2nNeUhanDu41/mytWeCuHd81ESsnF3ItGJWD625xZyHQm0Ny3uVmzUG2nZDZSlgJJyk0iKS8JnV53Rb+aMBuRUpKRlMdZwwzh3PE0CnI1OesFehLUVjMbNW3lh4t79SkzpSAU6PQ6jqYc1RzeiTvYm3Slw7skQko5vKufouIiLVrIRAmUOItNzULeLt40921+lX/AFmah2oxe6kkvSK8Rs5GcjALjDCHhmIlj2d+VoHb1DL4Efzx9Xa16DyqCUhCKq8jX5bM3aa8xpfmRlCNIJB5OHnRr1M04w1AOb+tRYhYydRDHZlxtFmri2eQK/0DJT323+jXKLFTbqexsxEE4UN+tvlnnen2HAJwu+JAbJ7h4Mpu08yaO5db+RqXg27BqjmVrYjcFIYQYCsxGKzn6lZTyrVLHnwImGjadgHZAgJQy9Vp9zaEUROUpcXiXFE0ydXj3atxLUxiBkTT1ampfQWs4RrOQiQIo+Xwp75KxnalZyHQ2EOoTWufMQrUZvdSTlm/eN5KUm0RSVjLygjv+KU1pmtGahtnNcMCRIodCknziyG54EX3TLLybONPQs2b6RuyiIIQQjsAJYBCQAMQA46WUR8poPxx4TEp5U0X7lqAUhPW4kHPBmD9qx/kdJOclAxDkFWRUFj0bX78O76LiIs5knbkqZLQss1Bp/0CgV6DdHwyKilPasXz+VAa6Ij3CAfyC3HAP1aMPzCbT/wJJBZWbjZRefNjQoyFeLl42uyZ7KYgoYKaUcohh+zkAKeWbZbRfDPwlpfyyon1LUArCNpQ4vEtmF7sv7L7C4V3iv7Cmw1vq9egzM3H087PKeJUlqzDrqtlAXEYcZ7POXmUWMlUCyixUNyhxLJsuULvCsdxGMxsFtvLD9RqO5WvNRkq2Mwszr+rr4eRR5noRf9cGFBb4EBXSvFLXaC8FMQYYKqW837A9CeglpXzYTFsPtJlCS4N5yeK+pigFUT3o9DpthbdhdrE3aS9F+iKcHJyIaBBBZKAWUtuxQcdKO7zP/+8l0pctw6VFCzwjI/HsHYVHz544entb+WrMm4VKlEF5ZqEShaDMQnWLch3LbS8vULOVYzlPl3eVb8RUgZSsKbliNlLsyZ67t+PiVHF/YXkKwpZzXHOvTWVpo+HANillakX7CiGmAFMAmjVrVlEZFZXAyUGLfIoIiOCBiAeMDu+SkNrP9n3Gp/s+xcPJg+6Nuxt9GK39W1v0Np2+YiXpy5bhPWgQ+vx80n/+mbTvvwcHB9zCO+IZGYVnVCTuXbrg4Gr5P2mJWaj0auK4jDhydbnGdt7O3oT5hdG3ad+rooWUWajuUZin49zJdOMCtdTEHABcPbQVy92GakqhuhzL7k7uNPNpRjOfq59nUkpi4tJYuP00606cRjqm0ylU0LetL05WXDxXQo0wMQkhVgDLpJSLK9rXFDWDqBlkFGRoKc0NCqO0wzsyUDNJmXN45584Qdwd43Dv1Ilm879GODoiCwvJ27+fnOhocqJ3kHfgABQXI1xd8ejWFY+oKDwjo3Br3w7h6EhWYdZVfoHYjNirzEKNPRtf5R9QZqG6T3GRngunM0g4nsbZo6kkxWch9RJHZwcCW/oaZwgNgr0rldvIFuQW6li5N5FF0XEcu5CFr7sz43oEc1evEJrVr9rs1V4mJic0R/NA4Byao3mClPJwqXa+QCwQLKXMqUjf0igFUTO5kHPBqCx2nt9pdHgHewfTq4k2u+jVuBe+xS7EjhlLcVYWzVf8jFNAgNnxirOzyd0VQ/LWjeRGR+MYew6APA8njoU6sSeokIOhgvP1wMnRmVCfUGUWuo6ResmlhGzjArXzJ9M1x7KAhqE+RrNR4+Y+ODnXrPUkcZdy+HZHPD/uPktWvo72TXy4p3cIIzo1xd3FOrLaxcQkpdQJIR4G/kALVZ0vpTwshJhqOD7P0HQ0sK5EOZTX11ayKmxLY8/GjGo5ilEtRyGl5HTGaWP+qN9jf+enEz+BlLz4uxfhcZlkvvcEQX6eOKGZhc5mnTUbLZQbkgsh4JvtSI8EN3qec6P1qTy6HNEykIqGDfDq3Rvv3n3waB+Jc8OG9r0RimrB6Fg+bvAjHE+jIEez1/s38aRd30CC2/oT2Nr/mo5le6DXSzafSOab6Dg2HU/GyUHwn/Am3B0VQrcQ/2qd3aqFcgq7UuLwjvvmc1p9tZEfBjixPErzczT2aMz5nPNlmoXCfMJo7tf8CrOQlJKiM2fIid5BTnQ0uTt2UJyhrZh1adlC81/0jsKjRw+bOLwV9iEno4Bzx9M4a3AuZ6eacSy38cfTz34rlq9Fem4hy3Yn8O2OeM6k5tLQ25WJvUIY3zOYhj5uNjuvWkmtqNHkHTpM/PjxeERF0mDuh+y7tJ+d53dyLvsczbybGZVAmE9Yhc1CUq+n4Ngxo/8id/duZH7+ZYe3wX/h3rULDi4uNrpChbUxOpYNkUamjuWmbfwJblu9juWqcDgxg2+j41m57xz5RXp6htbj7t4hDOnQGGdH22cxUApCUWMpzswk9rbbkcXFhP28HCd/f5ueT19YSN6+feTu2EHO9mjyDh7UHN5ubnh07YpHVCSeUb1xa9cW4Viz7NHXM8VFei7EZhjDTy/GXXYsN2nhS3C7mudYLo9CnZ4/Dl9gUXQcMXFpuDs7MqpLU+6OCqFdE59qlUUpCEWNREpJwiOPkL1pMyHfLsKjS5dql6HE4Z2zI5rc6GgKTp4CwMHXF89evfCMisQjMhKX0NAa/yZalzA6lo+lcu5YGomlHcuGBWo10bFcHhcz81m88wyLd50hOauAkPoeTIoMYWy3YHw97JMk017rIBSKckld+A3ZG/6k0XPP2kU5ADh6eeF9041433QjALrkZHJ27DSYpKLJWrcOAKcmTS4v2OvVSzm8rYyUkozkPOMM4dzxdPJztAJC/o09aNc3kKA2/jRt7YernR6klUVKye74NL7ZHsfvhy5QLCU3tmnI3VEh9GsVUKNnPGoGAez/8yz64rpzH2oDhefOkb50Ca4tWuIzaiTCzNpI4QAubk44uzle8dvFZNuxEitHLUVKSVF8PDkGc1Tuzp1XOryjemszDOXwrhS5mYWXU1gcSyMrNR8wOJbbXM58WpMdy+WRV1jMqn3n+CY6nqPnM/Fxc9LWLkSGEFLf097iGVEmpmvw+fRN6Ar1126oqHE4OjkYFIcjzibKw3TbuZRSKX3cUmUj9Xryjx4lt8ThvWeP5vB2dMS9Y0c8ehsc3l06K4e3GQrzdSSeSCfhWBpnj6Ve5VguqY3g18ijVpvz4lNy+DZaW7uQma+jXRMf7okKYWRn661dsCZKQVyDwnzdtRsprINeT8L0GeTu3k3IwgW4tm1bZlOplxTmF1OUX0xhvs74u7DUtun+IjPHLVX+jk4OuLg74uzqiIu7k/a7HGXj5CSR5+IpPnEY3cG96I4dwqkwFydniVfXLgb/RdR16/Au1um5GJvB2aPaDOFiXOYVjuWgtv4Et6tXaxzL5aHXSzafTGbR9jg2nUjGUQhuCW/CPXZYu1BRlA/iGri4qdtQXVz67DMKtm6i6Suv4N254zXbW8PerC/WU1RQbKFiufy5KF9HbmYh6UnXUjYtwKcF9Bxj3OMgdThuz8Px70M4y724eLrg6u+Ne6N6uNb31ZRMiRIy+e1SatvZzRHHagh1tAYljuXLNZbT0RVqjuWAEB+6Dm6m1Vhu4VurHMvlkZFbxLI9Z/l2RzzxKbkEeLsyY2ArJvRsZtO1C9WFejIqqo2cHTtI/nguPsOH43fH2Go7r4OjA64eDtWubPLTssk7l0R+choFGdlkZeaSlpBOsYsnxU7uFGPZQ9LR2cG8qczVEWdzSqWalI2UksxLmmP57FGtxvIVjuXegQS1rZ2O5WtxJDGTb3fEsWKvtnahR6g/Tw5uw5AOjSuVUbWmohSEolooSkri3JNP4RIWRpOZL1s25c66CPqaZf5zAFwBV0fA0/BzVYsS/4M7oOWTklJSdPYcOTH/kBPzFzl79qHLyqHY0RXHsJY4R3TGqW17HEKaoxMuFBXoKSzQG34XU1igpzBf2y4qKCA3VU+6yT5dkWWmYkcngYurA85uDri4aj/Org64uDng7KL9vnK/o/bb8OPo7EhSiquWxuLoZceyp58roeH1NYXQph5e/rXTsVweRcWGtQvb49kVl4qbswOjuzRlUmQo7QOrd+1CdaEUhMLmSJ2OxCeeRJ+TQ8jCBTh4WhDBseEV2PqB7YWrJgSa2nAB/BuBHAr56c7kXnQl50IauSsPUFAsQEjc6xXh06gAz8YFuNcvxKGsiYYT4KX96KUDRdKNQulBod6dIulBoWG7SO+u/TY5XpjjTlG2O4V6D3KlO+nSnULpTpHeAx3Xfri7Outo2sqHLoNb1wnHcnkkZeazeNcZFu88Q1JWAc3qefDisHZ2XbtQXSgFobA5yXM+JjcmhsC338K1Zctrdzj3D2z7CNoNh5aDbC6fPRBo8wt3oD6gL9SRd/IcOYfjyT0cR8rR86QckQgXJzzaBOPZMRSPDiG4hTRCmHHoGmc2lZaoGMgGstHrobBIUFTkQGGhA0VFgsJCB21fgY56GZsISPoJh9RiON0bvO8Ev1Hg5lvps9c0pJTsiU/jm+h4fjt4Hp1eMqBNAG9HhdK/dc1eu2BNVBSTwqZkb97M2Qen4jd2LE1ee/XaHYp18OUAyE6GaTvB3c/WItZIirOyyI2JIWd7NDk7oik89S8Ajn5+eBhWeHtGReHcrJl93twzEuDAj7B/CVw6AU5u0HYYdBoPzW8Ex9r57lmydmFRdDxHDGsX7uiurV0IbVBz1i5YExXmqrALRYmJxI6+DafAQEKXLMbBzYKojm1zYP3/4I5F0H6k7YWsJRRdTCJ35w5jllrdhQsAOAU2MSYc9IyKxKlBg+oVTEpI/Af2L4WDP0FeKng1gvCxmrJofO1ItZpAfEoO3+2I58fdCWTkFdG2sTf39A5lZOdAPFxqp7KzFKUgFNWOLCwkbtIkCk/9S9jPy3EJCbl2p7Q4+CQSWtwIdy6GOmrTripSSgrj4rR05tE7yNm5E32mVujetVUrQ8LBKDx69MTRqxrfenWFcHKdNqs48Qfoi6BROHQerykMr5qVnkSvl2w5mcyi6Hj+Op6EoxAM7diYu6NC6RFas9cuWBOlIBTVzoU33iBt0bc0nT0bnyGDr91BSvjudji7UzMt+QbZXsg6giwuJv/IUWPCwdw9/yALCrQV3hERxoSD7p2rcYV3Tgoc/hn2LdZmGMIRWg7UZhVt/gPO9lsjkJFXxLLdZ/luRzxxhrULE3o2Y0KvZjSqA2sXKopSEIpqJfOPdZybMQP/uyfR+PnnLet0YBn8fD/c8g70etC2AtZx9AUF5O3dpyUc3BFN/sFDoNcj3N3x6NZNM0lFReLati3CoRpi9pOPayaoAz9A5jlw9YUOo6DzBAjuVW0zxaPnM1kUHc/KvefIKyqme4g/d/cOZWgdW7tQUZSCUFQbhfHxxN4+BpcWzQn99luEJW+suakwtwf4h8L/raPsuE5FZSjOzNQc3gb/ReG/Jg7vyEhjllrn4GDbmlX0xRD3t6YsjqyGohzwD4NOd2o//qFWP2VRsZ51hy/yTXQcu2K1tQujOjdlUlQIHQLrTtRVVbCbghBCDAVmo9WV/kpK+ZaZNgOAjwBn4JKUsr9hfxyQhRZ/pyvrAkxRCsK+6PPziRs/AV1iImErfsY5MNCyjiunwYGlMGVzrXFq1maKLiaRuyP6ssP74kUAnAMDjQkHPSN72dbhXZANR9fA/sUQ+zcgoVlvzV/RfmSVQ2aTsvJZsvMsi3fFczFTW7swKTKEsd2D8PNQiRRNsYuCEEI4AieAQUACEAOMl1IeMWnjB2wHhkopzwghGkopkwzH4oDuUspLlp5TKQj7cv6ll0n/8UeC5n2G94ABlnU6vRkWjYC+j8PNL9tUPsXVSCkpjI0z+i9ydu667PBu3drov7Cpwzv9LBz8EfYtgZSTJiGzE6D5AItDZqWU/HMmjW+2x/PbofMUFUv6tw7gnt4h9G/dEMfrZO1CRbGXgogCZkophxi2nwOQUr5p0ua/QKCU8kUz/eNQCqLWkLF6NYlPP0P9KVNo+PhjlnUqyoPPemsO6v9Gg7O7bYVUXBPN4X1ES2e+w8Th7eSEe3g4nlFReA8ehFs5WXgrf3KpLZLcvwQO/QR5aZdDZjtPgEYdzHbLLypm9b5EvomO43BiJt4maxfC6ujaBWtiLwUxBm1mcL9hexLQS0r5sEmbj9BMSx0Ab2C2lHKR4VgskAZI4HMp5RdlnGcKMAWgWbNm3eLj421yPYqyKTh1itixd+DeoQPNFi5AOFkYN/7na/D3e3D3Ku1NUVHj0Bzeew0L9naQf0hzeLu2bYvvyJH43joMp4AA659YV2AImV0KJ37XcnI1DtdmFeFjwKshZ1Jy+W6nVnchPVdbu3B3VCijutT9tQvWxF4KYiwwpJSC6CmlfMSkzVygOzAQLetANDBMSnlCCBEopUwUQjQE1gOPSCm3lHdONYOofvQ5OcTeMY7i9HTN72BpKc6LR+DzGyD8Dhj9mW2FVFgNXVoamWvXkrFyFfkHD4KjI559++A3ciReN91k2WLIipKTAoeWa/6KxL1I4cgBt+58kdmLjbIbN3Vsxt2RIfQMq3fdrF2wJvaqB5EABJtsBwGJZtpcklLmADlCiC1AJ+CElDIRQEqZJIRYAfQEylUQiupFSsn5ma9QePo0zRbMt1w56IthzXTNETn4ddsKqbAqTv7+1Js4kXoTJ1Lw779krFpNxurVnHv8CRy8vfEZOhTfUSNx79rVeg9rz/pkRNzHT0WD2JL2N72y1nO73MonzjvRu/rg4H0bOE1Ae0QorIktFUQM0EoIEQacA+4EJpRqswqYK4RwQkt02Qv4UAjhCThIKbMMnwcDFiTyUVQn6T8uI3PNGhpMfwTPyEjLO+6eDwkxMPoL8KxvOwEVNsW1RQsaPv4YATOmk7trFxkrV5Lxyy+kL1uGc3CwZoIaOQKX4OBrD1YGxy5oaxdW/KOtXegW0pKmQwbi374hnN2Kw/6lWk6oPQsNIbPjodM4m4TMXo/YOsz1P2ghrI7AfCnlLCHEVAAp5TxDm6eA+wA9WijsR0KI5sAKwzBOwGIp5axrnU+ZmKqP/CNHiLtzPB49exL8xeeWL7jKOAef9IKg7jBphUqnUcfQ5+SQuX49GStXkbtzJ0iJe/du+I4cic/QoTh6e19zjKJiPeuPXOSb7XHsjE3F1eny2oWOTc2EvxZkGUJml1wOmQ3poymL9iPBrW7WarAWaqGcwqoUZ2URe/sYZEEBYSt+xqlePcs7L50Ip/7UopbqhdlOSIXdKUpMJGPNL2SsXElhbCzC1RXvgQPxHTUSz969rwpmSMrKZ+mus3y/U1u7EFzPXVu70C0Yf08L1y6kn9VWbO9fAimnDCGzt2rrK5rfqBZhmkEpCIXVkFJybvoMsv76i5BFi/Do2sXyzkfXwA93wc2vQN9HbSajomYhpST/4EEyVq4i89dfKc7IwDGgAb63Dsdn5AiOuDdiUXQcaw9qaxf6tQ7gnqgQBrSpwtoFKeHcHk1RHPwJ8tPBqzFEjNUioRq1t+o11maUglBYjdRvvuHim2/R8OmnqT/5Pss75mdopiWPBjDlL3Cs25W4FObRFxaSvXkzaT+vJGfLZkRxMf/6BrK1eU/8hw9n7KAImgd4WfekugItu+z+pXDyD0PIbIRmggofC142CNOtRSgFobAKefv2EXfXJLz69ydo7scVi1L59QmI+Roe+BOadrOdkIoazdnUXL7bEc8Pu8+iT0tnbOZRbkncg2fsSXB0xKtvX3xHGUJmXW1Q1zrnkiFkdgkk7tWyzLYapCmL1kPtmmXWXigFoagyurQ0Ym+7HeHoSNjPy3H0qYDj78xOmD8Eek2FW65Kx6Wo4+j1kq2nLrEoOo4/jyXhIARDOjTi7qhQehnWLhScOmUMmdVdvKiFzN5yixYy26WLbdY3JB29nGU267wWdt3hNm3VdlCP6yaAQikIRZWQej1np04lN3oHIUuW4N7RfMoDs+gK4fN+WqTJtB3geu0oFkXdIDO/iOV7Evg2Op7Tl3Jo4OXChJ7NGN+rGU18zadVkcXF5O7cScaqVWSuW4/My8O5WTN8R47Ad+RIXIJsUCdEXwyxmzVlcXQNFOVCvebarCJiHPhbUOyqFqMUhKJKXPr8C5I//JDGL7+E//jxFeu85V3Y+DqMXwptbrGNgIoaxfELWSyKjmPF3nPkFhbTtZkf9/QOZWjHxrg6WR5FVJydQ9b69WSsXKmFzAIe3bvjO2ok3kOH4uhlZV8FaC8yR1ZrJqi4v7V9IX21dOR1NGRWKQhFpcnZuYsz992Hzy23EPjeuxWb6l86pSXja3ML3PGN7YRU2J2StQuLouPYcVpbuzCiUyB3R4USHlT1ugtF585dDpmNi9NCZm+++XLIrKMNwlfTz2jmp31LIPVfcHKHdrdqM4vmA+pMyKxSEIpKoUtO5vRtt+Ho5U3osmUVS/csJXwzHM4fgId3gXdj2wmqsBvJWQUs3XWG73ee4UJmPkH+2tqFO7pXYO1CBZBSkn/gABmrVpHx61r0GRk4BQTgM3w4vqNG4ta6tdXPiZSQsNuQZXa5FjLr3eRyltmG7ax/zmpEKQhFhZHFxZyZ/H/k7d9P6I8/VPwfb+93sGoa3PoRdK9AOKyixiOlZO/ZdBZtj+NXw9qFG1o14J6oUG5sW311F/SFhWRv2kTGqtVkb94MOh2u7dvhN3IkPrfeilN9G6Rx0RVo2WX3L9Wyzep10KTT5ZBZTxsWWbIRSkEoKkzS7NmkfDaPJm++id/oURXrnJ0Mc7trb1b3roXqqHussDl6vWTlvnMs2BbHwXMZeLs6MaZ7EJMiQ6y/dqGC6FJTyfx1LRkrV5J/+LAWMnvDDVrI7I032iZkNjv5csjs+X3g4AQtB2n+ija3gJMNzmkDlIJQVIjsv//m7ANT8L39NgJnXTMF1tUsvx8Or4SHtkFAG6vLp6h+jl/I4vkVB9kTn0brRl7cHRXK6C5N8XSteXUXCk6eJGP1ajJWrUaXlISDj48WMjtyJO5dOtsmZPbiEa1s7oEfDSGzftDxNm3VdlD3Gh0yqxSEwmKKzp8ndvRtODVqROgPSyue3//kBvj+duj/LNz4nG2EVFQb+UXFzN14inmb/8XbzYkXh7Xntq5Na0XdBVlcTM6OHWSsWkXWuvXI/HycQ5ppWWZHjMQlqKn1T6ovhtObLofM6vKgXovLWWb9mln/nFVEKQiFRciiIuIn3U3ByZOE/rQM17AKJtMrzIFPI8HRVZs91JIptsI82/+9xAsrDhF7KYfbujblxWHtqWcDx3N1UJydQ9a6dWSsWnU5ZLZHDy1kdsgQ24TM5mfC0dWasigJmQ294XLIbA1ZE1QlBSGEuBVYK6XU20I4a6IURNW4+NbbpC5cSNMPP8DnlkqsWVj3Imz/WPM7hPaxvoCKaiEtp5BZa4/y054EQup7MGtUOH1b1T7na1loIbNryFixksL4eISbmxYyO3Iknr2jbBMymxavmZ/2m4bMDteUhZ1DZquqIL4DooDlwAIp5VHri2gdlIKoPJnr13Puken4T5xI4/+9WPEBEvfBlzdCl0kwYo7V5VPYHiklq/Yl8uovR8jMK2JKv+ZMH9gKN+e6Ee9fGikl+fv3k75qFZlrf7scMjtiOL4jbRkyG2MSMpuhhcxG3KGZoewQMltlE5MQwgcYj1bYRwILgCVSyixrClpVlIKoHIVnzhB7+xhcQkMJ+f47HFwqaEYo1sFXAzXn3LRd4O5nEzkVtuNMSi4vrDzI3ycv0TnYjzdvC6ddk7q3args9IWFZP+1iYyVK8n++2/Q6XBr3x7fUYaQ2YrUPLGUovwrQ2ZlMTTpbAiZHVNtIbNW8UEIIRoAdwGPAkeBlsAcKeXHVpKzyigFUXH0BQXEj59A4blzhC1fXjnHXfQn8MfzMHYhdBhtdRkVtqOoWM/XW2P5aMMJnBwceGpIG+6KDKm2tQw1EV1KihYyu2qVFjLr5KSFzI4ciddNN1b8BcoSspPh0E+GkNn9Wshsq8GaCar1UJv686pqYhoOTAZaAN8C30gpk4QQHsBRKWWNyWSlFETFOT9zJulLfyDos0/xvvHGig+QFq85psP6afmWakF0i0Jj/9l0nv35IEfPZzKofSNeHdmhzCR61yv5J06QuXo1GavXaCGzvr743DIUv1GjcOvUyXYhs/uXaD6L7AuGkNnbtZmFDUJmq6ogFqHVit5i5thAKeWf5fQdCsxGq0n9lZTyqlzPQogBaHWrnYFLUsr+lvYtjVIQFSNjzS8kPvUU9e//Pxo++WTFB5ASvh8D8dEwbSf4Vb44vaL6yC7Q8f6643yzPY4Ab1deGdGRoR1VKpTykMXF5EQbQmbXayGzLiEh+I4aie+IETg3tVXI7F+GkNlftJDZ+i21WUWE9UJmq6ogwoDzUsp8w7Y70EhKGXeNfo7ACWAQkADEAOOllEdM2vgB24GhUsozQoiGhtnJNfuaQykIyyn4919ix96BW7t2hCxcgHCuRIW3gz/B8v+DoW9B5EPWF1JhdTYcuchLqw5xPjOfSZEhPDmkDT5uqrpfRSjOzibrj3ValtmYGAA8evbEd2RJyGwFcpZZSn4mHFmlKYv4rdq+0Bu0WUX7EVUKma2qgtgN9JZSFhq2XYBtUsoe1+gXBcyUUg4xbD8HIKV806TNf4FAKeWLFe1rDqUgLEOfm0vcuHHoUlIJW/Ezzo0aVXyQ3FT4pCf4BsH9f9aZzJZ1laTMfGauOczagxdo08ibN24Lp1uIv73FqvUUJpwjc81qMlauuhwyO2iQFjIbFWmjkNk4k5DZ0+DsoYXMjpgLThX3j5SnICxZJ+9UohwApJSFBiVxLZoCZ022E4Bepdq0BpyFEJsAb2C2lHKRhX0BEEJMAaYANGtW81Yp1jSklFx45VUKTv1Ls6+/qpxyAFj/kqYk7vpZKYcajF4vWbzrDG//fowCnZ6nhrThgRua4+Kk8mNZA5egpjR46CHqT51K3r59WqGjtb+RuWYNTg0b4jtiOL6jRuHasqX1TuofCv2fhn5PaSGz+xZrqckroRyuhSUKIlkIMUJKuRpACDESuGRBP3OelNLTFSegGzAQcAeihRA7LOyr7ZTyC+AL0GYQFsh1XZOxfDkZq1bR4OGH8ezdu3KDxP4Ne7+FPjOgSYR1BVRYjRMXs3juZy1/Uu8W9Zk1OpywBjYwfygQQuDRpQseXbrQ6LnntJDZVatIWbCQlK++xq1DB3xHjsTn1mHWC5kVAoJ7aj82whIFMRX4XggxF+3BfRa424J+CYCp1zIISDTT5pKUMgfIEUJsATpZ2FdRQfKPHePCa6/j2TuKBg9NrdwgRfnwy6PgF6LlW1LUOPKLivn0r1N8tvlfPF2deG9sJ26vJfmT6gIOrq74DB2Cz9AhhpDZX0lfuZKLb7zBxXfewatfPy1k9sYBtgmZtSIVWQfhZWhv0eI4IYQTmqN5IHAOzdE8QUp52KRNO2AuMARwAXYBdwLHrtXXHMoHUTbF2dnE3n47Mi+fsBU/Vz5X/sZZsOUdzbTUcqB1hVRUmeh/U3hhxUFOX8phdJemvDisHfW9VE6smkD+8RNkrF5F5uo16JKTtZDZ/9yC38iRtguZtYCq+iAQQgwDOgBuJRchpXy1vD5SSp0Q4mHgD7RQ1flSysNCiKmG4/OklEeFEL8DBwA9WjjrIcM5r+priayKq5FScv6FFylKOEfIom8qrxySjsLWD7UQO6UcahTpuYW8sfYoP+5OoFk9D779v57c0CrA3mIpTHBr0xq3p56i4eOPk7M9WquKt2Il6UuW4hIaejlkNjDQ3qIasSSKaR7gAdwIfAWMAXZJKf/P9uJVDDWDME/qt99xcdYsGj71JPX/r5J/Nr0eFgyFSyfg4d21snJWXURKyer9ibz2yxHScot44IbmzBjYCncXFThQG9BCZv8gY+WqyyGzvXppIbODB9smZLYUVQ1zPSCljDD57QX8LKUcbAthq4JSEFeTt38/cXdNwqtvX4I+mYuobHW3mK/h18dh1GdaHV6F3TmbmsuLKw+x+UQynYL9eHN0OO0Dr5/8SXWNwoQEQ6GjVRTFn0G4u+M96Gb8Ro3Co1cv24TMUnUFsUtK2dMQXXQbkAIcklK2sr6oVUMpiCspTk/n9G23IYQDYT8vx9HXt3IDZZ7X1jwEdoa7V6t0GnZGV6xn/rZYPlh/AkcheGpIGyZFhV7X+ZPqElJK8vYaQmZ/+w19ZiZOjRpdDplt0cKq56uqD2KNYcXzu8A/aOGmX1pPPIUtkHo9ic8+hy75EqGLv6+8cgD47WkoLoRbP1LKwc4cSEjn2eUHOXI+k5vbafmTAv1U/qS6hBACj65d8OjahUbPP0f2X3+RsXIVKfMXkPLlV7h17Hg5ZNbftosdy51BCCEcgEgp5XbDtivgJqXMsKlUlUTNIC5z6csvSX7/Axq9+CL17ppY+YGO/QpLJ8DAl+CGJ6wnoKJC5BToeH/dCRZuj6WBlyuvjuzAkA6NVejqdYTu0iUtZHbVKgqOHNWyzPbvj++okXj171/pkNmqmpiipZRRlTpzNaMUhEZuTAzx996H9+BBNP3gg8o/RPIz4ZNeWn2HB7eAo8rZYw82HrvI/1Ye5lx6HndFNuPpoW1V/qTrnPzjJ7QoqDWrKU6+hFNAAC3/3ICohJKoqolpnRDidjTHtFqpXMPRXbrEucefwCUoiCavvVa1N8yNr2tFgO5YpJSDHUjKyueVNUf49cB5WjX04qepUXQPtUHhGkWtw61Na9yefoqGjz9GTnQ0hadPV0o5XAtLFMTjgCegE0Lko62mllJKFS5Rw5DFxZx76imKMzMJ/urLqhViT9gNu76Ang9AcLl5GRVWRq+XLI05y5u/HaVAp+fJwa2Z0q+Fyp+kuAphKGbEDTfYZPxrKggpZeXzyCqqlUuffEpu9A6azHodtzZtKj9QcRGsnq7Vyr3pf9YTUHFNTiVp+ZNi4tKIbF6PN0aH0zygCopeoagC11QQQoh+5vabKyCksB/ZW7dx6bPP8B09Gr/bb6/aYNs/hqTDcOdicFMTxeqgQFfMp3/9y6ebTuHh4sQ7YyIY2y1IOaEVdsUSE9NTJp/dgJ7AHuAmm0ikqDBFFy6Q+NRTuLZsSeOXqvjGn/IvbH5byy/fdph1BFSUy87TKTy34iCnk3MY1TmQF29tTwOVP0lRA7DExDTcdFsIEQy8YzOJFBVCFhVx7vEnkAUFNJ09Gwf3KsTESwm/PAaOLnDLu9YTUmGWjNwi3vztKEtjzhJcz51vJvekf2uVP0lRc7AoWV8pEoCO1hZEUTmSPvyIvH/+IfD993BtHla1wfYvgdjNMOwD8GliHQEVVyGlZM2B87y65jBpuUU82L85jw5srfInKWoclvggPuZysR4HoDOw34YyKSwk688/SZ0/H/8J4/EdVkVzUM4l+ON5CO4F3e6zjoCKqzibmsv/Vh1i0/FkIoJ8+WZyTzoEVmGVu0JhQyyZQZiuPNMBS6SU22wkj8JCChMSSHzuedw6dKDhs1Yo3PPH81CQDcNnQ2UT+inKRFesZ+H2ON5fdwIh4KVb23NPb5U/SVGzsURB/ATkSymLAYQQjkIIDyllrm1FU5SFvrCQczMeBSlpOvujqlelOvUnHPgB+j0NDdtZRUbFZQ4mZPDcigMcOpfJwLYNeXVUR5qq/EmKWoAlCuJP4GYg27DtDqwDKlnQWFFVkt56m/zDhwn6ZC4uQUFVG6wwV3NM12+pci1ZmZwCHR+uP8H8bbHU93Ll04lduaWjyp+kqD1YoiDcpJQlygEpZbYQwsOGMinKIXPtWtIWL6befffhPdAKVd02vwXp8XDvr+DsVvXxFAD8dSyJF1ce4lx6HhN6NeOZoW3xdVfpShS1C0sURI4QoquU8h8AIUQ3IM+2YinMUXA6lvMv/g/3Ll1o+PhjVR/w/AHYPhe6TILQvlUfT0FyVgGv/nKENfsTadnQi2VTo+ih8icpaimWKIhHgWVCiETDdhNgnCWDCyGGArPR6kp/JaV8q9TxAcAqINaw6+eSWtdCiDggCygGdGVlG7xe0OflcW7GDISrK00//ADhXMW3UX0xrJkOHvVgULnlxRUWoNdLftx9ljfWHiW/SM/jg1rzYP/muDqp0FVF7cWShXIxQoi2QBu0RH3HpJRF1+onhHAEPgEGoa2diBFCrJZSHinV9G8p5a1lDHOjlPLStc51PXDhtdcpOHWK4C+/xLlx46oPuOsLSNwLt3+tKQlFpTmVlM3zKw6yKzaVXmH1eOO2cFqo/EmKOoAl6yCmAd9LKQ8Ztv2FEOOllJ9eo2tP4JSU8rSh31JgJFBaQSiuQfryn8n4+Wca/PchvPr2scKAZ+HP16DlIOhYxbxN1zEFumI+2/Qvn/71L+4ujrxzewRju6v8SYq6gyUB7w9IKdNLNqSUacADFvRrCpw12U4w7CtNlBBivxDiNyFEB5P9Eq0WxR4hxJSyTiKEmCKE2C2E2J2cnGyBWLWL/OPHufDqq3hERtJg2rSqDygl/PoEIGHY+6qEaCXZFZvKf2b/zUcbTjK0Y2M2PN6fO3oEK+WgqFNY4oNwEEKIkmJBBtORJYH35v5TShcc+gcIMURG/QdYCbQyHOsjpUwUQjQE1gshjpnLICul/AL4ArSKchbIVWsozs7m3IxHcfTxoel77yIcrWDPPrISTv4Bg2eBf0jVx7vOyMgt4q3fj7Jk11mC/N1ZeF8PBrRpaG+xFAqbYImC+AP4UQgxD+0BPxX43YJ+CUCwyXYQkGjaQEqZafJ5rRDiUyFEAynlJSllomF/khBiBZrJ6rpJMS6l5MJLL1F45gwh3yzEqUGDqg+alwZrn4YmnaDX1KqPdx0hpeTXg+eZufoIqTkFTOnXnEdvboWHS2XSmSkUtQNLvt3PAA8CD6HNCtYBX1nQLwZoJYQIA84BdwITTBsIIRoDF6WUUgjRE83klSKE8AQcpJRZhs+Dgesq1CZt8WIy1/5GwOOP49HDShXdNsyE3EswcRk4qgebpSSk5fLSqsNsPJZEeFNfFt7Xg45NVf4kRd3HkigmPfCZ4cdipJQ6IcTDaDMQR2C+lPKwEGKq4fg8YAzwkBBCh7a24k6DsmgErDDYc52AxVJKS2YtdYK8gwe5+NbbePXvT/37/886g8Zvhz0LIephCOxsnTHrOMV6acifdBwp4cVh7bi3dyhOjipXleL6QBhcC2U3EKIV8CbQHq1gEABSyua2Fa3idO/eXe7evfvaDWswxRkZxN52O1LqCVu+HCd//6oPqiuAeX2hKB+m7QAXz6qPWcc5dC6D534+yMFzGdzUtiGvjuxAkL9KIKCoewgh9pS1zswSO8MC4GXgQ+BG4D7MO6AVVURKSeKzz1GUlETod99aRzkAbP0QLp2AiT8p5XANcgt1fLThJF9vjcXfw4W5E7owLLyJik5SXJdYoiDcpZR/GiKZ4oGZQoi/0ZSGwoqkzl9A9l9/0ej553Hv1Mk6gyYfh7/fh45joNUg64xZR9l0XMuflJCWx/iezXh2aFt8PVT+JMX1iyUKIl8I4QCcNPgUzgEqrs/K5O7ZQ9IHH+A9eDD+k+6yzqB6Pax5FJw9YOib1hmzDpKcVcBrvxxh9f5EWgR48uODUfQMU6vLFQpLczF5ANOB19DMTPfYUKbrDl1qKuceexznoKY0mfW69cwZexfBme0wYi54KZ1eGilL8icdI6+wmEdvbsVDA1qo/EkKhQGLcjEZPmaj+R8UVkQWF5P45FMUp6cT+vlSHL29rTNw1gVY9xKE3gBdrDQjqUP8m5zN8z8fZGdsKj1DtfxJLRuq/EkKhSkqGN7OXJo3j5zt22n82qu4tbNiNbffngFdPtz6kUqnYUKhTs+8zf8yd+Mp3JwdeOu2cO7oHoyDKv2pUFyFUhB2JGf7di7N/QTfkSPwGzPGegMf/01LqXHji9CgpfXGreXsjkvluZ8PcjIpm1sjmvDS8PY09FZFkhSKsrAkm2sfKeW2a+1TVIyii0mce/IpXFo0p/HLL1vP71CQBb8+CQHtoM8M64xZy8nIK+Lt34+xeOcZmvq5s+DeHtzYVvlkFIprYckM4mOgqwX7FBYidTrOPfE4+vx8QmbPxsHDiguwNs6CzHPwf+vAyZKcinUXKSW/HbrAy6sPk5JdwP19w3hsUGs8XdXEWaGwhDL/U4QQUUBvIEAI8bjJIR+01BmKSpI8ezZ5u/cQ+O67uLZoYb2BE/bAznnQ4/8guKf1xq2FJKbn8dKqQ2w4mkTHpj7Mv6cH4UEqf5JCURHKe5VyAbwMbUxDazLRcigpKkHWX3+R8uVX+I0bh+/wsgrpVYLiIlgzA7wbw8CXrDduLaNYL/lmexzvqfxJCkWVKVNBSCk3A5uFEAsNK6gxLJjzMk3TrbCcwoRzJD77HK7t29Ho+eesO3j0J3DxIIz7Dtyuzzflw4la/qQDCRkMaBPAayM7ElxP5U9SKCqLJcbYNw0ZWIuBPYCvEOIDKeW7thWtbqEvLOTcY49BcTFBH32Eg6ur9QZPPQ2b3oK2t0K74dYbt5aQV1jMRxtO8NXWWPw9nPl4fBdujahc/qSioiISEhLIz8+3gaQKhf1wc3MjKCgIZ2fL08dYoiDaSykzhRATgbVo9SH2AEpBVICkd94l/+BBms6ZjUuzZtYbWEr45XFwcIJb3rHeuLWEzSeSeXHlQc6m5nFnj2CevaUtfh6Vd84nJCTg7e1NaGioStCnqDNIKUlJSSEhIYGwsDCL+1miIJyFEM7AKGCulLJICFGnSnvamszffyftu++od889+AwebN3BD/wIp/+C/7wHvuZKftdNLmUX8PovR1i5L5HmAZ4snRJJZPP6VR43Pz9fKQdFnUMIQf369UlOTq5QP0sUxOdAHLAf2CKECEFzVCssoCA2lvMvvIh7p040fOLxa3eoCDkp8MdzENQDuk+27tg1FCkly/Yk8Mbao+QU6Jg+sBX/HdACN2frBdYp5aCoi1Tme21JLqY5wByTXfFCiBsrfKbrEH1+PucefQzh7EzTjz5EuFh5XcK6FyE/A4bPBoe6H3l8OjmbF1YcIvp0Cj1C/XljdDitGlkpd5VCobiKa8b+CSEaCSG+FkL8Zthuj4XZXIUQQ4UQx4UQp4QQz5o5PkAIkSGE2Gf4ecnSvrWBC6+/TsHx4wS+8zbOTZpYd/DTm2D/Ym21dKMO1h27hlGo0zN340mGzv6bQ4kZvDE6nB+mRCnloFDYGEuCwxei1ZUONGyfQEsBXi5CCEfgE+AWtHKl4w3KpTR/Syk7G35erWDfGkv6ipVk/LSc+lMfxKtfP+sOXpSn1Xmo1xz6PWXdsWsYe+JTufXjv3lv3QkGtW/En4/3Z0KvZiq5XgXx8tIy1SYmJjLGkPdr3759rF27tsJjzZw5k/fee8+q8tkCc9esqBhlKgghRIn5qYGU8kdADyCl1KGFvF6LnsApKeVpKWUhsBQYaaFcVelrd/JPnODCK6/g0bMnAQ8/bP0TbH4H0mK1TK3O7tYf387o9ZLTydm8uPIgt38WTXa+jq/v6c4nE7rS0Ecl16sKgYGB/PTTT0DlFURtw/SaFRWjPB/ELrR8SzlCiPqABBBCRAIZFozdFDhrsp0A9DLTLkoIsR9IBJ6UUh6uQF+EEFOAKQDNrBk+Wkn0OTmcm/EoDl5eNH3/PYSTlfP+XDgE2+dA54nQvL91x7YTSVn57D+bwf6z6exPSGf/2XQy83U4CPi/vmE8bqf8Sa+sOcyRROvGY7QP9OHl4eWbBEeNGsXZs2fJz89nxowZTJkyBS8vL6ZNm8aGDRvw9/fnjTfe4Omnn+bMmTN89NFHjBgxgoULF7JixQoKCgqIjY1lwoQJvPzylZWB4+LiuPXWW/nnn3946aWXyMvLY+vWrTz33HMcPXoULy8vnnzySQA6duzIL7/8QmhoKLNmzWLRokUEBwcTEBBAt27dAPj333+ZNm0aycnJeHh48OWXX9K2bVuz15WcnMzUqVM5c+YMAB999BF9+vRh5syZnDlzhtOnT3PmzBkeffRRpk+fDsCiRYt47733EEIQERHBt99+S3x8PJMnTyY5OZmAgAAWLFhAs2bNjNes0+kYOnToVdd86NAhFi5cyOrVq8nNzeXff/9l9OjRvPOOFh7+9ddf8/bbbxMYGEirVq1wdXVl7ty5lfgr1x3K+68rmcM/DqwGWgghtgEBWJZqw5wNoHR47D9AiJQyWwjxH2Al0MrCvtpOKb8AvgDo3r27XcNvpZScf+llCuPjabZgAU4BAdY9gb5YS6fh5guDX7fu2NVEVn4RB89lcCDBoBDOppOYoS1Kc3QQtGnkzbCIQDoH+9IrrD6hDTztLHH1M3/+fOrVq0deXh49evTg9ttvJycnhwEDBvD2228zevRoXnzxRdavX8+RI0e45557GDFiBAC7du3i0KFDeHh40KNHD4YNG0b37t2vOoeLiwuvvvoqu3fvNj4EZ86caVaePXv2sHTpUvbu3YtOp6Nr165GBTFlyhTmzZtHq1at2LlzJ//973/ZuHGj2XFmzJjBY489Rt++fTlz5gxDhgzh6NGjABw7doy//vqLrKws2rRpw0MPPcSJEyeYNWsW27Zto0GDBqSmpgLw8MMPc/fdd3PPPfcwf/58pk+fzsqVK5kxYwYPPfQQd999N5988kmZ93ffvn3s3bsXV1dX2rRpwyOPPIKjoyOvvfYa//zzD97e3tx00010slZd+FpMeQrCNEnfCrRFcgIoAG4GDlxj7AQg2GQ7CG2WYMQ0ZYeUcq0Q4lMhRANL+tZE0n/4gcxffyXg0Ufx7GWDZHkxX8O53XDbl+BR82smF+r0HL+QxT7DrGD/2XROJWcjDWq8WT0PuoXWY3KQL52D/egQ6Iu7S82JxrrWm76tmDNnDitWrADg7NmznDx5EhcXF+NbcXh4OK6urjg7OxMeHk5cXJyx76BBg6hfX1sPctttt7F161azCqIi/P3334wePRoPQ9bhEmWUnZ3N9u3bGTt2rLFtQUFBmeNs2LCBI0eOGLczMzPJysoCYNiwYbi6uuLq6krDhg25ePEiGzduZMyYMTRo0ACAevW073x0dDQ///wzAJMmTeLpp58GYNu2bSxfvty4/5lnnjErx8CBA/H11dLRtG/fnvj4eC5dukT//v2N5xg7diwnTpyoyG2qk5SnIBzRkvWVfpu3NLlNDNBKCBEGnAPuBCaYNhBCNAYuSimlEKInmk8kBUi/Vt+aRt6hw1yc9QaeN9xA/SkPWP8EGQnw5yvQ4iYIH3vt9tWMlJK4lFz2n01nn8FUdDgxk0KdHoD6ni50Cvbj1ohAOgX7EhHkRz3P6zsduTk2bdrEhg0biI6OxsPDgwEDBpCfn4+zs7Mxjt3BwQFXQ6oWBwcHdDqdsX/pWPeKxL47OTmh1+uN26bpRsyNo9fr8fPzY9++fRaNr9friY6Oxt39ar+Zq0nqGUdHR3Q6HVJKi+Q3bWNJ+7LOpbia8hTE+ZKoosogpdQJIR5Gi4ByBOZLKQ8b8johpZyHZqp6SAihA/KAO6X2lzLbt7Ky2JrizEzOPfoojvXrE/jO2wgHK2cOlRLWPqWZmIZ9UCNKiJb4DQ4kaArhQEIGGXlFALg7OxLe1Jd7okLoFOxHpyA/gvzd1QI0C8jIyMDf3x8PDw+OHTvGjh07KtR//fr1pKam4u7uzsqVK5k/f36Zbb29vY1v8AChoaH88ssvAPzzzz/ExsYC0K9fP+69916effZZdDoda9as4cEHH8THx4ewsDCWLVvG2LFjkVJy4MCBMk0zgwcPZu7cuTz1lBZ5t2/fPjp37lymfAMHDmT06NE89thj1K9fn9TUVOrVq0fv3r1ZunQpkyZN4vvvv6dv374A9OnTh6VLl3LXXXfx/fffV+i+9ezZk8cee4y0tDS8vb1Zvnw54eHhFRqjLmKJD6LSSCnXopmmTPfNM/k8FzDrBTLXtyYipSTx+ecpunCBkG8X4eTvb/2THF0Dx9fCoFehnuV5VKxFdoGOgwkZRgeyOb/Bf8Ib0ynIj07BfrRq6KXSa1eSoUOHMm/ePCIiImjTpg2RkZEV6t+3b18mTZrEqVOnmDBhQrnmpRtvvJG33nqLzp0789xzz3H77bezaNEiOnfuTI8ePWjdujUAXbt2Zdy4cXTu3JmQkBBuuOEG4xjff/89Dz30EK+//jpFRUXceeedZSqIOXPmMG3aNCIiItDpdPTr14958+aZbQvQoUMHXnjhBfr374+joyNdunRh4cKFzJkzh8mTJ/Puu+8andQAs2fPZsKECcyePZvbb7+9QvetadOmPP/88/Tq1YvAwEDat29vNENdz4iyplZCiHpSytRqlqdKdO/eXe7evbtaz5myYCFJb79Nw2efof6991r/BPkZMLcneAXAA5vA0bbRPEXFBr+BQRHsT0jnZNKVfgNtVlAz/QZV5ejRo7Rr187eYlSKhQsXXuF0VlSM7OxsvLy80Ol0jB49msmTJzN69Gh7i2VVzH2/hRB7pJRm3yTKqwdRq5SDPcj9Zy9J77+P96CbqXePRYvLK86GmZCTBOMXW105XMtvUM/ThU5BvvwnvInRVKT8Boq6ysyZM9mwYQP5+fkMHjyYUaNG2Vsku1PmDKI2Up0zCF1aGrGjb0M4OxO2/CccfXysf5L4aFgwFCL/C0PfrPJwyVkFxllBWX6DEgdy5+Dr029Qm2cQNYVZs2axbNmyK/aNHTuWF154wU4SKUqw2gxCUTZSryfxqacpTk0lZMli2ygHXYG25sE3GG6s+D9WdoGOQ+dMF59lcC49D9D8Bq2V30BhI1544QWlDOoISkFUgpTPPydn61Yaz5yJewcbxcpvmw2XjsOEH8HVq9ymlvgNujTz474+oXQK9qNDoA8eLupPr1Aoykc9JSpIzo4dJH88F5/hw/Ebd4dtTnLpJGx5FzrcBq2HXHFISkl8Sq7RTLT/rOY3KFB+A4VCYWWUgqgARUlJnHvyKVzCwmgy82Xb2Of1es205OwOQ98y+g0OJKSzz5CeosRv4ObsQHhTXyZFausNrle/gUKhsA1KQViI1OlIfOJJ9Dk5hCxcgIOn9XME5RTouLDpC1rEb+O7hk/w2SeHjX4DBwFtGvtwS8fGxplB60bKb6BQKGyHUhAWkjznY3JjYgh8+y1cW7as8nglfoPLi88ySEtKYL3La+yUbfkiq7fyGygqjWkG05rMvffey6233sqYMWO4//77efzxx2nfvlaVfqnTqCeOBWRv3kzKF1/gN3YMviMrXpbiWn4Dfw9nOgX7Mdt5Bd6pRbS+52u2hHS09mUoFDWar776yt4iKEqhFMQ1KEpMJPHpZ3Bt25ZGFobuJWcVcMAwM9iXoOUrSs+9ht/g5HpYvA4GPI+/Ug41g9+ehQsHrTtm43C45a1ym5RVD2LGjBn88ssvuLu7s2rVKho1asS///7LxIkTKS4u5pZbbuGDDz4gOzv7ivGKi4t59tln2bRpEwUFBUybNo0HH3ywzPO/++67/PjjjxQUFDB69GheeeUV4uLiuOWWW+jbty/bt2+nadOmrFq1Cnd3d06dOsXUqVNJTk7G0dGRZcuW0bx5c55++ml+++03hBC8+OKLjBs3DikljzzyCBs3biQsLOyKJHkDBgzgvffeo3v37lW6XoX1UAbscpCFhSQ89hhSpyPoow9xcLu6mllOgY6dp1P4Ysu/TPv+H/q8tZEeszbwf9/sZu5fp0jKzGdoh8a8eVs4a6ffwKGZQ1g2tTcv3tqe4Z0CCa7ngSjMgV+fgAZtoO+j1X+hihrF/Pnz2bNnD7t372bOnDmkpKSQk5NDZGQk+/fvp1+/fnz55ZeAVmNhxowZxMTEEBgYaHa8r7/+Gl9fX2JiYoiJieHLL780JuIrzbp16zh58iS7du1i37597Nmzhy1btgBw8uRJpk2bxuHDh/Hz8zOm1p44cSLTpk1j//79bN++nSZNmvDzzz+zb98+9u/fz4YNG3jqqac4f/48K1as4Pjx4xw8eJAvv/yS7du3m5WjKtersB5qBlEOF997j/z9B2j60Ue4hIaa9RucTMpCb3gJCvJ3p3MzP+7trfkNOja10G+w6U3IOAP3/Q5Ortdur6gervGmbyvKqgdx6623AtCtWzfWr18PaLURVq5cCcCECROM1eBMWbduHQcOHDCW3czIyODkyZOEhV2d+HHdunWsW7eOLl26AFp+opMnT9KsWTPCwsKM2Ve7detGXFwcWVlZnDt3zpizyM3wErV161bGjx+Po6MjjRo1on///sTExLBlyxbj/sDAQG666Saz96Aq16uwHkpBlEHGH3+Qtuhb0oaOZllRMPs/286hcxlX+Q2GdmxM52A/IoJ8qe9ViYd74l7Y8Sl0uw9Coqx8FYrahiX1IEpqGFiKlJKPP/6YIUOGWNT2ueeeu8oEFRcXd1Udhby8vDLrKJSXwseSMOyqXK/CeigTk4FL2QX8efQiH6w/wYz313DqyWc55h/M3S69WLwrHgHcFRnCnPFd2PLUjfzzv0EsvK8njw1qzY1tG1ZOORTrYPV08AyAm2da+5IUtZCK1oOIjIw0mnqWLl1qts2QIUP47LPPKCrS/GAnTpwgJyenzLbz58832vXPnTtHUlJSmef38fEhKCjI+FZfUFBAbm4u/fr144cffqC4uJjk5GS2bNlCz5496devH0uXLqW4uJjz58/z119/lXt9lblehfW47mcQhTo9Az/YxNlUbb2Bm76Ij7d9iqOTI7oXZ7GqS2taN/LG2RbrDXZ+BhcOwNhvwN3P+uMrah0VrQfx0Ucfcdddd/H+++8zbNgwszUM7r//fuLi4ujatStSSgICAowP9NIMHjyYo0ePEhWlzWa9vLz47rvvcHQsO6X7t99+y4MPPshLL72Es7Mzy5YtY/To0URHR9OpUyeEELzzzjs0btyY0aNHs3HjRsLDw2ndujX9+/e3/OZYeL0K66GyuQKvrjlCE183OgX70eTrD8n+6SeC5n2G94AB1heyhLQ4+DQKwvrD+CU1okqcovZlc83NzcXdXVs9v3TpUpYsWcKqVavsLZbNuN6u19qobK6V4KXh2sKcjNWrSfzpJ+o/8IBtlYOUWtSScIBh7ynloKg0e/bs4eGHH0ZKiZ+fX7klRusC19v12hubKgghxFBgNlpd6a+klGbDQoQQPYAdwDgp5U+GfXFAFlAM6MrScNai4NQpzr88E4/u3QmYMd2Wp4JDy+HUBhj6NvgG2fZcijrNDTfcwP79+yvc7+DBg0yaNOmKfa6uruzcudNaotmEyl6vonLYTEEIIRyBT4BBQAIQI4RYLaU8Yqbd28AfZoa5UUp5yVYylqDPySFhxqM4eHgQ+MH7CCcb6s3cVPjtGQjsCj0fsN15FIpyCA8PZ9++ffYWQ1HDsWUUU0/glJTytJSyEFgKmMtT8QiwHCg7VMKGSCk5P/MVCk+fpun77+HcsKFtT7j+f5CXBiPmgEPdqeWsUCjqHrZUEE2BsybbCYZ9RoQQTYHRwDwz/SWwTgixRwgxpayTCCGmCCF2CyF2JycnV1hIfUYG+QcP0uCRh/G8RsRIlYndAnu/g96PaCkXFAqFogZjSx+EOc9r6ZCpj4BnpJTFZhbP9JFSJgohGgLrhRDHpJRbrhpQyi+AL0CLYqqokI5+foQt/wnh7l7RrhWjKA/WPAr+odD/GdueS6FQKKyALRVEAhBssh0EJJZq0x1YalAODYD/CCF0UsqVUspEACllkhBiBZrJ6ioFYQ1sUdvhKra8B6n/wqQV4OJh+/MpFApFFbGliSkGaCWECBNCuAB3AqtNG0gpw6SUoVLKUOAn4L9SypVCCE8hhDeAEMITGAzU7MT25XHxCGz7CCLuhBbmc88oFNZk06ZNxlxGq1ev5q23qp5XauHChSQmln7Hu3a7+++/nyNHjpTTo2bj5aXVhE9MTGTMmDF2lqZ6sdkMQkqpE0I8jBad5AjMl1IeFkJMNRw353cooRGwwjCzcAIWSyl/t5WsNkWvhzXTwdUHhsyytzSK65ARI0YwYsQIi9rqdDqcyojiW7hwIR07drxmFtXS7epKnYfAwEBjwsPrBZuug5BSrgXWltpnVjFIKe81+Xwa6GRL2aqN3V9DQgyMmgeeDewtjaICvL3rbY6lHrPqmG3rteWZnmX7oOLi4hg6dCi9evVi7969tG7dmkWLFvHee++xZs0a8vLy6N27N59//jlCiCtqKFy6dInu3bsTFxd3xZgLFy5k9+7dzJ071+w57733XurVq8fevXvp2rUrkyZNYurUqeTm5tKiRQvmz5/Pn3/+ye7du5k4cSLu7u5ER0fz7rvvXiXT8uXLr2p3yy23GGVcsmQJb7zxBlJKhg0bxttvvw1QZv0HcyQnJzN16lTOnDkDaOk3+vTpw8yZMzlz5gynT5/mzJkzPProo0yfrq1pKrmHQggiIiL49ttviY+PZ/LkySQnJxMQEMCCBQto1qwZsbGxTJgwAZ1Ox9ChQ6/425RU6Vu4cCGrV68mNzeXf//9l9GjR/POO+8AWnr1t99+m8DAQFq1aoWrq2uZ976mo5L12ZLMRNjwCjQfAJ3utLc0ilrC8ePHmTJlCgcOHMDHx4dPP/2Uhx9+mJiYGA4dOkReXh6//PKLVc954sQJNmzYwPvvv8/dd9/N22+/zYEDBwgPD+eVV15hzJgxdO/ene+//559+/bh7u5uViZz7UpITEzkmWeeYePGjezbt4+YmBhjTqiy6j+YY8aMGTz22GPExMSwfPly7r//fuOxY8eO8ccff7Br1y5eeeUVioqKOHz4MLNmzWLjxo3s37+f2bNnA/Dwww9z9913c+DAASZOnGhUJjNmzOChhx4iJiaGxo0blynHvn37+OGHHzh48CA//PADZ8+eJTExkddee40dO3awfv16jh2z7gtGdaNSbdiStU+Bvghu/VCl06iFlPemb0uCg4Pp06cPAHfddRdz5swhLCyMd955h9zcXFJTU+nQoQPDhw+32jnHjh2Lo6MjGRkZpKenG5Po3XPPPYwdO9Zsn7/++qtCMsXExDBgwAACAgIArdDQli1bGDVqVJn1H8yxYcOGK3wamZmZZGVlATBs2DBcXV1xdXWlYcOGXLx4kY0bNzJmzBgaNNBm8PXq1QO02hI///wzAJMmTeLpp58GYNu2bcaMsZMmTeKZZ8x/DwYOHGhMFti+fXvi4+O5dOkS/fv3N55j7NixnDhxosxrqekoBWErjq6BY79oabzrNbe3NIpaROmQbyEE//3vf9m9ezfBwcHMnDmT/Px8AJycnNDrtRolJfsqg2cFI/ny8/PLlKksyksMWpH6D3q9nujo6CtmJyWUrlmh0+mQUlpUg8K0jSXtyzpXXUKZmGxBfqY2e2jUEaIetrc0ilrGmTNniI6OBmDJkiX07dsXgAYNGpCdnX2FozQ0NJQ9e/YAWMWB6uvri7+/P3///TegpfIumU14e3sb39RLlIE5mUzbmdKrVy82b97MpUuXKC4uZsmSJRVO9w1aSnJTm/61UoYMHDiQH3/8kZSUFABSU1MB6N27t7GmxPfff2+8z3369Llif0Xo2bMnmzdvJi0tDZ1OZ5yJ1FbUDMIW/PkqZF2Acd+Do7O9pVHUMtq1a8c333zDgw8+SKtWrXjooYdIS0sjPDyc0NBQevToYWz75JNPcscdd/Dtt9+WWb6zonzzzTdGJ3Xz5s1ZsGABoDmzp06danQ+P/DAA2ZlKt2uhCZNmvDmm29y4403IqXkP//5DyNHmsu+Uz5z5sxh2rRpREREoNPp6NevH/PmlR0U2aFDB1544QX69++Po6MjXbp0YeHChcyZM4fJkyfz7rvvGp3UALNnz2bChAnMnj2b22+/vUKyNW3alOeff55evXoRGBhI+/bta3XNClUPwtqc3QVfD4ZeD8Itb9tXFkWFsXc9CNNIGUXtJDs7Gy8vL3Q6HaNHj2by5MnGmt32pqL1IJSJyZroCmHNDPAJhJtetLc0CoXCDsycOZPOnTvTsWNHwsLCGDVqlL1FqjTKxGRNts+BpCMwfim4ettbGkUtJDQ01Gazh1mzZrFs2bIr9o0dO5YXXnjBJuerKrVN3hLee+89e4tgNZSJyVqk/KuVEG0zFO5YZB8ZFFXG3iYmhcKWKBOTPZBSMy05ucEt79hbGoVCobAKysRkDfYthri/tQVx3mWvvFQoFIrahJpBVJXsZFj3AgRHQtd77S2NQqFQWA2lIKrKH89DQTYMnw0O6nYqFIq6g3qiVYVTG+Dgj3DD49Cwrb2lUdQRSuoPABw+fJibbrqJ1q1b06JFC15++WVjao2FCxcSEBBA586dad++fbkJ7qqb0NBQLl26BGgrlhW1E+WDqCyFOfDLY1C/FfR93N7SKGzAhTfeoOCodbNxurZrS+Pnn7eobV5eHiNGjOCzzz5j8ODB5ObmcvvttzN79mwee+wxAMaNG8fcuXNJSkqiQ4cOjBgxosw02fZi+/bt9hZBUUnUDKKybHoL0s/A8I/A2c3e0ijqIIsXL6ZPnz4MHjwYAA8PD+bOncu77757VduGDRvSokUL4uPjzY6Vk5PD5MmT6dGjB126dGHVqlWANgu57bbbGDp0KK1atTJmNAX4/fff6dq1K506dWLgwIGAlsdo1KhRREREEBkZyYEDBwBISUlh8ODBdOnShQcffPCKpHUlM6JNmzYxYMAAxowZQ9u2bZk4caKx3dq1a2nbti19+/Zl+vTpxsyuCvuiZhCV4fx+iP4Eut4NoX3tLY3CRlj6pm8rDh8+TLdu3a7Y16JFC/Ly8khPT79i/+nTpzl9+jQtW7Y0O9asWbO46aabmD9/Punp6fTs2ZObb74Z0JLd7d27F1dXV9q0acMjjzyCm5sbDzzwAFu2bCEsLMyY4O7ll1+mS5curFy5ko0bN3L33Xezb98+XnnlFfr27ctLL73Er7/+yhdffGFWjr1793L48GECAwPp06cP27Zto3v37jz44IPGc40fP76Kd05hLZSCqCjFOlg9HTzqw6BX7S2Nog5TVppq07fzH374ga1bt+Lq6srnn39urENQmnXr1rF69WrjKt/8/HxjRTZzdQ3S0tLo168fYWFhwOUaClu3bjVmKL3ppptISUkhIyODLVu2GGsrDBs2DH9/f7Ny9OzZk6CgIAA6d+5MXFwcXl5eNG/e3Hiu8ePHl6lgFNWLTRWEEGIoMButJvVXUkqzldOFED2AHcA4KeVPFelb7ez6HM7vgzHzwd38P4FCYQ06dOjAli1brth3+vRpGjRogJ+fH3DZB3EtpJQsX76cNm3aXLF/586dFaqhYC7zQkk7VUOh7mEzH4QQwhH4BLgFaA+MF0K0L6Pd28AfFe1b7aTFw8bXodVg6HCbvaVR1HEmTpzI1q1b2bBhA6A5radPn84rr7xS4bGGDBnCxx9/bHwY7927t9z2UVFRbN68mdjYWOByDYV+/foZayRs2rSJBg0a4OPjc8X+3377jbS0NItla9u2LadPnzbW0v7hhx8qdG0K22FLJ3VP4JSU8rSUshBYCphL/v4IsBxIqkTf6kNK+PUJ7fOw91UJUYXNcXd3Z/Xq1cyaNYvWrVvToEED+vTpw8SJEys81v/+9z+KioqIiIigY8eO/O9//yu3fUBAAF988QW33XYbnTp1Yty4cYCWqXT37t1ERETw7LPP8s033wCab2LLli107dqVdevW0axZswpd56effsrQoUPp27cvjRo1qtU1FOoUUkqb/ABj0ExDJduTgLml2jQFNqOZkRYCYyzta3JsCrAb2N2sWTNpMw7+JOXLPlJun2u7cyjszpEjR+wtQpmsWLFChoWFybi4OHuLYnWysrKklFLq9Xr50EMPyQ8++MDOEtVNzH2/gd2yjOe4LWcQ5l6xSxsbPwKekVIWV6KvtlPKL6SU3aWU3UuKoVudvDT47Rlo0hl6PmibcygU12DUqFGcPn2akJAQe4tidb788ks6d+5Mhw4dyMjI4MEH1f9ZTcCWTuoEINhkOwhILNWmO7DU4NxqAPxHCKGzsG/1sf4lyE2Fu5aDowr8UtRcFixYwOzZs6/Y16dPHz755BM7SWQZjz32mHHxn6LmYMunXQzQSggRBpwD7gQmmDaQUoaVfBZCLAR+kVKuFEI4XatvtRG3Ff5ZBL0fgSad7CKCQmEp9913H/fdd5+9xVDUEWymIKSUOiHEw2jRSY7AfCnlYSHEVMPxMquMl9XXVrKWSVE+rHkU/EJgwHPVfnqFQqGwJza1l0gp1wJrS+0zqxiklPdeq2+1s/UDSDmpmZZcPO0qikKhUFQ3KhdTWSQdg78/gPA7oOXN9pZGoVAoqh2lIMyh12slRF29YMgb9pZGoVAo7IJSEOb4ZyGc3QGDZ4GXjUJnFQo7c++99/LTTz/Z7fybNm2yWSrwil5bXFwcHTt2tIkslWHAgAHs3r0bgP/85z9XJWesLlTMZmkyz8P6lyH0Buhsn8ApRc3g7x9PcOlstlXHbBDsxQ13tLbqmLWVTZs24eXlpQoKXYO1a+3nilUziNL8/gzoCrQSoiqdhsIOLFq0iIiICDp16sSkSZOIj49n4MCBREREMHDgQGMW1nvvvZeHHnqIG2+8kebNm7N582YmT55Mu3btuPfee43jeXl58cQTT9C1a1cGDhxIcnLyVefcs2cP/fv3p1u3bgwZMoTz58+TkZFBmzZtOH78OKBlWS2vat26deuIioqia9eujB07luxsTbmGhoby8ssv07VrV8LDwzl27BhxcXHMmzePDz/8kM6dO/P333+zZs0aevXqRZcuXbj55pu5ePEioKX3mDx5MgMGDKB58+bMmTPHeM7XXnuNtm3bMmjQIMaPH2/MVnutayvZ36lTJ6Kioq65TqS4uJinnnqKHj16EBERweeffw6UX+MiJiaG3r1706lTJ3r27ElWVhb5+fncd999hIeH06VLF/766y9Ay7N15513EhERwbhx48jLyzOeu6Q6X1xcHO3ateOBBx6gQ4cODB482NguJiaGiIgIoqKieOqpp6w3GypriXVt/OnWrZvla87NcfRXLZ3G5nerNo6i1mLvVBuHDh2SrVu3lsnJyVJKKVNSUuStt94qFy5cKKWU8uuvv5YjR46UUkp5zz33yHHjxkm9Xi9Xrlwpvb295YEDB2RxcbHs2rWr3Lt3r5RSSkB+9913UkopX3nlFTlt2jRj/2XLlsnCwkIZFRUlk5KSpJRSLl26VN53331SSinXrVsnIyMj5ZIlS+SQIUPKlDs5OVnecMMNMjs7W0op5VtvvSVfeeUVKaWUISEhcs6cOVJKKT/55BP5f//3f1JKKV9++WX57ruX/9dSU1OlXq+XUkr55Zdfyscff9zYLioqSubn58vk5GRZr149WVhYKGNiYmSnTp1kbm6uzMzMlC1btjSOZ8m1hYeHy02bNkkppXzyySdlhw4dyry+zz//XL722mtSSinz8/Nlt27d5OnTp+Vff/0lfXx85NmzZ2VxcbGMjIyUf//9tywoKJBhYWFy165dUkopMzIyZFFRkXzvvffkvffeK6WU8ujRozI4OFjm5eXJ999/3yjX/v37paOjo4yJiTHev+TkZBkbGysdHR2Nf9exY8fKb7/9VkopZYcOHeS2bduklFI+88wzZV5LRVNtKBNTCQVZsPZJaNgeek+3tzSK65SNGzcyZswYGjRoAGh1GKKjo421FiZNmnRF1bfhw4cjhCA8PJxGjRoRHh4OaKnC4+Li6Ny5Mw4ODsZke3fddRe33XZlJuLjx49z6NAhBg0aBGhvy02aNAFg0KBBLFu2jGnTprF///4y5d6xYwdHjhyhT58+ABQWFhIVFWU8XnLObt26Ga+lNAkJCYwbN47z589TWFhorA8BWo0JV1dXXF1dadiwIRcvXmTr1q2MHDkSd3d3470oTVnXlpGRQXp6Ov379zfe199++63M61u3bh0HDhww+jUyMjI4efIkLi4uZmtc+Pr60qRJE3r06AGAj48PoNXTeOSRRwAti21ISAgnTpxgy5YtTJ+uPXciIiKIiIgwK0dYWBidO3c23su4uDjS09PJysoymuomTJjAL7/8Uua1VASlIErY+DpkJsLYheDkYm9pFNcpsow6DKaYHi+pr+Dg4HBFrQUHBwd0Ot01+5ecs0OHDkRHR1/VVq/Xc/ToUdzd3UlNTTU+CM3JPWjQIJYsWWL2eIlsJTUgzPHII4/w+OOPM2LECDZt2sTMmTOv6m86hrSgjkRZ15aenm5R/QrTcT7++GOGDBlyxf5NmzZVuZ5GCZWpp5GXl2fTehrKBwGQsAd2fg497ofgnvaWRnEdM3DgQH788UdSUlIArQ5D7969Wbp0KQDff/89fftWrMytXq83vvkuXrz4qv5t2rQhOTnZ+BAtKiri8GEtccGHH35Iu3btWLJkCZMnT6aoqMjsOSIjI9m2bRunTp0CIDc3lxMnTpQrl7e3N1lZWcbtjIwMmjZtCmBMI14effv2Zc2aNeTn55Odnc2vv/56VZuyrs3Pzw9fX1+2bt0KYKxlURZDhgzhs88+M17/iRMnyMnJKbN927ZtSUxMJCYmBoCsrCx0Ot0VdTNOnDjBmTNnaNOmzRX7Dx06ZKz1bQn+/v54e3uzY8cOAON3xRqoGURxEayZDt5NYOBL9pZGcZ3ToUMHXnjhBfr374+joyNdunRhzpw5TJ48mXfffZeAgAAWLFhQoTE9PT2N9a19fX2vKsjj4uLCTz/9xPTp08nIyECn0/Hoo4/i7OzMV199xa5du/D29qZfv368/vrrZgsWBQQEsHDhQsaPH09BQQEAr7/+Oq1blx2xNXz4cMaMGcOqVav4+OOPmTlzJmPHjqVp06ZERkYaixWVRY8ePRgxYgSdOnUiJCSE7t27X1VHoqxr69ChAwsWLGDy5Ml4eHhcNTMozf33309cXBxdu3ZFSklAQAArV64ss72Liws//PADjzzyCHl5ebi7u7Nhwwb++9//MnXqVMLDw3FycmLhwoW4urry0EMPcd999xEREUHnzp3p2bNiL6pff/01DzzwAJ6engwYMMBq9TSELacn1U337t1lSeywxRRkwW/PQptboN2tthFMUWs4evQo7dq1s7cYVsXLy8sYUVTXyM7OxsvLi9zcXPr168cXX3xB165d7S1WtVNyHwDeeustzp8/f1VWXzD//RZC7JFSdjc3rppBuHrDqJqdClmhUJhnypQpHDlyhPz8fO65557rUjkA/Prrr7z55pvodDpCQkJYuHChVcZVCkKhqONYe/bQq1cvoxmphG+//dYYQVWdLF682Krj/fHHHzzzzDNX7AsLC2PFihVWPY+1GTdunDFSzZooBaFQlMKSSKLrmZ07d9pbBJsxZMiQa/ojaiuVcSeoKCaFwgQ3NzdSUlJsGjqoUFQ3UkpSUlJwc3OrUD81g1AoTAgKCiIhIcFsOgqFojbj5uZW5jqWslAKQqEwwdnZ+YoVvArF9YwyMSkUCoXCLEpBKBQKhcIsSkEoFAqFwix1aiW1ECIZiK9k9wbAJSuKY0/qyrXUlesAdS01kbpyHVC1awmRUpotnVmnFERVEELsLmu5eW2jrlxLXbkOUNdSE6kr1wG2uxZlYlIoFAqFWZSCUCgUCoVZlIK4zBf2FsCK1JVrqSvXAepaaiJ15TrARteifBAKhUKhMIuaQSgUCoXCLEpBKBQKhcIs172CEEIMFUIcF0KcEkI8a295KosQYr4QIkkIccjeslQVIUSwEOIvIcRRIcRhIcQMe8tUWYQQbkKIXUKI/YZrubpeZy1CCOEohNgrhPjF3rJUBSFEnBDioBBinxCigmUoaxZCCD8hxE9CiGOG/5koq419PfsghBCOwAlgEJAAxADjpZRH7CpYJRBC9AOygUVSyo72lqcqCCGaAE2klP8IIbyBPcCoWvp3EYCnlDJbCOEMbAVmSCl32Fm0SiGEeBzoDvhIKWttjV4hRBzQXUpZ6xfKCSG+Af6WUn4lhHABPKSU6dYY+3qfQfQETkkpT0spC4GlwEg7y1QppJRbgFR7y2ENpJTnpZT/GD5nAUeBpvaVqnJIjZKSbs6Gn1r5ViaECAKGAV/ZWxaFhhDCB+gHfA0gpSy0lnIApSCaAmdNthOopQ+iuooQIhToAtTaMmYGs8w+IAlYL6WsrdfyEfA0oLezHNZAAuuEEHuEEFPsLUwVaA4kAwsMpr+vhBCe1hr8elcQ5upK1sq3u7qIEMILWA48KqXMtLc8lUVKWSyl7AwEAT2FELXOBCiEuBVIklLusbcsVqKPlLIrcAswzWCirY04AV2Bz6SUXYAcwGq+1OtdQSQAwSbbQUCinWRRmGCw1y8HvpdS/mxveayBYeq/CRhqX0kqRR9ghMF2vxS4SQjxnX1FqjxSykTD7yRgBZq5uTaSACSYzEp/QlMYVuF6VxAxQCshRJjBuXMnsNrOMl33GBy7XwNHpZQf2FueqiCECBBC+Bk+uwM3A8fsKlQlkFI+J6UMklKGov2fbJRS3mVnsSqFEMLTEPyAwRwzGKiV0X9SygvAWSFEG8OugYDVgjmu65KjUkqdEOJh4A/AEZgvpTxsZ7EqhRBiCTAAaCCESABellJ+bV+pKk0fYBJw0GC7B3heSrnWfiJVmibAN4aIOQfgRyllrQ4RrQM0AlZo7yE4AYullL/bV6Qq8QjwveEl9zRwn7UGvq7DXBUKhUJRNte7iUmhUCgUZaAUhEKhUCjMohSEQqFQKMyiFIRCoVAozKIUhEKhUCjMohSEQmEGIUS24XeoEGKClcd+vtT2dmuOr1BYC6UgFIryCQUqpCAMax7K4woFIaXsXUGZFIpqQSkIhaJ83gJuMNQNeMyQeO9dIUSMEOKAEOJBACHEAEMNi8XAQcO+lYZkcIdLEsIJId4C3A3jfW/YVzJbEYaxDxlqFYwzGXuTSc7/7w2rzRUKm3Jdr6RWKCzgWeDJktoHhgd9hpSyhxDCFdgmhFhnaNsT6CiljDVsT5ZSphpSbMQIIZZLKZ8VQjxsSN5XmtuAzkAnoIGhzxbDsS5AB7RcYdvQVptvtfbFKhSmqBmEQlExBgN3G1KA7ATqA60Mx3aZKAeA6UKI/cAOtKSQrSifvsASQ/bXi8BmoIfJ2AlSSj2wD830pVDYFDWDUCgqhgAekVL+ccVOIQagpVo23b4ZiJJS5gohNgFuFoxdFgUmn4tR/7uKakDNIBSK8skCvE22/wAeMqQjRwjRuowCLb5AmkE5tAUiTY4VlfQvxRZgnMHPEYBWKWyXVa5CoagE6i1EoSifA4DOYCpaCMxGM+/8Y3AUJwOjzPT7HZgqhDgAHEczM5XwBXBACPGPlHKiyf4VQBSwH61w1dNSygsGBaNQVDsqm6tCoVAozKJMTAqFQqEwi1IQCoVCoTCLUhAKhUKhMItSEAqFQqEwi1IQCoVCoTCLUhAKhUKhMItSEAqFQqEwy/8DOOBa7IFG/2IAAAAASUVORK5CYII=\n", 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", 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    " ] @@ -1196,34 +1174,42 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 29, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/fluid/dygraph/math_op_patch.py:276: UserWarning: The dtype of left and right variables are not the same, left dtype is paddle.float32, but right dtype is paddle.int64, the right dtype will convert to paddle.float32\n", + " warnings.warn(\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "epoch: 0 iter: 0 loss: 0.3372 train acc: 0.5000 test acc: 0.5000\n", - "epoch: 0 iter: 5 loss: 0.2687 train acc: 0.2500 test acc: 0.5500\n", - "epoch: 0 iter: 10 loss: 0.0781 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 0 iter: 15 loss: 0.0786 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 1 iter: 0 loss: 0.0903 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 1 iter: 5 loss: 0.1020 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 1 iter: 10 loss: 0.0553 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 1 iter: 15 loss: 0.0559 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 2 iter: 0 loss: 0.0770 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 2 iter: 5 loss: 0.0879 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 2 iter: 10 loss: 0.0438 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 2 iter: 15 loss: 0.0538 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 3 iter: 0 loss: 0.0768 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 3 iter: 5 loss: 0.0887 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 3 iter: 10 loss: 0.0417 train acc: 1.0000 test acc: 1.0000\n", - "epoch: 3 iter: 15 loss: 0.0511 train acc: 1.0000 test acc: 1.0000\n" + "epoch: 0 iter: 0 loss: 0.1864 train acc: 0.7500 test acc: 0.9000\n", + "epoch: 0 iter: 5 loss: 0.0841 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 0 iter: 10 loss: 0.0490 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 0 iter: 15 loss: 0.0562 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 0 loss: 0.0800 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 5 loss: 0.0554 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 10 loss: 0.0421 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 1 iter: 15 loss: 0.0454 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 0 loss: 0.0752 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 5 loss: 0.0569 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 10 loss: 0.0413 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 2 iter: 15 loss: 0.0436 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 0 loss: 0.0775 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 5 loss: 0.0597 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 10 loss: 0.0419 train acc: 1.0000 test acc: 1.0000\n", + "epoch: 3 iter: 15 loss: 0.0425 train acc: 1.0000 test acc: 1.0000\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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", 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    " ] @@ -1274,33 +1260,33 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "epoch: 0 iter: 0 loss: 0.2345 train acc: 0.5750 test acc: 0.5350\n", - "epoch: 0 iter: 5 loss: 0.2322 train acc: 0.6500 test acc: 0.5800\n", - "epoch: 0 iter: 10 loss: 0.2423 train acc: 0.6250 test acc: 0.5550\n", - "epoch: 1 iter: 0 loss: 0.1909 train acc: 0.8000 test acc: 0.6900\n", - "epoch: 1 iter: 5 loss: 0.1938 train acc: 0.7250 test acc: 0.6450\n", - "epoch: 1 iter: 10 loss: 0.2055 train acc: 0.6750 test acc: 0.7250\n", - "epoch: 2 iter: 0 loss: 0.1855 train acc: 0.8000 test acc: 0.7400\n", - "epoch: 2 iter: 5 loss: 0.1627 train acc: 0.8000 test acc: 0.7650\n", - "epoch: 2 iter: 10 loss: 0.1684 train acc: 0.8250 test acc: 0.7900\n", - "epoch: 3 iter: 0 loss: 0.1676 train acc: 0.8250 test acc: 0.7750\n", - "epoch: 3 iter: 5 loss: 0.1387 train acc: 0.8500 test acc: 0.7500\n", - "epoch: 3 iter: 10 loss: 0.1679 train acc: 0.8500 test acc: 0.7950\n", - "epoch: 4 iter: 0 loss: 0.1584 train acc: 0.7250 test acc: 0.8050\n", - "epoch: 4 iter: 5 loss: 0.1408 train acc: 0.8500 test acc: 0.8150\n", - "epoch: 4 iter: 10 loss: 0.1603 train acc: 0.8500 test acc: 0.8100\n" + "epoch: 0 iter: 0 loss: 0.3369 train acc: 0.4500 test acc: 0.4700\n", + "epoch: 0 iter: 5 loss: 0.2124 train acc: 0.6250 test acc: 0.5750\n", + "epoch: 0 iter: 10 loss: 0.2885 train acc: 0.4500 test acc: 0.5550\n", + "epoch: 1 iter: 0 loss: 0.2455 train acc: 0.4750 test acc: 0.6300\n", + "epoch: 1 iter: 5 loss: 0.1831 train acc: 0.7750 test acc: 0.7550\n", + "epoch: 1 iter: 10 loss: 0.1584 train acc: 0.8000 test acc: 0.8000\n", + "epoch: 2 iter: 0 loss: 0.2106 train acc: 0.7000 test acc: 0.7800\n", + "epoch: 2 iter: 5 loss: 0.1612 train acc: 0.8250 test acc: 0.7600\n", + "epoch: 2 iter: 10 loss: 0.1550 train acc: 0.8250 test acc: 0.8300\n", + "epoch: 3 iter: 0 loss: 0.1663 train acc: 0.8000 test acc: 0.8400\n", + "epoch: 3 iter: 5 loss: 0.1485 train acc: 0.8500 test acc: 0.8450\n", + "epoch: 3 iter: 10 loss: 0.1655 train acc: 0.8000 test acc: 0.8350\n", + "epoch: 4 iter: 0 loss: 0.1625 train acc: 0.8000 test acc: 0.8700\n", + "epoch: 4 iter: 5 loss: 0.1297 train acc: 0.8500 test acc: 0.8400\n", + "epoch: 4 iter: 10 loss: 0.1646 train acc: 0.7750 test acc: 0.8850\n" ] }, { "data": { - "image/png": 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\n", + "image/png": 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", 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    " ] diff --git a/tutorials/machine_learning/QGAN_CN.ipynb b/tutorials/machine_learning/QGAN_CN.ipynb index c6a4bf8..a4e0869 100644 --- a/tutorials/machine_learning/QGAN_CN.ipynb +++ b/tutorials/machine_learning/QGAN_CN.ipynb @@ -183,6 +183,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -190,11 +191,11 @@ "\n", "判别器对数据进行判别并得到量子态$|\\phi\\rangle$,那么当输入为目标态时,$|\\phi\\rangle=D(|\\psi\\rangle\\otimes |00\\rangle)$;当输入为生成态时,$|\\phi\\rangle=D(G\\otimes I)|000\\rangle$。\n", "\n", - "对于判别器得到的量子态,我们还需要采用泡利 Z 门对第3个量子比特进行测量,从而得到判别器对输入量子态的判断结果(即判别器认为输入是目标态的概率)。首先有 $M_{z}=I\\otimes I\\otimes\\sigma_{z}$,而测量结果为 $\\text{disc_output}=\\langle\\phi|M_{z}|\\phi\\rangle$,所以测量结果为目标态的概率是 $P=(\\text{disc_output}+1)/2$。\n", + "对于判别器得到的量子态,我们还需要采用泡利 Z 门对第3个量子比特进行测量,从而得到判别器对输入量子态的判断结果(即判别器认为输入是目标态的概率)。首先有 $M_{z}=I\\otimes I\\otimes\\sigma_{z}$,而测量结果为 $\\text{disc}_\\text{output}=\\langle\\phi|M_{z}|\\phi\\rangle$,所以测量结果为目标态的概率是 $P=(\\text{disc}_\\text{output}+1)/2$。\n", "\n", - "我们定义判别器的损失函数为 $\\mathcal{L}_D=P_{G}(\\text{gen_theta}, \\text{disc_phi})-P_{T}(\\text{disc_phi})$,生成器的损失函数为 $\\mathcal{L}_{G}=-P_{G}(\\text{gen_theta}, \\text{disc_phi})$。这里的 $P_{G}$ 和 $P_{T}$ 分别是输入量子态为生成态和目标态时,$P=(\\text{disc_output}+1)/2$ 的表达式,gen\\_theta 和 disc\\_phi 分别是生成器和判别器线路的参数。\n", + "我们定义判别器的损失函数为 $\\mathcal{L}_D=P_{G}(\\text{gen}_\\theta, \\text{disc}_\\phi)-P_{T}(\\text{disc}_\\phi)$,生成器的损失函数为 $\\mathcal{L}_{G}=-P_{G}(\\text{gen}_\\theta, \\text{disc}_\\phi)$。这里的 $P_{G}$ 和 $P_{T}$ 分别是输入量子态为生成态和目标态时,$P=(\\text{disc}_\\text{output}+1)/2$ 的表达式,$\\text{gen}_\\theta$ 和 $\\text{disc}_\\phi$ 分别是生成器和判别器线路的参数。\n", "\n", - "因此我们只需要分别优化目标函数 $\\min_{\\text{disc_phi}}\\mathcal{L}_{D}$ 和 $\\min_{\\text{gen_theta}}\\mathcal{L}_{G}$ 即可交替训练判别器和生成器。" + "因此我们只需要分别优化目标函数 $\\min_{\\text{disc}_\\phi}\\mathcal{L}_{D}$ 和 $\\min_{\\text{gen}_\\theta}\\mathcal{L}_{G}$ 即可交替训练判别器和生成器。" ] }, { @@ -213,7 +214,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 31, "metadata": {}, "outputs": [], "source": [ @@ -225,6 +226,7 @@ "from paddle_quantum.state import zero_state\n", "from paddle_quantum.ansatz import Circuit\n", "from paddle_quantum import Hamiltonian\n", + "from paddle_quantum.gate import *\n", "from paddle_quantum.loss import ExpecVal\n", "from paddle_quantum.qinfo import partial_trace\n", "from tqdm import tqdm\n", @@ -241,17 +243,24 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "# 设置模拟方式为密度矩阵\n", - "paddle_quantum.set_backend('density_matrix')\n", + "paddle_quantum.set_backend(\"density_matrix\")\n", "\n", - "\n", - "class QGAN(paddle_quantum.gate.Gate):\n", - " def __init__(self, target_state):\n", - " super().__init__()\n", + "class QGAN:\n", + " def __init__(self, target_state, LR, ITR, ITR_D, ITR_G):\n", + " \"\"\"\n", + " 输入参数\n", + " target_state: 目标量子态\n", + " LR: 学习率\n", + " ITR: 总迭代次数\n", + " ITR_D: 判别器迭代次数\n", + " ITR_G: 生成器迭代次数\n", + " \"\"\"\n", + " \n", " self.target_state = target_state.clone()\n", "\n", " # 生成器的量子电路\n", @@ -265,14 +274,26 @@ " self.discriminator.u3([0, 2])\n", " self.discriminator.cnot([0, 2])\n", " self.discriminator.u3(0)\n", + " \n", + " # 训练参数\n", + " self.LR = LR\n", + " self.ITR = ITR\n", + " self.ITR_D = ITR_D\n", + " self.ITR_G = ITR_G\n", + "\n", + " # 优化器\n", + " self.optimizer = paddle.optimizer.SGD(\n", + " learning_rate=self.LR,\n", + " parameters=self.generator.parameters() + self.discriminator.parameters(),\n", + " )\n", "\n", " def disc_target_as_target(self):\n", " \"\"\"\n", " 判别器将目标态判断为目标态的概率\n", " \"\"\"\n", " state = self.discriminator(self.target_state)\n", - " expec_val_func = ExpecVal(Hamiltonian([[1.0, 'z2']]))\n", - " \n", + " expec_val_func = ExpecVal(Hamiltonian([[1.0, \"z2\"]]))\n", + "\n", " # 判别器对目标态的判断结果\n", " target_disc_output = expec_val_func(state)\n", " prob_as_target = (target_disc_output + 1) / 2\n", @@ -289,23 +310,25 @@ " # 判别器电路\n", " state = self.discriminator(gen_state)\n", " # 判别器对生成态的判断结果\n", - " expec_val_func = ExpecVal(Hamiltonian([[1.0, 'z2']]))\n", + " expec_val_func = ExpecVal(Hamiltonian([[1.0, \"z2\"]]))\n", " gen_disc_output = expec_val_func(state)\n", " prob_as_target = (gen_disc_output + 1) / 2\n", - " \n", + "\n", " return prob_as_target\n", "\n", - " def forward(self, model_name):\n", - " if model_name == 'gen':\n", - " # 计算生成器的损失函数,loss值的区间为[-1, 0],\n", - " # 0表示生成效果极差,为-1表示生成效果极好\n", - " loss = -1 * self.disc_gen_as_target()\n", - " else:\n", - " # 计算判别器的损失函数,loss值的区间为[-1, 1],\n", - " # 为-1表示完美区分,为0表示无法区分,为1表示区分颠倒\n", - " loss = self.disc_gen_as_target() - self.disc_target_as_target()\n", + " def gen_loss_func(self):\n", + " \"\"\"\n", + " 计算生成器的损失函数,loss值的区间为[-1, 0],\n", + " 0表示生成效果极差,为-1表示生成效果极好\n", + " \"\"\"\n", + " return -1 * self.disc_gen_as_target()\n", "\n", - " return loss\n", + " def disc_loss_func(self):\n", + " \"\"\"\n", + " 计算判别器的损失函数,loss值的区间为[-1, 1],\n", + " 为-1表示完美区分,为0表示无法区分,为1表示区分颠倒\n", + " \"\"\"\n", + " return self.disc_gen_as_target() - self.disc_target_as_target()\n", "\n", " def get_target_state(self):\n", " \"\"\"\n", @@ -322,7 +345,56 @@ " state = self.generator()\n", " state = partial_trace(state, 2, 4, 2)\n", "\n", - " return state.numpy()" + " return state.numpy()\n", + "\n", + " def train(self):\n", + " \"\"\"\n", + " 训练 QGAN 网络\n", + " \"\"\"\n", + " \n", + " # 用来记录 loss 值的变化\n", + " loss_history = []\n", + " pbar = tqdm(\n", + " desc=\"Training: \",\n", + " total=self.ITR * (self.ITR_G + self.ITR_D),\n", + " ncols=100,\n", + " ascii=True,\n", + " )\n", + "\n", + " for _ in range(self.ITR):\n", + " # 训练判别器\n", + " loss_disc_history = []\n", + " for _ in range(self.ITR_D):\n", + " pbar.update(1)\n", + " loss_disc = self.disc_loss_func()\n", + " loss_disc.backward()\n", + " self.optimizer.minimize(\n", + " loss_disc,\n", + " parameters=self.discriminator.parameters(),\n", + " no_grad_set=self.generator.parameters(),\n", + " )\n", + " self.optimizer.clear_grad()\n", + " loss_disc_history.append(loss_disc.numpy()[0])\n", + "\n", + " # 训练生成器\n", + " loss_gen_history = []\n", + " for _ in range(self.ITR_G):\n", + " pbar.update(1)\n", + " loss_gen = self.gen_loss_func()\n", + " loss_gen.backward()\n", + " self.optimizer.minimize(\n", + " loss_gen,\n", + " parameters=self.generator.parameters(),\n", + " no_grad_set=self.discriminator.parameters(),\n", + " )\n", + " self.optimizer.clear_grad()\n", + " loss_gen_history.append(loss_gen.numpy()[0])\n", + "\n", + " loss_history.append((loss_disc_history, loss_gen_history))\n", + "\n", + " pbar.close()\n", + "\n", + " return loss_history\n" ] }, { @@ -334,14 +406,14 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "Training: 100%|#################################################| 2250/2250 [00:39<00:00, 57.65it/s]\n" + "Training: 100%|#################################################| 2250/2250 [00:50<00:00, 44.19it/s]\n" ] }, { @@ -353,12 +425,12 @@ " [0.12500004+0.09081785j 0.97552836+0.j ]] \n", "\n", "the density matrix of the generated state:\n", - "[[0.02444258+3.7252903e-09j 0.12302095-9.3332648e-02j]\n", - " [0.12302095+9.3332678e-02j 0.97555757-7.4505806e-09j]] \n", + "[[0.02444273-1.0244548e-08j 0.12302139-9.3332976e-02j]\n", + " [0.12302142+9.3332976e-02j 0.9755573 +0.0000000e+00j]] \n", "\n", - "the distance between these two quantum states is 2.0483967e-05 \n", + "the distance between these two quantum states is 2.0483465e-05 \n", "\n", - "the fidelity between these two quantum states is 0.9999947358758301\n" + "the fidelity between these two quantum states is 0.9999945609564611\n" ] } ], @@ -374,50 +446,14 @@ "\n", "# 制备目标量子态\n", "target_state = zero_state(num_qubits=3)\n", - "target_state = paddle_quantum.gate.RY(0, param=0.9 * np.pi)(target_state)\n", - "target_state = paddle_quantum.gate.RZ(0, param=0.2 * np.pi)(target_state)\n", - "target_state.data = paddle.to_tensor(target_state.data.numpy())\n", + "target_state = RY(0, param=0.9 * np.pi)(target_state)\n", + "target_state = RZ(0, param=0.2 * np.pi)(target_state)\n", "\n", - "# 用来记录loss值的变化\n", - "loss_history = list()\n", "paddle.seed(18)\n", - "gan_demo = QGAN(target_state)\n", - "optimizer = paddle.optimizer.SGD(learning_rate=LR, parameters=gan_demo.parameters())\n", - "pbar = tqdm(desc=\"Training: \", total=ITR * (ITR1 + ITR2), ncols=100, ascii=True)\n", - "for itr0 in range(ITR):\n", - " \n", - " # 记录判别器loss值的变化\n", - " loss_disc_history = list()\n", - "\n", - " # 训练判别器\n", - " for itr1 in range(ITR1):\n", - " pbar.update(1)\n", - " loss_disc = gan_demo('disc')\n", - " loss_disc.backward()\n", - " optimizer.minimize(\n", - " loss_disc, parameters=gan_demo.discriminator.parameters(),\n", - " no_grad_set=gan_demo.generator.parameters()\n", - " )\n", - " gan_demo.clear_gradients()\n", - " loss_disc_history.append(loss_disc.numpy()[0])\n", - "\n", - " # 记录生成器loss值的变化\n", - " loss_gen_history = list()\n", - "\n", - " # 训练生成器\n", - " for itr2 in range(ITR2):\n", - " pbar.update(1)\n", - " loss_gen = gan_demo('gen')\n", - " loss_gen.backward()\n", - " optimizer.minimize(\n", - " loss_gen, parameters=gan_demo.generator.parameters(),\n", - " no_grad_set=gan_demo.discriminator.parameters()\n", - " )\n", - " optimizer.clear_grad()\n", - " loss_gen_history.append(loss_gen.numpy()[0])\n", "\n", - " loss_history.append((loss_disc_history, loss_gen_history))\n", - "pbar.close()\n", + "# 生成一个 QGAN 并进行训练\n", + "gan_demo = QGAN(target_state, LR, ITR, ITR1, ITR2)\n", + "loss_history = gan_demo.train()\n", "\n", "# 得到目标量子态\n", "target_state = gan_demo.get_target_state()\n", @@ -466,12 +502,12 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "from IPython.display import clear_output\n", - "!pip install celluloid\n", + "%pip install celluloid\n", "clear_output()" ] }, @@ -484,12 +520,12 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 35, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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    " ] @@ -518,23 +554,24 @@ " axes[1].set_ylim(-1, 0)\n", " for loss in loss_history:\n", " disc_data, gen_data = loss\n", - " disc_x_data = range(0, len(disc_data))\n", - " gen_x_data = range(0, len(gen_data))\n", + " disc_x_data = range(len(disc_data))\n", + " gen_x_data = range(len(gen_data))\n", " axes[0].plot(disc_x_data, disc_data, color='red')\n", " axes[1].plot(gen_x_data, gen_data, color='blue')\n", " camera.snap()\n", " animation = camera.animate(interval=600, \n", " repeat=True, repeat_delay=800)\n", - " animation.save(\"./figures/loss.gif\")\n", + " animation.save(\"./figures/QGAN-fig-loss.gif\")\n", "draw_pic(loss_history)\n", "clear_output()" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "![QGAN-fig-loss](figures/loss.gif)" + "![QGAN-fig-loss](figures/QGAN-fig-loss.gif)" ] }, { @@ -581,7 +618,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.13" }, "toc": { "base_numbering": 1, diff --git a/tutorials/machine_learning/QGAN_EN.ipynb b/tutorials/machine_learning/QGAN_EN.ipynb index 5956eee..2535712 100644 --- a/tutorials/machine_learning/QGAN_EN.ipynb +++ b/tutorials/machine_learning/QGAN_EN.ipynb @@ -190,6 +190,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -197,11 +198,11 @@ "\n", "The discriminator discriminates the data and obtains the quantum state $|\\phi\\rangle$ when the input is the target state, $|\\phi\\rangle=D(|\\psi\\rangle\\otimes |00\\rangle)$; When the input is generated state, $|\\phi\\rangle=D(G\\otimes I)|000\\rangle$.\n", "\n", - "For the quantum state obtained by the discriminator, we also need to use the Pauli Z gate to measure the third qubit so as to obtain the judgment result of the input quantum state by the discriminator (that is, the probability that the discriminator thinks the input is the target state). First there is $M_{z}=I\\otimes I\\otimes\\sigma_{z}$, and the measurement result is $\\text{disc_output}=\\langle\\phi|M_{z}|\\phi\\rangle$, so the probability of the measurement that the result is the target state is $P=(\\text{disc_output}+1)/2$.\n", + "For the quantum state obtained by the discriminator, we also need to use the Pauli Z gate to measure the third qubit so as to obtain the judgment result of the input quantum state by the discriminator (that is, the probability that the discriminator thinks the input is the target state). First there is $M_{z}=I\\otimes I\\otimes\\sigma_{z}$, and the measurement result is $\\text{disc}_\\text{output}=\\langle\\phi|M_{z}|\\phi\\rangle$, so the probability of the measurement that the result is the target state is $P=(\\text{disc}_\\text{output}+1)/2$.\n", "\n", - "We define the loss function of the discriminator as $\\mathcal{L}_{D}=P_{G}(\\text{gen_theta}, \\text{disc_phi})-P_{T}(\\text{disc_phi})$, The loss function of the generator is $\\mathcal{L}_{G}=-P_{G}(\\text{gen_theta}, \\text{disc_phi})$. Here, $P_{G}$ and $P_{T}$ are the expressions of $P=(\\text{disc_output}+1)/2$, when the input quantum state is the generated state and the target state, respectively. gen\\_theta and disc\\_phi are the parameters of the generator and discriminator circuits.\n", + "We define the loss function of the discriminator as $\\mathcal{L}_{D}=P_{G}(\\text{gen}_\\theta, \\text{disc}_\\phi)-P_{T}(\\text{disc}_\\phi)$, The loss function of the generator is $\\mathcal{L}_{G}=-P_{G}(\\text{gen}_\\theta, \\text{disc}_\\phi)$. Here, $P_{G}$ and $P_{T}$ are the expressions of $P=(\\text{disc}_\\text{output}+1)/2$, when the input quantum state is the generated state and the target state, respectively. gen\\_theta and disc\\_phi are the parameters of the generator and discriminator circuits.\n", "\n", - "So we only need to optimize the objective function $\\min_{\\text{disc_phi}}\\mathcal{L}_{D}$ and $\\min_{\\text{gen_theta}}\\mathcal{L}_{G}$ respectively. The discriminator and generator can be alternately trained." + "So we only need to optimize the objective function $\\min_{\\text{disc}_\\phi}\\mathcal{L}_{D}$ and $\\min_{\\text{gen}_\\theta}\\mathcal{L}_{G}$ respectively. The discriminator and generator can be alternately trained." ] }, { @@ -220,7 +221,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 11, "metadata": { "ExecuteTime": { "end_time": "2021-01-09T10:49:41.308412Z", @@ -237,6 +238,7 @@ "from paddle_quantum.state import zero_state\n", "from paddle_quantum.ansatz import Circuit\n", "from paddle_quantum import Hamiltonian\n", + "from paddle_quantum.gate import *\n", "from paddle_quantum.loss import ExpecVal\n", "from paddle_quantum.qinfo import partial_trace\n", "from tqdm import tqdm\n", @@ -253,7 +255,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 12, "metadata": { "ExecuteTime": { "end_time": "2021-01-09T10:49:43.091496Z", @@ -265,10 +267,16 @@ "# set the backend to density_matrix\n", "paddle_quantum.set_backend('density_matrix')\n", "\n", - "\n", - "class QGAN(paddle_quantum.gate.Gate):\n", - " def __init__(self, target_state):\n", - " super().__init__()\n", + "class QGAN():\n", + " def __init__(self, target_state, LR, ITR, ITR_D, ITR_G):\n", + " \"\"\"\n", + " parameters\n", + " target_state: target state\n", + " LR: learning rate\n", + " ITR: number of iterations\n", + " ITR_D: number of iterations for discriminator\n", + " ITR_G: number of iterations for generator\n", + " \"\"\"\n", " self.target_state = target_state.clone()\n", "\n", " # Quantum circuit of generator\n", @@ -282,6 +290,18 @@ " self.discriminator.u3([0, 2])\n", " self.discriminator.cnot([0, 2])\n", " self.discriminator.u3(0)\n", + " \n", + " # Hyperparameters of training\n", + " self.LR = LR\n", + " self.ITR = ITR\n", + " self.ITR_D = ITR_D\n", + " self.ITR_G = ITR_G\n", + " \n", + " # Optimizer\n", + " self.optimizer = paddle.optimizer.SGD(\n", + " learning_rate=self.LR,\n", + " parameters=self.generator.parameters() + self.discriminator.parameters(),\n", + " )\n", "\n", " def disc_target_as_target(self):\n", " \"\"\"\n", @@ -310,19 +330,20 @@ " prob_as_target = (gen_disc_output + 1) / 2\n", "\n", " return prob_as_target\n", + " \n", + " def gen_loss_func(self):\n", + " \"\"\"\n", + " Calculate the loss function of the generator, the interval of the loss value is [-1, 0],\n", + " 0 means extremely poor generation effect, -1 means excellent generation effect\n", + " \"\"\"\n", + " return -1 * self.disc_gen_as_target()\n", "\n", - " def forward(self, model_name):\n", - " if model_name == 'gen':\n", - " # Calculate the loss function of the generator, the interval of the loss value is [-1, 0],\n", - " # 0 means extremely poor generation effect, -1 means excellent generation effect\n", - " loss = -1 * self.disc_gen_as_target()\n", - " else:\n", - " # Calculate the loss function of the discriminator, the loss value range is [-1, 1],\n", - " # -1 means perfect distinction, 0 means indistinguishable, 1 means inverted distinction\n", - " loss = self.disc_gen_as_target() - self.disc_target_as_target()\n", - " loss = self.disc_gen_as_target() - self.disc_target_as_target()\n", - "\n", - " return loss\n", + " def disc_loss_func(self):\n", + " \"\"\"\n", + " Calculate the loss function of the discriminator, the loss value range is [-1, 1],\n", + " -1 means perfect distinction, 0 means indistinguishable, 1 means inverted distinction\n", + " \"\"\"\n", + " return self.disc_gen_as_target() - self.disc_target_as_target()\n", "\n", " def get_target_state(self):\n", " \"\"\"\n", @@ -339,7 +360,56 @@ " state = self.generator()\n", " state = partial_trace(state, 2, 4, 2)\n", "\n", - " return state.numpy()" + " return state.numpy()\n", + " \n", + " def train(self):\n", + " \"\"\"\n", + " Train the QGAN\n", + " \"\"\"\n", + " \n", + " # Used to record the change of loss value\n", + " loss_history = []\n", + " pbar = tqdm(\n", + " desc=\"Training: \",\n", + " total=self.ITR * (self.ITR_G + self.ITR_D),\n", + " ncols=100,\n", + " ascii=True,\n", + " )\n", + "\n", + " for _ in range(self.ITR):\n", + " # Train the discriminator\n", + " loss_disc_history = []\n", + " for _ in range(self.ITR_D):\n", + " pbar.update(1)\n", + " loss_disc = self.disc_loss_func()\n", + " loss_disc.backward()\n", + " self.optimizer.minimize(\n", + " loss_disc,\n", + " parameters=self.discriminator.parameters(),\n", + " no_grad_set=self.generator.parameters(),\n", + " )\n", + " self.optimizer.clear_grad()\n", + " loss_disc_history.append(loss_disc.numpy()[0])\n", + "\n", + " # Train the generator\n", + " loss_gen_history = []\n", + " for _ in range(self.ITR_G):\n", + " pbar.update(1)\n", + " loss_gen = self.gen_loss_func()\n", + " loss_gen.backward()\n", + " self.optimizer.minimize(\n", + " loss_gen,\n", + " parameters=self.generator.parameters(),\n", + " no_grad_set=self.discriminator.parameters(),\n", + " )\n", + " self.optimizer.clear_grad()\n", + " loss_gen_history.append(loss_gen.numpy()[0])\n", + "\n", + " loss_history.append((loss_disc_history, loss_gen_history))\n", + "\n", + " pbar.close()\n", + "\n", + " return loss_history" ] }, { @@ -351,7 +421,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 13, "metadata": { "ExecuteTime": { "end_time": "2021-01-09T10:52:15.221809Z", @@ -363,7 +433,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Training: 100%|#################################################| 2250/2250 [00:57<00:00, 39.44it/s]\n" + "Training: 100%|#################################################| 2250/2250 [00:51<00:00, 43.51it/s]" ] }, { @@ -375,12 +445,19 @@ " [0.12500004+0.09081785j 0.97552836+0.j ]] \n", "\n", "the density matrix of the generated state:\n", - "[[0.02444258+3.7252903e-09j 0.12302095-9.3332648e-02j]\n", - " [0.12302095+9.3332678e-02j 0.97555757-7.4505806e-09j]] \n", + "[[0.02444273-1.0244548e-08j 0.12302139-9.3332976e-02j]\n", + " [0.12302142+9.3332976e-02j 0.9755573 +0.0000000e+00j]] \n", "\n", - "the distance between these two quantum states is 2.0483967e-05 \n", + "the distance between these two quantum states is 2.0483465e-05 \n", "\n", - "the fidelity between these two quantum states is 0.9999947358758301\n" + "the fidelity between these two quantum states is 0.9999945609564611\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "\n" ] } ], @@ -396,51 +473,14 @@ "\n", "# prepare the target quantum state\n", "target_state = zero_state(num_qubits=3)\n", - "target_state = paddle_quantum.gate.RY(0, param=0.9 * np.pi)(target_state)\n", - "target_state = paddle_quantum.gate.RZ(0, param=0.2 * np.pi)(target_state)\n", - "target_state.data = paddle.to_tensor(target_state.data.numpy())\n", + "target_state = RY(0, param=0.9 * np.pi)(target_state)\n", + "target_state = RZ(0, param=0.2 * np.pi)(target_state)\n", "\n", - "# Used to record the change of loss value\n", - "loss_history = list()\n", "paddle.seed(18)\n", - "gan_demo = QGAN(target_state)\n", - "optimizer = paddle.optimizer.SGD(learning_rate=LR, parameters=gan_demo.parameters())\n", - "pbar = tqdm(desc=\"Training: \", total=ITR * (ITR1 + ITR2), ncols=100, ascii=True)\n", - "for itr0 in range(ITR):\n", - "\n", - " # Record the change in the loss value of the discriminator\n", - " loss_disc_history = list()\n", - "\n", - " # Train the discriminator\n", - " for itr1 in range(ITR1):\n", - " pbar.update(1)\n", - " loss_disc = gan_demo('disc')\n", - " loss_disc.backward()\n", - " optimizer.minimize(\n", - " loss_disc, parameters=gan_demo.discriminator.parameters(),\n", - " no_grad_set=gan_demo.generator.parameters()\n", - " )\n", - " gan_demo.clear_gradients()\n", - " loss_disc_history.append(loss_disc.numpy()[0])\n", - "\n", - " # Record the change of the generator loss value\n", - " loss_gen_history = list()\n", - "\n", - " # Training generator\n", - " for itr2 in range(ITR2):\n", - " pbar.update(1)\n", - " loss_gen = gan_demo('gen')\n", - " loss_gen.backward()\n", - " optimizer.minimize(\n", - " loss_gen, parameters=gan_demo.generator.parameters(),\n", - " no_grad_set=gan_demo.discriminator.parameters()\n", - " )\n", - " optimizer.clear_grad()\n", - " loss_gen_history.append(loss_gen.numpy()[0])\n", - "\n", "\n", - " loss_history.append((loss_disc_history, loss_gen_history))\n", - "pbar.close()\n", + "# Construct a QGAN and train\n", + "gan_demo = QGAN(target_state, LR, ITR, ITR1, ITR2)\n", + "loss_history = gan_demo.train()\n", "\n", "# Get the target quantum state\n", "target_state = gan_demo.get_target_state()\n", @@ -488,12 +528,12 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "from IPython.display import clear_output\n", - "!pip install celluloid\n", + "%pip install celluloid\n", "clear_output()" ] }, @@ -506,12 +546,12 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "
    " ] @@ -540,23 +580,24 @@ " axes[1].set_ylim(-1, 0)\n", " for loss in loss_history:\n", " disc_data, gen_data = loss\n", - " disc_x_data = range(0, len(disc_data))\n", - " gen_x_data = range(0, len(gen_data))\n", + " disc_x_data = range(len(disc_data))\n", + " gen_x_data = range(len(gen_data))\n", " axes[0].plot(disc_x_data, disc_data, color='red')\n", " axes[1].plot(gen_x_data, gen_data, color='blue')\n", " camera.snap()\n", " animation = camera.animate(interval=600, \n", " repeat=True, repeat_delay=800)\n", - " animation.save(\"./figures/loss.gif\")\n", + " animation.save(\"./figures/QGAN-fig-loss.gif\")\n", "draw_pic(loss_history)\n", "clear_output()" ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "![QGAN-fig-loss](./figures/loss.gif)" + "![QGAN-fig-loss](figures/QGAN-fig-loss.gif)" ] }, { @@ -603,7 +644,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.13" }, "toc": { "base_numbering": 1, diff --git a/tutorials/machine_learning/VQSVD_CN.ipynb b/tutorials/machine_learning/VQSVD_CN.ipynb index 421d134..8009b5c 100644 --- a/tutorials/machine_learning/VQSVD_CN.ipynb +++ b/tutorials/machine_learning/VQSVD_CN.ipynb @@ -72,7 +72,7 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 154, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:47:34.433321Z", @@ -94,7 +94,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 155, "metadata": {}, "outputs": [], "source": [ @@ -121,7 +121,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 156, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:47:34.469286Z", @@ -158,7 +158,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 157, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:47:34.541244Z", @@ -201,7 +201,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 158, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:47:34.600873Z", @@ -264,7 +264,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 159, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:47:34.656799Z", @@ -319,7 +319,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 160, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:47:34.692350Z", @@ -338,14 +338,13 @@ ], "source": [ "# 超参数设置\n", - "N = 3 # 量子比特数量\n", - "T = 8 # 设置想要学习的阶数\n", + "RANK = 8 # 设置想要学习的阶数\n", "ITR = 100 # 迭代次数\n", "LR = 0.02 # 学习速率\n", "SEED = 14 # 随机数种子\n", "\n", "# 设置等差的学习权重\n", - "weight = np.arange(3 * T, 0, -3).astype('complex128')\n", + "weight = np.arange(3 * RANK, 0, -3).astype('complex128')\n", "print('选取的等差权重为:')\n", "print(weight)" ] @@ -359,7 +358,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 161, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:47:34.725007Z", @@ -369,24 +368,24 @@ "outputs": [], "source": [ "# 设置电路参数\n", - "cir_depth = 20 # 电路深度\n", - "block_len = 2 # 每个模组的长度" + "num_qubits = 3 # 量子比特数量\n", + "cir_depth = 20 # 电路深度" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 162, "metadata": {}, "outputs": [], "source": [ "# 定义量子神经网络\n", - "def U_theta() -> Circuit:\n", + "def U_theta(num_qubits: int, depth: int) -> Circuit:\n", "\n", - " # 用 UAnsatz 初始化网络\n", - " cir = Circuit(N)\n", + " # 用 Circuit 初始化网络\n", + " cir = Circuit(num_qubits)\n", " \n", - " # 搭建层级结构:\n", - " for _ in range(cir_depth):\n", + " # 搭建层级结构\n", + " for _ in range(depth):\n", " cir.ry()\n", " cir.rz()\n", " cir.cnot()\n", @@ -404,7 +403,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 163, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:49:24.011232Z", @@ -413,67 +412,89 @@ }, "outputs": [], "source": [ - "class NET(paddle.nn.Layer):\n", - " def __init__(self, matrix: np.ndarray, weights: np.ndarray) -> None:\n", - " super(NET, self).__init__()\n", + "class VQSVD():\n", + " def __init__(self, matrix: np.ndarray, weights: np.ndarray, num_qubits: int, depth: int, rank: int, lr: float, itr: int, seed: int):\n", + " \n", + " # 超参数\n", + " self.rank = rank\n", + " self.lr = lr\n", + " self.itr = itr\n", + " \n", + " paddle.seed(seed)\n", " \n", " # 创建用来学习 U_dagger 的量子神经网络\n", - " self.cir_U = U_theta()\n", + " self.cir_U = U_theta(num_qubits, depth)\n", " \n", " # 创建用来学习 V_dagger 的量子神经网络\n", - " self.cir_V = U_theta()\n", + " self.cir_V = U_theta(num_qubits, depth)\n", " \n", " # 将 Numpy array 转换成 Paddle 支持的 Tensor\n", " self.M = paddle.to_tensor(matrix)\n", " self.weight = paddle.to_tensor(weights)\n", - "\n", - " # 定义损失函数和前向传播机制\n", - " def forward(self):\n", " \n", + " # 定义损失函数\n", + " def loss_func(self):\n", " # 获取量子神经网络的酉矩阵表示\n", " U = self.cir_U.unitary_matrix()\n", - " U_dagger = dagger(U)\n", - " \n", " V = self.cir_V.unitary_matrix()\n", - " V_dagger = dagger(V)\n", " \n", " # 初始化损失函数和奇异值存储器\n", - " loss = 0 \n", - " singular_values = np.zeros(T)\n", - " \n", - " # 定义损失函数\n", - " for i in range(T):\n", - " loss -= paddle.real(self.weight)[i] * paddle.real(U_dagger @ self.M @ V)[i][i]\n", - " singular_values[i] = paddle.real(U_dagger @ self.M @ V)[i][i].numpy()\n", + " loss = paddle.to_tensor(0.0)\n", + " singular_values = np.zeros(self.rank)\n", + "\n", + " for i in range(self.rank):\n", + " loss -= paddle.real(self.weight)[i] * paddle.real(dagger(U) @ self.M @ V)[i][i]\n", + " singular_values[i] = paddle.real(dagger(U) @ self.M @ V)[i][i].numpy()\n", " \n", - " # 函数返回两个矩阵 U 和 V_dagger 学习的奇异值以及损失函数 \n", - " return U, V_dagger, loss, singular_values\n" + " return loss, singular_values\n", + " \n", + " def get_matrix_U(self):\n", + " return self.cir_U.unitary_matrix()\n", + " \n", + " def get_matrix_V(self):\n", + " return self.cir_V.unitary_matrix()\n", + "\n", + " # 训练 VQSVD 网络\n", + " def train(self):\n", + " loss_list, singular_value_list = [], []\n", + " optimizer = paddle.optimizer.Adam(learning_rate=self.lr, parameters=self.cir_U.parameters()+self.cir_V.parameters())\n", + " for itr in range(self.itr):\n", + " loss, singular_values = self.loss_func()\n", + " loss.backward()\n", + " optimizer.minimize(loss)\n", + " optimizer.clear_grad()\n", + " loss_list.append(loss.numpy()[0])\n", + " singular_value_list.append(singular_values)\n", + " if itr% 10 == 0:\n", + " print('iter:', itr,'loss:','%.4f'% loss.numpy()[0])\n", + "\n", + " return loss_list, singular_value_list" ] }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 164, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "iter: 0 loss: -262.8009\n", - "iter: 10 loss: -1886.9825\n", - "iter: 20 loss: -2182.6929\n", - "iter: 30 loss: -2280.7289\n", - "iter: 40 loss: -2315.2391\n", - "iter: 50 loss: -2333.0160\n", - "iter: 60 loss: -2342.7280\n", - "iter: 70 loss: -2348.7263\n", - "iter: 80 loss: -2353.2796\n", - "iter: 90 loss: -2356.9237\n" + "iter: 0 loss: -88.4531\n", + "iter: 10 loss: -1795.0786\n", + "iter: 20 loss: -2059.0496\n", + "iter: 30 loss: -2202.6445\n", + "iter: 40 loss: -2269.9832\n", + "iter: 50 loss: -2304.1875\n", + "iter: 60 loss: -2320.8447\n", + "iter: 70 loss: -2331.9180\n", + "iter: 80 loss: -2340.2454\n", + "iter: 90 loss: -2348.0549\n" ] }, { "data": { - "image/png": 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", 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", 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    " ] @@ -489,37 +510,16 @@ "loss_list, singular_value_list = [], []\n", "U_learned, V_dagger_learned = [], []\n", " \n", - "# 确定网络的参数维度\n", - "net = NET(M, weight)\n", - "\n", - "# 一般来说,我们利用 Adam 优化器来获得相对好的收敛\n", - "# 当然你可以改成 SGD 或者是 RMS prop.\n", - "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())\n", - "\n", - "# 优化循环\n", - "for itr in range(ITR):\n", - "\n", - " # 前向传播计算损失函数\n", - " U, V_dagger, loss, singular_values = net()\n", - "\n", - " # 反向传播极小化损失函数\n", - " loss.backward()\n", - " opt.minimize(loss)\n", - " opt.clear_grad()\n", - "\n", - " # 记录优化中间结果\n", - " loss_list.append(loss[0][0].numpy())\n", - " singular_value_list.append(singular_values)\n", - " \n", - " if itr% 10 == 0:\n", - " print('iter:', itr,'loss:','%.4f'% loss.numpy()[0])\n", + "# 创建 VQSVD 网络并进行训练\n", + "net = VQSVD(matrix=M, weights=weight, num_qubits=num_qubits, depth=cir_depth, rank=RANK, lr=LR, itr=ITR, seed=SEED)\n", + "loss_list, singular_value_list = net.train()\n", " \n", "# 绘制学习曲线\n", "loss_plot(loss_list)\n", "\n", "# 记录最后学出的两个酉矩阵 \n", - "U_learned = U.numpy()\n", - "V_dagger_learned = V_dagger.numpy()" + "U_learned = net.get_matrix_U().numpy()\n", + "V_dagger_learned = dagger(net.get_matrix_V()).numpy()" ] }, { @@ -549,7 +549,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 165, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:49:24.407257Z", @@ -559,7 +559,7 @@ "outputs": [ { "data": { - "image/png": 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o9ifvP/25PoiIiFBV1fT0dB00aJD+73//U1XVnj176s8//6yqqgsXLtQePXqoquqQIUP0pZdeyn5OUlKSLl68WNu1a6fJycl65MgRbdOmjS5dulS3bt2qwcHBumzZMlVVHTx4sI4dO1ZVVevUqaPHjx9XVdVDhw6pqurjjz+uzz//fHZsN910k1555ZWanp6e5/62bdvq1q1bdfXq1dq8eXPdt2+fqqoeOHAg+/mffPLJKef75JNPNCUlRevXr68bNmxQVdXhw4dnv6aGDRvqK6+8oqqqr732mt56662nvWdjxozRxx57TFVVd+3apS1atFBV1XfffVfvvvtuVVU9ePCgZmZmqqrqW2+9pSNHjjztPMuWLdPo6Gjt2rWrPvroo9nvt6rqlVdeqVOnus+Sp59+Wv/85z+rqurWrVu1bdu2p5zn0KFDGh4eftr5z1Zen5PAYs3jM9VKBJ52vW4giSoc/XFsoEMx56rD2yFrdhVVSNp+1qe0aagDNw11bGwsW7Zs4YEHHuDgwYOcf/75rFu3Djh1gZmc1UJ50VIw35nNwewJC4/g43av8vxSYfbh49SuFh7okExZc/OX+e878SscT+LkwHl1j5t5dd4RUQU/Px82DXX+MZfENNRZiXPgwIEEBQXx1Vdf0bp1a66++mruv/9+li5dyrFjx+jcuXO+8S5btozWrVuf2Yv1EysR5HB5j74cywxl/E9n/03NmFPMew401+I0mum3tgKbhrrkp6H+/vvvOXToEACpqamsXbuWhg0bAi5B9OjRg1tuuaXA0kBCQgKjRo3i3nvvLVL8/maJIIcGUZUYWX89F31/C+lpZ7dylDGn2PEjZKSeui0j1W33E5uG2nf+mIZ68+bNdO/ePft9iI+P59prr83eP2zYMFasWHFaIti8eXN299EhQ4Zw3333cfPNNxcpfn8rsWmo/ckf01DnZ/n094j94Y/s+s371L3gmmK5hjk32DTUpjQrrdNQlwnte/4OrRxD3U3jAh2KMcaUCEsEuQSHVkDihqM/T+dY4tZAh2OMMcXOEkEejnccjgLLpv4z0KGYUiwoKIg0a0sypVBaWhpBRZhM0xJBHsJrNuKnBr+ncvOLAx2KKcVatWrF2LFjLRmYUiUtLY2xY8fSqlUrn59jjcXGnKHExERGjRrF+vXrT+kfb0wgBQUF0apVK1544QVq1ap1yr78GottQFkBEnduZeuPX9Llt/cEOhRTCtWqVYsPPvgg0GEYc9asaqgACTP+Q5cVj7Jt48pAh2KMMcXGEkEBmvW7k3QNYsdMW9PYGHPuskRQgBq1G7K6ysW02fs5KceOBTocY4wpFpYIChHW9fdU5wgrZlhdsDHm3GSJoBCtLuzPtqD6bNuwPNChGGNMsbBEUAgJCmZuj8k8dPAqVu88HOhwjDHG7ywR+OCazk0IDw3i0wWnL05hjDFlnSUCH1SrFMqYOrP50+pBHPk1KdDhGGOMX1ki8FGL83tTTY6SserTQIdijDF+ZYnAR83ie0N0KyLXfBjoUIwxxq9KNBGISIKIrBKR5SKy2NtWQ0RmiMhG72f1kozJZyIQfwvsWsrOtT8EOhpjjPGbQJQIeqhqbI6Jjx4GZqlqc2CW97hUOt5mMClage3fvBboUIwxxm9Kw6RzVwOXefffB+YCDwUqmIKEV6nB6p5v0KrNhYEOxRhj/KakSwQKfCMiS0Tkdm9bjKru9u7vAWLyeqKI3C4ii0Vk8b59+0oi1jy1634t1aPrBOz6xhjjbyWdCC5W1U7AFcDdInJpzp3qFkfIc4EEVX1TVeNVNT46OroEQs3fqrmTWDhmKGpz0BtjzgElmghUdaf3MxGYAlwA7BWROgDez8SSjOlMpB3cTtdfv2bVjzMDHYoxxpy1EksEIhIhIlWy7gN9gNXA58BN3mE3AZ+VVExnqk3fW0mmIse+fyvQoRhjzFkrycbiGGCKiGRd92NV/VpEfgImisitwDZgSAnGdEbCI6qxOPoK4hKnsS9xN9G1rM3AGFN2lViJQFW3qGpH79ZWVZ/yth9Q1ctVtbmq9lLVgyUV09mI6XknYZLGhulvBjoUY4w5K0VKBCISLyJDvaqdrOqe0tAFtcSd1/oC5lTqx9fbg8jIzLN92xhjygSfEoGIxIjIQuBH4GNOdvEcA7xYTLGVesf6vcyHRzox/+fAdWc1xpiz5WuJ4CVgLxAF5Fyz8RNco2+51LtNDA0jMlg+Z1KgQzHGmDPma7XO5cDlqnrIa+zNshlo4PeoyogKIUE8X+tr4naNZ/fO/tSpV27fCmNMGeZriaAikJrH9mjguP/CKXsa9r6TUMmg5saJgQ7FGGPOiK+JYD4wIsdjFZFg3JxAs/wdVFkS06Q9NLqE0OXvg400NsaUQb4mggeB20RkBhCGayBeC1wEPFJMsZUZaZ1GQNJ2Vn87OdChGGNMkfmUCFR1LdAeWAB8A4TjGorjVHVz8YVXNgS1voqDVOPw2rmBDsUYY4rM5zEAqroHeLwYYymzgkPDCL5nERfVtBHGxpiyx9dxBPeIyA15bL9BRO7yf1hlTzUvCaSeOBHgSIwxpmh8bSP4E/BLHtsTgPv9FUxZ99PHT5D4dHuOWzIwxpQhviaC+rgJ4XLb4e0zQOU6LajPXlbMGh/oUIwxxme+JoI9QGwe2zsB+/0WTRnX8pJB7JMowpa/H+hQjDHGZ74mgo+BV0Skt4iEerc+wMvAR8UWXRkTFBLK9kaDiU1dwpafVwc6HGOM8YmvieBx4HtgOm6uoWPA/3DdSf9aPKGVTU363kW6BrFz5uuBDsUYY3ziU/dRVU0DhonIY0Acbl3h5aq6sTiDK4uq127Ix3Uf5MNddemcmk6lCuVylm5jTBlSpPUIVHWjqk5U1U8sCeSvRd8/sPZETaat2BXoUIwxplA+f10VkaG4WUhrkSuBqOoAP8dVpnVuWJ1ra26H2Z/D+f8JdDjGGFMgXweUPQ98CDQCkoADuW4mBxHh+jq7GZoynp0/Lw90OMYYUyBfSwQ3AsNU1VZg8VHLK+5EN/+belsmQIvYQIdjjDH58rWNIAhYXoxxnHMiatRB2gyA5R+hqccKf4IxxgSIr4ngTeC0uYZMwY53vBGOH+b7z98OdCjGGJMvX6uGIoHfiUhvYCWQlnOnqt7n57jOCeHNurO2YidCgqTwg40xJkB8TQRtOFk11CrXPvVbNOcaEdo8NCfQURhjTIF8HVDWw18X9Ja4XAzsVNX+ItIYGA9EAUuA4aqa1/rIZVZa6gm2rF1My9iLAh2KMcacpkgDyvzkj8C6HI+fBV5S1WbAIeDWAMRUrFa+czf1pgzkwEHraWuMKX18TgQi0kNE3hSRr0Vkds5bEc5RH7gSeNt7LEBPIKtb6vvANT5HX0ZEX3gDleU4a762RmNjTOnj64CyEbhJ5qoAlwH7gOq4aajXFuF6LwMPApne4yggSVXTvcc7gHr5xHC7iCwWkcX79u0rwiUDr0GH7iSENKHOpo/JzMgs/AnGGFOCfC0RjALuUdVhuB5Dj6hqHG60cbIvJxCR/kCiqi45k0BV9U1VjVfV+Ojo6DM5ReCIcLjtDTTPTGDlj7MCHY0xxpzC10TQBJjp3T8BVPbu/wsY4eM5LgIGiEgCrnG4J/BPIFJEshqt6wM7fTxfmdKqz60cJZzEhRMDHYoxxpzC10RwAFctBO6Dup13Pwqo6MsJVPURVa2vqo2A64DZqno9MAcY5B12E/CZjzGVKWERkXzY4X3u2nc1ew4fD3Q4xhiTzddE8C3Qx7s/Ebda2bvAOGDGWcbwEDBSRDbhEss7Z3m+Uqtf90tIzxQm/Lg90KEYY0w2XweU3QOEe/efBtJxVT0Tgb8X9aKqOheY693fAlxQ1HOURQ2jInii9gJiF/yN9B4LCAkJDnRIxhjj84CygznuZ+L6/psz0KlZPdovXk/iujnUat8r0OEYY4zP3UczRKRWHtujRCTD/2Gdu9r2vgkNr0atDeMCHYoxxgC+txHkN2taGHBOTQdR3ILCIpCOw9C1n/HrPlvK0hgTeAVWDYnISO+uAneISM4xA8HAJcD6YortnHW0w3AiFr3B0mmvcdktTwU6HGNMOVdYG8G93k8Bfg/krAZKBRKAO/wf1rktol47Fje9h3rt+wU6FGOMKTgRqGpjABGZAwxU1UMlElU5ED/cSgLGmNLBpzYCVe2ROwmISDMRCc/vOaZwW1cv5LuPnwl0GMaYcs7XXkP/EJGbvPsiIjOBn4HdItKlOAM8lx1a9DFdNzzL1i0bAx2KMaYc87XX0PXABu/+FUBHoCvwAWBfac9Qwz53ESKZbJv5RqBDMcaUY74mghjcFNEAvwEmquqPwKtAXHEEVh5EndeKdZXiabVrCsdPnAh0OMaYcqook8419O73AbLmUg4h/zEGxgdB599KbQ6wdOaEQIdijCmnfE0EnwIfi8gMoAYw3dseC2wqhrjKjRaXDGJbUH1WrrfhGMaYwPA1EYwEXsGtRtZbVY962+sArxdHYOWFhFRgZo/PeWbfRazZdTjQ4RhjyiFfu4+mq+qLqvpHVV2WY/tLqmoL8Z6lazufR1iI8OW3PwU6FGNMOZTvgDIR6QQsV9VM736+VHWp3yMrRyIrVeCd6E9otXYWycfWU7lSpUCHZIwpRwoaWbwYqA0keveVvBuGFTfvkDkL9S4YQM3pk0le/yV0GhzocIwx5UhBiaAxsC/HfVOMGncZAAsbUHnVB5YIjDElKt9EoKrb8rpviklQMJmdbiJozpMkrF9Oo1axgY7IGFNO+DrFRBMRGSki/xKRV0XkfhGxUoKfpbQbRpoGs232W4EOxRhTjhS6VKWI/Bm3TnEwrr1AgGjgWRF5SFVfKt4Qy4+IqHps6j+eru0vDnQoxphypMASgYhcDDwHPA9Eq2odVa0N1AJeBJ4XkYuKP8zyo9n5fQgLt15DxpiSU1jV0J3AB6r6aK4F7A+o6iPAh8BdxRlgebTss1f54blrUNVAh2KMKQcKSwRdgfcK2P+ed4zxo+ATh+l2bA53PPkSix7rwlVPf8rUZTsDHZYx5hxVWCKoDWwpYP9m3DQTxo+21r+aExrK/envcL5sYPDRj3lk8ipLBsaYYlFYIqgIFDQ/cioQ5suFRCRcRH4UkRUiskZEnvC2NxaRRSKySUQmiEgF30I/dz03fx8zM+NoKTsIEmVw8Hwqpx3g+ekbCn+yMcYUUaG9hoArRSS/2dAii3CtE0BPVU0WkVDgOxH5H25Cu5dUdbyIvAHcSjmfyG5XUgoScrJ9IIhM7g2ZzONJtwQwKmPMucqXRPBOIft9atFU1/KZ7D0M9W4K9AR+521/HxhNOU8E7aul0PP4csSb0CNM0hkSPI8DQTXYvKsLTevWDGyAxphzSoFVQ6oa5MPN53mGRCRYRJbjxiPMwLUxJKlqunfIDqBePs+9XUQWi8jiffv25XXIOePlOjOQXPk1hAzuD5pIzHvdYPF/ISMtQNEZY841vq5H4BeqmqGqsUB94AKgVRGe+6aqxqtqfHR0dHGFWCo0Ob6GMEk/ZVuIZJIe2YiK0Q3hi/s5NiaO8W89S/JxSwjGmLPjS9WQ36lqkojMAboBkSIS4pUK6gPWNeaO7/LcHAKgChtncOzzv9J67xdUrPAgACfSMwgLsUlgjTFFV2IlAhGJFpFI735FoDewDpgDDPIOuwn4rKRiKpNEoEUfao78gXZ/mkpwkJCcmMDPT3Xl47Fvkng4JdARGmPKmJKsGqoDzBGRlcBPwAxV/QJ4CBgpIpuAKApvnDYAQUEEV44CICNpJ3VDkvnd5gfYNeYSPhr3PgeSC+r1a4wxJ0lZnMYgPj5eFy9eHOgwSpeMNPZ/9y7B3z5H9fR9LND2fN/1DX5/aQuqR5T7oRnGGEBElqhqfO7tJdpYbIpRcCg1u99O9YdWs+/iv3GsRlv+PX8blzw3h3emzeZwijUqG2Py5lNjsYhUx/Xv74GbefSUBKKqtfwemTkzoeFE9/ojvXrB13uOMPmLL7h58Z0sXXcx8SNegFo+d9QyxpQTvvYa+gBoixvwtRcfB5GZwGpZuwqP3PAbEr+5j7hVb8O/u3K89bVMrjaca3peTKUKAek0ZowpZXxqIxCRI0B3VV1a/CEVztoIzsDRA/D9y6QvfJMjGSEcuWsFDWJshLIx5cnZthFsLsKxpjSKiII+TxJy/wrSBrzhkoAq/3vjISbOXcKJ9IxAR2iMCRBfP9z/CDwtIh1FxEYtlWVValOr81UAnNixnD573qT/nCuY8PTvmfTtKtIyMgMcoDGmpPmaCDbhpqReCqSKSEbOW/GFZ4pT2HlxBN3zI8mN+nBDxhT6zOzNB8/cyeRFP5NuCcGYcsPXNoL5QHXgDfJoLFbVT4slunxYG4H/6Z7V7J/2OJm7V3LJseepXzOSP17ejP4d6xEcJIEOzxjjB/m1EfjabSQeuEBVV/s3LFNaSO12RN/2KZqSxKtbjvOvb1bTcMpVvD2rL7fdN5qgCuGBDtEYU0x8rRpaC1QtzkBM6SAVI+nbtjafjWjJebWi+EPy6wS9Fo8ueZ/vf95DWRyJbowpmK+J4P+AMSLSS0RiRKRGzltxBmgCI6j6eUTdPQOGT4HKtZBp91Hnw+7M/HFFoEMzxviZr1VDX3k/v+HU9gHxHltPonORCDTtCU16kLHuS4IXTuKyzu0B+HbB91CzORc3j+az5bt4fvoGdiWlUDeyIg/0bck1cXmuL2SMKYV8TQQ9ijUKU7qJENymPw3b9AdAk/cRP2MgGzPq8HClG5mS3Ipq6QcZX+FV7km6j0cmpwJYMjCmjCi011DWQvPAjaq6oUSiKoT1GgqwjHTSlo/j+Mx/UCVlF4syW5GUGUHv4KV8mHE5j6XfQr3Iinz/cM9AR2qMyeGMRxarahrQGJtfyGQJDiG083Cq/HkFf027mSayi74hSwgSZXDwfKJJYmdSCpsSjwQ6UmOMD3xtLH4fuK04AzFlUEgFZlcZwIyMzqSpayYKIpMPKzzFAyHjSd2/FYB5P+/jj+OX2WI5xpRSvrYRRADXi0hvYAlwNOdOVb3P34GZsuH/utegx9ffEeoNMA+TdJqxixYhu2DiNGjWi5DqA1i1vS5VwkMBeHnmz6zccZj4RtU5v1EN2terRnio9TcwJlB8TQStcdNLADTJtc+qjMqxKw58QEYQp/4VBIUg7a+F6o1g6ftctGkGsy9/HEJ6ARAWEsz2g8eYvT4RgArBQXQ8rxrxjWpwfqPqdG5Qg2qVQkv8tRhTXtlSlebsvHEx7Fl1+vba7eGO7yAjHX7+Gup1gqp1YcP/YNmHcP6tHKjVjSXbD7N42yF+SjjIqh2HSc90f4+928Tw1o2uTevQ0VRbbtMYPzjbKSayThIONMN9/9usqsf9FJ8pq+74ruD9wSHQuv/Jx8cOwvYfYP0XRFVvTJ/4m+nT/Xr4TWtSUjNYsSOJxQkHsxfNycxUerw4l2s71eev/dugqmzYe4QWtaoQZHMgGeMXvk46Fwr8A7gHqIAbSHYCeBV41OtZVGKsRFDGpZ+AddNg8X9h2/dQsyXcvcgNYMslNT2TcT9up0VMFbo1jWJTYjK9xsyjangInRtW96qTatChvrUzGFOY/EoEviaCMcAw4GHcmAKAS4CngY9UdZQfYy2UJYJzSOI6OLIHmvaAtOMw9rfQ9hroMBQqRp52+OGUNGat28tPCYdYnHCQjYnJgGtn6FD/ZDtDlyZRVA6zpTiNyelsE8Ee4BZV/SrX9iuBt1W1jt8i9YElgnPUwS0w6VbYtRRCK0G7ayH+Fte+kN9TjqayZJtLCj8lHGTVzsOkZSif3NGN8xvVYO2uX/l57xH6tatNeGgwU5fttOkwTLl1tm0E1XDLVea2GYg8i7iMOalGE7h9DuxaBovfhVWfwLKxcPtcqBuX91MiKtC7TQy928QAcDwtg+W/JNG+XjUAvli5i7e+3UK/drWZumwnD0xaQVqG+/KzMymFRya7hm5LBqY887VEsBBYoqp359r+OhCrqt18OMd5wAdADK6x+U1V/ac3e+kEoBGQAAxR1UMFnctKBOXE8cOul1GHoa79YMZjkHoM4m+GmLY+nSIjU9l+8BiNa0Zw0TOz2ZmUctoxdaqF88Mjl/s7emNKnbNdvP5B4CYR2SAi73u3DcANwAM+niMd+LOqtgG6AneLSBtcu8MsVW0OzPIeGwPh1aDjdScbkU8kw9IP4PUL4Z2+sGKCa1coQHCQ0LhmBAC78kgCALsPH+dP45excMsBW2/BlEs+JQJVnQ+0ACYBlb3bJ0BLVS2k/2D2OXar6lLv/hFgHVAPuBo3hQXez2uKEL8pT/qPgZHroM/f4WgiTLkdZo72+el1IyvmuT2iQjCz1iVy3ZsLufzFecxYu9dPARtTNvjcrUJVdwGP+uOiItIIiAMWATGqutvbtQdXdZTXc24Hbgdo0KCBP8IwZVFEFFx4L3S9GxLmQ7Xz3Pbti2DuP1zjcsvfQPDpI5Mf6NuSRyavIiUtI3tbxdBgnvpte/q0jeHLlbsZ/9MvhAa7EsjOpBS27EvmoqY1bcyCOacV2Ebg6+pjqnrQ5wuKVAbmAU+p6mQRSVLVyBz7D6lq9YLOYW0E5jTrv4KvHoBfd0DlGOh0I3S6CSLPO+WwovQaevGbDfx77mZ+eLgntaqGk5GpBFtCMGXYGXUfFZFMCp9LSFXVp5KFNzDtC2C6qo7xtm0ALlPV3SJSB5irqi0LOo8lApOnzAzYOMMNVNv4DUTUhJHr3ejmM3AiPYPl25Po0iQKgOHvLCIsJJhhF5xH9xbRhAT72sRmTOlwpt1HC1qZrB/wR1wjsC8BCPAOsC4rCXg+B24CnvF+fubL+Yw5TVAwtOznbknbYd8GlwQyM2HsNdD4UogbDihMuhkGvQdV8qyJBNzkeFlJIDNTaV+vGhMX72Dmur3UrhrOkPj6DDn/POpXr1QiL8+Y4lLkSedEJA54Hjey+D/Ak6q6z4fnXQx8C6wCMr3Nf8G1E0wEGgDbcN1HC6xqshKBKZKj+2HSLbB1HgSFQLX6cGiba0/oP6bw5+eQlpHJrHWJjP9pO/N+dn/2lzSPZtj553F56xgqhFgpwZReZzWy2DtBY+ApYDAwGfiLquY1yKzYWSIwZ2T/JvjhX7DkXfc4uAL8aTWEhEFIOISGF+l0O5NSmPjTL0xc/Au7Dx+nZuUKvHVjPHENCmziMiZgznhksYhEAY8BdwDfAxeq6k/+D9GYYlazGUiQSwAZqW7bvGehYnVY9AY06wWt+kOLPm4MQyHqRVbk/t4tuO/y5sz/eR+Tlu6gWa3KAMxcu5ejqelc1aGu9TgypV6BiUBEHsUNGEsArlbVr0siKGOKxZE9sPyjk0kgI9U9HvQutB8MG76CtVMhKBRa9IWhH+Y5I2puwUFCj1a16NGqVva28T/9wu7DKVwd63okJR45Tq0qRStxGFNSCisRPAmkADuAu0TkrrwOUtUB/g7MGL+b9xxo5qnbNBM2zYSrXoYrx8COn2D9F5CRdjIJTL0LarZwpYWazXy61JvDO7PfW6P5yPE0uj83l9Z1qnDdBQ3o36FO9noLxpQGhf01foAtRWnOFTt+PFkayJKR6rYDBAVBgy7uliX1GCSudSWHmY9DdCtodSV0uA6iW+R7qaAgoVZVVwIQEf7cpwXjftzOg5NW8uS0tQyIrcuwCxrQrl7hVVDGFDdbqtIYXyT94qqO1n8BCd/DVf+ETsMheR8kroGGF+U5mjknVWXxtkOM+3E7X67czYn0TNrVq8p15zfg6ti6VAm3dZpN8TrrXkOliSUCE1DHDroG57DK8ONb8NUoCI+EFv1caaHZ5VAhosBTHE5J47PlOxn34y+s2/0rlSoEs+DhnkRWsrWZTfHxy5rFxhigUo6ZV2Kvhyp1YP2X8PP/YOV4t6jOn9e7nkeZma7KKZdqFUO5sVsjhndtyModh/kp4WB2Evj7F2tpUbsKQ+LPs4V0TImwRGDM2ahQCVr3d7eMdLcG8+4VJ7ufjv8dpCa7huZWv4HIUydMFBE6nhdJx/MiAUjPyGTZL0mEBAcxddlOHpm8kpQ018BtC+mY4mJVQ8YUp3nPwerJsG+de1ynI1zwB4i7vsCnpWdk0v35uXkupFM3MpwFD9tCOqboznZhGmPMmej+INy9EO5dCr3/BsFhkOytd5B6FL75K2xf6CbMyyEkOCjfhXR2JR1n5MTlfL16N8dSfZrqy5gCWYnAmJKm6sYobFsA7w+AzDSIiHbrKLTqD026Q0hY9tKa0RziXxVe5Z7U+9hHJBVDgwkLDSLpWBphIUFc0rwm/7wujogwq+k1BbMSgTGlRdZAtYYXwoNb4Np3oNHFsPpT+Hgw7P8ZgL9eWp2aoSe4L2QK58sG7g2ZTMXQYJ4e2J7Fj/Zi3G1d+V2XBqSkZVCpQjAAr83ZxMeLtgfqlZkyyr5CGBNI4VWh/SB3Sz/hGptj2gHQL/Ft+gSPQ8kkCGVoyDyi+/6VK7yG4m5No+jWNOqU0323cT91Iyvyuy4NUFXemLeFC5tG0aF+NcSH6TJM+WSJwJjSIiQMmvY8+Tj+FoJ2L4e9qwEII40rfroZui3L9xTjbu9KWobrZfTLwRRe+GYDGZlK7arh9G4TQ5+2MXRpHGXTZZtTWCIwprSqVg8ObDp1W9J2OLLXtSmMG+qql1oPgKim2YeEeiunNYiqxOJHezF7fSLfrN3DpCU7GLtwG1XCQ+jZqhZ92tSme8toKlvbQrlnjcXGlFZfjIRlY0+dHym4gltlrfuDMO462OWVDmLaQeurIPZ3p41VyHI8LYPvNu7nm7V7mLkukYNHU6kQHMSUuy+kbd1qqKpVH53jbGSxMWVNQZPkVakNt891JYR1X8C6z2HuM1A/3iWCpO1uZba6cdmN0+GhwfRqE0OvNjFkZCpLtx9i1rpEWsRUAeDZrzewbPshxt3W1dZQKGcsERhTWt3xXeHHRDaAbne525E9UMlrPF78Lnw3Bqqd50oKra+C87q4dZ1xayic36gG5zc6OV1Gw6hKnEjPyE4CIycuJ6ZqOH3axNCxfqQlh3OYVQ0Zcy46dhB+/hrWfg6bZ0PGCaje2A1sy2Puo9zSMzK5+b2f+GHzAdIzlVpVwujVJoY+bWLo1jSKsJDgEngRxt9s9lFjyqsTR2DjN66RuZu3ttR7/V1poc0AaNIj3/WaDx9LY86GRGas3cvcDYkcTc2gclgI3VtG06dNDD1a1aKqN322TZBX+lkiMMY46anw+b2w4X9w4jBUqAzN+8AFt0PDbvk+7XhaBj9sPsA3a/cwY+1e9ien8vLQWK6Jq8fHi7bxt2lrOZ5+cgW4rMFvlgxKD0sExphTpadCwnxYN81No93rCTcZ3q+7YctcaNkPKlbP86kZmcryXw7RIqYKVcJD6fjEdA6nnD7vUb3Iinz/cM88zmACwRKBMSZ/mRnuFlIBFv8XvrgfgkKg8aVunEKrK6FyrXyf3vjhL/Nd07Z7i2ha16lKm7pVaVOnKo1rRhBsDc8BYd1HjTH5CwrO7lFEpxFQuyOs+8w1Nn/xJ7cK2wObXAkhPdUljBzqRlbMc8rsiqHB7DtyggWbt5CW4VJFeGgQLWtXpVuTKB6+ohUAaRmZ2QPhTMkrsUQgIv8F+gOJqtrO21YDmAA0AhKAIap6qKRiMsbkISgI6nd2t15PwN41sHPJyWqicUPh+GGvW6ob1fxA35Y8MnkVldP2Z8+Umhwald1GkJqeyabEZNbu/pW1u35l3e5f+eXQsexLXvnKt8Q3qsE/ftsecHMmNatVmZiqYTbIrQSUWNWQiFwKJAMf5EgEzwEHVfUZEXkYqK6qDxV2LqsaMiaAFrzqFtvZtdQ9rtUWut7JVOlJ5hcjuSZ9OlNC+hLcf4xPDcWqyr/nbqZhVCX6d6jL4ZQ0Oj7xDQA1IirQuk4V2nhVS63rVKVpdGUrPZyhUtFGICKNgC9yJIINwGWqultE6gBzVbVlYeexRGBMKZD0C6z/wlUftewHHYbCPzu4WVSDK8A9S6B63tNdFCQ1PZMVO5JY55Ue1u7+lQ17jnDC65FUITiIFrUrc/dlzbiifR3SMjI5lppBtYqh/n6F55zS2kYQo6q7vft7gJhABmOMKYLI86Drne6mCl/++eRKaxmp8EosNL4EGnd3cyBVqe3TaSuEBJ026jk9I5Ot+4+6qiUvQWTNoLpyx2GufX0B799yAd1bRLP9wDHW7fmVNnWqUr96xXyrlmzcw0mBTgTZVFVFJN/iiYjcDtwO0KBB0b9lGGOKUfJeWP4RZObqQnp4F8x6Alpe4RJBwveQuBaaXAZRzU4u0lOIkOAgmsdUoXlMFa6OPfXDOqZqGA/2a0nrOm7OpG/W7uHvX7o1oquEh7geS1m3ulVpVqsyX6/ewyOTV5GS5hLXzqQUHpm8CqBcJoNAJ4K9IlInR9VQYn4HquqbwJvgqoZKKkBjjA/mPQeaeeq2oGBXIrj5SzdtNrjxCgtfc/er1HXLcjbu7qqVfJj6Ii/1q1firsuaZT++vktDOjesfkrD9ISffsn+0A8OEgRIzzz1YyQlLYPnp2+wRBAAnwM3Ac94Pz8LbDjGmDNS0EypOccf9H0Kzr8Vts6DLfPg5+mwfSHEDnP7l30I4ZFu6c6KkWcUSsUKwcQ1qE5cg5OD4TIylW0HjrJu9xHW7j7Ma3M25/ncXUkpvDl/MwePptGkZgRNoiNoXDOCGhEVzuneSyXZa2gccBlQE9gLPA5MBSYCDYBtuO6jBws7lzUWG3OOyMyE5D1Qta5rZ/hnBzeFtgS5KbQbd3eD2eqf1r55Vi56Znae4x7qRVakXb2qzF6fmD3uAaBqeAhNoivTpKZLDO3qVaNHq/wH2JVWAW8sVtVh+ey6vKRiMMaUMkFBLgmAay+4ZwnsXOymuNgyDxa84noh1Y+HjDT44V/Q6FKoG3tyANwZyBr3kFVdBG7wW1aDcXpGJjuTUtiy/yhb9h1l6/5ktu4/yg9bDjB52U66NYnKTgQ3vL2ITg0iGdnHdXj8ftN+6levSP3qlcrMCOpAVw0ZY8xJIRXc8psNL4Qef3Ezp6afcPv2roGZo939sGqu+qjJZW4GVR97JGXJagfIr9dQSHAQDaMiaBgVQY9cHdqPpabza455lepXr0jNKmHZ+65/exHgurk2iKpEY6+KyZUmKtMkOoKoUlbVZHMNGWPKjuRE2DrflRi2znPVSDd94Rql966B3StdA3RWKaOEpWVksvyXJLbuO8rm/cls3XeUrfuPsu3AMVIzTjam33d5c0b2bsHRE+m8891WftO+Ns1qVcn3vP7q6hrwqiFjjDlrlWtB+0HuBnBwK1T1PhDXTIX5z7n7Uc1dQmhyGbToB8ElM9gsNPj0MRDgGqt3Hkphy/5ktuw7SmyDSAC2HTjGmBk/0yKmCs1qVWHB5v38eeIKGnttEY1rRpD463He/2Fb9oC64ujqaiUCY8y5ITMTEte4toUtc2HbAggOgQe3uvaE9V9BaEVo0NX9BLe856SbYdB7UCUw41lTUjMQcWtKr955mP9+v5Ut+46yZV8yvx4/fWrvLGcyxXepmGLCXywRGGMKlZ4Kh7ZCtFfJ/+9ubjBbcBicd4ErMexZ5dZj6Hwz9B8T2HhzUVUOHUuj85Mz8pziW4Ctz1xZpHNa1ZAxpnwJqXAyCQDc+g1s+8EbwzAXZv/ddVPVTDcqutp50KIPRLc+48Ft/iQi1IiokO8U33UjK/rvWlYiMMaUS1PuhFWfQGYaBIW6nwCVanpzJF0KLa6AqnUCGubUZTvz7Op6JsuA5lciCHzaM8aYknZkD6yZfPLDPzMNQsKg79PQrJcb7fzF/fDLQrf/UAIsHweHd5Z4qNfE1ePpge2pF1kRwbUN+HstaKsaMsaUP3nNjaQKBzbBwP949zefbEDe8DV87S2VUqOpKy006e56JIX6r4omP9fE1SvWOZAsERhjyp+C5kYCN8q55smJ7LjgdjeAbes8N45h1SRYNhYe2ub2b5rpRj43vAjCq5bMa/AjSwTGmPLnju+KdnxQENRu527d7oaMdNj/M4RVdvu/f8UlCQn25ki6FJpd7pJHGWCJwBhjiio4BGLanHz8u4mw4ydXWtg6382RtHv5yUTw0zsQ0xbqdnK9mUoZSwTGGHO2QsO9nkaXAI/CiWQ4tt/tO/4rfPUAaAaERkDDbq7E0Ko/RDUNaNhZLBEYY4y/hVU+WW0UXhUe2AQJ350sMcx4DEIruURwZC+s/cwlh+iWPq/a5k+WCIwxprhVquFmSW0zwD0+ssd1VwXY9j387wF3v3KMSwiNL4U2V0N4tZPnKMbpMCwRGGNMScs5bXa7gVCv08nSwtb5bqBb08tdItg63yWBzbPd+IZ5z/p9OgxLBMYYE2jVG7lbpxtPjmGo5o0bWPYhrJxw8tjlH0H3h/xaKrCRxcYYU5rkHsNwzevQ+mrXNRXcQLh5z/r1kpYIjDGmNDu6DzZOd72OwA18W/6Ra2T2E0sExhhTmuU5HYZ/SwWWCIwxpjQrbDoMP7DGYmOMKc2KOh3GGbASgTHGlHOWCIwxppyzRGCMMeWcJQJjjCnnLBEYY0w5VyYXrxeRfcC2M3x6TWC/H8MpbmUpXou1+JSleMtSrFC24j3bWBuqanTujWUyEZwNEVmsqvGBjsNXZSlei7X4lKV4y1KsULbiLa5YrWrIGGPKOUsExhhTzpXHRPBmoAMoorIUr8VafMpSvGUpVihb8RZLrOWujcAYY8ypymOJwBhjTA6WCIwxppwrN4lARP4rIokisjrQsRRGRM4TkTkislZE1ojIHwMdU0FEJFxEfhSRFV68TwQ6psKISLCILBORLwIdS2FEJEFEVonIchFZHOh4CiIikSIySUTWi8g6EekW6JjyIyItvfc06/ariPwp0HHlR0Tu9/6/VovIOBEJ99u5y0sbgYhcCiQDH6hqu0DHUxARqQPUUdWlIlIFWAJco6prAxxankREgAhVTRaRUOA74I+qujDAoeVLREYC8UBVVe0f6HgKIiIJQLyqlvpBTyLyPvCtqr4tIhWASqqaFOCwCiUiwcBOoIuqnulg1WIjIvVw/1dtVDVFRCYCX6nqe/44f7kpEajqfOBgoOPwharuVtWl3v0jwDqgXmCjyp86yd7DUO9War9hiEh94Erg7UDHci4RkWrApcA7AKqaWhaSgOdyYHNpTAI5hAAVRSQEqATs8teJy00iKKtEpBEQBywKcCgF8qpalgOJwAxVLc3xvgw8CGQWclxpocA3IrJERG4PdDAFaAzsA971qt3eFpGIQAflo+uAcYEOIj+quhN4AdgO7AYOq+o3/jq/JYJSTEQqA58Cf1LVXwMdT0FUNUNVY4H6wAUiUiqr30SkP5CoqksCHUsRXKyqnYArgLu9as7SKAToBLyuqnHAUeDhwIZUOK8KawDwSaBjyY+IVAeuxiXbukCEiNzgr/NbIiilvLr2T4GPVHVyoOPxlVcVMAfoF+BQ8nMRMMCrdx8P9BSRDwMbUsG8b4OoaiIwBbggsBHlawewI0dpcBIuMZR2VwBLVXVvoAMpQC9gq6ruU9U0YDJwob9ObomgFPIaX98B1qnqmEDHUxgRiRaRSO9+RaA3sD6gQeVDVR9R1fqq2ghXHTBbVf32zcrfRCTC6zCAV83SByiVPd9UdQ/wi4i09DZdDpTKDg65DKMUVwt5tgNdRaSS9/lwOa7t0C/KTSIQkXHAD0BLEdkhIrcGOqYCXAQMx31bzera9ptAB1WAOsAcEVkJ/IRrIyj13TLLiBjgOxFZAfwIfKmqXwc4poLcC3zk/S3EAv8IbDgF85Jrb9w37FLLK2VNApYCq3Cf3X6bbqLcdB81xhiTt3JTIjDGGJM3SwTGGFPOWSIwxphyzhKBMcaUc5YIjDGmnLNEUI6JyFwR+VeArq0iMigQ1/ZFaY/PH7xZLEf7cNwcEbmxBELK69oF/h68WW+vLcmYzkWWCM5R3iCvf3tTGJ8Qkb0iMktEeuc4bCDwSKBi9DcR6eR9cFySz/4JIrKgpOMqSH4fdCLyXmmYIltErgTOAz7KsS3Bi1tFJMWbcvoBb6BTSXsSeEZE7LPsLNibd+76FDcVwa1AC6A/8D8gKusAVT3ozW5a5ohISO4PHm/G1uXALXkcHwVcg804WlR/BN5T1Yxc2/+GG0jYGjcZ2j+AQEyI9xVQBTdNhDlDlgjOQd50D5cAD6vqLFXdpqo/qeoLqjo+x3GnVA153/T+T0T+4y3SsUNEHsh17hYiMk9EjovIBhH5jYgki8gIb38j75tifK7nFVbEf8Y7X4oXx3M5F94QkdFeVcYIEdkMnADymtnybWCwN2FfTjd4z5kgIv1E5FsROSQiB0Vkuoi0LiA2n16TiNQTkfHeeQ+JyJci0jy/8xaFiAwUkZXe+3PQ+x3E5Nh/lbjZSY+LyFYReUrcZGpZ+2uJyGfe87eJyGnJMo9rRuPmuJmWx+4jqrpHVRNU9W1gJW76i6znNvWut0dEjorIUnET/uU8f6F/b3nE9JCI7BeRruAmO8Qlg2GFvR6TP0sE56Zk7zZAir6K0f24IeydgGeB58RbZcorfk8B0oGuwAjgcSDMDzEfxX2Tbw3chZsH6NFcxzQGfgcMBjoCx/M4z0dAMDA01/ZbgQmqehSXQF7GlZguAw4D03J+cBaViFTCTbZ3HOgOdMNNFzzT23fGRKQ2boK893Hvz6XA2Bz7++Je97+Atrj3cRCnTu/wHtAM98F+DXAj0KiQS1+MS575zm0kzmVeXGk5dlXGlUB7435XnwKTRaRVrlPk+/eWx3VewE1h0T3Xokc/4t5zc6ZU1W7n4A24FrcQz3HcHEsv4FZfynnMXOBfOR4nAONyHbMR+D/vfl9cEqiXY/+FuPnyR3iPG3mP43OdR4FB+T3OI/47gE05Ho/GfdDE+PDaPwQW5Hh8vne9LvkcHwFk4KZ7Pi0+X14T7sN3I960Ld62YOAAMKSAWPN8H3Af3F949zt5xzXM5xzzgb/m2nYN7suA4KoGFbgox/6G3mseXUBsfwK25bE9AZcgkoFU79wpwIWF/F4WZv0t+fL3luP9GQq8C/yc13uAm0I6Ewgp6f+zc+VmJYJzlKp+ipu3/CrcN7MLgYUi8pdCnroy1+NdQC3vfitgl3rTInt+wg8LvIjIIBH5zqtKSAZeAhrkOmyH+jZV8NtAtxzfPm8BVqs3PbJXbfGxiGwWkV+BvbjSce7rFUVnXInliFdVlowraVQHmp7FeQFWADOB1SLyqYjc6VXb5Lz2o1nX9a79MS7B1cZ9W8/EfXMGQN1KXIWtcFWRvEtdAGNwk8p1x5WEnlDV7IZ4cbOmPidu3e1DXkzxnP4eF/T3luUFXMntYs17BbEUXMLz2xq+5Y0lgnOYqh5X1Rmq+jdVvRA3tfXoQqpA0nI9Vor2d5KVFLIbcsWtrZAvr753PDAdl7jigP/DLXmZ01EfY5gHbAJuETct9jC85RM9XwDRwB+ALt710oH83hdfXlMQrqE6NtetBfCfAmI9AlTLY3skLpGgrh68j3dbiavm2igiHXNc+4lc1+0ANMetGJalqDNM7sclsrwcUNVNqvoDrvQ5SkR65Nj/Aq4K76+4ZBGLS0S532Nf/t5m4BJafjPw1gCO68nlUk0RhQQ6AFOi1uJ+5+G4In1RrQfqikhdVc36NhnPqf+4WR88dXJsiy3kvBcBO1X1yawNItLwDOID3BrKIvJfXI+X9bhvtmO980bhSjZ3qeocb1snCv5f8OU1LcUlnP1atHV6N+C+0WcnKnELqXfEVYdkvyZcFd8PIvI3YA2uymSFd+1WqroprwuIyHrc7+gCYIG3rQGuxFiQZUC0iNRU1f35HaSqh8R1OnhJROK8WC8GPvBKpnhtVU1x1TtF9RVumuhPRERV9f1c+9vh3gNzhqxEcA4SkSgRmS0iN4hIBxFpLCKDcev0ztIzX/ZyBu6D630R6eh9kx+D+zbtKnRVU3B1wQ+JSFsRuRD37bAgPwP1ROR6EWkiIndy9r1A3gdqeteeqqoHvO2HcN90bxORZiLSHXjDew158vE1fYSrYvpMRLp77/mlIvJiIT2HxuBKLneL65EVi5tnvob3ExHp6vWuOd/7AB+A69uftejL34DficjfRKSdiLTyqtqe8+LfAHwN/EdEunnXeA9XpVKQZbg1qC8u5DiAfwMtcaUAcL/T34ob29Ee125zxlU36ta3GAy8IacPbrsE9/rMGbJEcG5Kxn1w/RFXTbIG14PkY07vTeMzVc0EfovrJfQj7sP2KVwSyFmXnNU18Sdctcj/FXLeacDzuJ48K3E9TR470zi9c+7CfZOsTo6xA95rGIqrOlkNvIarvjhRyCkLfE2qegzXm2cLbu3b9bj3pzou+eQX5zjgZu+2GPeBVhu4RN2KX+CqiC7CVWltBF4EnlTVD71zTAeuBHrgfi8/4tYK3p7jUiOArcBsXHfQj3GNtfnyqqT+C1xf0HHesYm4Utdor3fZSFwS+RbXRrXQu3/GvGQwBJfQbgTXZRfX/vVuQc81BbOFacxZ8eqpl+N61JSlBeGND0SkFq7kcb6qbg10PLmJyPNANVUNxGC2c4a1EZgiEZHf4hptN+K6VY7hZD21OceoaqK4wWcNcCWK0iaRwqseTSGsRGCKxCuS/x+ujvoQbizC/T526zTGlEKWCIwxppyzxmJjjCnnLBEYY0w5Z4nAGGPKOUsExhhTzlkiMMaYcu7/AXkI/NK2++0sAAAAAElFTkSuQmCC", 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", "text/plain": [ "
    " ] @@ -576,7 +576,7 @@ "U, D, V_dagger = np.linalg.svd(M, full_matrices=True)\n", "\n", "# 计算 Frobenius-norm 误差\n", - "for i in range(T):\n", + "for i in range(RANK):\n", " lowrank_mat = np.matrix(U[:, :i]) * np.diag(D[:i])* np.matrix(V_dagger[:i, :])\n", " recons_mat = np.matrix(U_learned[:, :i]) * np.diag(singular_value[:i])* np.matrix(V_dagger_learned[:i, :])\n", " err_local.append(norm(lowrank_mat - recons_mat)) \n", @@ -586,9 +586,9 @@ "\n", "# 画图 \n", "fig, ax = plt.subplots()\n", - "ax.plot(list(range(1, T+1)), err_subfull, \"o-.\", \n", + "ax.plot(list(range(1, RANK+1)), err_subfull, \"o-.\", \n", " label = 'Reconstruction via VQSVD')\n", - "ax.plot(list(range(1, T+1)), err_SVD, \"^--\", \n", + "ax.plot(list(range(1, RANK+1)), err_SVD, \"^--\", \n", " label='Reconstruction via SVD')\n", "plt.xlabel('Singular Value Used (Rank)', fontsize = 14)\n", "plt.ylabel('Norm Distance', fontsize = 14)\n", @@ -608,7 +608,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 166, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:50:17.225100Z", @@ -629,7 +629,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 167, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:50:18.337792Z", @@ -681,14 +681,14 @@ "for i in range(5, 16, 5):\n", " reconstimg = np.matrix(U[:, :i]) * np.diag(sigma[:i]) * np.matrix(V[:i, :])\n", " plt.imshow(reconstimg, cmap='gray')\n", - " title = \"n = %s\" % i\n", + " title = f\"n = {i}\"\n", " plt.title(title)\n", " plt.show()" ] }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 168, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:50:18.966739Z", @@ -699,16 +699,18 @@ "source": [ "# 然后我们再来看看量子版本的分解效果:\n", "\n", + "# 设置电路参数\n", + "cir_depth = 40 # 电路深度\n", + "num_qubits = 5 # 量子比特数量\n", + "\n", "# 超参数设置\n", - "N = 5 # 量子比特数量\n", - "T = 8 # 设置想要学习的阶数\n", - "ITR = 200 # 迭代次数\n", - "LR = 0.02 # 学习速率\n", - "SEED = 14 # 随机数种子\n", + "RANK = 8 # 设置想要学习的阶数\n", + "ITR = 200 # 迭代次数\n", + "LR = 0.02 # 学习速率\n", + "SEED = 14 # 随机数种子\n", "\n", "# 设置等差的学习权重\n", - "weight = np.arange(2 * T, 0, -2).astype('complex128')\n", - "\n", + "weight = np.arange(2 * RANK, 0, -2).astype('complex128')\n", "\n", "def Mat_generator():\n", " imgmat = np.array(list(img.getdata(band=0)), float)\n", @@ -717,16 +719,12 @@ " return lenna.astype('complex128')\n", "\n", "M_err = Mat_generator()\n", - "U, D, V_dagger = np.linalg.svd(Mat_generator(), full_matrices=True)\n", - "\n", - "# 设置电路参数\n", - "cir_depth = 40 # 电路深度\n", - "block_len = 1 # 每个模组的长度" + "U, D, V_dagger = np.linalg.svd(Mat_generator(), full_matrices=True)" ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 169, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:50:19.553293Z", @@ -736,13 +734,13 @@ "outputs": [], "source": [ "# 重新定义量子神经网络\n", - "def U_theta():\n", + "def U_theta(num_qubits: int, depth: int) -> Circuit:\n", "\n", " # 用 Circuit 初始化网络\n", - " cir = Circuit(N)\n", + " cir = Circuit(num_qubits)\n", " \n", " # 搭建层级结构:\n", - " for _ in range(cir_depth):\n", + " for _ in range(depth):\n", " cir.ry()\n", " cir.cnot()\n", "\n", @@ -751,7 +749,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 170, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:59:58.649381Z", @@ -763,41 +761,41 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 0 loss: -4291.2284\n", - "iter: 10 loss: -103444.3877\n", - "iter: 20 loss: -126821.2327\n", - "iter: 30 loss: -135986.5470\n", - "iter: 40 loss: -141457.8124\n", - "iter: 50 loss: -145045.8896\n", - "iter: 60 loss: -147249.5471\n", - "iter: 70 loss: -149020.3769\n", - "iter: 80 loss: -150570.5096\n", - "iter: 90 loss: -151898.1960\n", - "iter: 100 loss: -152989.3110\n", - "iter: 110 loss: -153869.6654\n", - "iter: 120 loss: -154547.8973\n", - "iter: 130 loss: -155069.0768\n", - "iter: 140 loss: -155459.7348\n", - "iter: 150 loss: -155744.3048\n", - "iter: 160 loss: -155957.9127\n", - "iter: 170 loss: -156124.0155\n", - "iter: 180 loss: -156257.4063\n", - "iter: 190 loss: -156367.2717\n" + "iter: 0 loss: 3902.7036\n", + "iter: 10 loss: -109067.9844\n", + "iter: 20 loss: -124662.9922\n", + "iter: 30 loss: -136021.7188\n", + "iter: 40 loss: -143259.4844\n", + "iter: 50 loss: -147684.2812\n", + "iter: 60 loss: -150412.4688\n", + "iter: 70 loss: -151939.5781\n", + "iter: 80 loss: -152878.7969\n", + "iter: 90 loss: -153509.0000\n", + "iter: 100 loss: -153973.1875\n", + "iter: 110 loss: -154308.6562\n", + "iter: 120 loss: -154568.4688\n", + "iter: 130 loss: -154789.6094\n", + "iter: 140 loss: -154995.1719\n", + "iter: 150 loss: -155195.5625\n", + "iter: 160 loss: -155395.0156\n", + "iter: 170 loss: -155593.9375\n", + "iter: 180 loss: -155790.7188\n", + "iter: 190 loss: -155982.7812\n" ] }, { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 17, + "execution_count": 170, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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2zL5kveTGjx8fxth1dezYsfOex/JIsd5GFbu7/wFA9Ai3jDZfCHFhoG/QCZEJErsQmSCxC5EJErsQmSCxC5EJpTacBOJGecPDw+GcqGJr//794RxWgcQsI5ZHlPukSZPCOUNDQ2GMbWk0Z86cMMaqod59992q4y+++GI4Z8eOHWGMncebbropjEUWG2uWyThy5EgYS6k6pBYVqXpjNiuzythWZZFdymy+aI62fxJCSOxC5ILELkQmSOxCZILELkQmSOxCZMIFY70xyyCq8GEWFLPXmLXCbJyoOin1WKxKKtr/CwB6e3vD2LZt26qO9/f3Vx0HgI6OjjDGrDK2b1tkebEKNVbpx2IpDSLZHPZ6steFxZg9Gz03lkdUzSfrTQghsQuRCxK7EJkgsQuRCRK7EJlQ6mq8uyf1ZIuKMdiWRgy2Cp5SQMOeE+tpx2AFNHv37g1jUcEIe84zZ84MY/PmzQtjCxYsCGMzZsyoOs5WmNl5ZEUmLNZoWAENizEiZ4C9ZtGqe73bPwkhLgIkdiEyQWIXIhMkdiEyQWIXIhMkdiEyYVTrzcy6APwKlS2ZHcAad3/KzB4F8BMAZxrBPezub7LHYtYbKyKI7CtWtMIKD9ixmI0TzWNFFWyLKtZjbHBwMIy99957YWzt2rVVx9n2TzfeeGMYu+aaa8LYypUrw1i0XRPrG8isVFaQM23atDAWWansdWZ95pg1y+ax/CO7lD2vlB50tfjsJwH83N3Xm1k7gHVm9nYRe9Ld/6WGxxBCtJha9nrrB9Bf3B4ys60Aqu/aJ4S4YDmvz+xmNh/A1QA+KIYeMLNNZvacmcV9kYUQLadmsZtZG4BXATzo7oMAngawCMAKVP7yPx7MW21mPWbWc/jw4fozFkIkUZPYzWwcKkJ/wd1/AwDuvs/dT7n7aQDPALi22lx3X+Pu3e7ezTZFEEI0l1HFbpVv1j8LYKu7PzFifOSWJXcC2Nz49IQQjaKW1fjvA7gXwMdmtqEYexjAPWa2AhU7bheAn9aTCKvwiWLUZiB2WGqVVJRH6rGiPmIAcPDgwTB24MCBMBZZMp2dneGcRYsWhbGrrroqjM2ePTuM7d69u+r4sWPHwjmsYotZqcwOY7GI1NcztSIuspZZhSCz+SJqWY3/A4BqmVJPXQhxYaFv0AmRCRK7EJkgsQuRCRK7EJkgsQuRCaU2nDSz0E5IsUhSG/ylbDXF5qVaecxC27hxYxiLbC0AmDhxYtXxFStWhHOWLVsWxpi9xhpERlV7zG5ksOsjpTEjm8OeF8uDXTvsGkm59pPmnPcMIcR3EoldiEyQ2IXIBIldiEyQ2IXIBIldiEwo3XqLLA9W1XTixImq46w+nlk8rOEkyyOq2IryA3jlUm9vbxiLGkcCwOeffx7Goio11jiSNTZkNuWePXvCWGQ1zZo1K5wzefLkMJZaARa91pFFyeaMNo81zGTNUaMqO3YNR+dDe70JISR2IXJBYhciEyR2ITJBYhciEyR2ITKhVOvN3ZMa5UVVSNEeWQCvamLWStSwEYjtJNagkFlXKZYRwKurIvsqZQ7A96Njll2UP6vWmjJlShhjVWPsHEfXDrNLWdXb0NBQGGPXQUq1X8rzYnP0l12ITJDYhcgEiV2ITJDYhcgEiV2ITBh1Nd7MJgBYC2B8cf9fu/sjZrYAwEsAOgGsA3Cvu8dL2QXRKjlb9Y1WMlnRCis8YLBV62j1nK3sMtgWT6zPHFtx7erqqjrOetCx1XjmTrD8o1V3VrzEVuqZ88K2lIpW8dn1lrqtGCuSYddIdP7ZuW9WIczXAH7g7stR2Z75VjO7DsAvADzp7n8G4DCA+2t4LCFEixhV7F5huPhxXPHPAfwAwK+L8ecB3NGMBIUQjaHW/dnHFju4DgB4G8DnAI64+xlnvxfA3KZkKIRoCDWJ3d1PufsKAPMAXAvgz2s9gJmtNrMeM+s5dOhQWpZCiLo5r9V4dz8C4PcArgcwzczOrFbMA9AXzFnj7t3u3t3R0VFPrkKIOhhV7GY2w8ymFbcnAvghgK2oiP6vi7vdB+D1JuUohGgAtRTCzAHwvJmNReWXwyvu/lsz+wTAS2b2TwA+AvBsLQeMrAFW+BHZJ8wiYaTOi2xD1nuM2UmsH9uSJUvCWLS1EntM1sONFQ0xqyml8IPZZAxWCMNstJSCHHYtMmsrdV5KUUvK1mejit3dNwG4usr4DlQ+vwshvgPoG3RCZILELkQmSOxCZILELkQmSOxCZIKl2lBJBzPbD+BMOdd0AAdKO3iM8jgb5XE237U8rnT3GdUCpYr9rAOb9bh7d0sOrjyUR4Z56G28EJkgsQuRCa0U+5oWHnskyuNslMfZXDR5tOwzuxCiXPQ2XohMaInYzexWM/vMzLab2UOtyKHIY5eZfWxmG8ysp8TjPmdmA2a2ecRYh5m9bWbbiv/jzozNzeNRM+srzskGM7uthDy6zOz3ZvaJmW0xs78txks9JySPUs+JmU0wsz+a2cYij38sxheY2QeFbl42s7g7ajXcvdR/AMai0tZqIYBLAWwEsLTsPIpcdgGY3oLj3gRgJYDNI8b+GcBDxe2HAPyiRXk8CuDvSj4fcwCsLG63A/g/AEvLPickj1LPCQAD0FbcHgfgAwDXAXgFwN3F+L8B+JvzedxW/GW/FsB2d9/hldbTLwG4vQV5tAx3Xwvg3B5dt6PSuBMoqYFnkEfpuHu/u68vbg+h0hxlLko+JySPUvEKDW/y2gqxzwXw5YifW9ms0gH8zszWmdnqFuVwhlnu3l/c3gsg7mzRfB4ws03F2/ymf5wYiZnNR6V/wgdo4Tk5Jw+g5HPSjCavuS/Q3eDuKwH8FYCfmdlNrU4IqPxmR+UXUSt4GsAiVPYI6AfweFkHNrM2AK8CeNDdz2rHU+Y5qZJH6efE62jyGtEKsfcBGLltSdisstm4e1/x/wCA19Dazjv7zGwOABT/D7QiCXffV1xopwE8g5LOiZmNQ0VgL7j7b4rh0s9JtTxadU6KYx/BeTZ5jWiF2D8EsLhYWbwUwN0A3ig7CTObbGbtZ24D+BGAzXxWU3kDlcadQAsbeJ4RV8GdKOGcWKWh2rMAtrr7EyNCpZ6TKI+yz0nTmryWtcJ4zmrjbaisdH4O4O9blMNCVJyAjQC2lJkHgBdReTv4LSqfve5HZc+8dwBsA/C/ADpalMd/APgYwCZUxDanhDxuQOUt+iYAG4p/t5V9TkgepZ4TAH+BShPXTaj8YvmHEdfsHwFsB/BfAMafz+PqG3RCZELuC3RCZIPELkQmSOxCZILELkQmSOxCZILELkQmSOxCZILELkQm/D965hTK7FIF7QAAAABJRU5ErkJggg==", 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", 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    " ] @@ -812,37 +810,17 @@ "# 记录优化中间过程\n", "loss_list, singular_value_list = [], []\n", "U_learned, V_dagger_learned = [], []\n", - " \n", - "net = NET(Mat_generator(), weight)\n", - "\n", - "# 一般来说,我们利用 Adam 优化器来获得相对好的收敛\n", - "# 当然你可以改成 SGD 或者是 RMS prop.\n", - "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())\n", - "\n", - "# 优化循环\n", - "for itr in range(ITR):\n", "\n", - " # 前向传播计算损失函数\n", - " U, V_dagger, loss, singular_values = net()\n", - "\n", - " # 反向传播极小化损失函数\n", - " loss.backward()\n", - " opt.minimize(loss)\n", - " opt.clear_grad()\n", - "\n", - " # 记录优化中间结果\n", - " loss_list.append(loss[0][0].numpy())\n", - " singular_value_list.append(singular_values)\n", - " \n", - " if itr% 10 == 0:\n", - " print('iter:', itr,'loss:','%.4f'% loss.numpy()[0])\n", + "# 创建 VQSVD 网络并训练\n", + "net = VQSVD(matrix=Mat_generator(), weights=weight, num_qubits=num_qubits, depth=cir_depth, rank=RANK, lr=LR, itr=ITR, seed=SEED)\n", + "loss_list, singular_value_list = net.train()\n", "\n", "# 记录最后学出的两个酉矩阵 \n", - "U_learned = U.numpy()\n", - "V_dagger_learned = V_dagger.numpy()\n", + "U_learned = net.get_matrix_U().numpy()\n", + "V_dagger_learned = dagger(net.get_matrix_V()).numpy()\n", "\n", "singular_value = singular_value_list[-1]\n", - "mat = np.matrix(U_learned.real[:, :T]) * np.diag(singular_value[:T])* np.matrix(V_dagger_learned.real[:T, :])\n", + "mat = np.matrix(U_learned.real[:, :RANK]) * np.diag(singular_value[:RANK])* np.matrix(V_dagger_learned.real[:RANK, :])\n", "\n", "reconstimg = mat\n", "plt.imshow(reconstimg, cmap='gray')" diff --git a/tutorials/machine_learning/VQSVD_EN.ipynb b/tutorials/machine_learning/VQSVD_EN.ipynb index c243bad..cdbfb9e 100644 --- a/tutorials/machine_learning/VQSVD_EN.ipynb +++ b/tutorials/machine_learning/VQSVD_EN.ipynb @@ -76,14 +76,27 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2021-03-09T03:44:34.008567Z", "start_time": "2021-03-09T03:44:29.796997Z" } }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import numpy as np\n", "from numpy import pi as PI\n", @@ -344,14 +357,13 @@ ], "source": [ "# Hyperparameter settings\n", - "N = 3 # Number of qubits\n", - "T = 8 # Set the number of rank you want to learn\n", + "RANK = 8 # Set the number of rank you want to learn\n", "ITR = 100 # Number of iterations\n", "LR = 0.02 # Learning rate\n", "SEED = 14 # Random seed\n", "\n", "# Set the learning weight \n", - "weight = np.arange(3 * T, 0, -3).astype('complex128')\n", + "weight = np.arange(3 * RANK, 0, -3).astype('complex128')\n", "print('The selected weight is:')\n", "print(weight)" ] @@ -375,8 +387,8 @@ "outputs": [], "source": [ "# Set circuit parameters\n", - "cir_depth = 20 # circuit depth\n", - "block_len = 2 # length of each block" + "num_qubits = 3 # number of qubits\n", + "cir_depth = 20 # circuit depth" ] }, { @@ -386,13 +398,13 @@ "outputs": [], "source": [ "# Define quantum neural network\n", - "def U_theta() -> Circuit:\n", + "def U_theta(num_qubits: int, depth: int) -> Circuit:\n", "\n", " # Initialize the network with Circuit\n", - " cir = Circuit(N)\n", + " cir = Circuit(num_qubits)\n", " \n", " # Build a hierarchy:\n", - " for _ in range(cir_depth):\n", + " for _ in range(depth):\n", " cir.ry()\n", " cir.rz()\n", " cir.cnot()\n", @@ -418,42 +430,66 @@ }, "outputs": [], "source": [ - "class NET(paddle.nn.Layer):\n", - " def __init__(self, matrix: np.ndarray, weights: np.ndarray) -> None:\n", - " super(NET, self).__init__()\n", + "class VQSVD():\n", + " def __init__(self, matrix: np.ndarray, weights: np.ndarray, num_qubits: int, depth: int, rank: int, lr: float, itr: int, seed: int):\n", + " \n", + " # Hyperparameters\n", + " self.rank = rank\n", + " self.lr = lr\n", + " self.itr = itr\n", + " \n", + " paddle.seed(seed)\n", " \n", " # Create the parameter theta for learning U\n", - " self.cir_U = U_theta()\n", + " self.cir_U = U_theta(num_qubits, depth)\n", " \n", " # Create a parameter phi to learn V_dagger\n", - " self.cir_V = U_theta()\n", + " self.cir_V = U_theta(num_qubits, depth)\n", " \n", " # Convert Numpy array to Tensor supported in Paddle\n", " self.M = paddle.to_tensor(matrix)\n", " self.weight = paddle.to_tensor(weights)\n", "\n", - " # Define loss function and forward propagation mechanism\n", - " def forward(self):\n", + " # Define the loss function\n", + " def loss_func(self):\n", " \n", " # Get the unitary matrix representation of the quantum neural network\n", " U = self.cir_U.unitary_matrix()\n", - " U_dagger = dagger(U)\n", - " \n", - " \n", " V = self.cir_V.unitary_matrix()\n", - " V_dagger = dagger(V)\n", - " \n", + " \n", " # Initialize the loss function and singular value memory\n", - " loss = 0\n", - " singular_values = np.zeros(T)\n", + " loss = paddle.to_tensor(0.0)\n", + " singular_values = np.zeros(self.rank)\n", " \n", " # Define loss function\n", - " for i in range(T):\n", - " loss -= paddle.real(self.weight)[i] * paddle.real(U_dagger @ self.M @ V)[i][i]\n", - " singular_values[i] = paddle.real(U_dagger @ self.M @ V)[i][i].numpy()\n", + " for i in range(self.rank):\n", + " loss -= paddle.real(self.weight)[i] * paddle.real(dagger(U) @ self.M @ V)[i][i]\n", + " singular_values[i] = paddle.real(dagger(U) @ self.M @ V)[i][i].numpy()\n", " \n", - " # Function returns two matrices U and V_dagger, learned singular values and loss function\n", - " return U, V_dagger, loss, singular_values" + " # Function returns learned singular values and loss function\n", + " return loss, singular_values\n", + " \n", + " def get_matrix_U(self):\n", + " return self.cir_U.unitary_matrix()\n", + " \n", + " def get_matrix_V(self):\n", + " return self.cir_V.unitary_matrix()\n", + " \n", + " # Train the VQSVD network\n", + " def train(self):\n", + " loss_list, singular_value_list = [], []\n", + " optimizer = paddle.optimizer.Adam(learning_rate=self.lr, parameters=self.cir_U.parameters()+self.cir_V.parameters())\n", + " for itr in range(self.itr):\n", + " loss, singular_values = self.loss_func()\n", + " loss.backward()\n", + " optimizer.minimize(loss)\n", + " optimizer.clear_grad()\n", + " loss_list.append(loss.numpy()[0])\n", + " singular_value_list.append(singular_values)\n", + " if itr% 10 == 0:\n", + " print('iter:', itr,'loss:','%.4f'% loss.numpy()[0])\n", + " \n", + " return loss_list, singular_value_list" ] }, { @@ -461,25 +497,36 @@ "execution_count": 11, "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " elif dtype == np.bool:\n", + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/fluid/dygraph/math_op_patch.py:276: UserWarning: The dtype of left and right variables are not the same, left dtype is paddle.float32, but right dtype is paddle.float64, the right dtype will convert to paddle.float32\n", + " warnings.warn(\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "iter: 0 loss: -43.6754\n", - "iter: 10 loss: -1533.6699\n", - "iter: 20 loss: -2002.1223\n", - "iter: 30 loss: -2137.2044\n", - "iter: 40 loss: -2200.9439\n", - "iter: 50 loss: -2267.5643\n", - "iter: 60 loss: -2329.0521\n", - "iter: 70 loss: -2359.0386\n", - "iter: 80 loss: -2367.3676\n", - "iter: 90 loss: -2372.0702\n" + "iter: 0 loss: -88.4531\n", + "iter: 10 loss: -1795.0786\n", + "iter: 20 loss: -2059.0496\n", + "iter: 30 loss: -2202.6445\n", + "iter: 40 loss: -2269.9832\n", + "iter: 50 loss: -2304.1875\n", + "iter: 60 loss: -2320.8447\n", + "iter: 70 loss: -2331.9180\n", + "iter: 80 loss: -2340.2454\n", + "iter: 90 loss: -2348.0549\n" ] }, { "data": { - "image/png": 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", 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", 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    " ] @@ -495,38 +542,16 @@ "loss_list, singular_value_list = [], []\n", "U_learned, V_dagger_learned = [], []\n", "\n", - " \n", - "# Determine the parameter dimension of the network\n", - "net = NET(M, weight)\n", - "\n", - "# We use Adam optimizer for better performance\n", - "# One can change it to SGD or RMSprop.\n", - "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())\n", - "\n", - "# Optimization cycle\n", - "for itr in range(ITR):\n", - "\n", - " # Forward propagation to calculate loss function\n", - " U, V_dagger, loss, singular_values = net()\n", - "\n", - " # Back propagation minimizes the loss function\n", - " loss.backward()\n", - " opt.minimize(loss)\n", - " opt.clear_grad()\n", - "\n", - " # Record optimization intermediate results\n", - " loss_list.append(loss[0][0].numpy())\n", - " singular_value_list.append(singular_values)\n", - " \n", - " if itr% 10 == 0:\n", - " print('iter:', itr,'loss:','%.4f'% loss.numpy()[0])\n", + "# Construct the VQSVD network and train\n", + "net = VQSVD(matrix=M, weights=weight, num_qubits=num_qubits, depth=cir_depth, rank=RANK, lr=LR, itr=ITR, seed=SEED)\n", + "loss_list, singular_value_list = net.train()\n", "\n", "# Draw a learning curve\n", "loss_plot(loss_list)\n", "\n", "# Record the last two learned unitary matrices\n", - "U_learned = U.numpy()\n", - "V_dagger_learned = V_dagger.numpy()" + "U_learned = net.get_matrix_U().numpy()\n", + "V_dagger_learned = dagger(net.get_matrix_V()).numpy()" ] }, { @@ -566,7 +591,7 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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    " ] @@ -584,7 +609,7 @@ "\n", "\n", "# Calculate the Frobenius-norm error\n", - "for i in range(T):\n", + "for i in range(RANK):\n", " lowrank_mat = np.matrix(U[:, :i]) * np.diag(D[:i])* np.matrix(V_dagger[:i, :])\n", " recons_mat = np.matrix(U_learned[:, :i]) * np.diag(singular_value[:i])* np.matrix(V_dagger_learned[:i, :])\n", " err_local.append(norm(lowrank_mat - recons_mat)) \n", @@ -594,9 +619,9 @@ "\n", "# Plot\n", "fig, ax = plt.subplots()\n", - "ax.plot(list(range(1, T+1)), err_subfull, \"o-.\", \n", + "ax.plot(list(range(1, RANK+1)), err_subfull, \"o-.\", \n", " label = 'Reconstruction via VQSVD')\n", - "ax.plot(list(range(1, T+1)), err_SVD, \"^--\", \n", + "ax.plot(list(range(1, RANK+1)), err_SVD, \"^--\", \n", " label='Reconstruction via SVD')\n", "plt.xlabel('Singular Value Used (Rank)', fontsize = 14)\n", "plt.ylabel('Norm Distance', fontsize = 14)\n", @@ -690,7 +715,7 @@ "for i in range(5, 16, 5):\n", " reconstimg = np.matrix(U[:, :i]) * np.diag(sigma[:i]) * np.matrix(V[:i, :])\n", " plt.imshow(reconstimg, cmap='gray')\n", - " title = \"n = %s\" % i\n", + " title = f\"n = {i}\"\n", " plt.title(title)\n", " plt.show()" ] @@ -706,15 +731,18 @@ }, "outputs": [], "source": [ + "# Set circuit parameters\n", + "cir_depth = 40 # depth of circuit\n", + "num_qubits = 5 # Number of qubits\n", + "\n", "# Hyper-parameters\n", - "N = 5 # Number of qubits\n", - "T = 8 # Set the number of rank you want to learn\n", - "ITR = 200 # Number of iterations\n", - "LR = 0.02 # Learning rate\n", - "SEED = 14 # Random number seed\n", + "RANK = 8 # Set the number of rank you want to learn\n", + "ITR = 200 # Number of iterations\n", + "LR = 0.02 # Learning rate\n", + "SEED = 14 # Random number seed\n", "\n", "# Set the learning weight\n", - "weight = np.arange(2 * T, 0, -2).astype('complex128')\n", + "weight = np.arange(2 * RANK, 0, -2).astype('complex128')\n", "\n", "# Convert the image into numpy array\n", "def Mat_generator():\n", @@ -724,11 +752,7 @@ " return lenna.astype('complex128')\n", "\n", "M_err = Mat_generator()\n", - "U, D, V_dagger = np.linalg.svd(Mat_generator(), full_matrices=True)\n", - "\n", - "# Set circuit parameters\n", - "cir_depth = 40 # Circuit depth\n", - "block_len = 1 # The length of each module" + "U, D, V_dagger = np.linalg.svd(Mat_generator(), full_matrices=True)" ] }, { @@ -742,14 +766,14 @@ }, "outputs": [], "source": [ - "# Define quantum neural network\n", - "def U_theta():\n", + "# Define circuit of quantum neural network\n", + "def U_theta(num_qubits: int, depth: int) -> Circuit:\n", "\n", " # Initialize the network with Circuit\n", - " cir = Circuit(N)\n", + " cir = Circuit(num_qubits)\n", " \n", " # Build a hierarchy:\n", - " for _ in range(cir_depth):\n", + " for _ in range(depth):\n", " cir.ry()\n", " cir.cnot()\n", "\n", @@ -770,32 +794,32 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 0 loss: -5052.6035\n", - "iter: 10 loss: -108312.2634\n", - "iter: 20 loss: -127067.9950\n", - "iter: 30 loss: -138785.3241\n", - "iter: 40 loss: -144992.7031\n", - "iter: 50 loss: -148297.3650\n", - "iter: 60 loss: -150532.9232\n", - "iter: 70 loss: -152235.0095\n", - "iter: 80 loss: -153425.8656\n", - "iter: 90 loss: -154247.9781\n", - "iter: 100 loss: -154813.1122\n", - "iter: 110 loss: -155224.0510\n", - "iter: 120 loss: -155530.3507\n", - "iter: 130 loss: -155773.2695\n", - "iter: 140 loss: -155976.5740\n", - "iter: 150 loss: -156153.5143\n", - "iter: 160 loss: -156310.1349\n", - "iter: 170 loss: -156450.4223\n", - "iter: 180 loss: -156576.0634\n", - "iter: 190 loss: -156689.3533\n" + "iter: 0 loss: 3902.7036\n", + "iter: 10 loss: -109067.9844\n", + "iter: 20 loss: -124662.9922\n", + "iter: 30 loss: -136021.7188\n", + "iter: 40 loss: -143259.4844\n", + "iter: 50 loss: -147684.2812\n", + "iter: 60 loss: -150412.4688\n", + "iter: 70 loss: -151939.5781\n", + "iter: 80 loss: -152878.7969\n", + "iter: 90 loss: -153509.0000\n", + "iter: 100 loss: -153973.1875\n", + "iter: 110 loss: -154308.6562\n", + "iter: 120 loss: -154568.4688\n", + "iter: 130 loss: -154789.6094\n", + "iter: 140 loss: -154995.1719\n", + "iter: 150 loss: -155195.5625\n", + "iter: 160 loss: -155395.0156\n", + "iter: 170 loss: -155593.9375\n", + "iter: 180 loss: -155790.7188\n", + "iter: 190 loss: -155982.7812\n" ] }, { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 17, @@ -804,7 +828,7 @@ }, { "data": { - "image/png": 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", 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", 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    " ] @@ -820,36 +844,16 @@ "loss_list, singular_value_list = [], []\n", "U_learned, V_dagger_learned = [], []\n", " \n", - "net = NET(Mat_generator(), weight)\n", - "\n", - "# We use Adam optimizer for better performance\n", - "# One can change it to SGD or RMSprop.\n", - "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())\n", - "\n", - "# Optimization loop\n", - "for itr in range(ITR):\n", - "\n", - " # Forward propagation to calculate loss function\n", - " U, V_dagger, loss, singular_values = net()\n", - "\n", - " # Back propagation minimizes the loss function\n", - " loss.backward()\n", - " opt.minimize(loss)\n", - " opt.clear_grad()\n", - "\n", - " # Record optimization intermediate results\n", - " loss_list.append(loss[0][0].numpy())\n", - " singular_value_list.append(singular_values)\n", - " \n", - " if itr% 10 == 0:\n", - " print('iter:', itr,'loss:','%.4f'% loss.numpy()[0])\n", + "# Construct the VQSVD network and train\n", + "net = VQSVD(matrix=Mat_generator(), weights=weight, num_qubits=num_qubits, depth=cir_depth, rank=RANK, lr=LR, itr=ITR, seed=SEED)\n", + "loss_list, singular_value_list = net.train()\n", "\n", "# Record the last two unitary matrices learned\n", - "U_learned = U.numpy()\n", - "V_dagger_learned = V_dagger.numpy()\n", + "U_learned = net.get_matrix_U().numpy()\n", + "V_dagger_learned = dagger(net.get_matrix_V()).numpy()\n", "\n", "singular_value = singular_value_list[-1]\n", - "mat = np.matrix(U_learned.real[:, :T]) * np.diag(singular_value[:T])* np.matrix(V_dagger_learned.real[:T, :])\n", + "mat = np.matrix(U_learned.real[:, :RANK]) * np.diag(singular_value[:RANK])* np.matrix(V_dagger_learned.real[:RANK, :])\n", "\n", "reconstimg = mat\n", "plt.imshow(reconstimg, cmap='gray')" diff --git a/tutorials/machine_learning/figures/QGAN-fig-loss.gif b/tutorials/machine_learning/figures/QGAN-fig-loss.gif index 4f66f308c239361fe94f3482f798322dc8227c2c..91b1e04034d1aa2428b6fd9f860abec0cf96935d 100644 GIT binary patch delta 1146 zcmdn{i|OEWCSG?>Hw(+e4U7tmtqcs46Iv7}>dl{Av`Cm;@h1zT4Flt5b>>T=Tsme9 zH4MIt6%4IFB}$VmB|XcynCEAxU4Bv%WRD+kLdP7YR{50>*(E5eZbsiTynq4EFt z@&DoB|CcZS-`@Uz`t<+l>Hl}^XlrY`apT5+aq+gc|NqO&XUzDouKr(ERyH{~+1>sB z%9SfKGyhjq{0|HJfAZwXkdP1wiT~#2|M%?K@D)bk?q2XNe`2*`BXi7acM>Nq6rhsRy%HAxP6|V@9l?gZmqPR@#E*g$?FY5 z0;aO-Zh3IK{*!2iLabRtf+MR)n8m?XiKGP&+hj^!EaXsVT5+&LB`@Jor{t0qN$fh? zDh_t*2Pr)6;lGmcxS3%FdqRW7GWX^-iKGa{Rw1#>$-#z7CK^he%JVW7bxB@uXlBXT z#`&1l_!Y;3X4^@w>P}|YEFSmd@4J!IospKXtTUxgV;M(6*$dUlD-By1H74sBDKI(m zOb#$ol*#6K!q~u+@{8PLd_W-2{-o2kBhn*;0gwQo}VKQxIuh;8Z%)k&Uy z`pz?}?>jH_t}E$XHJQas8Gb=nP<1Eo-y zzA_JpT#ok~3^}(zh@4GG1BTqMNQm5rm?*d$%)X8!keuY^hEzKYxj$JDeV=lZ!Ezu! z6hYlNxfmkXS>}SFkGlpU$5`)#CU;#M1?mys{BVl|P|sV2cMQ`Qm>3{(hPzxRi|thh096sV A{Qv*} delta 2104 zcmX>&ooVkcCSG?>Hw(+e4U7tm?Fdl|LKF4eFh8$07w1e!J{6uU%R>NVICPYPS zo+bW*4Tn*+K%>f`My-`2Y*ey*5h0@J4B!ih-_ldkzxJ$rF!MfSYOiRvPZ3n!PU zhZu#j>uz~)yZ)1ChC-}qOo1b-NSMXJR*AF)58Gr)ULSF3@OURG<7+LxJfa_hfNRMVZ&!PZ$fBQhvy--n2{J{ObnB zD}PN34;h!=HeMw=IYcvnQFilE%`m3=B?lNE#;707X=q}V5M@O)mPaFV znyL2WS{;4)E(O-jH_t}E%CHTkrTHjV^Y4@{7y z&;+TdOE^JZ*L}u{$EXshQ7?=M8#T{lH!h<<*#zdQ7AwL=Sy|5^#wbQd!bWX(Y#?mZ z0YceevxG+!K4W0vG}o7~i-P?e2pI(`0}ckyA?T`-kYrp&ff7OyF!mls;`Q9-gebg0 z4fB|K0%4EcO>n~H8c+g&8ReBm(5Ox6`nXK$1DccwO_fnOgiLbT{3pkg1xEr08I=Sz zs-TbQp5p^w1_Zr+kIg62)W)fm5dX?ZMmyUX4(yknTgzy$Q< Z!dAJ-5#3IcU;73UG_t{jWAf~7H2@tk7h?bb diff --git a/tutorials/qnn_research/BarrenPlateaus_CN.ipynb b/tutorials/qnn_research/BarrenPlateaus_CN.ipynb index 8f7acf2..d248b16 100644 --- a/tutorials/qnn_research/BarrenPlateaus_CN.ipynb +++ b/tutorials/qnn_research/BarrenPlateaus_CN.ipynb @@ -44,8 +44,12 @@ "name": "stderr", "output_type": "stream", "text": [ - "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\openfermion\\hamiltonians\\hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", - " from scipy.optimize.optimize import OptimizeResult\n" + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" ] } ], @@ -59,9 +63,10 @@ "import numpy as np\n", "from math import pi\n", "import paddle\n", - "from paddle_quantum.state import zero_state\n", "from paddle_quantum.ansatz import Circuit\n", "from paddle_quantum.linalg import dagger\n", + "from paddle_quantum.loss import ExpecVal\n", + "from paddle_quantum.state import zero_state\n", "# 画图工具\n", "from matplotlib import pyplot as plt \n" ] @@ -161,21 +166,18 @@ "name": "stderr", "output_type": "stream", "text": [ - "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", - " elif dtype == np.bool:\n", - "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", - "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", - " if data.dtype == np.object:\n" + " elif dtype == np.bool:\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "主程序段总共运行了 2.7961888313293457 秒\n", - "采样 300 个随机网络关于第一个参数梯度的均值是: -0.025778826\n", - "采样 300 个随机网络关于第一个参数梯度的方差是: 0.11283756\n" + "主程序段总共运行了 2.0201921463012695 秒\n", + "采样 300 个随机网络关于第一个参数梯度的均值是: -0.002514134\n", + "采样 300 个随机网络关于第一个参数梯度的方差是: 0.11258849\n" ] } ], @@ -282,21 +284,19 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ - "主程序段总共运行了 1.4345674514770508 秒\n" + "主程序段总共运行了 1.368649959564209 秒\n" ] } ], @@ -453,7 +453,8 @@ "source": [ "# 要优化的目标函数,其中参数分别是电路和哈密顿量\n", "def loss_func(circuit: Circuit, H: Hamiltonian) -> paddle.Tensor:\n", - " return circuit().expec_val(H, shots = 0)" + " expec_val = ExpecVal(H)\n", + " return expec_val(circuit())" ] }, { @@ -495,17 +496,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "--Ry(0.785)----Rx(0.557)----*--\n", + "--Ry(0.785)----Ry(5.090)----*--\n", " | \n", - "--Ry(0.785)----Rz(1.090)----z--\n", + "--Ry(0.785)----Rz(4.853)----z--\n", " \n", - "Hamiltonian info: -0.5460435438880067 X0\n", - "-0.06715081059031625 Z1, Z0\n", - "-0.7710366768893184 Z1, X0\n", - "-0.7873104687630661 Z1, Y0\n", - "0.9563406325371104 Y0\n", - "0.8230280338420977 Y1\n", - "-0.7909293184638813 Y0, Y1\n" + "Hamiltonian info: \n", + " -0.11659613736881846 X0\n", + "0.7564519922877542 Z0\n", + "-0.5665789011512152 Y0, Y1\n", + "0.47839020497319384 Z0, Y1\n", + "0.8831698245631991 X0, Z1\n", + "-0.37755591215283 Y0\n", + "0.5686545814476456 Z0, X1\n" ] } ], @@ -517,7 +519,7 @@ "print(cir)\n", "# 随机生成哈密顿量\n", "H_l = Hamiltonian(random_pauli_str_generator(N, terms=7))\n", - "print('Hamiltonian info: ', H_l)" + "print('Hamiltonian info: \\n', H_l)" ] }, { @@ -545,7 +547,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 100%|###################################################| 300/300 [00:03<00:00, 83.25it/s]" + "Sampling: 100%|##################################################| 300/300 [00:02<00:00, 105.66it/s]\n" ] }, { @@ -553,30 +555,21 @@ "output_type": "stream", "text": [ "Mean of gradient for all parameters: \n", - "theta 1 : 0.010323498\n", - "theta 2 : -0.023893388\n", + "theta 1 : 0.008229507\n", + "theta 2 : -0.015562029\n", "Variance of gradient for all parameters: \n", - "theta 1 : 0.04497918\n", - "theta 2 : 0.1173012\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n" + "theta 1 : 0.64334434\n", + "theta 2 : 0.18892294\n" ] }, { "data": { - "image/png": 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", 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", 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", 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -654,22 +643,15 @@ "name": "stderr", "output_type": "stream", "text": [ - "Training: 100%|###################################################| 120/120 [00:01<00:00, 93.13it/s]" + "Training: 100%|##################################################| 120/120 [00:01<00:00, 104.60it/s]\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "最终的优化结果: -1.431776\n", - "实际的基态能量: -2.935288\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n" + "最终的优化结果: -1.8954318\n", + "实际的基态能量: -2.3761654\n" ] } ], @@ -706,7 +688,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 100%|###################################################| 300/300 [00:03<00:00, 89.26it/s]" + "Sampling: 100%|###################################################| 300/300 [00:03<00:00, 99.81it/s]\n" ] }, { @@ -714,41 +696,32 @@ "output_type": "stream", "text": [ "Mean of max gradient\n", - "0.7397743\n", + "0.93205416\n", "Variance of max gradient\n", - "0.16580562\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n" + "0.1852078\n" ] }, { "data": { - "image/png": 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", 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 0%| | 0/300 [00:00" + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 0%| | 0/300 [00:00" + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 0%| | 0/300 [00:00" + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -900,14 +853,12 @@ }, { "data": { - "image/png": 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", + "image/png": 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    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -1092,9 +1043,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "--Rz(0.812)----Ry(1.897)----Rz(4.609)----*----x----Ry(1.629)--\n", + "--Rz(0.907)----Ry(2.993)----Rz(0.103)----*----x----Ry(5.857)--\n", " | | \n", - "--Rz(0.351)----Ry(2.939)----Rz(5.847)----x----*----Ry(0.576)--\n", + "--Rz(5.250)----Ry(2.564)----Rz(4.133)----x----*----Ry(5.153)--\n", " \n" ] }, @@ -1102,7 +1053,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", " elif dtype == np.bool:\n" ] @@ -1148,37 +1099,24 @@ "execution_count": 18, "metadata": {}, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", - "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", - " if data.dtype == np.object:\n" - ] - }, { "data": { - "image/png": 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", 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", 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", + "image/png": 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -1209,7 +1147,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 100%|###################################################| 300/300 [00:03<00:00, 76.54it/s]" + "Sampling: 100%|##################################################| 300/300 [00:02<00:00, 112.23it/s]\n" ] }, { @@ -1217,28 +1155,19 @@ "output_type": "stream", "text": [ "Mean of max gradient\n", - "0.15144292\n", + "0.14334632\n", "Variance of max gradient\n", - "0.0035474023\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n" + "0.0034603078\n" ] }, { "data": { - "image/png": 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", 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], diff --git a/tutorials/qnn_research/BarrenPlateaus_EN.ipynb b/tutorials/qnn_research/BarrenPlateaus_EN.ipynb index 3af2e1e..6c57fa5 100644 --- a/tutorials/qnn_research/BarrenPlateaus_EN.ipynb +++ b/tutorials/qnn_research/BarrenPlateaus_EN.ipynb @@ -42,8 +42,12 @@ "name": "stderr", "output_type": "stream", "text": [ - "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\openfermion\\hamiltonians\\hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", - " from scipy.optimize.optimize import OptimizeResult\n" + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" ] } ], @@ -57,9 +61,10 @@ "import numpy as np\n", "from math import pi\n", "import paddle\n", - "from paddle_quantum.state import zero_state\n", "from paddle_quantum.ansatz import Circuit\n", "from paddle_quantum.linalg import dagger\n", + "from paddle_quantum.loss import ExpecVal\n", + "from paddle_quantum.state import zero_state\n", "\n", "# Drawing tools\n", "from matplotlib import pyplot as plt " @@ -160,21 +165,18 @@ "name": "stderr", "output_type": "stream", "text": [ - "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", - "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", - " elif dtype == np.bool:\n", - "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", - " if data.dtype == np.object:\n" + " elif dtype == np.bool:\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "The main program segment has run in total 3.090050458908081 seconds\n", - "Use 300 samples to get the mean value of the gradient of the random network's first parameter, and we have: 0.016533764\n", - "Use 300 samples to get the variance of the gradient of the random network's first parameter, and we have: 0.09683221\n" + "The main program segment has run in total 2.2558279037475586 seconds\n", + "Use 300 samples to get the mean value of the gradient of the random network's first parameter, and we have: -0.0032896693\n", + "Use 300 samples to get the variance of the gradient of the random network's first parameter, and we have: 0.098623686\n" ] } ], @@ -280,21 +282,19 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ - "The main program segment has run in total 1.7086431980133057 seconds\n" + "The main program segment has run in total 1.5701446533203125 seconds\n" ] } ], @@ -452,7 +452,8 @@ "source": [ "# objective function\n", "def loss_func(circuit: Circuit, H: Hamiltonian) -> paddle.Tensor:\n", - " return circuit().expec_val(H, shots = 0)" + " expec_val = ExpecVal(H)\n", + " return expec_val(circuit())" ] }, { @@ -494,16 +495,18 @@ "name": "stdout", "output_type": "stream", "text": [ - "--Ry(0.785)----Rx(1.077)----*--\n", + "--Ry(0.785)----Rz(5.325)----*--\n", " | \n", - "--Ry(0.785)----Rz(0.623)----z--\n", + "--Ry(0.785)----Rx(3.479)----z--\n", " \n", - "Hamiltonian info: -0.6880109593275947 Z1\n", - "0.7323522915498704 Z0\n", - "-0.8871768419457995 Y0, Y1\n", - "-0.7724600283015672 X1\n", - "-0.39151551408092455 Y1\n", - "0.22370578944475894 Y0, Z1\n" + "Hamiltonian info: \n", + " 0.7469285407889965 X0, X1\n", + "-0.36732514676253114 Y0\n", + "0.14368811242599788 Z0\n", + "0.5751598291922848 Y0, Y1\n", + "0.12302397651276697 Y0, Z1\n", + "-0.07083710973626145 Y1\n", + "-0.054905066805228886 X0\n" ] } ], @@ -515,7 +518,7 @@ "print(cir)\n", "# Random generate Hamiltonian information, in Pauli string format\n", "H_l = Hamiltonian(random_pauli_str_generator(N, terms=7))\n", - "print('Hamiltonian info: ', H_l)" + "print('Hamiltonian info: \\n', H_l)" ] }, { @@ -544,7 +547,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 100%|###################################################| 300/300 [00:03<00:00, 77.68it/s]" + "Sampling: 100%|##################################################| 300/300 [00:02<00:00, 111.88it/s]\n" ] }, { @@ -552,30 +555,21 @@ "output_type": "stream", "text": [ "Mean of gradient for all parameters: \n", - "theta 1 : 0.015548194\n", - "theta 2 : -0.026560133\n", + "theta 1 : -0.00420132\n", + "theta 2 : -0.004461403\n", "Variance of gradient for all parameters: \n", - "theta 1 : 0.20417707\n", - "theta 2 : 0.13769649\n" - ] - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - "\n" + "theta 1 : 0.08278141\n", + "theta 2 : 0.04159966\n" ] }, { "data": { - "image/png": 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", + "image/png": 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", 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", 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -654,15 +644,15 @@ "name": "stderr", "output_type": "stream", "text": [ - "Training: 100%|###################################################| 120/120 [00:01<00:00, 87.80it/s]" + "Training: 100%|##################################################| 120/120 [00:01<00:00, 115.10it/s]" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "optimal result: -1.2294903\n", - "real energy: -2.064555\n" + "optimal result: -0.5158533\n", + "real energy: -1.400689\n" ] }, { @@ -706,7 +696,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 100%|###################################################| 300/300 [00:03<00:00, 75.81it/s]\n" + "Sampling: 100%|##################################################| 300/300 [00:02<00:00, 114.13it/s]\n" ] }, { @@ -714,34 +704,32 @@ "output_type": "stream", "text": [ "Mean of max gradient\n", - "0.72318614\n", + "0.48790267\n", "Variance of max gradient\n", - "0.0966615\n" + "0.05380149\n" ] }, { "data": { - "image/png": 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", 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", 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    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 0%| | 0/300 [00:00" + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" }, { "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 0%| | 0/300 [00:00" + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -879,14 +875,12 @@ }, { "data": { - "image/png": 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", + "image/png": 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oy8zMFOrWrStYWFgIWVlZgiAIQlRUlABA2Lhxo6Jeq1atBE9PT6XXgFwuF3x9fQUXFxdF2fjx4wUAwuXLlxVl8fHxgpGRUZ54VPH09BTs7OyE1NRURdnp06cFAIKDg4OiLDdGQ0NDIT4+Xuka2dnZQmZmplLZixcvBEtLS6Xncs+ePQIAYeHChUrnNmvWLM/j//HHH4W3P/YePnwoqKmpCXPmzFG6n5CQEEFdXV2pvKDvlatXr+a5XyIiopKUnZ0tWFtbCz4+Pkrla9asEQAIR44cEQRBEDIyMpT6UoLw5rNYS0tLmDlzpqLs1KlTAgDB2dk5T/8m99ipU6cUZar6nfPmzRMkEonw6NEjRdngwYMFAEr3JQiCUK9ePcHLy0tx++TJkwIA4euvv85zXblcLghC4T7DVenevbugqakp3L9/X1EWExMjGBgYCH5+foqy3L7Kzz///N7rve2vv/5S9GEBCA0aNBBu3bqlVKegfdPC9HdVqVOnjtL3CVVUPX+5j+Hs2bOKstx+1KhRoxRl2dnZgp2dnSCRSIT58+cryl+8eCHo6OgIgwcPVpTlvnZsbW2V+rv//POPAEBYtmyZomzw4MFKfcaCfg+Kj48XNDU1hU6dOileK4IgCN9//70AQCkeVXbu3CkAEJYuXaooy8nJEVq2bJmnf5f7ep4yZUqe6xT0PVG3bl3B2tpaSE5OVpQdPXo0T59ZEN58h/jxxx8Vt4cPHy5YW1sLCQkJSvU+/fRTwcjISBFDbrvXrFlTqW+9bNkyAYAQEhKiKOvUqVOe+yUqLZzWTSSivn37Ij09HQcOHEBqaioOHDiQ75Tu7du3w8jICG3atEFCQoLiz8vLC/r6+krTXd/+1TE1NRUJCQlo1qwZ0tLSEBERoXRdfX19DBw4UHFbU1MTjRo1woMHD94b+8GDBwEAEydOVCqfNGkSgDej5z7Gxo0bcfjwYaxatQo1a9ZEenq60pSf3GkRqjYO0tbWVpo2kZ6enm+9t6+lSu6v7gcOHFC502Kut9v8xYsXePnyJZo1a6Zy18VWrVopTZPw9vYGAPTq1QsGBgZ5yt99LtTV1fH5558rbmtqauLzzz9HfHw8rl+/rjK+pKQknDx5En379lW8JhISEpCYmIh27drh7t27iI6OBvDmuW3cuDEaNWqkON/c3LxA61XFxMQgJCQEgwYNUvq1tXnz5vmOTu3VqxfMzc2VytTU1BQjNORyOZKSkpCdnY0GDRootenBgwehrq6uNNpCTU0NY8eO/WCsu3btglwuR9++fZXeU1ZWVnBxcckzhbyo7xUiIqKSpKamhk8//RSXLl1SWg5m69atsLS0VMw80dLSUozUy8nJQWJiIvT19VGjRg2V/ZXBgwcXaNbE23Vev36NhIQE+Pr6QhAElSP7Ro8erXS7WbNmSp+lO3fuhEQiwY8//pjn3NxRfIX9DH9bTk4Ojh49iu7du8PZ2VlRbm1tjf79++P8+fNISUn54OPOj7+/P44dO4bt27dj9OjR0NDQwOvXr5XqFLRvWpj+rirGxsYICwvD3bt3863z9vOXkZGBhIQENG7cGABUvi5GjBih+LeamhoaNGgAQRAwfPhwpfutUaOGyj7SoEGDlPq7vXv3hrW1teK7hSoF/R50/PhxZGVlYezYsUojPgu6wcvhw4ehoaGBkSNHKsqkUqlitpMqb/dBcxXkPfHs2TMEBQVh8ODBMDIyUtRv06YN3N3d3xunIAjYuXMnunTpAkEQlNqkXbt2ePnyZZ7nbujQoUqjn3Nn+LAfS2UFp3UTicjc3BytW7fG1q1bkZaWhpycHMWi2O+6e/cuXr58CQsLC5XH315nKCwsDNOmTcPJkyfzdK5evnypdNvOzi7PdI0qVarg1q1b74390aNHkEqlSlNUAMDKygrGxsZ49OjRe8//EB8fH8W/P/30U9SsWRPAm7Udgf8+9FWtF5mRkaHUKdDR0cm33tvXUqV58+bo1asXAgICsGTJErRo0QLdu3dH//79lTqKBw4cwOzZsxEUFJRnzc13Va1aVel2bofE3t5eZfm7a+nY2NjkWWzb1dUVwJt1HHM7lG+7d+8eBEHA9OnTMX36dJWPNT4+Hra2tnj06JEiMfq2GjVqqDzvbbnP+7uvi9wyVZ1cJycnldfavHkzfvnlF0RERCglht+u/+jRI1hbW+eZdlKQWO/evQtBEPLdrT13elCuor5XiIiIStqAAQOwZMkSbN26Fd9//z2ePn2Kc+fO4euvv4aamhqA/9ZxXLVqFaKiopR+9FW1k3d+n8/vevz4MWbMmIF9+/bl6bO82+/MXT/ybVWqVFE67/79+7CxsYGJiUm+91nYz/C3PX/+HGlpaSr7CjVr1oRcLseTJ09Qq1atfK/xPpaWlrC0tATwJvE2d+5ctGnTBnfv3lVsiFPQvmlh+ruqzJw5E926dYOrqys8PDzQvn17fPbZZ6hdu7aiTlJSEgICArBt27Y865a++/wBqvux2traMDMzy1P+7rqVAPI8ZxKJBNWrV8+zzvrbCvo9KLcf+u59mJubo0qVKvleP1duvzJ3enYuVf1a4M2AAVVTsAvynsgvVgD5/mCQ6/nz50hOTsa6deuwbt06lXXefS7ffd5y2+Pd+IjEwuQkkcj69++PkSNHIjY2Fh06dMh3fRy5XA4LCwts2bJF5fHcjl5ycjKaN28OQ0NDzJw5E9WqVYO2tjZu3LiB7777Ls+mJrkd1ncJglCg+FUl34pblSpV0LJlS2zZskWRnLS2tgbw5lfHd5N6z549Uxr1Z21tjWfPnuW5bm7Zu2ssvU0ikWDHjh0IDAzE/v37ceTIEQwbNgy//PILAgMDoa+vj3PnzqFr167w8/PDqlWrYG1tDQ0NDWzcuFHlTuD5tfnHPhfvk/u8T548Ge3atVNZJ7+OV0lT1bH+888/MWTIEHTv3h3ffPMNLCwsoKamhnnz5uH+/fvFcr9yuRwSiQSHDh1S2fbvJjxL8vkhIiL6GF5eXnBzc8Nff/2F77//Hn/99RcEQVCa9TB37lxMnz4dw4YNw6xZs2BiYgKpVIrx48er3PSuIKMmc3Jy0KZNGyQlJeG7776Dm5sb9PT0EB0djSFDhhS431lYhf0MF1Pv3r3xww8/YO/evYqZLwXtmxamv6uKn58f7t+/j7179+Lo0aP4/fffsWTJEqxZs0YxArJv3764ePEivvnmG9StWxf6+vqQy+Vo3769yteFqvYu6T5SQb8Hlba3RyPnKux7oihyrzFw4MB818N8OwENsB9LZR+Tk0Qi69GjBz7//HMEBgbi77//zrdetWrVcPz4cTRp0uS9ncXTp08jMTERu3btUlqAOioqqljjdnBwgFwux927dxWjGoE3izMnJycrdjcsLunp6Uq/3uZuiHLt2jWljllMTAyePn2KUaNGKdU9d+4c5HK5Ugfi8uXL0NXVVYw6fJ/GjRujcePGmDNnDrZu3YoBAwZg27ZtGDFiBHbu3AltbW0cOXJEaTTlxo0bP+Yh5ysmJgavX79WGj15584dAMh3V73caUsaGhpo3br1e6/v4OCgcvpPZGTkB2PLfd7f3v0vl6qy/OzYsQPOzs7YtWuXUgL83SleDg4OOHHiBF69eqX0RaQgsVarVg2CIMDJyalAr4GCKI1kPRERkSoDBgzA9OnTcevWLWzduhUuLi5o2LCh4viOHTvg7++P9evXK52XnJycZ9RbQYWEhODOnTvYvHkzBg0apCh/ezfowqpWrRqOHDmCpKSkfEdPfsxnuLm5OXR1dVX2FSIiIiCVSvMkAj9G7tTrd/uxBembFqa/mx8TExMMHToUQ4cOxatXr+Dn54effvoJI0aMwIsXL3DixAkEBARgxowZinPeNw38Y717bUEQcO/evTzJtLcV9HtQbj/07t27SlP2nz9/XqARgg4ODjh16hTS0tKURk8Wpg9b0PfE27G+60P9WHNzcxgYGCAnJ+eD/frCYD+WxMQ1J4lEpq+vj9WrV+Onn35Cly5d8q3Xt29f5OTkYNasWXmOZWdnIzk5GcB/v4q9/StYVlYWVq1aVaxxd+zYEQCwdOlSpfLFixcDQJ4dqgvq3SkIwJupyidOnFDaqbBWrVpwc3PDunXrlKYlrV69GhKJRGl6fO/evREXF6e0w3ZCQgK2b9+OLl26qFzHJ9eLFy/y/KKY21HMnWKjpqYGiUSiFMfDhw+xZ8+egj3oQsrOzsbatWsVt7OysrB27VqYm5vDy8tL5TkWFhZo0aIF1q5dq/KX+ufPnyv+3bFjRwQGBuLKlStKx/P7tfptNjY28PDwwB9//IFXr14pys+cOYOQkJACPT5A9ev48uXLuHTpklK9jh07Ijs7G6tXr1aU5eTk4Ndff/3gffTs2RNqamoICAjI8xwLgqByKtKH5CaMc9+PREREpSV3lOSMGTMQFBSUZ61oNTW1PJ9327dvV6w5XRSqPq8FQcCyZcuKfM1evXpBEAQEBATkOZZ7Px/zGa6mpoa2bdti7969SlOJ4+LisHXrVjRt2hSGhoaFjjshIUHlKLTff/8dgPKO2wXtmxamv6vKu+2gr6+P6tWrK/Vhgbyj597t3xenP/74A6mpqYrbO3bswLNnz9ChQ4d8zyno96DWrVtDQ0MDv/76q9JjKujjadeuHWQyGX777TdFmVwux8qVKwt0PlDw94S1tTXq1q2LzZs3KyWujx07hvDw8A/eR69evbBz506EhobmOf52v74w9PT0VE7lJyoNHDlJVAbkNxz/bc2bN8fnn3+OefPmISgoCG3btoWGhgbu3r2L7du3Y9myZejduzd8fX1RpUoVDB48GF9//TUkEgn+97//FfuQ/Tp16mDw4MFYt26dYir5lStXsHnzZnTv3h3+/v5Fuq6npydatWqFunXrokqVKrh79y7Wr18PmUyG+fPnK9X9+eef0bVrV7Rt2xaffvopQkNDsWLFCowYMUJpNGfv3r3RuHFjDB06FOHh4TAzM8OqVauQk5OjsuP7ts2bN2PVqlXo0aMHqlWrhtTUVPz2228wNDRUJGg7deqExYsXo3379ujfvz/i4+OxcuVKVK9evUTWI7SxscGCBQvw8OFDuLq64u+//0ZQUBDWrVv33jWWVq5ciaZNm8LT0xMjR46Es7Mz4uLicOnSJTx9+hTBwcEAgG+//Rb/+9//0L59e4wbNw56enpYt24dHBwcCvR45s6di27duqFJkyYYOnQoXrx4gRUrVsDDw0MpYfk+nTt3xq5du9CjRw906tQJUVFRWLNmDdzd3ZWu0aVLFzRp0gRTpkzBw4cP4e7ujl27dhWoY1WtWjXMnj0bU6dOxcOHD9G9e3cYGBggKioKu3fvxqhRozB58uQCxfv2NY2NjbFmzRoYGBhAT08P3t7eBV63i4iIqKicnJzg6+uLvXv3AkCe5GTnzp0xc+ZMDB06FL6+vggJCcGWLVuURpgVlpubG6pVq4bJkycjOjoahoaG2Llz50etY+fv74/PPvsMy5cvx927dxXTi8+dOwd/f3989dVXH/0ZPnv2bBw7dgxNmzbFF198AXV1daxduxaZmZlYuHBhkeL+888/sWbNGsVGO6mpqThy5AiOHTuGLl26oGXLloq6hembFrS/q4q7uztatGgBLy8vmJiY4Nq1a9ixYwe++uorAIChoSH8/PywcOFCyGQy2Nra4ujRo8U+4+ptJiYmaNq0KYYOHYq4uDgsXboU1atXV9qE5l0F/R5kbm6OyZMnY968eejcuTM6duyImzdv4tChQwUaHdy9e3c0atQIkyZNwr179+Dm5oZ9+/YhKSkJQMFGFhbmPTFv3jx06tQJTZs2xbBhw5CUlIRff/0VtWrV+mCfef78+Th16hS8vb0xcuRIuLu7IykpCTdu3MDx48cVMReGl5cX/v77b0ycOBENGzaEvr7+ewfPEBWrEt4NnIjesXHjRgGAcPXq1ffWc3BwEDp16pSnfN26dYKXl5ego6MjGBgYCJ6ensK3334rxMTEKOpcuHBBaNy4saCjoyPY2NgI3377rXDkyBEBgHDq1ClFvebNmwu1atXKcx+DBw8WHBwcPvhYZDKZEBAQIDg5OQkaGhqCvb29MHXqVCEjIyPP9fT09D54PUEQhB9//FFo0KCBUKVKFUFdXV2wsbERPv30U+HWrVsq6+/evVuoW7euoKWlJdjZ2QnTpk0TsrKy8tRLSkoShg8fLpiamgq6urpC8+bNP/gcCIIg3LhxQ+jXr59QtWpVQUtLS7CwsBA6d+4sXLt2Tane+vXrBRcXF0FLS0twc3MTNm7cKPz444/Cu//NAhC+/PJLpbKoqCgBgPDzzz8rlZ86dUoAIGzfvl1RlvucXbt2TfDx8RG0tbUFBwcHYcWKFSqvuXHjRqXy+/fvC4MGDRKsrKwEDQ0NwdbWVujcubOwY8cOpXq3bt0SmjdvLmhrawu2trbCrFmzhPXr1wsAhKioqA+227Zt2wQ3NzdBS0tL8PDwEPbt2yf06tVLcHNz++DjFgRBkMvlwty5cwUHBwdBS0tLqFevnnDgwAGVr83ExEThs88+EwwNDQUjIyPhs88+E27evJnn8at6PgRBEHbu3Ck0bdpU0NPTE/T09AQ3Nzfhyy+/FCIjIxV1CvNe2bt3r+Du7i6oq6urfA6IiIhKysqVKwUAQqNGjfIcy8jIECZNmiRYW1sLOjo6QpMmTYRLly4JzZs3F5o3b66op6r/8e6xt/uT4eHhQuvWrQV9fX3BzMxMGDlypBAcHJznMzC//qCqz+fs7Gzh559/Ftzc3ARNTU3B3Nxc6NChg3D9+nWlegX5DM/PjRs3hHbt2gn6+vqCrq6u4O/vL1y8eFGpzvv6Ku+6evWq0KdPH0WfUU9PT6hfv76wePFiQSaT5alfmL5pQfu775o9e7bQqFEjwdjYWNDR0RHc3NyEOXPmKJ379OlToUePHoKxsbFgZGQk9OnTR4iJiREACD/++KOiXu7z9Pz5c6X7yO95fbfvlPva+euvv4SpU6cKFhYWgo6OjtCpUyfh0aNHea6p6rtIQb4H5eTkCAEBAYrXeYsWLYTQ0FDBwcFBGDx48Afb7Pnz50L//v0FAwMDwcjISBgyZIhw4cIFAYCwbdu2Dz5uQSj4e0IQ3ryGa9asKWhpaQnu7u7Crl27VD7+d58PQRCEuLg44csvvxTs7e0FDQ0NwcrKSmjVqpWwbt06RZ383s+qviu8evVK6N+/v2BsbCwAKND3QaLiIhEEroBKRFRetGjRAgkJCSqncJR1devWhbm5+UetQ0VERERE5c/p06fh7++P7du3f3A6elmzZ88e9OjRA+fPn0eTJk3EDoeoQuKak0REVKxkMhmys7OVyk6fPo3g4GC0aNFCnKCIiIiIiD4gdwOjXLlrmRsaGqJ+/foiRUVU8XHNSSIiKlbR0dFo3bo1Bg4cCBsbG0RERGDNmjWwsrLC6NGjxQ6PiIiIiEilsWPHIj09HT4+PsjMzMSuXbtw8eJFzJ079707hRPRx2FykoiIilWVKlXg5eWF33//Hc+fP4eenh46deqE+fPnw9TUVOzwiIiIiIhUatmyJX755RccOHAAGRkZqF69On799VfFJkJEVDK45iQRERERERERERGJgmtOEhERERERERERkSiYnCQiIiIiIiIiIiJRVPo1J+VyOWJiYmBgYACJRCJ2OERERESFJggCUlNTYWNjA6mUvz2XR+yTEhERUXn2Mf3RSp+cjImJgb29vdhhEBEREX20J0+ewM7OTuwwqAjYJyUiIqKKoCj90UqfnDQwMAAAREVFwcTERORoyhaZTIajR4+ibdu20NDQEDucMoPtkj+2jWpsF9XYLvlj26jGdslfUlISnJycFP0aKn/YJ1WN73vV2C75Y9uoxnbJH9tGNbZL/tg2qn1Mf7TSJydzp80YGBjA0NBQ5GjKFplMBl1dXRgaGvIN9xa2S/7YNqqxXVRju+SPbaMa2yV/MpkMADgduBxjn1Q1vu9VY7vkj22jGtslf2wb1dgu+WPbqPYx/VEuSkRERERERERERESiYHKSiIiIiIiIiIiIRMHkJBEREREREREREYmCyUkiIiIiIiIiIiISBZOTREREREREREREJAomJ4mIiIiIiIiIiEgUTE4SERERERERERGRKJicJCIiIiIiIiIiIlEwOUlERERERERERESiUBc7ACKqGHLkAi5HJeF6ggSmUUnwqW4BNalE7LCIiIiIqIKLSU5H0ussAEB2djaevALCYlKgrv7m666pviasjXTEDJGIiN6DyUki+miHQ58hYH84nr3MAKCGP+5eg7WRNn7s4o72HtZih0dERFQgDx8+xKxZs3Dy5EnExsbCxsYGAwcOxA8//ABNTc18z2vRogXOnDmjVPb5559jzZo1JR0yUaWXmZ2DrivOI+FV1lul6lgUEqi4Za6vhfNT/KGlrlb6ARIR0QcxOUlEH+Vw6DOM+fMGhHfKY19mYMyfN7B6YH0mKImIqFyIiIiAXC7H2rVrUb16dYSGhmLkyJF4/fo1Fi1a9N5zR44ciZkzZypu6+rqlnS4RARAU00KG2MdJL7OgvBuhxSARAJYG2tDU40rmhERlVVMThJRkeXIBQTsD8+TmAQAAYAEQMD+cLRxt+IUbyIiKvPat2+P9u3bK247OzsjMjISq1ev/mByUldXF1ZWViUdIhG9QyKRYFLbGhi84YrK44IATGpbAxIJ+6JERGUVk5NEVGRXopL+fyq3agKAZy8zcCUqCT7VTEsvMCIiomLy8uVLmJiYfLDeli1b8Oeff8LKygpdunTB9OnT3zt6MjMzE5mZmYrbKSkpAACZTAaZTPbxgVcQuW3BNlHGdlFW3VQbNkbaiHmnXyqVALVsDOHjaFTp24qvmfyxbVRju+SPbaPax7QHk5NEVGTxqfknJotSj4iIqCy5d+8efv311w+Omuzfvz8cHBxgY2ODW7du4bvvvkNkZCR27dqV7znz5s1DQEBAnvJTp05xSrgKx44dEzuEMqkyt8uLTCA4SYJbiVI8SAUE5B0ZKReA+rovcOjQIREiLJsq82vmQ9g2qrFd8se2UZaWllbkc5mcJKICy8qW40hYLGyr6KB+1SqwMNAu0HkFrUdERFQSpkyZggULFry3zu3bt+Hm5qa4HR0djfbt26NPnz4YOXLke88dNWqU4t+enp6wtrZGq1atcP/+fVSrVk3lOVOnTsXEiRMVt1NSUmBvbw9/f3+YmnK2QS6ZTIZjx46hTZs20NDQEDucMqOytsujpDQcCYvDkfA43HqaonTM08YA8a+y8Dw1E/K31hza80QLNT1qoGc9m0o9tbuyvmYKgm2jGtslf2wb1RITE4t8LpOTRPRBT5LSsPXKY2y/9gQJr7LQuqYFfh/cEI2cTGBtpI3Ylxkq150EADUJVPyOTUREVHomTZqEIUOGvLeOs7Oz4t8xMTHw9/eHr68v1q1bV+j78/b2BvBm5GV+yUktLS1oaWnlKdfQ0OAXHRXYLqpVhna5G5eKQ6GxOBQai9vP/ktISiRAA4cqaO9hjfYeVrA11sGZO8+V1p60N9HFk6Q0TNkdhv0hsZjbwxMOpnpiPIwyozK8ZoqKbaMa2yV/bBtlH9MWTE4SkUo5cgGnIuLx5+VHOHPnuWL3QwsDLXjaGkMQBKhJJfixizvG/HkDEkBlgjJHAPr9HohRzZwxsa0rtNTVSvNhEBERwdzcHObm5gWqGx0dDX9/f3h5eWHjxo2QSgu/w29QUBAAwNrautDnElV2giAgLCYFh0NjcSj0Ge4/f604piaVoLGzCdp7WKOduyUsDJVn5/i5mMHT1hAh0SnwtDXEzjG+WH/+IZYev4ML9xLRdslZjG/tihHNnKDB3buJiMoMJieJSEl8Sgb+vvoEf115rLSoeDMXMwzwropWNS2VOnPtPayxemB9BOwPV9ocx9pIG9+2q4GL9xOx/fpTrD37AKcjn2PxJ3VQy8aoVB8TERFRQURHR6NFixZwcHDAokWL8Pz5c8Wx3J24o6Oj0apVK/zxxx9o1KgR7t+/j61bt6Jjx44wNTXFrVu3MGHCBPj5+aF27dpiPRSickUuFxD0NBmHQ2NxODQWj5P+W7dMQ02CptXN0MHDGq3dLWGip5nvdSQSCSa1ccF3f1/DpDYu0FRXw5gW1dDBwwo/7AnBhXuJWHA4AvuCY7Cglydq2xmXwqMjIqIPYXKSiCAIAi7dT8Sflx/haFgcsv9/oR5jXQ30bWCPfo2qwsks/ykw7T2s0cbdCpfuxePoucto28wbPtUtoCaVoEd9O7Rxt8TUXSGIjEtF95UXML61K0Y3rwY1KSd8ExFR2XHs2DHcu3cP9+7dg52dndIx4f+nEMhkMkRGRioWfdfU1MTx48exdOlSvH79Gvb29ujVqxemTZtW6vETlSc5cgFXHyYpEpKxKf/9yK2lLkVzV3N09LRGy5oWMNQu+FTBJtVM8X3dHDSp9t/arY5mevhzuDd2XH+KOQdv4/azFHRfeQFDmzhhYhtX6GnxazERkZj4vzBRJSfLkaPT8nO4E/dKUeblUAUDG1dFBw9raGsUbBq2mlQCbycTJN4W4O1kopR4bFvLCvUdquD7XSE4Gh6Hn49E4mREPH7pUweO70l6EhERlaYhQ4Z8cG1KR0dHRaISAOzt7XHmzJkSjoyoYpDlyBH4IBGHQmNxNCwWCa+yFMf0NNXg72aBDh7WaFHDvNgThhKJBH0a2MPfzQIz94djX3AM1p+PwuHQWMzp4YEWNSyK9f6IiKjgmJwkqmQEQcDd+FdwtTQAAGioSVHdQh/RL9LRo74tBng7oKa1YbHfr5m+FtZ+5oWdN6IRsC8M1x+9QIdl5/BDp5oY4F21Uu+eSERERFRRZchycOFeAg6FxuJYeBxepssUxwy11dHa3RIdPKzRzMWswD+KfwwzfS0s71cPPerbYtruUEQnp2PIxqvoVtcG0zu7w0w/70ZVRERUspicJKpEMrNz0Gv1RYRGp+DkpOZwNtcHAEzv7I6FvTWgX8JTWiQSCXp72aGxswm+2X4Llx4k4nTkcwzwrlqi90tEREREpSctKxtnIp/jUGgsTkbE41VmtuKYqZ4m2tayRHsPa/g4m0JTXZyNafxrWODoBD/8cvQONl2Mwt6gGJy58xzTOrmjV31b/nBORFSKmJwkquCeJKXB3kQXAKClrgYLA21oqb9CSPRLRXLS2kinVGOyq6KLLSO88eflR+jgYa3o/Mly5Nw5kYiIiKgcSs2Q4WREPA6FxOL0nXhkyOSKY5aGWmhfywrtPazR6J3lf8Skp6WOGV3c0a2uDb7beQsRsamYvD0Ye25GY04PDziYcvkhIqLSwOQkUQWUIcvBwZBn+DPwEYKeJOPst/6wq/ImQfljF3cY6WjAWDf/nQ5Lg1QqwSAfR6Wyb3fcQrZcwKxutUSPj4iIiIje78XrLBy7HYfDobE4fzcBWTn/JSTtquigg8ebhGQ9e2NIy0hCUpU69sbYP7Ypfj8XhaXH7+D8vQS0W3oW41u7YnhTJ/54TkRUwpicJKpAohJeY+vlR9h+/SmS096s56MuleD6oxeK5GRZ/QX4Xvwr7AuOgSAIGNrEEfWrMjlJREREVNbEp2bgaNibhOSlB4nIkf+3QZSzuR46eFihg4c1atkYlqup0RpqUoxpUQ0dPKzw/e4QXLyfiPmHIrA3KAYLenmitp2x2CESEVVYTE4SlXOyHDmOh8dhy+XHOH8vQVFua6yDfo3s0beBPSwMtUWMsGCqW+hj1xhfBD1JRv2qVRTlcrlQpn9pJyIiIqroYpLTcTg0FodDY3H1URLe2rAeblYG6OBhjQ6eVnCx0C9XCUlVHM30sGWEN3Zcf4rZ/97G7Wcp6L7yAoY2ccKktq7Q1eRXaCKi4sb/WYnKqZjkdGy78hjbrj5BfGomAEAiAVq4mmNgYwe0qGFRZtbzKag69saoY2+suH03LhVfbb2JuT094OVgIl5gRERERJXMo8TXOBQai0OhsQh+kqx0rI6dEdp7WKODhxUczcrmrJyPIZFI0KeBPfzdLDBzfzj2Bcdg/fkoHA6NxZweHmhRw0LsEImIKhQmJ4nKmdDol1h6/C5ORsQhdxaNmb4m+jawR79GVRWb31QEC49EIjIuFX3WXMLo5tUwvrWraDs6EhEREVV0d+NSFQnJ289SFOUSCdDAoQrae1ijvYcVbI1LdzNFsZjpa2F5v3roUc8W0/aEIjo5HUM2XkW3ujaY0dkdpvpaYodIRFQhMDlJVM6kZMhw/HYcAKCxswkGeDugXS2rCpm0W9SnDgL2hWHXzWisOn0fpyKfY8kndeBmZSh2aERERETlniAICItJweHQWBwKfYb7z18rjqlJJWjsbIL2HtZo525ZLpYJKin+bhY4OsEPvxy9g00Xo7A3KAZn7jzHtE7u6FXfttxPZSciEhuTk0Rl2O1nKVhz5j5sjHXwXXs3AICPsykmtHZFp9pWqG5hIHKEJctIRwOLP6mLNu6W+H53CG4/S0HXXy9gUltXjGjmXO6mrRMRERGJTS4XEPw0GYf+fw3Jx0lpimMaahI0rW6GDh7WaO1uCRM9blCYS09LHTO6uKNbXRt8t/MWImJTMXl7MPbcjMacHh5ldtNJIqLygMlJojIs9mUG9gbFwEhHA+NauUBbQw0SiQTjWruIHVqp6uBpDS/HKpi6MwQnIuIx71AEjt+Owy996qKqacWZxk5ERERUEnLkAq4+TMLh0FgcCYvFs5cZimNa6lK0qGGODh7WaFnTAobaGiJGWvbVsTfG/rFN8du5B1h2/C7O30tAu6VnMb61K0Y0dYK6WsWbzUREVNKYnCQqI0KevsSWy49gV0UHX7V8k3z0czXHKD9ndKltA20NNZEjFJeFgTZ+H9wA/1x7gpn7w3H14Qt0WHYW0zu745OG9pxOQ0RERPQWWY4cgQ8ScSg0FkfDYpHwKktxTE9TDS1rWqKDhxVa1DDnDtSFpKEmxRctqqOjhzW+3x2Ci/cTMf9QBPYFxWBBr9rwtDMSO0QionKFn0JEIkrPysH+4BhsufwIwU9fAnizuc0ov2rQVJdCTSrB9x1rihxl2SGRSPBJw6rwrWaGSduDcSUqCVN2heBoeBzm9/KEhUHlXQuJiIiIKDM7B+fvJuBQaCyOhcfhZbpMccxQWx2t3S3RwcMazVzMKv0P38XB0UwPW0Z4Y/v1p5jz722EP0tBt5XnMayJEya2dWXSl4iogPi/JZEI7sWn4s/Ax9h54ylSM7IBvFnjp4OHNQY2doCGGkcBvo+9iS62jWyM9eej8PORSJyMiEeHpedwclILGOlyKhIRERFVHmlZ2TgT+RyHQmNxMiIerzKzFcdM9TTRtpYl2ntYw8fZtEJuoCg2iUSCvg3s4V/DArMOhGNfcAx+Px+Fw2GxmNPDE81dzcUOkYiozGNykqiUZGXLcSQsFn8GPsLlqCRFub2JDvo3ckCfBnYw09cSMcLyRSqVYKSfM/xczTHxnyA0djZlYpKIiIgqhdSMbFx7LsG/fwXh7N0EZMjkimOWhlpoX8sK7T2s0cjJhBsIlhJzAy0s71cPPerZYtqeUDx9kY7BG66ge10bTO/sDlP284mI8sXkJFEJe5KUhr+uPMY/154o1vqRSoBWNS0xwLsq/FzMIWWnschqWBlg9xdNIBcERdmjxNd4nJSGZi78pZqIiIgqhhevs3DsdhwOh8bi3N3nkOWoAYgHANhV0UEHjzcJyXr2xuxbisjfzQJHJ/jhl6N3sOliFPYExeD0neeY1skdverbcp10IiIVmJwkKkGCIGD45qu4E/cKAGBhoIVPG1XFpw3tYWOsI3J0FcfbU5Ry5AIm/ROMa49eYFa3WvjMx1G8wIiIiIg+wvPUTBwJi8Xh0FhcepCIHPl/P8ZaaAvo1cgZnerYopaNIZNeZYieljpmdHFHt7o2+G7nLUTEpmLy9mDsuRmNOT084GCqJ3aIRERlCpOTRMUoPjUD2689xbAmTtDRVINEIkG/RlVxMiIeA7yrolVNS2ioca2fkiTLkcPdxhCRsaloUcNC7HCIiIiICiUmOR2HQ98kJK8+SsJbk0PgZmWADh7WaONmhjvXzqJTGxdoaHBZm7Kqjr0x9o9tit/OPcCy43dx/l4C2i09i/GtXTGiqRPU+b2AiAgAk5NExUYQBHy6NhAPEl7DwkALfRrYAwCG+DpiaBMnkaOrPLQ11DCzmwfGtnSBucF/a/ucjIhDMxdzJoeJiIiozHmU+BqHQmNxKDQWwU+SlY7VsTNCew9rdPCwgqPZmxF3MpkMdzlQslzQUJPiixbV0cHDGt/vCsGlB4mYfygC+4NjML9nbXjaGYkdIhGR6JicJCqi5DQZ/g19iv7eDtBUl0IikaB3AzucuB0PC0NtRT1OsRHH24nJc3efY9ima/CwNcSSvnXhYmkgYmREREREwN24VEVC8vazFEW5RAI0cKiC9h7WaO9hBVsuBVQhOJnpYetIb2y//hRz/r2NsJgUdFt5HsOaOGFiW1foavKrORFVXvwfkKgQBEHAzSfJ+POeFN9cPYOsbDlM9LXQtY4NAGC0XzV80aK6yFHSuzJlchjraiA0OgWdfj2Pb9vVwLAmTlwsnoiIiEqNIAgIi0nB4dBYHAp9hvvPXyuOqUklaOxsgvYe1mjnbqn0QzdVHBKJBH0b2MO/hgVmHgjH/uAY/H4+CofDYjGnhyeau3IzRyKqnJicJCqAV5nZ2BsUjT8DH///L9tSAHLUtDaEnqaaoh6TXWVTa3dLHB3vh+923sKpyOeY/e9tHAuPw6I+dWBvoit2eERERFRByeUCgp8m49D/ryH5OClNcUxDTYKm1c3QwcMard0tYaKnKWKkVJrMDbTwa7966FnPFtP2hOLpi3QM3nAF3evaYHpnd5jqa334IkREFQiTk0TvcftZCrZcfoQ9N2PwKjMbAKClLkWdKtmY3KMxGjqZcdp2OWFhqI0NQxpi29UnmHUgHJejktBh2TnM6OKOPl52fB6JiIioWOTIBVx7mIRDobE4EhaLZy8zFMe01KVoUcMcHTys0bKmBQy1uZlNZebvZoGjE/yw6GgkNl18iD1BMThz5zmmdXJHz/q27J8SUaXB5CTROzJkOTgY8gxbLj/G9UcvFOXOZnro710V3Wpb4eLpY6hnb8wOQzmTu3u6bzVTTPonGNcevcC3O27haFgc5vX0VFqnkoiIiKigZDlyBD5IxKHQWBwNi0XCqyzFMT1NNbSsaYkOHlZoUcOcawuSEj0tdfzYpRa61bXFlJ23EBGbiknbg7EnKBpzunuiqiln+RBRxcdPRqK3XH2YhJF/XENymgwAoC6VoF0tKwzwrgqfaqaQSCSQyWQiR0kfy8FUD39/7oPfzj3A4qN3cPx2HG4ufYE5PTzR3sNK7PCIiIioHMjMzsH5uwk4FBqL47fjFP1HADDUVkcbdyt08LBCUxczaGuovedKREBde2PsH9sU684+wLITd3HubgLaLj2DCa1dMbypE9TVpGKHSERUYpicpEotO0eOuNRMxS6IrpYGyJDlwNZYB/0a2aNvA3suSF5BqUklGN28Gpq7mmPC30GIiE3F6D+vo1d9O/zY1Z3TrIiIiCiPtKxsnIl8jkOhsTgZEa9Y9gcATPU00bbWm4SkTzVTaDCZRIWkoSbFl/7V0dHTGt/vCsGlB4mYdygC+4JjML9nbXjaGYkdIhFRiWBykiqtaw+T8OXWG7Ay1Mber5oCAIx0NLBrTBPUsDKAGje3qRRqWhti71dNsOz4Xaw5cx//hsTgS/9qTE4SERERACA1Q4aTEfE4FBKL03fikSGTK45ZGWqjvYcV2ntYoaGjCfuPVCyczPSwdaQ3tl9/ijn/3kZYTAq6rTyP4U2dMKGNK5cGIKIKh/+rUaUhlwtIfJ2lWFfQyUwPL17LkCMX8Dw1U1HubmMoZpgkAi11NXzb3g2talrg6Yt0OJvrK47lyAV+0SAiIqpkXrzOwrHbcTgcGovzdxOQlfNfQtKuig46elqjvYcV6toZQ8p+ApUAiUSCvg3s4V/DAjMPhGN/cAx+OxeFQ6GxmNvDE36u5mKHSERUbJicpAov8VUmtl9/iq2XH8PKUBv/jPYBAJjqa+GvUY3haWsETXVOuyHAy8EEXg7/3b4SlYRpe0KwqE8d1LYzFi0uIiIiKnnPUzNxJCwWh0NjcelBInLkguKYs7keOnhYoYOHNWrZGHJTRCo15gZa+LVfPfSoZ4Npu0Px9EU6Bm24gh71bDGtU02Y6nNDRyIq/5icpApJEARcffgCWy4/wqGQWMWv3S/SspD4KlPxIe7lUEXMMKmMW3g4AnfiXmFL4GPU7m0sdjhERERUzGKS03E49E1C8uqjJAj/5SPhZmWADh7W6OhpBRdLA/GCJALQ0s0SxyaaYtHRSGy6+BC7b0bjdGQ8pnd2R496tkyYE1G5xuQkVSgpGTLsvhGNLZcf4U7cK0V5bTsjDPR2QOc61lyjhQrst0ENsOzEXUxq66ooEwSBnT8iIqJy7HFiGg6FPsPB0FgEP0lWOlbHzgjtPazRwcMKjmZ64gRIlA89LXX82KUWutW1xZSdtxARm4qJ/wRj981ozOnuiaqmumKHSERUJMzSUIUQGv0SfwY+wt6gGKTLcgAA2hpSdKtjiwGNq3JKLhVJFT1N/NS1luK2IAgY/ed1eDuZYoivI9eYIiIiKifuxafiUEgsDoXGIvxZiqJcIgEaOFRBe483a0jaGuuIGCVRwdS1N8b+sU2x7uwDLDtxF+fuJqDt0jOY0NoVw5s6QZ07xRNROcPkJJVre4OiseF8FIKfvlSUuVjoY4B3VfSobwcjHe64TMXn+O14HAmLw5GwOBy/HYef+9ThlxgiIqIySBAEhD9LweHQNwnJe/H/zahRk0rQ2NkE7T2s0a6WJSwMtEWMlKhoNNSk+NK/Ojp6WuP7XSG49CAR8w5FYF9wDBb0qg0PWyOxQyQiKjAmJ6lcu3Q/EcFPX0JDTYIOHtYY2NgBDR2rcNotlYjWNS0wq7sH5v57GxfvJ6L9krP4qWst9KzPdX6IiIjEJggCgp4kKxKSj5PSFMc01CRoWt0MHTys0drdEiZ6miJGSlR8nMz0sHWkN7Zfe4o5B28jLCYFXVecx/CmTpjQxpVLWhFRucD/qajcOBwai80XH2JqRzfFNO1BPo5wMNVDnwZ2MONOdVTCJBIJPmvsgKbVzTDxnyDcfJyMSduDcTQ8FnN7eHK3RCIiomIQk5yOpNdZAIDs7Gw8eQWExaRAXf3NVxdTfU1YG72ZuZAjF3DtYRIOhcbiSFgsnr3MUFxHW0OK5q7m6OBhjZY1LWCozRk1VDFJJBL0bWgPfzcLBOwPw4Fbz/DbuSgcDovFnO6e8HM1FztEIqL3YnKSyo3Doc9w6UEi/gx8hIX/v3Oyu40h3G0MxQ2MKh0nMz1s/9wHa88+wNLjd3AkLA7XH73AvJ610cbdUuzwiIiIyq3M7Bx0XXEeCa+y3ipVx6KQQMUtM31NLOxdG8dvx+NoWKxSXT1NNbSsaYkOHlZoUcOco8aoUjE30MKK/vXRs34cpu0OxZOkdAzacAU96tniu3YuYodHRJSvMrdS7sqVK+Ho6AhtbW14e3vjypUr+dbdtGkTJBKJ0p+2NteMKe9y5AJO3I7DsE1XERmbqigf0sQJX7esjvGtXd9zNlHpUP//dX72fNkENSwNkPAqCyP/uIZvdwQjNUMmdnhERETlkqaaFDbGOnjfaikvXmdh2KZr2Hr5MRJeZcFIRwO96tvh90ENcH16G/zarx46elozMUmVVks3Sxyd2BxDfB0hkQC7b0ajw/ILuPpcAkEQxA6PiCiPMvWJ/ffff2PixIlYs2YNvL29sXTpUrRr1w6RkZGwsLBQeY6hoSEiIyMVt7nuW/kVn5qBf64+wV9XniA6OR0AYF9FBwHdPAC82ZWurr2xiBES5VXLxgh7v2qCxcfu4LdzD/DPtae4cC8Rv/Stg8bOpmKHR0REVK5IJBJMalsDgzfkP0AhRwBM9TTRtpYVOnhYwaeaKTS4OzGREn0tdfzUtRa61bXB1F0hiIhNxZ/31BC1+Qbm9ayNqqa6YodIRKRQpj7FFy9ejJEjR2Lo0KFwd3fHmjVroKuriw0bNuR7jkQigZWVleLP0pJTKssTQRBw8X4CvtxyA77zTmLR0TuITk6Hsa4GRvk5Y0gTJ7FDJPogbQ01fN+xJraNbAy7KjqITk5Hv98CsedmtNihERERlTt+LmaobWcEqYoxB6Z6mvhrpDeu/NAa83q+WUuPiUmi/NWrWgX7xzbFxNbVoS4RcOF+ItouPYN1Z+8jO0cudnhERADKUHIyKysL169fR+vWrRVlUqkUrVu3xqVLl/I979WrV3BwcIC9vT26deuGsLCw0giXPtLLNBnWn49Cq8Vn0P+3y/g35Bmy5QK8HKpgySd1EDi1Fb7vWBNOZnpih0pUYN7Opjg83g+fNrSHhYEWWtTg4uNERESFlTt6Uq5i9uniT+rCp5oZ1FRlLolIJQ01KcY0d8Z3dXLg7VQFGTI55h6MQPdVFxAa/VLs8IiIys607oSEBOTk5OQZ+WhpaYmIiAiV59SoUQMbNmxA7dq18fLlSyxatAi+vr4ICwuDnZ2dynMyMzORmZmpuJ2SkgIAkMlkkMm4TtzbctujuNpFEAQEP32Jv64+xb8hscjMfvNLnZ6mGrrVtUa/hvZwszL4/9pyyGRl85e84m6XioRtA2hJgVlda+JFWjXoaUggk8mQlZWFmwkS+L/1fw/x9fI+bBvV2C75Y5tQRZM7ejI0+iXkAiCVAB62RvBzMRM7NKJyy0IH+F/PBtgTHIc5B28jNDoF3VZewPCmThjf2oXrtBKRaMr1/z4+Pj7w8fFR3Pb19UXNmjWxdu1azJo1S+U58+bNQ0BAQJ7yU6dOQVeX626ocuzYsWK5zrM0YH7wfy85W10BTazk8DLLhrbaQzy48RAPiuWeSkdxtUtFxLZRduW5BFvuqeHsstMYWytH5TS1yoyvl/yxbVRju+SVlpYmdghExerdtSflAjCpbQ2uL0/0kSQSCfo2tIe/mwUC9ofhwK1nWHf2AQ6FPsOc7m+WSiAiKm1lJjlpZmYGNTU1xMXFKZXHxcXBysqqQNfQ0NBAvXr1cO/evXzrTJ06FRMnTlTcTklJgb29Pfz9/WFqys0r3iaTyXDs2DG0adMGGhoahT4/MjYVEbGp6FbXRlF28uVV2FbRQb+GdqhrZ1QuO5gf2y4VGdtGteygaOyKCkWXBs7o3NJF7HDKDL5e8se2UY3tkr/ExESxQyAqdn4uZvC0NURIdAo8bQ05apKoGJkbaGFF//roWT8O03aH4klSOgZtuIIe9WwxvbM7TPQ0xQ6RiCqRMpOc1NTUhJeXF06cOIHu3bsDAORyOU6cOIGvvvqqQNfIyclBSEgIOnbsmG8dLS0taGlp5SnX0NDgF518FKVtwmNS0HnlJWhrSNGmlg2MdN+cv22UD6QVZNgYXzP5Y9so61rXFq+igtG3eTVFu9yLT4WeljqsjXREjk58fL3kj22jGtslL7ZH8enatSuCgoIQHx+PKlWqoHXr1liwYAFsbGzyPScjIwOTJk3Ctm3bkJmZiXbt2mHVqlXcqPEjSSQSTGrjgu/+voZJbVzK5Y/aRGVdSzdLHJ1oikVHIrH50kPsvhmN05HxmN7ZHT3q2fJ9R0SlosxsiAMAEydOxG+//YbNmzfj9u3bGDNmDF6/fo2hQ4cCAAYNGoSpU6cq6s+cORNHjx7FgwcPcOPGDQwcOBCPHj3CiBEjxHoIldbDhNc4HBqruF3T2gAetoZo6WaB1Mz/1sGqKIlJosIy1gLU/3830QxZDr7cchNtl5zFnpvREAQVK/4TEZEo/P398c8//yAyMhI7d+7E/fv30bt37/eeM2HCBOzfvx/bt2/HmTNnEBMTg549e5ZSxBVbk2qm+L5uDppU4wwnopKir6WOn7rWwq4xvnCzMsCLNBkm/hOMQRuu4EkSlw0hopJXZkZOAsAnn3yC58+fY8aMGYiNjUXdunVx+PBhxa/Ojx8/hlT6Xz71xYsXGDlyJGJjY1GlShV4eXnh4sWLcHd3F+shVBg5cgGXo5JwPUEC06gk+FS3yLMrYnaOHMdvx2PL5Uc4dzcB+lrqaOZiBj0tdUgkEuz+ogk01MpU/puoTHiZLoO2phpSM7Ix/u8gHA2Pxezunpw+Q0RUBkyYMEHxbwcHB0yZMgXdu3eHTCZTOUL15cuXWL9+PbZu3YqWLVsCADZu3IiaNWsiMDAQjRs3LrXYiYg+Rr2qVbB/bFOsO/sAy07cxbm7CWiz5AwmtnHFsCZOih/aiYiKW5lKTgLAV199le807tOnTyvdXrJkCZYsWVIKUVUuh0OfIWB/OJ69zACghj/uXoO1kTZ+7OKO9h7WePYyHduuPMG2q48Rl/Jm92GJBGjgWAVJr7Ogp/XmZcXEJJFqloba2DnaB6tO38fyE3dxMCQWVx++wIJenmjpximARERlRVJSErZs2QJfX998p85fv34dMpkMrVu3VpS5ubmhatWquHTpUr7JyczMTGRmZipup6SkAHiztip3X/9PbluwTZSxXfLHtlGtMO0yqqkD2riZYfq+cFyOeoG5ByOwNygac7rVQi0bw5IOtdTxNaMa2yV/bBvVPqY9ylxyksR1OPQZxvx5A+9OMo19mYHRf95AHTsjhMakIEf+poapnib6NrRH/0ZVYW/C3c6JCkpdTYqvW7nAv4YFJvwThHvxrzBs0zX0a2SPHzq5Q1+L/z0TEYnlu+++w4oVK5CWlobGjRvjwIED+daNjY2FpqYmjI2NlcotLS0RGxur+iQA8+bNQ0BAQJ7yU6dOQVeXfap3HTt2TOwQyiS2S/7YNqoVpl36WQJOEgn2PpIiLCYVPVdfQgtrAR3s5dBUK8EgRcLXjGpsl/yxbZSlpRV9GQh++yWFHLmAgP3heRKTABRlwU9fAgC8nUwwoLED2tWyhJZ6BfxkIiolnnZGODC2KRYdicT6C1H468oTnL+XgF/61EUjJxOxwyMiqhCmTJmCBQsWvLfO7du34ebmBgD45ptvMHz4cDx69AgBAQEYNGgQDhw4UKwbQ0ydOhUTJ05U3E5JSYG9vT38/f1hasr1FXPJZDIcO3YMbdq04cZPb2G75I9to1pR26UTgK9TMzH7YAQOhsbh5DMJ7mToYVZXdzStXjH+r+JrRjW2S/7YNqolJiYW+VwmJ0nhSlTS/0/lfr9FvWujdwP7UoiIqHLQ1lDDtM7uaFXTEpO3B+NJUjo+WXcJo/ycMbGNK38AICL6SJMmTcKQIUPeW8fZ2VnxbzMzM5iZmcHV1RU1a9aEvb09AgMD4ePjk+c8KysrZGVlITk5WWn0ZFxcHKysrPK9Py0tLWhpaeUp5270qrFdVGO75I9to1pR2sXGRAOrBjbAidtxmLYnFE9fpGPo5uvoWc8W0zq7V5h10/maUY3tkj+2jbKPaQsmJ0khPvXDiUkA0FDnWpJEJcGnmikOj2+GmfvDsf36U6w98wBnIp9jcd+6cK+A6/sQEZUWc3NzmJubF+lcuVwOAErrQ77Ny8sLGhoaOHHiBHr16gUAiIyMxOPHj1UmM4mIyqtWNS3h7WyKRUcisfnSQ+y6GY3Td55jeuea6F7XtlhHlxNR5cIsEylYGGgXaz0iKjwDbQ383KcO1n3mBVM9TUTEpuJgyDOxwyIiqhQuX76MFStWICgoCI8ePcLJkyfRr18/VKtWTZFojI6OhpubG65cuQIAMDIywvDhwzFx4kScOnUK169fx9ChQ+Hj48OduomowtHXUsdPXWth1xhfuFkZIOl1Fib8HYzBG6/iSVLR15sjosqNyUlSaORkAmsjbeT3e5cEgLWRNtfBIyoFbWtZ4cgEP4zyc8bXrVwU5YKgalVYIiIqDrq6uti1axdatWqFGjVqYPjw4ahduzbOnDmjmIItk8kQGRmptOj7kiVL0LlzZ/Tq1Qt+fn6wsrLCrl27xHoYREQlrl7VKtg/tim+aVcDmupSnL3zHG2WnMG6s/eRnSMXOzwiKmc4rZsU1KQS/NjFHWP+vAEJoLQxTm7C8scu7lCTcrg+UWkw09fC9x1rKm7LcuQY8PtldK1jgwHeVTl1hoiomHl6euLkyZPvrePo6JjnhyJtbW2sXLkSK1euLMnwiIjKFA01Kb70r44OHlb4fncIAh8kYe7BCOwLjsH8nrXhYWskdohEVE5w5CQpae9hjdUD68PKSHnqtpWRNlYPrI/2HtYiRUZEu248xZWoJCw6Gomk11lih0NEREREBGdzffw1sjEW9PKEobY6QqNT0G3lBcw9eBvpWTlih0dE5QBHTlIe7T2s0cbdCpfuxePoucto28wbPtUtOGKSSGR9vOzxKjMH1kbaMNXPu8MrEREREZEYJBIJPmlYFf5uFgjYH45/bz3DurMPcCj0Geb28EQzl6JtSkZElQNHTpJKalIJvJ1M4GUmwNvJhIlJojJAKpVgeFMndPT8bwTzsfA4jP3rJpLTOJKSiIiIiMRlYaCNlf3r4/dBDWBtpI0nSen4bP0VTPw7iDN/iChfTE4SEZVTmdk5mLYnBPuDY9B2yVmcjowXOyQiIiIiIrR2t8Sxic0xxNcREgmw62Y0Wi8+g903n3KDRyLKg8lJIqJySktdDes+awBncz3Ep2ZiyMar+GF3CNKyssUOjYiIiIgqOX0tdfzUtRZ2jvFFDUsDJL3OwoS/gzF441U8SUoTOzwiKkOYnCQiKsfq2Bvj37HNMMTXEQCw5fJjdFx2DtcfvRA3MCIiIiIiAPWrVsH+sU0xua0rNNWlOHvnOdouOYvfzj5Ado5c7PCIqAxgcpKIqJzT0VTDT11rYcsIb1gbaeNhYhr6rLmIn49EICubHT4iIiIiEpemuhRftXTB4XHN4O1kgnRZDuYcvI0eqy4iNPql2OERkciYnCQiqiCaVDfD4fF+6FnfFnIBWHnqPrqtvICI2BSxQyMiIiIigrO5Pv4a2Rjze3rCUFsdIdEv0W3lBcw7eBvpWTlih0dEImFykoioAjHS0cDivnWxZmB9mOhp4vazFHT99QLWnrmPHDkXHyciIiIicUmlEnzaqCqOT2qOTrWtkSMXsPbsA7Rdegbn7j4XOzwiEgGTk0REFVB7D2scHt8MrWtaICtHjnmHIjDyj2vcHZGIiIiIygQLA22s7F8fvw9qAGsjbTxJSsdn669g4j9BSHqdJXZ4RFSKmJwkIqqgLAy08dugBljYqzb0NNXQwcMKEolE7LCIiIiIiBRau1vi2MTmGOLrCIkE2HUjGq0Xn8Gem9H8YZ2okmBykoioApNIJOjb0B6nvmmB3l52ivLgJ8mIT80QMTIiIiIiojf0tdTxU9da2DnGF66W+kh6nYXxfwdh8MareJKUJnZ4RFTCmJwkIqoELAy0FaMmX6bJ8Pn/rqPdkrMIecrdEYmIiIiobKhftQoOjG2GyW1doakuxdk7z9F2yVn8fu4BsnPkYodHRCWEyUkiokrmZboMpvqaqKKrieoW+mKHQ0RERESkoKkuxVctXXB4XDN4O5kgXZaD2f/eRo9VFxEazR/WiSoiJieJiCqZqqa62P1FE2we1gg6mmoAALlcwI3HL0SOjIiIiIjoDWdzffw1sjHm9/SEobY6QqJfotvKC5h38DbSs3LEDo+IihGTk0RElZCmuhT2JrqK2xsuRKHnqov4cW8oO3tEREREVCZIpRJ82qgqjk9qjk6e1siRC1h79gHaLT2L83cTxA6PiIoJk5NERIS4lDeb42y+9Aidlp/DTY6iJCIiIqIywsJAGysH1MfvgxrA2kgbj5PSMHD9ZUz8JwgvXmeJHR4RfSQmJ4mICD90cscfwxrBylAbDxJeo9fqi/jlaCSysrnwOBERERGVDa3dLXF0gh8G+zhAIgF23YhGq8VnsOdmNARBEDs8IioiJieJiAgA4OdqjiPj/dCtrg3kAvDryXvoufoC7sSlih0aEREREREAwEBbAwHdPLBjtC9cLfWR9DoL4/8OwpCNV/EkKU3s8IioCJicJCIiBSNdDSz7tB5W9K8HY10NhEanoPOv5/H7uQeQy/lrNBERERGVDV4OVXBgbDNMauMKTTUpztx5jrZLzuL3cw+QncPZP0TlCZOTRESUR+faNjg63g/+NcyRlS3H7H9vo99vgfw1moiIiIjKDE11Kca2csGh8c3QyMkE6bIczP73NnqsuoiwmJdih0dEBcTkJBERqWRhqI0NQxpiXk9P6Gqq4XJUEjosO4d/rj7hmj5EREREVGZUM9fHtpGNMa+nJwy01RES/RJdV1zAvEO3kZ6VI3Z4RPQBTE4SEVG+JBIJ+jWqikPjmqGBQxW8yszGshN3kS5jJ4+IiIiIyg6p9E2/9cTE5ujoaYUcuYC1Zx6g3dKzOH83QezwiOg9mJwkIqIPcjDVw9+f+2BKBzcs6lMHuprqAMARlERERERUplgYamPVAC/8NqgBrI208TgpDQPXX8akf4Lx4nWW2OERkQrqYgdARETlg5pUgtHNqymVbbn8GDcfJ+PHru4w1NYQKTIiIiIiImVt3C3R2NkEi45E4o/AR9h54ylORcZjRmd3NHSsghdpMgBAdnY2nrwCwmJSoK7+JkViqq8JayMdMcMnqlSYnCQioiJ5mS7D/EMReJWZjXpVjTGwsYPYIRERERERKRhoayCgmwe61rXF1F23cCfuFcb/HQQNNQlkOW/PAFLHopBAxS1zfS2cn+IPLXW10g+aqBLitG4iIioSIx0NbBraEH0b2KF/o6pih0NEREREpJKXQxUcGNsMk9q4QkP6bmJSmUQCWBtrQ1ON6RKi0sJ3GxERFVkDRxMs7F0HUqkEAJCWlY3hm64i+EmyuIEREREREb1FU12Ksa1ccHiCH1wt9fOtJwjApLY1IJFISjE6osqNyUkiIio2y0/cw4mIePRcfRFLj9+BLEcudkhERERERArVzPVx6OtmsDXOu6akVALUtjOCn4uZCJERVV5MThIRUbH53M8ZnWpbI0cuYOnxu+i1+iLuxb8SOywiIiIiIgU1NSnm9vTMUy7nqEkiUTA5SURExaaKniZW9q+P5f3qwVBbHbeevkSn5eew4XwU5PL81/YhIiIiIipNfi5mqG1nhLfzkDWtDThqkkgETE4SEVGx61rHBkcnNEczFzNkZssx80A4Bq6/jOjkdABAjlzA5agkXE+Q4HJUEnKYuCQiIiKiUiSRSDCpbQ0Ib3VDq+hqctQkkQjUxQ6AiIgqJisjbfwxrBH+vPwYc/+9jYv3E9F+yVn08rLF4bA4xL7MAKCGP+5eg7WRNn7s4o72HtZih01ERERElYSfixk8bQ0REp0CALh4PxE3H79AvapVRI6MqHLhyEkiIioxEokEnzV2wMFxzVCvqjFSM7Ox6eKj/09M/if2ZQbG/HkDh0OfiRQpEREREVU2EokEk9q4wFJHQNNqpgCAmQfCIQic1UNUmpicJCKiEudkpodtIxtDX0v1gP3c7l/A/nBO8SYiIiKiUtOkmim+r5uDBb08oKuphpuPk7EvOEbssIgqFSYniYioVNx4nIxXmdn5HhcAPHuZgStRSaUXFBERERERAAsDLXzpXx0AMP9QBNKy8u+3ElHxYnKSiIhKRXxqxocrFaIeEREREVFxGt7UCbbGOnj2MgPrzj4QOxyiSoPJSSIiKhUWBtrFWo+IiIiIqDhpa6jh+441AQBrztxHTHK6yBERVQ5MThIRUalo5GQCayNtSN5Tx9pIG42cTEotJiIiIiKit3X0tEIjRxNkyORYeDhC7HCIKgUmJ4mIqFSoSSX4sYs7AOSboPyxizvUpO9LXxIRERERlRyJRILpnd0hkQB7gmJw4/ELsUMiqvCYnCQiolLT3sMaqwfWh5WR8tRtCwMtrBlYH+09rEWKjIiIiIjoDU87I/SubwcAmLk/HHK5IHJERBWbutgBEBFR5dLewxpt3K1w6V48jp67jLbNvOFT3YIjJomIiIiozPimXQ0cDHmGoCfJ2BscjR717MQOiajC4shJIiIqdWpSCbydTOBlJsDbyUSRmLz+6AW2Xn4scnREVJl17doVVatWhba2NqytrfHZZ58hJibmvee0aNECEolE6W/06NGlFDEREZUEC0NtfOFfHQCw4FAk0rKyRY6IqOJicpKIiMqEkKcv0Wv1Rfy0LwwPE16LHQ4RiejcuXMYOHAgfHx8EB0dDQD43//+h/Pnz5f4ffv7++Off/5BZGQkdu7cifv376N3794fPG/kyJF49uyZ4m/hwoUlHisREZWs4U2dYFdFB7EpGVhz5oHY4RBVWExOEhFRmeBha4hmLmbIypFj1oFwscMhIpHs3LkT7dq1g46ODm7evInMzEwAwMuXLzF37twSv/8JEyagcePGcHBwgK+vL6ZMmYLAwEDIZLL3nqerqwsrKyvFn6GhYYnHSkREJUtbQw3fd6wJAFh75j6ik9NFjoioYmJykoiIygSJRIIfu9SCulSCExHxOBURL3ZIRCSC2bNnY82aNfjtt9+goaGhKG/SpAlu3LhRqrEkJSVhy5Yt8PX1VYpFlS1btsDMzAweHh6YOnUq0tLSSilKIiIqSR08rNDIyQSZ2XIsPBwhdjhEFRI3xCEiojKjuoU+hjV1wrqzDxCwPwy+1U2hpa4mdlhEVIoiIyPh5+eXp9zIyAjJycmlEsN3332HFStWIC0tDY0bN8aBAwfeW79///5wcHCAjY0Nbt26he+++w6RkZHYtWtXvudkZmYqRoUCQEpKCgBAJpN9cJRmZZLbFmwTZWyX/LFtVGO75K8gbfN9e1f0WBOIvUExGNDQDvWqGpdSdOLhayZ/bBvVPqY9mJwkIqIyZWzL6th9MxoPE9Ow/nwUvmhRXeyQiKgUWVlZ4d69e3B0dFQqP3/+PJydnYt0zSlTpmDBggXvrXP79m24ubkBAL755hsMHz4cjx49QkBAAAYNGoQDBw5AIpGoPHfUqFGKf3t6esLa2hqtWrXC/fv3Ua1aNZXnzJs3DwEBAXnKT506BV1d3YI+tErj2LFjYodQJrFd8se2UY3tkr8PtY23uRSB8VJ889dljPfIgVT1R0KFw9dM/tg2yj5m1giTk0REVKYYaGtgSns3TNoejBUn76FnPTtYGWmLHRYRlZKRI0di3Lhx2LBhAyQSCWJiYnDp0iVMnjwZ06dPL9I1J02ahCFDhry3ztuJTzMzM5iZmcHV1RU1a9aEvb09AgMD4ePjU6D78/b2BgDcu3cv3+Tk1KlTMXHiRMXtlJQU2Nvbw9/fH6ampgW6n8pAJpPh2LFjaNOmzQen1lcmbJf8sW1UY7vkr6Bt0zA1E22WncejVznItq2L7nVtSjHK0sfXTP7YNqolJiYW+VwmJ4mIqMzpUc8WWy4/wo3HyZh36DaWfVpP7JCIqJRMmTIFcrkcrVq1QlpaGvz8/KClpYXJkydj7NixRbqmubk5zM3Ni3SuXC4HAKUp2B8SFBQEALC2ts63jpaWFrS0tPKUa2ho8IuOCmwX1dgu+WPbqMZ2yd+H2sbGRANf+btgweEILDp2F53q2EJXs+KnVPiayR/bRtnHtAU3xCEiojJHKpVgZjcPSCTA3qAYXIlKEjskIiolEokEP/zwA5KSkhAaGorAwEA8f/4cs2bNKvH7vnz5MlasWIGgoCA8evQIJ0+eRL9+/VCtWjXFqMno6Gi4ubnhypUrAID79+9j1qxZuH79Oh4+fIh9+/Zh0KBB8PPzQ+3atUs8ZiIiKj1DmzjC3kQHcSmZWHP6vtjhEFUYTE4SEVGZ5GFrhE8bVgUA/LgvDDlyQeSIiKg0zJs3Dxs2bICmpibc3d3RqFEj6OvrY8OGDR9cN/Jj6erqYteuXWjVqhVq1KiB4cOHo3bt2jhz5oxilKNMJkNkZKRiXSVNTU0cP34cbdu2hZubGyZNmoRevXph//79JRorERGVPm0NNXzfoSYAYO3ZB4hOThc5IqKKoeKPQSYionLrm3Y1cDDkGW4/S8HWy4/wmY+j2CERUQlbu3Yttm7dmqe8Vq1a+PTTT/Hdd9+V2H17enri5MmT763j6OgIQfjvxxJ7e3ucOXOmxGIiIqKypb2HFbydTHA5KgnzD0Xg135cfojoY3HkJBERlVkmepqY1NYVALDsxF1kZueIHBERlbTY2FiVazWam5vj2bNnIkRERET0H4lEgumd3SGRAPuDY3D9EZcfIvpYHzVy8sSJEzhx4gTi4+MVi4Xn2rBhw0cFRkREBAD9G1XF3bhXGOzrAC11NbHDIaISZm9vjwsXLsDJyUmp/MKFC7Cxqdg7oxIRUfngYWuETxrYY9vVJwjYH449XzSBVCoROyyicqvIycmAgADMnDkTDRo0gLW1NSQSvhGJiKj4qatJMau7h9hhEFEpGTlyJMaPHw+ZTIaWLVsCePOD+LfffotJkyaJHB0REdEbk9rWwIFbz3Dr6UvsvhmNXl52YodEVG4VOTm5Zs0abNq0CZ999llxxkNERPRe9+JTUc1cnz+KEVVQ33zzDRITE/HFF18gKysLAKCtrY3vvvsOU6dOFTk6IiKiN8wNtPBVy+qYfygCC49EoL2HFfS0uK0HUVEUec3JrKws+Pr6FmcsRERE7zXv4G20XXIWe4KixQ6FiEqIRCLBggUL8Pz5cwQGBiI4OBhJSUmYMWOG2KEREREpGdrEEVVNdBGXkok1Z+6LHQ5RuVXk5OSIESNU7qRIRERUUgx1NCAXgOAnL8UOhYhKmL6+Pho2bAgPDw9oaWmJHQ4REVEeWupq+L5jTQDAurMP8PRFmsgREZVPRR5znJGRgXXr1uH48eOoXbs2NDQ0lI4vXrz4o4MjIiJ624hmTmjkZIKGjiZih0JEJYibLhIRUXnRrpYlGjubIPBBEuYfisCK/vXFDomo3ClycvLWrVuoW7cuACA0NFTpGNcBIyKikqClrsbEJFEFx00XiYioPJFIJJjRuRY6/XoOB249wxDfJDRgf5WoUIqcnDx16lRxxkFERFQoMcnp2BMUjTHNqzF5QVSBcNNFIiIqb9xtDPFpQ3v8deUJAvaHY++XTSCVsn9KVFBFXnOSiIhILK8zs9Fh2TksPByJo+FxYodDRMWImy4SEVF5NLFNDehrqSMk+iV23eTmjUSF8dHJyfDwcBw+fBj79u1T+iuqlStXwtHREdra2vD29saVK1cKdN62bdsgkUjQvXv3It83ERGVD3pa6hjgXRUAMOtAODJkOSJHRETFhZsuEhFReWRuoIWxLasDABYejsDrzGyRIyIqP4o8rfvBgwfo0aMHQkJCIJFIIAgCgP/Wm8zJKfwXxb///hsTJ07EmjVr4O3tjaVLl6Jdu3aIjIyEhYVFvuc9fPgQkydPRrNmzYr2YIiIqNz50r86dt2IxtMX6Vh39gG+buUidkhEVAy46SIREZVXQ5o4YuuVx3iUmIbVp+9jcrsaYodEVC4UeeTkuHHj4OTkhPj4eOjq6iIsLAxnz55FgwYNcPr06SJdc/HixRg5ciSGDh0Kd3d3rFmzBrq6uu/dlTEnJwcDBgxAQEAAnJ2di/hoiIiovNHTUsf3nWoCAFadvoenL9JEjoiIikPupotSqRShoaG4efOm4i8oKEjs8IiIiPKlpa6G7zu+6Z+uO/cAT5LYPyUqiCKPnLx06RJOnjwJMzMzSKVSSKVSNG3aFPPmzcPXX3+NmzdvFup6WVlZuH79OqZOnaook0qlaN26NS5dupTveTNnzoSFhQWGDx+Oc+fOFfXhEBFROdSltjW2BD7C5agkzD14G6sGeIkdEhF9JG66SERE5Vlbd0v4OJvi0oNEzD8cgZX964sdElGZV+TkZE5ODgwMDAAAZmZmiImJQY0aNeDg4IDIyMhCXy8hIQE5OTmwtLRUKre0tERERITKc86fP4/169cX6lf0zMxMZGZmKm6npKQAAGQyGWQyWaHjrshy24Ptooztkj+2jWpsF9WKq12mdayBbqsu4WBILM5ExMK3mmlxhCcqvmZUY7vkj21CRERUNkgkEszo4o5Oy8/h31vPMNgnCY2cTMQOi6hMK3Jy0sPDA8HBwXBycoK3tzcWLlwITU1NrFu3rlSmV6empuKzzz7Db7/9BjMzswKfN2/ePAQEBOQpP3XqFHR1dYszxArj2LFjYodQJrFd8se2UY3tolpxtEsTSynOxUrx3d/X8G3tHKh99HZvZQNfM6qxXfJKS6t408bCw8Px+PFjZGVlKZV37dpVpIiIiIgKpqa1IT5pWBV/XXmMmQfCsO/LppBKJWKHRVRmFTk5OW3aNLx+/RoAEBAQgC5duqBZs2YwNTXF33//XejrmZmZQU1NDXFxcUrlcXFxsLKyylP//v37ePjwIbp06aIok8vlAAB1dXVERkaiWrVqec6bOnUqJk6cqLidkpICe3t7+Pv7w9S0/I+2KU4ymQzHjh1DmzZt8ixGX5mxXfLHtlGN7aJacbZLk3QZ2iw9j9g0GRJMamGor0MxRSkOvmZUY7vkLzExUewQik1JbLpIRERU2ia1dcWB4BiERqdg542n6NPAXuyQiMqsIicn27Vrp/i3i4sLIiIikJSUhCpVqig6j4WhqakJLy8vnDhxAt27dwfwJtl44sQJfPXVV3nqu7m5ISQkRKls2rRpSE1NxbJly2Bvr/qNr6WlBS0trTzlGhoa/KKTD7aNamyX/LFtVGO7qFYc7WKmoYFv27th6q4Q/HryPnp62cNMP+//9eUNXzOqsV3yqkjtkbvp4okTJ+Dk5IQrV64gMTERkyZNwqJFi8QOj4iIqEDM9LUwtlV1zD0YgYVHItHB0xr6WkVOwRBVaB818e3cuXMYOHAgfHx8EB0dDRMTE/z55584f/58ka43ceJE/Pbbb9i8eTNu376NMWPG4PXr1xg6dCgAYNCgQYoNc7S1teHh4aH0Z2xsDAMDA3h4eEBTU/NjHhoREZUzfRvYw9PWCKmZ2Vh4WPVaxURU9l26dAkzZ87Md9NFIiKi8mKIrxMcTXXxPDUTq0/fEzscojKryMnJnTt3ol27dtDR0cHNmzcVm8y8fPkSc+fOLdI1P/nkEyxatAgzZsxA3bp1ERQUhMOHDys2yXn8+DGePXtW1JCJiKgCU5NKENCtFgDgn2tPcS/+lcgREVFRqNp0EUCRN10kIiISi6a6FN93rAkA+O1cFJ4kVbw1oomKQ5HHFM+ePRtr1qzBoEGDsG3bNkV5kyZNMHv27CIH9NVXX6mcxg0Ap0+ffu+5mzZtKvL9EhFR+Ve/ahV83bI66lWtguoW+mKHQ0RFIPami0RERMWpjbslmlQ3xYV7iZh/KAIrB9QXOySiMqfIIycjIyPh5+eXp9zIyAjJyckfExMREVGRTWxbA/5uFmKHQURFNG3aNMUmhzNnzkRUVBSaNWuGgwcPYtmyZSJHR0REVDgSiQTTOrlDKgH+DXmGyw8qziZ2RMWlyMlJKysr3LuXd82E8+fP81dtIiIqExJeZSIlQyZ2GERUCO3atUPPnj0BANWrV0dERAQSEhIQHx+PVq1aiRwdERFR4dW0NsSnjaoCAGYeCEeOXBA5IqKypcjTukeOHIlx48Zhw4YNkEgkiImJwaVLlzB58mRMnz69OGMkIiIqtL1B0Zi2JxS9vezwY5daYodDRO8xceJEzJo1C3p6epg4ceJ76y5evLiUoiIiIio+k9q4Yn9QDMJiUrDz+lP0bWgvdkhEZUaRk5NTpkyBXC5Hq1atkJaWBj8/P2hpaWHy5MkYO3ZsccZIRERUaCZ6mkjNyMbNx8nIzpFDXa3IkwWIqITdvHkTMtmbUc43btyARCJRWS+/ciIiorLOVF8LX7dywZyDt7HwSCQ61raGvlaRUzJEFUqR3wkSiQQ//PADvvnmG9y7dw+vXr2Cu7s79PW5AQEREYmvmYs5Ng9rhKbVzaAmZUKDqCw7deqU4t8f2gCRiIiovBrs64gtlx/hYWIaVp66h+/au4kdElGZ8NHDSDQ1NeHu7o5GjRoxMUlERGVKc1dzJiaJyhGZTIZWrVrh7t27YodCRERU7DTVpfihkzsAYP25KDxJShM5IqKyodAjJ4cNG1agehs2bCh0MERERCUhPSsHmy4+xGBfB+hqcvoMUVmloaGBW7duiR0GERFRiWld0wJNq5vh/L0EzDt0G6sGeIkdEpHoCj1yctOmTTh16hSSk5Px4sWLfP+IiIjKisEbr2DB4QisPn1f7FCI6AMGDhyI9evXix0GERFRiZBIJJjWuSakEuBgSCwCHySKHRKR6Ao9fGTMmDH466+/EBUVhaFDh2LgwIEwMTEpidiIiIiKxVBfR1yJSsLasw/Qx8seVU11xQ6JiPKRnZ2NDRs24Pjx4/Dy8oKenp7Sce7WTURE5Z2blSH6e1fFn4GPMetAOPZ91ZRLEVGlVuiRkytXrsSzZ8/w7bffYv/+/bC3t0ffvn1x5MgRCIJQEjESERF9lPYeVmhS3RRZ2XLMPBAudjhE9B6hoaGoX78+DAwMcOfOHdy8eVPxFxQUJHZ4RERExWJCa1cYaKsjLCYFO64/ETscIlEVaeEtLS0t9OvXD/369cOjR4+wadMmfPHFF8jOzkZYWBg3xiEiojJFIpHgpy610GHZORy/HYfTkfFoUcNC7LCISIW3d+4mIiKqqEz1tTCulQtm/3sbPx+5g46e1jDQ1hA7LCJRfPRu3VKpFBKJBIIgICcnpzhiIiIiKnYulgYY7OsIAJi5PxxZ2XJxAyIiIiKiSm2QjyOczPSQ8CoTK09xbXSqvIqUnMzMzMRff/2FNm3awNXVFSEhIVixYgUeP37MUZNERFRmjWvtAjN9LTxIeI2NF6LEDoeI3iM8PByHDx/Gvn37lP6IiIgqCk11KX7oWBMAsOF8FB4npokcEZE4Cj2t+4svvsC2bdtgb2+PYcOG4a+//oKZmVlJxEZERFSsDLU18F37Gvhmxy0sP3EX3evZwtJQW+ywiOgtDx48QI8ePRASEqKYnQO8WZ4BAGfqEBFRhdKqpgWauZjh3N0EzD14G2s+8xI7JKJSV+iRk2vWrIGhoSGcnZ1x5swZjBo1Cj179szzR0REVBb1qm+HelWN8TorB/MPRYgdDhG9Y9y4cXByckJ8fDx0dXURFhaGs2fPokGDBjh9+rTY4RERERUriUSCaZ3cIZUAh8Nicel+otghEZW6QicnBw0aBH9/fxgbG8PIyCjfPyIiorJIKpUgoGstSCTA7pvRuPYwSeyQiOgtly5dwsyZM2FmZgapVAqpVIqmTZti3rx5+Prrr8UOj4iIqNjVsDLAAG8HAMDMA+HIkQsiR0RUugo9rXvTpk0lEAYREVHpqW1njE8a2GPb1SeYsTcM+8c2hZpUInZYRIQ307YNDAwAAGZmZoiJiUGNGjXg4OCAyMhIkaMjIiIqGRPauGJvUDRuP0vB9mtP8GmjqmKHRFRqPnq3biIiovLom3Y1YKitjvBnKdgXHC12OET0/zw8PBAcHAwA8Pb2xsKFC3HhwgXMnDkTzs7OIkdHRERUMkz0NDGutSsAYNHRSKRmyESOiKj0MDlJRESVkqm+Fn7oVBPTO7ujc20bscMhov83bdo0yOVyAMDMmTMRFRWFZs2a4eDBg1i+fLnI0REREZWczxo7wNlMDwmvsrDi1D2xwyEqNYWe1k1ERFRRfNKQ02WIyorQ0FB4eHigXbt2irLq1asjIiICSUlJqFKlimLHbiIioopIU12KaZ1rYtima9h4/iH6N6oKB1M9scMiKnEcOUlERAQgMzsHcSkZYodBVGnVrl0b3t7e+O2335Camqp0zMTEhIlJIiKqFPxrWKCZixmycuSYe/C22OEQlQomJ4mIqNILefoS7Zeew1dbb0AQuDsikRjOnDmDWrVqYdKkSbC2tsbgwYNx7tw5scMiIiIqVRKJBNM7u0NNKsGRsDhcvJ8gdkhEJa5YkpNJSUmKtYGIiIjKG1N9TcS+zEBUQhqevkgXOxyiSqlZs2bYsGEDnj17hl9//RUPHz5E8+bN4erqigULFiA2NrZU48nMzETdunUhkUgQFBT03roZGRn48ssvYWpqCn19ffTq1QtxcXGlEygREVU4rpYGGOD9ZvmhWQduI0fOH8+pYitycjI8PBzz58+Hr68vzM3NYWFhgUGDBmHnzp14/fp1ccZIRERUomyMdfD74AY4Nbk57E10xQ6HqFLT09PD0KFDcebMGdy5cwd9+vTBypUrUbVqVXTt2rXU4vj2229hY1OwzbImTJiA/fv3Y/v27Thz5gxiYmLQs2fPEo6QiIgqsvGtXWGorY7bz1Lwz7UnYodDVKIKlZyMjIzEpEmT4OLigsaNG+Pq1asYPXo04uLicPDgQTg4OGDmzJkwMzNDhw4dsHr16pKKm4iIqFg1qW4GA20NscMgordUr14d33//PaZNmwYDAwP8+++/pXK/hw4dwtGjR7Fo0aIP1n358iXWr1+PxYsXo2XLlvDy8sLGjRtx8eJFBAYGlkK0RERUEZnoaWJ8a1cAwKIjkUjJkIkcEVHJKdRu3RcvXsTr16+xfPlytGrVCpqamopjZmZmaNSoEWbNmoWHDx9i79692LVrF8aMGVPsQRMREZUUQRCwNygGte2M4GyuL3Y4RJXW2bNnsWHDBuzcuRNSqRR9+/bF8OHDS/x+4+LiMHLkSOzZswe6uh8eSX39+nXIZDK0bt1aUebm5oaqVavi0qVLaNy4scrzMjMzkZmZqbidkpICAJDJZJDJ+AU0V25bsE2UsV3yx7ZRje2Sv7LcNp82sMGfgQ/xICENy4/fwXftXEvtvstyu4iNbaPax7RHoZKTQ4cOxdChQz9Yz9HREePGjcO4ceOKHBgREZEYFhyOxJoz99Hc1RybhjbkDsFEpSgmJgabNm3Cpk2bcO/ePfj6+mL58uXo27cv9PT0Svz+BUHAkCFDMHr0aDRo0AAPHz784DmxsbHQ1NSEsbGxUrmlpeV718mcN28eAgIC8pSfOnWqQEnRyubYsWNih1AmsV3yx7ZRje2Sv7LaNq3NJFiXoIaNF6Jg9eoezHVK9/7LaruUBWwbZWlpaUU+t1DJSSIiooqubwM7rD//AGfuPMeJ2/Fo7W4pdkhElUKHDh1w/PhxmJmZYdCgQRg2bBhq1KhRLNeeMmUKFixY8N46t2/fxtGjR5GamoqpU6cWy/2+z9SpUzFx4kTF7ZSUFNjb28Pf3x+mpqYlfv/lhUwmw7Fjx9CmTRtoaHDpjVxsl/yxbVRju+SvrLdNB0HA7T9u4Ny9RFzOtMGqXnVL5X7LeruIiW2jWmJiYpHPLVJyMiEhARs2bMClS5cUvwhbWVnB19cXQ4YMgbm5eZEDIiIiEpOzuT6GN3XGmjP3MfNAOJq6mEFbQ03ssIgqPA0NDezYsQOdO3eGmlrxvucmTZqEIUOGvLeOs7MzTp48iUuXLkFLS0vpWIMGDTBgwABs3rw5z3lWVlbIyspCcnKy0ujJuLg4WFlZ5Xt/Wlpaee4HeNMO/KKTF9tFNbZL/tg2qrFd8leW22ZGl1pov+wcjt2Ox9VHL+Fb3azU7rsst4vY2DbKPqYtCp2cvHr1Ktq1awddXV20bt0arq5v1jyIi4vD8uXLMX/+fBw5cgQNGjQoclBERERiGtuyOnbffIrHSWn4/dwDfNXSReyQiCq8ffv2ldi1zc3NC/Tj+fLlyzF79mzF7ZiYGLRr1w5///03vL29VZ7j5eUFDQ0NnDhxAr169QLwZhPJx48fw8fHp3geABERVWoulgYY6F0Vmy89wswD4fj362ZQk3LpIao4Cp2cHDt2LPr06YM1a9bkWYdLEASMHj0aY8eOxaVLl4otSCIiotKkp6WO7zvWxLhtQVh56j561reDjXEpL/BDRKWuatWqSrf19d9silWtWjXY2dkBAKKjo9GqVSv88ccfaNSoEYyMjDB8+HBMnDgRJiYmMDQ0xNixY+Hj45PvZjhERESFNb61K/YExSAiNhV/X32C/t5VP3wSUTkhLewJwcHBmDBhgsoNAiQSCSZMmICgoKDiiI2IiEg0XevYoJGjCdJlOZhz8LbY4RBRGSGTyRAZGam06PuSJUvQuXNn9OrVC35+frCyssKuXbtEjJKIiCqaKnqaGN/6zWyeX45GIiWDO0VTxVHo5KSVlRWuXLmS7/ErV67A0pKbBxARUfkmkUjwU9dakEqAf289w8X7CWKHRESlzNHREYIgoG7dunnKWrRooSjT1tbGypUrkZSUhNevX2PXrl3vXW+SiIioKAY2dkA1cz0kvs7CipP3xA6HqNgUOjk5efJkjBo1CuPGjcO+fftw+fJlXL58Gfv27cO4ceMwevRofPvttyURKxERUalytzHEAG8HAEDAvnBk58hFjoiIiIiIKisNNSmmdXYHAGy8EIWohNciR0RUPAqdnPzyyy+xefNmXL58Gb169YKPjw98fHzQq1cvXL58GZs2bcIXX3xRErESERGVukltXVFFVwORcan4M/CR2OEQVSpJSUmQy/mjABERUS7/GhZo7moOWY6AuVx6iCqIQicnAeCTTz5BYGAg0tLSEB0djejoaKSlpSEwMBB9+/Yt7hiJiIhEY6yricntagAAFh+7g8RXmSJHRFSxhYeHY/78+fD19YW5uTksLCwwaNAg7Ny5E69fc4QIERHR9M41oSaV4Fh4HC7c49JDVP4VKTmZS0NDA9bW1rC2toaGhkZxxURERFSmfNqwKjxsDZGSkY1fub4PUbGLjIzEpEmT4OLigsaNG+Pq1asYPXo04uLicPDgQTg4OGDmzJkwMzNDhw4dsHr1arFDJiIiEk11CwN81vjN0kMz93PpISr/1AtT2cnJSeUu3R8yfvx4fP3114U+j4iIqCxQk0oQ0LUWdt+MxrhWLmKHQ1ThXLx4Ea9fv8by5cvRqlUraGpqKo6ZmZmhUaNGmDVrFh4+fIi9e/di165dGDNmjIgRExERiWt8axfsvhmNyLhUbLv6BAP/P1lJVB4VKjm5adOmIt2Jo6Njkc4jIiIqK7wcTODlYCJ2GEQV0tChQzF06NAP1nN0dMS4ceMwbty4UoiKiIio7DLW1cSE1i74aX84Fh+7gy51bGCkwxmtVD4VKjnZvHnzkoqDiIio3BAEAbEpGbA20hE7FCIiIiKqpAY0dsCflx/jXvwr/HrirmInb6Ly5qPWnCQiIqpsEl5lYtCGK+jy63mkZMjEDoeoQklISMDChQvRo0cP+Pj4wMfHBz169MDPP/+M58+fix0eERFRmaKhJsW0TjUBAJsuPsSD569EjoioaAqdnDQwMICfnx8mTJiA//3vfwgLC4MgCCURGxERUZljqK2B6OR0pKRn4/rDF2KHQ1RhXL16Fa6urli+fDmMjIzg5+cHPz8/GBkZYfny5XBzc8O1a9fEDpOIiKhMaVHDAv41zJEtFzD3YITY4RAVSaGmdQPAggULcP36dZw8eRIrVqyAXC6Hjo4OateuDS8vL9SvXx/169dHnTp1SiJeIiIiUWmqS7Gkb10Y62rAwVRP7HCIKoyxY8eiT58+WLNmTZ4NGAVBwOjRozF27FhcunRJpAiJiIjKph86uePc3bM4fjsO5+8moKmLmdghERVKoZOTX3zxheLf6enp0NPTw9ixY5GUlITAwED8/vvvyMrKQk5OTrEGSkREVFbUsTcWOwSiCic4OBibNm3Kk5gEAIlEggkTJqBevXoiREZERFS2VbfQx2c+Dth44SFmHQjHv183hboaV/Gj8uOjXq06Om82AujXrx/Wrl2Lq1evIjU1FTdv3iyW4IiIiMq6oCfJuHAvQewwiMo9KysrXLlyJd/jV65cgaWlZSlGREREVH6Ma+UCY10NRMal4q+rT8QOh6hQCj1y8oMXVFdH7dq1i/uyREREZc6RsFh8/r/rsDXWwfGJzaGjqSZ2SETl1uTJkzFq1Chcv34drVq1UiQi4+LicOLECfz2229YtGiRyFESERGVTca6mpjYxhUz9oZh8dFIdK1jAyMdDbHDIiqQYk9OEhERVRZ+LuawNdZBdHI6Vp+5j4ltXMUOiajc+vLLL2FmZoYlS5Zg1apViiWC1NTU4OXlhU2bNqFv374iR0lERFR29W9UFf+79Ah3419h+Ym7mN7ZXeyQiAqk0NO6R4wYgdWrV+Pq1avIzMwEAJVrAxEREVV0Oppq+KFTTQDAmjP38SQpTeSIiMq3Tz75BIGBgUhLS0N0dDSio6ORlpaGwMBAJiaJiIg+QF1Nimn/n5DcfPEhHjx/JXJERAVT6OTk3bt3MWXKFHh7e8PAwAAAEBAQgBUrVuDixYtIS+MXMyIiqjw6eFjBt5opsrLlmHUgXOxwiCoEDQ0NWFtbw9raGhoanJJGRERUUM1dzdHSzQLZcgFz/r0tdjhEBVLoad1nzpwB8CZJef36ddy4cQM3btzAjBkzkJycDDU1Nbi6uiIsLKzYgyUiIiprJBIJfupaCx2WncPR8DicvfMcfq7mYodFVK44OTkVaSbO+PHj8fXXX5dAREREROXXD51q4uyd5zgREc++KZULRV5z0sXFBS4uLvj0008VZQ8ePMD169e5WzcREVUqrpYGGOzjiA0XovDT/jAcHucHTfVCT04gqrQ2bdpUpPMcHR2LNQ4iIqKKoJq5Pgb9f9909r/hOFitGdTV2DelsqtYN8RxdnaGs7Mz+vTpU5yXJSIiKvPGt3HBvuBoPHj+GpsuRmGUXzWxQyIqN5o3by52CERERBXKuFYu2H3zKe7EvcJfVx7jMx9HsUMiylehkpOcckNERKSaobYGvm3vhm933MKy43fRva4tLAy1xQ6LiIiIiCohI10NTGzjiul7w7D42B10rWMLI12u40xlU6GSk5xyQ0RElL/e9e2w9fJjBD1JxvxDEVj8SV2xQyIqNwwMDFCvXj14eXmhfv36qF+/Ptzd3Yv0wzgREREB/RpVxf8CH+FO3CssO3EXM7q4ix0SkUqFSk5yyg0REVH+pFIJArrWQreVF7DrZjQGNK4KLwcTscMiKhcWLFiA69ev4+TJk1ixYgXkcjl0dHRQu3ZtpYRlnTp1xA6ViIioXFBXk2J6Z3d8tv4K/rj0EAMaV0U1c32xwyLKgyuiEhERFaM69sbo28AOADDzwG0IgiByRETlwxdffIH169cjODgYKSkpEAQBY8eOhaenJwIDA/HFF1+gfv36YodJRERUrjRzMUcrNwtkywXM+fe22OEQqVSkDXESEhKwYcMGXLp0CbGxsQAAKysr+Pr6YsiQITA35zb1RERUeX3b3g3JaTJMbleDU1KJikBHRwcA0K9fP9SuXRsAkJ2djfDwcDHDIiIiKpd+6FQTZ+48x8mIeJy58xzNXZmzobKl0CMnr169CldXVyxfvhxGRkbw8/ODn58fjIyMsHz5cri5ueHatWslESsREVG5YKavhXWDGsD1/9q787iq6vyP4+972VVAWQREBBEVxS01CU3N3LeaFrPJfqWW5eSWWKk1adoiOo41Taat2jpWM5Vp7qaYpWkomoq47+CuqCgg3N8fTRTjvSqKfC/c1/Px4PHwnnvOvW8+YX743HO+J8TXdBSg3HB3dy8cVAIAgKsXHVxJD7eMkiS9NHeLLuYXmA0E/I9inzk5ZMgQ9erVS9OnT7/kbBCbzaaBAwdqyJAhWrVqVYmFBACgLDty5oKq+nLnbgAAAJgx9Pba+nLdAW0/clafrtmnhxKiTEcCChX7zMkNGzZo+PDhdi9Ts1gsGj58uFJTU0siGwAAZVp+gU1jZ2/SrUnLtOVQluk4gFN79NFHNW3aNK1du1Y5OTmSxLIIAACUEP8KHkrsVFeSNGXxNp3KzjWcCPhdsYeToaGhWrNmjcPn16xZo5CQkOsKBQBAeeBmtejo2Rzl5hdoSdph03EAp7Z9+3aNGjVK8fHx8vX9dUmEcePG6Y033tCPP/6o7OxswwkBACjb/nxzhOqG+OpUdp7+sXS76ThAoWJf1v3UU0/pscceU0pKitq3b184iDx8+LCWLl2qd955R5MnTy7xoAAAlEXPda+vB+Mj1TImyHQUwKklJydL+nVImZKSonXr1mndunUaM2aMTp06JTc3N9WpU0ebN282nBQAgLLJ3c2qv/aop/97b40+WrVXfeIjFVO1kulYQPGHk4MGDVJQUJBeffVVvfnmm8rPz5ckubm5qVmzZpo5c6buu+++Eg8KAEBZFF7ZR+GVfUzHAMqM2rVrq3bt2rr//vsLt+3atUspKSlav369wWQAAJR9rWsHq0O9qlqSdkQvf7tFM/q1MB0JKP5wUpJ69+6t3r17Ky8vT8eOHZMkBQUFycPDo0TDAQBQnmSevqCf955Qj0bVTEcBypTo6GhFR0erV69epqMAAFDmPde9vpK3HdWy9KNann5Et9WtajoSXNw1DSd/4+HhobCwsJLKAgBAubXveLa6/GOF8vILFFfNXzWDKpqOBDiNmjVrXtPNb5588kkNHTr0BiQCAKD8qhlUUQ8nROndlbv10rdpahUTJA+3Yt+SBCgxxRpOZmZmqkqVKvLy8rqq/Xft2qXo6OhrCgYAQHkSEeCjm6MClLztqMbP2cwlNMAfzJw585qOi4qKKtEcAAC4iiHta+vL9Qe148hZffrTPj3cMsp0JLiwYg0n//3vf2vkyJHq1KmT7rjjDvXo0UPBwcFF9vnpp580e/ZszZ49W/v27dOZM2dKNDAAAGWRxWLR2J711fm1FVqWflTfbT2s22NDTMcCnELbtm1NRwAAwKX4+3gosWMd/fXrTXp1yTbd2aSaKlfwNB0LLqpY5+0OHjxYGzZsUOvWrTVz5kxVr15dt956q1555RUNGDBAYWFh+tOf/qQjR44oKSlJR48evVG5AQAoc6KDK6n/rTUlSePnbFHOxXzDiQAAAOCq7r85QrGhvjqVnafXlmw3HQcurNiLCsTExCgxMVHJyck6dOiQHn30UW3YsEEBAQH6z3/+o0OHDundd99Vz5495e3tfSMyAwBQZg25vbaq+nppz/Fsvfv9btNxAKdy7NgxTZo0SXfddZcSEhKUkJCgu+66S3/729/40BsAgBLm7mbV8z3qS5I+Wr1XO45w5SvMuK4VTwMDA9W3b1999tlnmjhxolq2bHlNi5kDAOAqKnm5a3S3WEnSG9/tUMbp84YTAc5h7dq1qlOnjl5//XX5+/urTZs2atOmjfz9/fX6668rNjZWP//8s+mYAACUK61igtShXojyC2x66ds003Hgoq77dkyvvvqqJGnz5s3Kz+fyNAAAruRPTcLVPLKKzufl65V5W03HAZzCkCFD1KtXL+3fv18zZ87UxIkTNXHiRM2cOVP79u3TvffeqyFDhpiOCQBAufNc93rycLNoefpRLUs/YjoOXNB1DyebNGkiSXr22WdVv359NWnSRH369FFSUpLmzp1b7NebOnWqoqKi5O3trfj4eK1Zs8bhvl9++aWaN2+uypUrq2LFimrSpIk++uija/1WAAAoFRaLRS/cESeLRZqz4ZBW7zpuOhJg3IYNGzR8+HC7V+FYLBYNHz5cqamppR8MAIByrmZQRfX97926X5q7RXn5BWYDweVc93CyXbt2kqTZs2crPT1dK1eu1NChQxUUFKQlS5YU67U+++wzJSYmauzYsVq3bp0aN26szp0768gR+5P7gIAAPffcc1q1apU2btyofv36qV+/flq4cOH1flsAANxQDcL99UCLGpKkF77ZrIs0gXBxoaGhl/1Qes2aNQoJ4Q73AADcCEPa11ZgRU/tPHpOH6/eazoOXIx7cXY+c+aMXnjhBc2bN0/Hjh2Tv7+/6tSpo1atWunee+9V3bp1ValSJcXHxys+Pr7YYaZMmaIBAwaoX79+kqTp06fr22+/1fvvv69Ro0Zdsv9tt91W5PGwYcP0wQcfaOXKlercuXOx3x8AgNL0VKe6+vaXDG3NPKNPftqnh//7iTXgip566ik99thjSklJUfv27QsHkYcPH9bSpUv1zjvvaPLkyYZTAgBQPvl5eyixUx0999UmvbZku7o3qGo6ElxIsYaTDz30kFJSUjRgwACFhITo/PnzGjlypHbt2qUxY8aoe/fumjZtmsLDw4sdJDc3VykpKRo9enThNqvVqg4dOmjVqlVXPN5ms+m7775Tenq6Jk6c6HC/nJwc5eTkFD7OysqSJOXl5SkvL6/Yucuz3+pBXYqiLo5RG/uoi33URarkadGT7WP0wpw0/X1Runo0qCo/Hw9q4wB1caw81GTQoEEKCgrSq6++qjfffLNwLXM3Nzc1a9ZMM2fO1H333Wc4JQAA5df9N9fQR6v2amvmGf3zu51qft3X2gJXp1jDyUWLFmnlypW66aabCrf99a9/1bx58+Tm5qaXX35ZLVq00MqVK1WzZs1iBTl27Jjy8/MvuVwnJCREW7c6vlnA6dOnFR4erpycHLm5uenNN99Ux44dHe4/YcIEjRs37pLty5YtU4UKFYqV2VUsXrzYdASnRF0cozb2URf7XL0u/japcYBVLarm6PvvFuuPy+25em0coS6Xys7ONh2hRPTu3Vu9e/dWXl6ejh07JkkKCgqSh4eH4WQAAJR/blaLxvSorwfe/Umfrj2g6g1NJ4KrKNZwMiQkxGHzGxkZqbffflsvvfSShg0bpm+++aZEAl6Jr6+vUlNTdfbsWS1dulSJiYmKjo6+5JLv34wePVqJiYmFj7OyshQREaF27dopMDCwVDKXFXl5eVq8eLE6duzILwV/QF0cozb2URf7qMvvenQv+pja2EddHDt+vHzdVMnDw0NhYWFGM+Tk5Cg+Pl4bNmzQ+vXrC28Cac9tt92m5OTkItsef/xxTZ8+/QanBACgZLWMCVKn+iFatOWwvtpjVT+bzXQkuIBiDScHDx6s/v376/PPP1fjxo3t7vPggw8qKSmp2EGCgoLk5uamw4cPF9l++PBhhYaGOjzOarUqJiZG0q93Dk9LS9OECRMcDie9vLzk5eV1yXYPDw9+0XGA2thHXRyjNvZRF/uoS1Enz+Wqgvuv/zxTG/uoy6XKej0yMzNVpUoVuz2aPbt27VJ0dPQNzfTMM8+oWrVq2rBhw1XtP2DAAI0fP77wMVfkAADKqme71dOy9CPaetqq5O3H1DGumulIKOeKtYJAYmKievbsqaZNm6pLly6aPn26CgoKZPnDNWizZs1SUFBQsYN4enqqWbNmWrp0aeG2goICLV26VAkJCVf9OgUFBUXWlAQAoKz4bO0+tf3bMs3ekGE6ClCq/v3vfysgIEB33XWXZsyYoaNHj16yz08//aRnn31WcXFxDj8kLynz58/XokWLinUDngoVKig0NLTwy8/P7wYmBADgxokKqqiHEyIlSRPmpysvv8BwIpR3xTpzUpImT56sXr16afLkyRoxYoTOnz+vxo0bKygoSKdPn9aFCxc0c+bMawqTmJiohx9+WM2bN1eLFi302muv6dy5c4V3737ooYcUHh6uCRMmSPp1/cjmzZurVq1aysnJ0bx58/TRRx9p2rRp1/T+AACYdDI7T1kXLmruLxm6p/if8wFl1uDBg9WlSxd98803mjlzpgYOHKibb75Z3bp10+7duzV37lxJUvfu3ZWUlHTZ9cWv1+HDhzVgwAB9/fXXxTr78ZNPPtHHH3+s0NBQ9ezZU88///xlj+cmjVeHG2HZR10cozb2URfHqI19A1pGaNbq3dp1LFszf9ilvv8dVoKfGUeupx7FHk5KUnx8vL744gvl5uZq3bp12rZtm7KyshQUFKTbb79dVate2y3ne/furaNHj2rMmDHKzMxUkyZNtGDBgsKb5Ozbt09W6+8ne547d05PPPGEDhw4IB8fH8XGxurjjz9W7969r+n9AQAwqV+rKAVV8lKPBlW1cMF803GAUhUTE6PExEQlJibq+PHjmjNnjubPn6+oqCj95z//UUJCQpGrdW4Em82mvn37auDAgWrevLn27NlzVcc98MADioyMVLVq1bRx40aNHDlS6enp+vLLLx0ew00ai4cbYdlHXRyjNvZRF8eozaW617Dos11umrJwqyoe2ayKZXsVmRLHz0xR13ODxmsaTkrSwYMHNX/+fB0/flwhISFKSEhQs2bNrjnIbwYPHqzBgwfbfW758uVFHr/00kt66aWXrvs9AQBwBl7ubrq3WXU+hYXLCwwMVN++fdW3b98Seb1Ro0Zp4sSJl90nLS1NixYt0pkzZzR69Ohivf5jjz1W+OeGDRsqLCxM7du3186dO1WrVi27x3CTxqvDjbDsoy6OURv7qItj1Ma+vLw8FSxarNRzFZV++Jy2uNXU2G71TMdyCvzM2Hc9N2i8puHkl19+qQcffFDR0dEKDAwsvFt2ZGSkkpKSdN99911zIAAAIOXmS1+uP6j7bo684WeLAc7o1Vdf1fDhw7V582bFxsbKzc3tml9rxIgRVxx0RkdH67vvvtOqVasuuTFP8+bN1adPH33wwQdX9X7x8fGSpB07djgcTnKTxuKhLvZRF8eojX3UxTFqcymrRfprt3r6vxk/619rD+ihljVVJ8TXdCynwc9MUddTi2saTg4bNkyTJ0/WE088offee0+hoaEaP3685s2bpyeeeEIXLlzQQw89dM2hAABwZXn5BZr8i5sOr9ks/wre6tIg1HQkoNQ1adJEkvTss89q69at8vHxUVxcnBo2bKgGDRqoR48eV/1awcHBCg4OvuJ+r7/+epGrcg4dOqTOnTvrs88+Kxw4Xo3U1FRJUlhY2FUfAwCAM7olOkCd40K0cPNhvTh3iz7s34IPzlHiij2czM3N1cGDB/XII49IkiZNmqS1a9fKz89PdevWVdeuXXXnnXcynAQA4Bp5uFnVOMCmRQcteunbLbqtbrC8Pa79rDGgLGrXrp0kafbs2ZKks2fPavPmzfrll1+0ZMmSYg0nr1aNGjWKPK5UqZIkqVatWqpevbqkX5c2at++vT788EO1aNFCO3fu1Keffqpu3bopMDBQGzdu1PDhw9WmTRs1atSoxDMCAFDanu1WT8u2HtX3249pWfoR3R4bYjoSyhnrlXcpytPTU/Xq1dPRo0clSX5+fnr//fdVUPDrreXDwsKUm5tbsikBAHAxHcILFObvrQMnz2t68k7TcYAb6syZMxoxYoTq1aun4OBgxcTEqFu3bnr55ZeVnp4u6ddBYXx8vB599FG99tprxrLm5eUpPT29cNF3T09PLVmyRJ06dVJsbKxGjBihe+65R3PmzDGWEQCAkhQZWFH9bo2SJL00N025FwvMBkK5c02XdW/evLnwz1OnTtX999+vcePGqVatWtq7d6/++te/llhAAABckZebNKpzHQ37fKOmLd+pe5pWV0QAd/BF+fTQQw8pJSVFAwYMUEhIiM6fP6+RI0dq165dGjNmjLp3765p06YpPDy8VHNFRUXJZrNddltERISSk5NLNRcAAKVtcLsY/SflgHYdO6ePVu/VI7fWNB0J5Uixz5z8Xy1atNCOHTv0zTffaOTIkfr+++81bNiwksgGAIBL69ogRAnRgcq5WKCXv00zHQe4YRYtWqTZs2fr+eef12OPPaZhw4bJw8ND8+bN065duxQaGqoWLVpo9+7dpqMCAOCSfL099FSnupKkfyzZphPnuGIWJee6h5OSZLVa1bp1a/Xq1UuxsbEl8ZIAALg8i8WiF+6Ik5vVogWbM7Vy+zHTkYAbIiQkpPAy6f8VGRmpt99+W3/5y1/4ABwAAIN6NY9QvTA/ZV24qFcXbzMdB+VIiQwnAQDAjVE31Ff/d0ukJOmFOZuVl88aPyh/Bg8erP79+2vDhg0O93nwwQf13XfflWIqAADwR25Wi8b0qC9J+uSnvUrPPGM4EcoLhpMAADi54R3rKLCip3YcOasPftxjOg5Q4hITE9WzZ081bdpUXbp00fTp01VQUCCLxVK4z6xZsxQUFGQwJQAASKgVqC5xoSqwSS99u+WStZmBa8FwEgAAJ+fv46Fnuvy6xs9rS7bryJkLhhMBJW/y5Mn68ccf5evrqxEjRuj8+fNq3LixoqOjFRgYqBdffFF/+9vfTMcEAMDlPdutnjzdrPp++zF9t/WI6TgoB67pbt0AAKB09WoWoU9+2qeNB05r0oJ0Te7V2HQkoMTFx8friy++UG5urtatW6dt27YpKytLQUFBuv3221W1alXTEQEAcHk1Aiuo/601NT15p176Nk2tawfL051z33Dt+OkBAKAMsFotGndHnCTp3ykHtGH/KbOBgBvk4MGD+vDDD5WcnKyCggIlJCTo/vvvZzAJAIATGdSuloIqeWn3sXP6cNUe03FQxjGcBACgjLipRhX1bRml57rVU70wP9NxgBL35Zdfqnbt2nrttdc0b948DRs2TC1atFB0dLQ+//xz0/EAAMB/+Xp76OnOdSRJ/1i6XcfP5hhOhLKM4SQAAGXIC3fEaUCbaC6dQbk0bNgwTZ48WZs2bdJDDz2kLl26aMuWLRoyZIieeOIJffjhh6YjAgCA/7q3WYTqh/npzIWLenXJNtNxUIbxmw0AAGVU7sUCZedeNB0DKBG5ubk6ePCgHnnkEUnSpEmT9M4776hu3boaPny4Vq5cqZdfftlwSgAA8Bs3q0VjetaXJH360z5tzcwynAhlFcNJAADKoDW7T6jLP1Zo0oJ001GAEuHp6al69erp6NGjkiQ/Pz+9//77KigokCSFhYUpNzfXZEQAAPA/bokOVNcGoSqwSS/O3SKbzWY6EsoghpMAAJRBefkF2nX0nOZvytC5HM6eRPmwefNmVa9eXZI0depUvf766woMDFTz5s0VExOjJ5980mxAAABwiWe71ZOnm1U/7DiuJWlHTMdBGeRuOgAAACi+VjFBmnRvI3VpEKqKXvxzjvKnRYsW2rFjh3744QdlZmaqYcOGio2NNR0LAAD8j4iACnqkdU1NW75TL3+7RW3rBLM+OoqF32YAACij7mseYToCcENZrVa1bt3adAwAAHAFg9rF6IufD2jP8Wx98OMeDWgTbToSyhBG2QAAlHE2m03fbszg5jgAAAAwopKXu57pXFeS9PrS7Tp+NsdwIpQlDCcBACjjRnyxQYM+Xaepy3aYjgIAAAAXdW+z6oqr5qczORc1ZfE203FQhjCcBACgjOscFypJemfFbu09fs5wGgAAALgiq9WiMT3qS5L+tWaf0jKyDCdCWcFwEgCAMq5T/RC1rh2k3PwCvTh3i+k4AAAAcFHx0YHq1jBUBTbppW+3yGazmY6EMoDhJAAAZZzFYtHYnnFyt1q0JO2IlqUfMR0JAAAALmp013rydLfqhx3HtXjLYdNxUAYwnAQAoByIqVpJ/VpFSZLGz9minIv5ZgMBAADAJUUEVNCjt9aUJL08L42+FFfEcBIAgHJiaPvaCvb10u5j5/T+yj2m4wAAAMBFPdEuRsG+Xtp7PFsf/LjHdBw4OYaTAACUE77eHhrVJVaS9M/vtivz9AXDiQAAAOCKKnm56+nOdSVJ/1y6Q8fO5hhOBGfGcBIAgHLkrpvC1bRGZWXn5mvC/DTTcQAAAOCi7m1aXQ3C/XQm56L+vmib6ThwYgwnAQAoR6xWi8bf2UAWizQ79ZDW7D5hOhIAAABckNVq0ZgecZKkz9bu05ZDWYYTwVkxnAQAoJxpEO6v+2+uIUka+81m5RfYDCcCAACAK2pRM0DdG4WpwCa9OHeLbDb6UlyK4SQAAOXQ053ryt/HQ2kZWfrXmn2m4wAAAMBFjeoSK093q1btOq5FWw6bjgMnxHASAIByKKCip57qXFd/blFDXRuEmo4DAAAAFxURUEGPtY6WJL0yL005F/MNJ4KzYTgJAEA59X+3RGrC3Q0VWMnLdBQAAAC4sL/cVkvBvl7aezxbM3/YYzoOnAzDSQAAXIDNZtOZC3mmYwAAAMAFVfRy1zOd60qS/vndDh09k2M4EZwJw0kAAMq5Ayez1W/mWvWdsZZFyAEAAGDEPU2rq2G4v87mXNSUxemm48CJMJwEAKCcc7datWb3CW08cEqbD2WZjgMAAAAXZLVaNKZnfUnSrLX7tfnQacOJ4CwYTgIAUM6F+nvr770aa9HwtmoQ7m86DgAAAFzUzVEB6tEoTDab9OLcLVzVA0kMJwEAcAldG4apZlBF0zEAAADg4kZ1jZWXu1Wrd53Qws2HTceBE2A4CQCAi9l44JR2HztnOgYAAABcUPUqFfRYm2hJ0ivz0pRzMd9wIpjGcBIAABfy0eq9unPqDxozexOX0QAAAMCIgW1rqaqvl/adyNaMH/aYjgPDGE4CAOBCWscEycNq1ffbj2nRFi6jAQAAQOmr6OWukV1iJUlvfLdDR8/kGE4EkxhOAgDgQqKCKurR1jUl/boI+YU8LqMBAABA6bvrpnA1ru6vszkX9fdF6abjwCCGkwAAuJhB7WIU6uetAyfP6+0Vu0zHAQAAgAuyWi0a07O+JOmzn/dr08HThhPBFIaTAAC4mIpe7nq2ez1J0pvLd+jAyWzDiQAAAOCKmkUGqGfjarLZfr2qhzXRXRPDSQAAXFDPRmGKrxmgC3kFemVemuk4AAAAcFGjusbKy92qn3af0MLNmabjwACGkwAAuCCLxaIX7oiT1SLN+yVTP+w4ZjoSAAAAXFB4ZR893iZakvTyvDTWRHdBDCcBAHBR9cL89H+3REqSXvhms/LyCwwnAgAAgCt6vG0thfh5af+J85rxwx7TcVDKGE4CAODCEjvWVUBFT20/clYfrtprOg5gXFRUlCwWS5GvpKSkyx5z4cIFDRo0SIGBgapUqZLuueceHT58uJQSAwBQ9lX0ctfILrGSpDe+264jZy4YToTSxHASAAAX5l/BQ093ritJem3xNh07m2M4EWDe+PHjlZGRUfg1ZMiQy+4/fPhwzZkzR1988YWSk5N16NAh3X333aWUFgCA8uFPTcLVOKKyzuXm6+8Lt5mOg1LEcBIAABd3X/MINQz315mci/rbgnTTcQDjfH19FRoaWvhVsWJFh/uePn1a7733nqZMmaLbb79dzZo104wZM/Tjjz9q9erVpZgaAICyzWq1aEyP+pKkz1P2a9PB04YTobQwnAQAwMW5WS0ad2ecEqID1e/WKNNxAOOSkpIUGBiom266SX/729908eJFh/umpKQoLy9PHTp0KNwWGxurGjVqaNWqVaURFwCAcqNZZBXd0biabDZp/NwtstlspiOhFLibDgAAAMxrWqOK/vXYLaZjAMYNHTpUTZs2VUBAgH788UeNHj1aGRkZmjJlit39MzMz5enpqcqVKxfZHhISoszMTIfvk5OTo5yc35dRyMrKkiTl5eUpLy/v+r+RcuK3WlCToqiLY9TGPuriGLWxz2RdnuoYo0VbMrVm9wnNST2grg1CSz3D5fAzY9/11IPhJAAAuER27kVV8KRNQPkwatQoTZw48bL7pKWlKTY2VomJiYXbGjVqJE9PTz3++OOaMGGCvLy8SizThAkTNG7cuEu2L1u2TBUqVCix9ykvFi9ebDqCU6IujlEb+6iLY9TGPlN1aRti1cIDVr3w9Qbl7lknDye87pefmaKys7Ov+Vh+6wAAAIWycy/qbwvTNe+XDC0a3lb+Ph6mIwHXbcSIEerbt+9l94mOjra7PT4+XhcvXtSePXtUt27dS54PDQ1Vbm6uTp06VeTsycOHDys01PGZHqNHjy4yCM3KylJERITatWunwMDAy39DLiQvL0+LFy9Wx44d5eHB/49+Q10cozb2URfHqI19putyW+5Fpf7jBx3OylGGb6wGtrX/77QJpmvjrI4fP37NxzKcBAAAhdytVq3YdlSHs3K0YFOGet9cw3Qk4LoFBwcrODj4mo5NTU2V1WpV1apV7T7frFkzeXh4aOnSpbrnnnskSenp6dq3b58SEhIcvq6Xl5fdMzE9PDz4RccO6mIfdXGM2thHXRyjNvaZqou/h4dGdY3V8M82aPqK3erdIlJV/bxLPcfl8DNT1PXUguEkAAAo5OluVdI9jXQhL1+ta1/bMAcoq1atWqWffvpJ7dq1k6+vr1atWqXhw4frwQcfVJUqVSRJBw8eVPv27fXhhx+qRYsW8vf31yOPPKLExEQFBATIz89PQ4YMUUJCgm65hXVcAQC4Vnc2DtfMH/dqw/5TmrwoXZPubWw6Em4QhpMAAKCIm6MCTEcAjPDy8tKsWbP0wgsvKCcnRzVr1tTw4cOLXH6dl5en9PT0Iusqvfrqq7JarbrnnnuUk5Ojzp0768033zTxLQAAUG5YrRaN7Vlfd7/5o75IOaCHEqLUINzfdCzcAAwnAQCAQ0eyLujAqfNqWqOK6SjADde0aVOtXr36svtERUXJZrMV2ebt7a2pU6dq6tSpNzIeAAAup2mNKrqzSTXNTj2k8XO26LPHb5HFYjEdCyXMCe93BAAAnEHK3hNqN3m5Bn+yTtm5F03HAQAAgAsa2SVW3h5WrdlzQvN+yTQdBzcAw0kAAGBXXDV/Va7gqUOnL2ja8p2m4wAAAMAFVavso8fb1JIkvTIvTRfy8g0nQkljOAkAAOzy9nDT8z3qSZLeWrFL+45nX+EIAAAAoOQNbFtLYf7eOnjqvN5budt0HJQwhpMAAMChznGhujUmSLkXCzR+7hbTcQAAAOCCfDzdNLJLrCRp6rIdOpJ1wXAilCSGkwAAwCGLxaIX7qgvd6tFS9IOa3n6EdORAAAA4ILubFJNN9WorOzcfE1amG46DkoQw0kAAHBZMVV91bdllCRp/Jwtyr1YYDYQAAAAXI7FYtGYHvUlSf9OOaBfDpw2nAglheEkAAC4omEdaiuokpd2HTunGT+wzg8AAABK3001quium8IlSePmbJbNZjOcCCWB4SQAALgiX28Pjer66zo/ry/drsOs8wMAAAADnulSVz4ebvp570l9+0uG6TgoAQwnAQDAVbn7pnDdVKOyzuXmK2n+VtNxAAAA4ILC/H00sG0tSdKEeVt1IS/fcCJcL4aTAADgqlitFo2/o4EsFumr9Qf1854TpiMBAADABT3WJlph/t46eOq83v1+l+k4uE4MJwEAwFVrWN1f998cIUkaM3uz8gtY5wcAAACly8fTrXDJoTeX72TJoTKO4SQAACiWpzrVVYNwPz3ZobasFtNpAAAA4IruaFxNN9WorOzcfE1akG46Dq6D0w0np06dqqioKHl7eys+Pl5r1qxxuO8777yj1q1bq0qVKqpSpYo6dOhw2f0BAMD1C6zkpTmDb1WnuFBZLEwnAQAAUPosFovG9oyTJP1n3QFtPHDKbCBcM6caTn722WdKTEzU2LFjtW7dOjVu3FidO3fWkSNH7O6/fPly/fnPf9ayZcu0atUqRUREqFOnTjp48GApJwcAwLX8cSjJIuQAAAAwoUlEZd19U7gkafycLbLZWHKoLHKq4eSUKVM0YMAA9evXT/Xr19f06dNVoUIFvf/++3b3/+STT/TEE0+oSZMmio2N1bvvvquCggItXbq0lJMDAOB6bDabPl69V62SvtPmQ6dNxwEAAIALeqZLrHw83PTz3pOauzHDdBxcA3fTAX6Tm5urlJQUjR49unCb1WpVhw4dtGrVqqt6jezsbOXl5SkgIMDhPjk5OcrJySl8nJWVJUnKy8tTXl7eNaYvn36rB3Upiro4Rm3soy72URfHylJtVu04puPncjXzh9165U9xN/S9ylJdShs1AQAArirU31t/ua2WpizepqT5W9Wxfoi8PdxMx0IxOM1w8tixY8rPz1dISEiR7SEhIdq6detVvcbIkSNVrVo1dejQweE+EyZM0Lhx4y7ZvmzZMlWoUKF4oV3E4sWLTUdwStTFMWpjH3Wxj7o4VhZq08JT8qlpUYLHXs2bt7dU3rMs1KW0ZWdnm44AAABgzIDW0Zq1Zp8Onjqvd1bs0pD2tU1HQjE4zXDyeiUlJWnWrFlavny5vL29He43evRoJSYmFj7OyspSRESE2rVrp8DAwNKIWmbk5eVp8eLF6tixozw8PEzHcRrUxTFqYx91sY+6OEZt7KMujh0/ftx0BAAAAGN8PN00qls9Df3Xer25fKd6NY9QqL/j2RCci9MMJ4OCguTm5qbDhw8X2X748GGFhoZe9tjJkycrKSlJS5YsUaNGjS67r5eXl7y8vC7Z7uHhwS86DlAb+6iLY9TGPupiH3VxrKzV5kJevtbtPamWMUE39H3KWl1KA/UAAACurmejMH3w4x6l7D2pSQu3asp9TUxHwlVymhvieHp6qlmzZkVuZvPbzW0SEhIcHjdp0iS9+OKLWrBggZo3b14aUQEAwP84fjZHnV5doYdnrNHOo2dNxwEAAICLsVgsGtOjviTpy3UHlbr/lNlAuGpOM5yUpMTERL3zzjv64IMPlJaWpr/85S86d+6c+vXrJ0l66KGHitwwZ+LEiXr++ef1/vvvKyoqSpmZmcrMzNTZs/xSBABAaQqo6Kno4IrKy7dp/JwtstlspiMBAADAxTSOqKy7m4ZLksbP2UxPWkY41XCyd+/emjx5ssaMGaMmTZooNTVVCxYsKLxJzr59+5SR8ftt4adNm6bc3Fzde++9CgsLK/yaPHmyqW8BAACX9Nsn1R5uFiVvO6qlaUdMRwIAAIALeqZzrHw83LRu3ynN2Zhx5QNgnNOsOfmbwYMHa/DgwXafW758eZHHe/bsufGBAADAVYkOrqRHbo3W9OSdGj93i26tHSRvDzfTsQAAAOBCQv299cRttfT3xduUNC9NHeuFyMeTntSZOdWZkwAAoGwbcnuMQvy8tO9Ett79fpfpOAAAAHBBA9pEK7yyjw6dvqB36EmdHsNJAABQYip6uevZbvUkSVOX7dShU+cNJwIAAICr8fZw06iusZKkact3KvP0BcOJcDkMJwEAQIm6o3E1tYgK0Pm8fL08L810HAAAALigHo3C1Dyyis7n5WvSgq2m4+AyGE4CAIASZbFY9MIdcbJapG83ZujHncdMRwIAAICLsVgsGtOzviTpy/UHtX7fScOJ4AjDSQAAUOLqV/NTn/hISdK4b7boYn6B4UQAAABwNY2qV9Y9TatLksbP3SKbzWY4EexhOAkAAG6IEZ3qqEoFD6UfPqOPV+81HQcAAAAu6JkudVXB003r953SNxsOmY4DOxhOAgCAG6JyBU891bmuJGnK4m06fjbHcCIAAAC4mhA/bz1xWy1JUtL8rTqfm284Ef4Xw0kAAHDD3H9zDcXXDNAT7WLk6+1hOg4AAABc0KOtoxVe2UcZpy/orRU7TcfB/2A4CQAAbhg3q0WzHrtFA9vWkqc7bQcAAABKn7eHm0Z3i5UkTU/eqYzT5w0nwh/xWwIAALihLBZL4Z/z8gtUUMBC5AAAAChd3RuG6eaoKrqQV6BJC9JNx8EfMJwEAACl4sedx9TtH9/rP+sOmI4CAAAAF2OxWDSmR5wsFumr9Qe1bt9J05HwXwwnAQBAqfjlwGltP3JW736/WzYbZ08CAACgdDWs7q97mlaXJI2fs4We1EkwnAQAAKWiX6uaGt6hjj5/PKHIpd4AAABAaXmmc11V8HRT6v5Tmp16yHQciOEkAAAoJZ7uVg3rUFv+FbhrNwAAAMyo6uetQe1iJElJ87cqO/ei4URgOAkAAEqdzWbTDzuOcSkNAAAASt0jt9ZUeGUfZWZd0FvJu0zHcXkMJwEAQKmy2WzqN3Ot+rz7kxZsyjQdBwAAAC7G28NNz3arJ0l6a8VOHTp13nAi18ZwEgAAlCqLxaJG4f6SpJe+TdP53HzDiQAAAOBqujUMVYuoAF3IK9DEBVtNx3FpDCcBAECp+8ttMQqv7KODp85rWvJO03EAAADgYiwWi8b0rC+LRZqdekgpe0+ajuSyGE4CAIBS5+Pppue6/3opzfTkndp/IttwIgAAALiaBuH+6tWsuiRp/NwtKihgPXQTGE4CAAAjujYIVctagcq9WKAX524xHQcAAAAu6KlOdVXR000b9p/S7A0HTcdxSQwnAQCAERaLRS/cESc3q0WLthzWim1HTUcCFBUVJYvFUuQrKSnpssfcdtttlxwzcODAUkoMAACuR1U/bz3RLkaSNHF+urJzLxpO5HoYTgIAAGPqhPjq4YQoSdK4OZuVe7HAbCBA0vjx45WRkVH4NWTIkCseM2DAgCLHTJo0qRSSAgCAkvDIrTVVvYqPMrMuaHryLtNxXA7DSQAAYNSTHWsrqJKndh49pw9+3GM6DiBfX1+FhoYWflWsWPGKx1SoUKHIMX5+fqWQFAAAlARvDzc92+3X9dDfSt6pg6fOG07kWtxNBwAAAK7Nz9tDz3SJ1TP/3qh/LN2uO5tUU1U/b9Ox4MKSkpL04osvqkaNGnrggQc0fPhwubtfvm3+5JNP9PHHHys0NFQ9e/bU888/rwoVKjjcPycnRzk5OYWPs7KyJEl5eXnKy8srmW+kHPitFtSkKOriGLWxj7o4Rm3sc8W6dKgbqJujqmjtnpOa8O0WvXpfI7v7uWJtrsb11IPhJAAAMO7eptX1yU/7tGH/KSUt2Kop9zUxHQkuaujQoWratKkCAgL0448/avTo0crIyNCUKVMcHvPAAw8oMjJS1apV08aNGzVy5Eilp6fryy+/dHjMhAkTNG7cuEu2L1u27LJDTVe1ePFi0xGcEnVxjNrYR10cozb2uVpdbvOTfpab5v6SqRjbAdX0dbyvq9XmSrKzs6/5WIaTAADAOKvVonF3xOlPU3/Ql+sOqk98DTWLDDAdC+XEqFGjNHHixMvuk5aWptjYWCUmJhZua9SokTw9PfX4449rwoQJ8vLysnvsY489Vvjnhg0bKiwsTO3bt9fOnTtVq1Ytu8eMHj26yHtlZWUpIiJC7dq1U2BgYHG+vXItLy9PixcvVseOHeXh4WE6jtOgLo5RG/uoi2PUxj5Xrssej836IuWgvjsZoC96xctqtRR53pVrcznHjx+/5mMZTgIAAKfQJKKy7r85QjabFBl45TX+gKs1YsQI9e3b97L7REdH290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    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -1069,9 +1063,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "--Rz(0.275)----Ry(1.589)----Rz(5.910)----*----x----Ry(0.235)--\n", + "--Rz(5.714)----Ry(4.260)----Rz(5.514)----*----x----Ry(4.171)--\n", " | | \n", - "--Rz(2.328)----Ry(2.518)----Rz(5.586)----x----*----Ry(2.902)--\n", + "--Rz(0.917)----Ry(0.867)----Rz(4.504)----x----*----Ry(3.387)--\n", " \n" ] }, @@ -1079,7 +1073,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\fluid\\framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", " elif dtype == np.bool:\n" ] @@ -1126,37 +1120,24 @@ "execution_count": 18, "metadata": {}, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "c:\\Users\\jingmingrui\\Anaconda3\\envs\\pd_dep\\lib\\site-packages\\paddle\\tensor\\creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", - "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", - " if data.dtype == np.object:\n" - ] - }, { "data": { - "image/png": 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", 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", 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", 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", 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    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -1187,7 +1168,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Sampling: 100%|###################################################| 300/300 [00:03<00:00, 92.32it/s]\n" + "Sampling: 100%|##################################################| 300/300 [00:02<00:00, 122.85it/s]\n" ] }, { @@ -1195,21 +1176,19 @@ "output_type": "stream", "text": [ "Mean of max gradient\n", - "0.15071002\n", + "0.15121777\n", "Variance of max gradient\n", - "0.0035270636\n" + "0.0036665837\n" ] }, { "data": { - "image/png": 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", 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KjIzUokWLNHbsWC1dulTXXXed7Ha7o89//vMfeXl56eOPP3Zqnz9/fg235k9LlixRXFycnnvuOUfbH3/8Ue4xkv48xiff3XXkyBHt27dPV199dYXraNeunX744QcNHDjwtMf1dOcs6i++lsI5LTw8XO3atdOzzz6rI0eOlHn/5FufyxMTE6O9e/c63U79xx9/6OWXX65yDaX/gjv5X9pFRUWaM2eOU7+IiAi1aNFCKSkpKioqcrS/9tprFX54l2rZsqX69++vF198Ufv27Svz/um2syKNGzc+7bpLXX311Tpx4oTmzp3raCsuLtbMmTNPu+zBgwfLtJVeaSu9/bZx48aSVOV6TueNN97Q4cOHHT8vWbJE+/bt01VXXeVoa9eunb755hun4/Hhhx+WuWW8OrVdffXVKi4u1qxZs5zaZ8yYIZvN5rT+M3H11VcrKyvLaX7MiRMnNHPmTHl7e6tfv341Hjs2NlbffPON5s2bp9zc3DJfSbm7u8tmszk96mDnzp2OO41qyt3dvcwVq5kzZ5b7SAXpz8cqHD9+3PHz3LlzdeLEiUr38U033aS9e/eW+//4sWPHVFBQIKlq5yzqL67c4Jzm5uamV155RVdddZW6dOmi+Ph4BQYGau/evVq5cqV8fHz0f//3fxUuf8cdd2jWrFkaNmyYxo0bp1atWumtt95yPFysKv9i7927t5o1a6a4uDjde++9stlsWrBgQZkPaQ8PDz3xxBO64447NGDAAMXGxmrHjh2aP3/+aefcSNLs2bPVt29fdevWTaNGjdIFF1yg7Oxspaena8+ePfrhhx9OO8apwsPDNXfuXD3xxBNq3769WrZs6XRV6WSDBw9Wnz59NHHiRO3cuVOhoaFaunRppXOaSk2dOlWrV6/WoEGDFBwcrJycHM2ZM0dt2rRR3759Jf0ZNJo2baqUlBQ1adJEjRs3Vq9evao8X+NUzZs3V9++fRUfH6/s7GwlJyerffv2TpPFR44cqSVLlujKK6/UTTfdpF9//VVvvvmm0wTf6tY2ePBgXXbZZXr44Ye1c+dOde/eXZ988ok++OAD3XfffWXGrqnRo0frxRdf1G233aaMjAyFhIRoyZIl+uqrr5ScnFxmzk913HTTTZowYYImTJig5s2bl7lKMWjQIE2fPl1XXnmlbr75ZuXk5Gj27Nlq3769NmzYUOP1XnPNNVqwYIF8fX0VGhqq9PR0ffbZZxXeEl9UVKSBAwfqpptu0pYtWzRnzhz17dvX6QaBUw0fPlyLFy/WmDFjtHLlSvXp00fFxcXavHmzFi9erI8//lgRERFVOmdRj7nqNi2gKreCv/vuu07t5d0ibYwx69atMzfccIM577zzjN1uN8HBweamm24yaWlpp61j+/btZtCgQaZhw4amRYsW5v777zf/+c9/jCTzzTffOPr169fPdOnSpdwxvvrqK3PxxRebhg0bmtatW5t//etf5uOPPy5zO7kxxsyZM8e0bdvW2O12ExERYVavXl3mdtWKtvPXX381I0aMMAEBAcbDw8MEBgaaa665xixZssTRp/Q22e+++85p2dJ9enI9WVlZZtCgQaZJkyZlbkcvz4EDB8zw4cONj4+P8fX1NcOHDzfr1q077a3gaWlp5tprrzWtW7c2np6epnXr1mbYsGFm69atTuN/8MEHJjQ01DRo0MBpzMr2fUW3gr/zzjtm0qRJpmXLlqZhw4Zm0KBBJjMzs8zyzz33nAkMDDR2u9306dPHfP/992XGrKy2U28FN8aYw4cPm/Hjx5vWrVsbDw8P06FDB/PMM8843ZpvzJ+3Qt99991laqroFvVTZWdnm/j4eOPn52c8PT1Nt27dyr1dvaq3gp+sT58+RpIZOXJkue+/+uqrpkOHDsZut5tOnTqZ+fPnlznuxlS8jaXvnXwr+O+//+7YHm9vbxMTE2M2b95cZn+UnuOff/65GT16tGnWrJnx9vY2t9xyizlw4IDTOso7lkVFRebf//636dKli7Hb7aZZs2YmPDzcTJkyxeTl5Rljqn7Oon6yGeOiWWtAPZacnKzx48drz549CgwMdHU5AIBqINzgL+/YsWNOd3P88ccf6tGjh4qLi7V161YXVgYAqAnm3OAv74YbbtD555+vsLAw5eXl6c0339TmzZv11ltvubo0AEANEG7wlxcTE6NXXnlFb731loqLixUaGqqFCxeWuUMEAHBu4GspAABgKTznBgAAWArhBgAAWMpfbs5NSUmJfvvtNzVp0qTWH/cOAADODmOMDh8+rNatW5f5g7Gn+suFm99++83xh9EAAMC5Zffu3WrTpk2lfVwebmbPnq1nnnlGWVlZ6t69u2bOnKnIyMgK+ycnJ2vu3LnatWuX/Pz8dOONNyopKcnxuPzTKX0k+e7du+Xj41Mr2wAAAM6u/Px8BQUFVelPi7g03CxatEgJCQlKSUlRr169lJycrJiYGG3ZskUtW7Ys0//tt9/WxIkTNW/ePPXu3Vtbt27VbbfdJpvNVuGfrz9V6VdRPj4+hBsAAM4xVZlS4tIJxdOnT9eoUaMUHx+v0NBQpaSkqFGjRpo3b165/b/++mv16dNHN998s0JCQnTFFVdo2LBhWrNmTR1XDgAA6iuXhZuioiJlZGQ4/bVZNzc3RUdHKz09vdxlevfurYyMDEeY2b59u5YvX66rr766wvUUFhYqPz/f6QUAAKzLZV9L5ebmqri4WP7+/k7t/v7+2rx5c7nL3HzzzcrNzVXfvn1ljNGJEyc0ZswYPfTQQxWuJykpSVOmTKnV2gEAQP11Tj3nZtWqVXrqqac0Z84crV27VkuXLtWyZcv0+OOPV7jMpEmTlJeX53jt3r27DisGAAB1zWVXbvz8/OTu7q7s7Gyn9uzsbAUEBJS7zKOPPqrhw4dr5MiRkqRu3bqpoKBAo0eP1sMPP1zufe92u112u732NwAAANRLLrty4+npqfDwcKWlpTnaSkpKlJaWpqioqHKXOXr0aJkA4+7uLunPh/sAAAC49FbwhIQExcXFKSIiQpGRkUpOTlZBQYHi4+MlSSNGjFBgYKCSkpIkSYMHD9b06dPVo0cP9erVS9u2bdOjjz6qwYMHO0IOAAD4a3NpuImNjdX+/fs1efJkZWVlKSwsTKmpqY5Jxrt27XK6UvPII4/IZrPpkUce0d69e9WiRQsNHjxYTz75pKs2AQAA1DM28xf7Pic/P1++vr7Ky8vjIX4AAJwjqvP7+5y6WwoAAOB0CDcAAMBSCDcAAMBSCDcAAMBSCDcAAMBSXHorOAAA+J+QictcXUKt2DltkEvXz5UbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKYQbAABgKfUi3MyePVshISHy8vJSr169tGbNmgr79u/fXzabrcxr0KBBdVgxAACor1webhYtWqSEhAQlJiZq7dq16t69u2JiYpSTk1Nu/6VLl2rfvn2O18aNG+Xu7q5//OMfdVw5AACoj1webqZPn65Ro0YpPj5eoaGhSklJUaNGjTRv3rxy+zdv3lwBAQGO16effqpGjRoRbgAAgCQXh5uioiJlZGQoOjra0ebm5qbo6Gilp6dXaYxXX31VQ4cOVePGjct9v7CwUPn5+U4vAABgXS4NN7m5uSouLpa/v79Tu7+/v7Kysk67/Jo1a7Rx40aNHDmywj5JSUny9fV1vIKCgs64bgAAUH+5/GupM/Hqq6+qW7duioyMrLDPpEmTlJeX53jt3r27DisEAAB1rYErV+7n5yd3d3dlZ2c7tWdnZysgIKDSZQsKCrRw4UJNnTq10n52u112u/2MawUAAOcGl1658fT0VHh4uNLS0hxtJSUlSktLU1RUVKXLvvvuuyosLNStt956tssEAADnEJdeuZGkhIQExcXFKSIiQpGRkUpOTlZBQYHi4+MlSSNGjFBgYKCSkpKclnv11Vd13XXX6bzzznNF2QAAoJ5yebiJjY3V/v37NXnyZGVlZSksLEypqamOSca7du2Sm5vzBaYtW7boyy+/1CeffOKKkgEAQD1mM8YYVxdRl/Lz8+Xr66u8vDz5+Pi4uhwAABxCJi5zdQm1Yue02v+rAdX5/X1O3y0FAABwKsINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFJeHm9mzZyskJEReXl7q1auX1qxZU2n/Q4cO6e6771arVq1kt9t14YUXavny5XVULQAAqO8auHLlixYtUkJCglJSUtSrVy8lJycrJiZGW7ZsUcuWLcv0Lyoq0uWXX66WLVtqyZIlCgwMVGZmppo2bVr3xQMAgHrJpeFm+vTpGjVqlOLj4yVJKSkpWrZsmebNm6eJEyeW6T9v3jwdPHhQX3/9tTw8PCRJISEhdVkyAACo51z2tVRRUZEyMjIUHR39v2Lc3BQdHa309PRyl/nvf/+rqKgo3X333fL391fXrl311FNPqbi4uML1FBYWKj8/3+kFAACsy2XhJjc3V8XFxfL393dq9/f3V1ZWVrnLbN++XUuWLFFxcbGWL1+uRx99VM8995yeeOKJCteTlJQkX19fxysoKKhWtwMAANQvLp9QXB0lJSVq2bKlXnrpJYWHhys2NlYPP/ywUlJSKlxm0qRJysvLc7x2795dhxUDAIC65rI5N35+fnJ3d1d2drZTe3Z2tgICAspdplWrVvLw8JC7u7ujrXPnzsrKylJRUZE8PT3LLGO322W322u3eAAAUG+57MqNp6enwsPDlZaW5mgrKSlRWlqaoqKiyl2mT58+2rZtm0pKShxtW7duVatWrcoNNgAA4K/HpV9LJSQk6OWXX9brr7+un3/+WXfeeacKCgocd0+NGDFCkyZNcvS/8847dfDgQY0bN05bt27VsmXL9NRTT+nuu+921SYAAIB6xqW3gsfGxmr//v2aPHmysrKyFBYWptTUVMck4127dsnN7X/5KygoSB9//LHGjx+viy66SIGBgRo3bpwefPBBV20CAACoZ2zGGOPqIupSfn6+fH19lZeXJx8fH1eXAwCAQ8jEZa4uoVbsnDao1seszu/vc+puKQAAgNMh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEsh3AAAAEupF+Fm9uzZCgkJkZeXl3r16qU1a9ZU2Pe1116TzWZzenl5edVhtQAAoD5zebhZtGiREhISlJiYqLVr16p79+6KiYlRTk5Ohcv4+Pho3759jldmZmYdVgwAAOozl4eb6dOna9SoUYqPj1doaKhSUlLUqFEjzZs3r8JlbDabAgICHC9/f/86rBgAANRnLg03RUVFysjIUHR0tKPNzc1N0dHRSk9Pr3C5I0eOKDg4WEFBQbr22mu1adOmCvsWFhYqPz/f6QUAAKzLpeEmNzdXxcXFZa68+Pv7Kysrq9xlOnbsqHnz5umDDz7Qm2++qZKSEvXu3Vt79uwpt39SUpJ8fX0dr6CgoFrfDgAAUH+4/Gup6oqKitKIESMUFhamfv36aenSpWrRooVefPHFcvtPmjRJeXl5jtfu3bvruGIAAFCXGrhy5X5+fnJ3d1d2drZTe3Z2tgICAqo0hoeHh3r06KFt27aV+77dbpfdbj/jWgEAwLnBpVduPD09FR4errS0NEdbSUmJ0tLSFBUVVaUxiouL9eOPP6pVq1Znq0wAAHAOcemVG0lKSEhQXFycIiIiFBkZqeTkZBUUFCg+Pl6SNGLECAUGBiopKUmSNHXqVF188cVq3769Dh06pGeeeUaZmZkaOXKkKzcDAADUEy4PN7Gxsdq/f78mT56srKwshYWFKTU11THJeNeuXXJz+98Fpt9//12jRo1SVlaWmjVrpvDwcH399dcKDQ111SYAAIB6xGaMMa4uoi7l5+fL19dXeXl58vHxcXU5AAA4hExc5uoSasXOaYNqfczq/P4+5+6WAgAAqAzhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWArhBgAAWEqDM1k4IyNDP//8syQpNDRUPXv2rJWiAAAAaqpG4SYnJ0dDhw7VqlWr1LRpU0nSoUOHdNlll2nhwoVq0aJFbdYIAABQZTX6Wuqee+7R4cOHtWnTJh08eFAHDx7Uxo0blZ+fr3vvvbe2awQAAKiyGl25SU1N1WeffabOnTs72kJDQzV79mxdccUVtVYcAABAddXoyk1JSYk8PDzKtHt4eKikpOSMiwIAAKipGoWbAQMGaNy4cfrtt98cbXv37tX48eM1cODAWisOAACgumoUbmbNmqX8/HyFhISoXbt2ateundq2bav8/HzNnDmztmsEAACoshrNuQkKCtLatWv12WefafPmzZKkzp07Kzo6ulaLAwAAqK4aP+fGZrPp8ssv1+WXX16b9QAAAJyRKoebF154QaNHj5aXl5deeOGFSvtyOzgAAHCVKoebGTNm6JZbbpGXl5dmzJhRYT+bzUa4AQAALlPlCcU7duzQeeed5/jvil7bt2+vdhGzZ89WSEiIvLy81KtXL61Zs6ZKyy1cuFA2m03XXXddtdcJAACsqUZ3S02dOlVHjx4t037s2DFNnTq1WmMtWrRICQkJSkxM1Nq1a9W9e3fFxMQoJyen0uV27typCRMm6JJLLqnW+gAAgLXVKNxMmTJFR44cKdN+9OhRTZkypVpjTZ8+XaNGjVJ8fLxCQ0OVkpKiRo0aad68eRUuU1xcrFtuuUVTpkzRBRdcUO36AQCAddUo3BhjZLPZyrT/8MMPat68eZXHKSoqUkZGhtMt5G5uboqOjlZ6enqFy02dOlUtW7bU7bffftp1FBYWKj8/3+kFAACsq1q3gjdr1kw2m002m00XXnihU8ApLi7WkSNHNGbMmCqPl5ubq+LiYvn7+zu1+/v7O56fc6ovv/xSr776qtavX1+ldSQlJVX7ahIAADh3VSvcJCcnyxijf/7zn5oyZYp8fX0d73l6eiokJERRUVG1XmSpw4cPa/jw4Xr55Zfl5+dXpWUmTZqkhIQEx8/5+fkKCgo6WyUCAAAXq1a4iYuLkyS1bdtWvXv3LvePZ1aHn5+f3N3dlZ2d7dSenZ2tgICAMv1//fVX7dy5U4MHD3a0lf6hzgYNGmjLli1q166d0zJ2u112u/2M6gQAAOeOGs256devnyPY/PHHHzWe0+Lp6anw8HClpaU52kpKSpSWllbuFaBOnTrpxx9/1Pr16x2vIUOG6LLLLtP69eu5IgMAAGr25xeOHj2qf/3rX1q8eLEOHDhQ5v3i4uIqj5WQkKC4uDhFREQoMjJSycnJKigoUHx8vCRpxIgRCgwMVFJSkry8vNS1a1en5Zs2bSpJZdoBAMBfU43CzQMPPKCVK1dq7ty5Gj58uGbPnq29e/fqxRdf1LRp06o1VmxsrPbv36/JkycrKytLYWFhSk1NdUwy3rVrl9zcanSBCQAA/AXZjDGmugudf/75euONN9S/f3/5+Pho7dq1at++vRYsWKB33nlHy5cvPxu11or8/Hz5+voqLy9PPj4+ri4HAACHkInLXF1Crdg5bVCtj1md3981uiRy8OBBx8PzfHx8dPDgQUlS3759tXr16poMCQAAUCtqFG4uuOAC7dixQ9Kfk3wXL14sSfq///s/xxwYAAAAV6hRuImPj9cPP/wgSZo4caJmz54tLy8vjR8/Xg888ECtFggAAFAd1Z5QfPz4cX344YdKSUmRJEVHR2vz5s3KyMhQ+/btddFFF9V6kQAAAFVV7XDj4eGhDRs2OLUFBwcrODi41ooCAACoqRp9LXXrrbfq1Vdfre1aAAAAzliNnnNz4sQJzZs3T5999pnCw8PVuHFjp/enT59eK8UBAABUV43CzcaNG9WzZ09J0tatW53eO/kvhQMAANS1GoWblStX1nYdAAAAtYK/awAAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACyFcAMAACylXoSb2bNnKyQkRF5eXurVq5fWrFlTYd+lS5cqIiJCTZs2VePGjRUWFqYFCxbUYbUAAKA+c3m4WbRokRISEpSYmKi1a9eqe/fuiomJUU5OTrn9mzdvrocffljp6enasGGD4uPjFR8fr48//riOKwcAAPWRzRhjXFlAr1699Le//U2zZs2SJJWUlCgoKEj33HOPJk6cWKUxevbsqUGDBunxxx8/bd/8/Hz5+voqLy9PPj4+Z1Q7AAC1KWTiMleXUCt2ThtU62NW5/e3S6/cFBUVKSMjQ9HR0Y42Nzc3RUdHKz09/bTLG2OUlpamLVu26NJLLy23T2FhofLz851eAADAulwabnJzc1VcXCx/f3+ndn9/f2VlZVW4XF5enry9veXp6alBgwZp5syZuvzyy8vtm5SUJF9fX8crKCioVrcBAADULy6fc1MTTZo00fr16/Xdd9/pySefVEJCglatWlVu30mTJikvL8/x2r17d90WCwAA6lQDV67cz89P7u7uys7OdmrPzs5WQEBAhcu5ubmpffv2kqSwsDD9/PPPSkpKUv/+/cv0tdvtstvttVo3AACov1x65cbT01Ph4eFKS0tztJWUlCgtLU1RUVFVHqekpESFhYVno0QAAHCOcemVG0lKSEhQXFycIiIiFBkZqeTkZBUUFCg+Pl6SNGLECAUGBiopKUnSn3NoIiIi1K5dOxUWFmr58uVasGCB5s6d68rNAAAA9YTLw01sbKz279+vyZMnKysrS2FhYUpNTXVMMt61a5fc3P53gamgoEB33XWX9uzZo4YNG6pTp0568803FRsb66pNAAAA9YjLn3NT13jODQCgvuI5NxU7Z55zAwAAUNsINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIINwAAwFIauLoAAIBrhExc5uoSas3OaYNcXQLqEa7cAAAASyHcAAAASyHcAAAASyHcAAAASyHcAAAASyHcAAAASyHcAAAAS6kX4Wb27NkKCQmRl5eXevXqpTVr1lTY9+WXX9Yll1yiZs2aqVmzZoqOjq60PwAA+GtxebhZtGiREhISlJiYqLVr16p79+6KiYlRTk5Ouf1XrVqlYcOGaeXKlUpPT1dQUJCuuOIK7d27t44rBwAA9ZHLw8306dM1atQoxcfHKzQ0VCkpKWrUqJHmzZtXbv+33npLd911l8LCwtSpUye98sorKikpUVpaWh1XDgAA6iOXhpuioiJlZGQoOjra0ebm5qbo6Gilp6dXaYyjR4/q+PHjat68ebnvFxYWKj8/3+kFAACsy6XhJjc3V8XFxfL393dq9/f3V1ZWVpXGePDBB9W6dWungHSypKQk+fr6Ol5BQUFnXDcAAKi/XP611JmYNm2aFi5cqPfee09eXl7l9pk0aZLy8vIcr927d9dxlQAAoC659K+C+/n5yd3dXdnZ2U7t2dnZCggIqHTZZ599VtOmTdNnn32miy66qMJ+drtddru9VuoFAAD1n0uv3Hh6eio8PNxpMnDp5OCoqKgKl3v66af1+OOPKzU1VREREXVRKgAAOEe49MqNJCUkJCguLk4RERGKjIxUcnKyCgoKFB8fL0kaMWKEAgMDlZSUJEn697//rcmTJ+vtt99WSEiIY26Ot7e3vL29XbYdAACgfnB5uImNjdX+/fs1efJkZWVlKSwsTKmpqY5Jxrt27ZKb2/8uMM2dO1dFRUW68cYbncZJTEzUY489VpelAwCAesjl4UaSxo4dq7Fjx5b73qpVq5x+3rlz59kvCAAAnLPO6bulAAAATkW4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAlkK4AQAAluLycDN79myFhITIy8tLvXr10po1ayrsu2nTJv39739XSEiIbDabkpOT665QAABwTnBpuFm0aJESEhKUmJiotWvXqnv37oqJiVFOTk65/Y8ePaoLLrhA06ZNU0BAQB1XCwAAzgUuDTfTp0/XqFGjFB8fr9DQUKWkpKhRo0aaN29euf3/9re/6ZlnntHQoUNlt9vruFoAAHAucFm4KSoqUkZGhqKjo/9XjJuboqOjlZ6eXmvrKSwsVH5+vtMLAABYl8vCTW5uroqLi+Xv7+/U7u/vr6ysrFpbT1JSknx9fR2voKCgWhsbAADUPy6fUHy2TZo0SXl5eY7X7t27XV0SAAA4ixq4asV+fn5yd3dXdna2U3t2dnatTha22+3MzwEA4C/EZVduPD09FR4errS0NEdbSUmJ0tLSFBUV5aqyAADAOc5lV24kKSEhQXFxcYqIiFBkZKSSk5NVUFCg+Ph4SdKIESMUGBiopKQkSX9OQv7pp58c/713716tX79e3t7eat++vcu2AwAA1B8uDTexsbHav3+/Jk+erKysLIWFhSk1NdUxyXjXrl1yc/vfxaXffvtNPXr0cPz87LPP6tlnn1W/fv20atWqui4fAADUQy4NN5I0duxYjR07ttz3Tg0sISEhMsbUQVUAAOBcZfm7pQAAwF8L4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFgK4QYAAFhKvQg3s2fPVkhIiLy8vNSrVy+tWbOm0v7vvvuuOnXqJC8vL3Xr1k3Lly+vo0oBAEB95/Jws2jRIiUkJCgxMVFr165V9+7dFRMTo5ycnHL7f/311xo2bJhuv/12rVu3Ttddd52uu+46bdy4sY4rBwAA9ZHLw8306dM1atQoxcfHKzQ0VCkpKWrUqJHmzZtXbv/nn39eV155pR544AF17txZjz/+uHr27KlZs2bVceUAAKA+auDKlRcVFSkjI0OTJk1ytLm5uSk6Olrp6enlLpOenq6EhASntpiYGL3//vvl9i8sLFRhYaHj57y8PElSfn7+GVYPAOe2ksKjri6h1ljlM90qx+RsHI/SMY0xp+3r0nCTm5ur4uJi+fv7O7X7+/tr8+bN5S6TlZVVbv+srKxy+yclJWnKlCll2oOCgmpYNQCgvvFNdnUFONnZPB6HDx+Wr69vpX1cGm7qwqRJk5yu9JSUlOjgwYM677zzZLPZXFhZzeTn5ysoKEi7d++Wj4+Pq8v5y+N41C8cj/qF41H/nMvHxBijw4cPq3Xr1qft69Jw4+fnJ3d3d2VnZzu1Z2dnKyAgoNxlAgICqtXfbrfLbrc7tTVt2rTmRdcTPj4+59yJaWUcj/qF41G/cDzqn3P1mJzuik0pl04o9vT0VHh4uNLS0hxtJSUlSktLU1RUVLnLREVFOfWXpE8//bTC/gAA4K/F5V9LJSQkKC4uThEREYqMjFRycrIKCgoUHx8vSRoxYoQCAwOVlJQkSRo3bpz69eun5557ToMGDdLChQv1/fff66WXXnLlZgAAgHrC5eEmNjZW+/fv1+TJk5WVlaWwsDClpqY6Jg3v2rVLbm7/u8DUu3dvvf3223rkkUf00EMPqUOHDnr//ffVtWtXV21CnbLb7UpMTCzzVRtcg+NRv3A86heOR/3zVzkmNlOVe6oAAADOES5/iB8AAEBtItwAAABLIdwAAABLIdwAAABLIdygXhg+fLieeuopV5fxlzV06FA999xzVep74MABtWzZUjt37jy7RVnMxIkTdc8997hk3X+1Y5abm6uWLVtqz549ri4FrmJQZw4cOGBuvvlm06RJE+Pr62v++c9/msOHD1e6zLFjx8xdd91lmjdvbho3bmxuuOEGk5WV5dQnMzPTXH311aZhw4amRYsWZsKECeb48eNOfVauXGl69OhhPD09Tbt27cz8+fOd3v/888/NNddcY1q1amUkmffee682NrlK1q9fb5o3b+60L0pKSsyjjz5qAgICjJeXlxk4cKDZunXraceaNWuWCQ4ONna73URGRppvv/3W6f3a2J+//fabGTZsmOnQoYOx2Wxm3LhxVdrOqhynU1XlnPnhhx9M3759jd1uN23atDH//ve/nd7fuHGjueGGG0xwcLCRZGbMmFFmPT/++KNp1qyZOXTo0Gm3Y/z48WbkyJHnxHaV53Tjlqc2zon9+/ebJk2amF9//bVKddamujhmx44dM3FxcaZr167G3d3dXHvttVWqrSafiy+++KLp16+fadKkiZFkfv/99zJ97r//fvPPf/6zSjVY2dnav/Ud4eYsO3jwoONEuvLKK0337t3NN998Y7744gvTvn17M2zYsEqXHzNmjAkKCjJpaWnm+++/NxdffLHp3bu34/0TJ06Yrl27mujoaLNu3TqzfPly4+fnZyZNmuTos337dtOoUSOTkJBgfvrpJzNz5kzj7u5uUlNTHX2WL19uHn74YbN06dI6Dze33367ueOOO5zapk2bZnx9fc37779vfvjhBzNkyBDTtm1bc+zYsQrHWbhwofH09DTz5s0zmzZtMqNGjTJNmzY12dnZjj61sT937Nhh7r33XvP666+bsLCwKoWbqoxbntOdM3l5ecbf39/ccsstZuPGjeadd94xDRs2NC+++KKjz5o1a8yECRPMO++8YwICAioMAREREWbWrFmV1lNQUGB8fHxMenr6ObNdJ6vKuKeqzXPixhtvNBMmTDhtnbWpro7ZkSNHzJgxY8xLL71kYmJiqhxuavK5OGPGDJOUlGSSkpIq/OW7ceNGY7fbzYEDB6pUx7lk7969pw2jpc7W/q3vCDdnwfHjx82HH35obrzxRmO328369evNTz/9ZCSZ7777ztHvo48+Mjabzezdu7fccQ4dOmQ8PDzMu+++62j7+eefjSTHB9Xy5cuNm5ub09WHuXPnGh8fH1NYWGiMMeZf//qX6dKli9PYsbGxJiYmptz11mW4OXHihPH19TUffviho62kpMQEBASYZ555xtF26NAhY7fbzTvvvFPhWJGRkebuu+92/FxcXGxat25tkpKSHGPUxv48Wb9+/aoUbqo7rjGmSufMnDlzTLNmzZzGePDBB03Hjh3LHTM4OLjCEDBlyhTTt2/fSrfj3XffNS1atDintutk1R23JttY2Tnx+uuvmzZt2py2ztpUV8fsZHFxcVUKNzX5XDzZypUrK/3l27ZtW/PKK6+cdpxzzWOPPWb8/f3N/fffbzZs2FBhv7O9f+sz5tzUoh9//FH333+/2rRpoxEjRqhFixZauXKlunfvrvT0dDVt2lQRERGO/tHR0XJzc9O3335b7ngZGRk6fvy4oqOjHW2dOnXS+eefr/T0dElSenq6unXr5niisyTFxMQoPz9fmzZtcvQ5eYzSPqVjuNKGDRuUl5fntF927NihrKwsp5p9fX3Vq1evCmsuKipSRkaG0zJubm6Kjo52LFNb+7MmajJuVc6Z9PR0XXrppfL09HQad8uWLfr999+rVWNkZKTWrFmjwsLCCvt88cUXCg8PP6e269R1V3fc2jwnIiMjtWfPnjqd+1JXx6wmzta4pSIjI/XFF1+c8Tj1zYMPPqjnn39eP//8s3r27KmePXvqhRde0P79+536ne39W58Rbs7QgQMH9Pzzz6tnz56KiIjQ9u3bNWfOHO3bt09z5sxx/EHPrKwstWzZ0mnZBg0aqHnz5srKyip37KysLHl6epb5K+b+/v6OZbKyspw+pErfL32vsj75+fk6duxYzTa8lmRmZsrd3d1p35TWXV7NFe2r3NxcFRcXV7pMbe3PmqjJuFU5Z2qz3tatW6uoqKjS5TIzM9W6dWunGuv7dp267prUW5v7WPpzP9aVujpmNXG2xi3VunXrOt3XdcXLy0uxsbFatmyZ9u7dqxEjRui1115TYGCgrrvuOr333ns6ceLEWd+/9Rnh5gzNnDlT9913n7y9vbVt2za99957uuGGG5z+ZYiKHTt2THa7XTabzdWl/OU1bNhQknT06NEK+xw7dkxeXl51VZLlVGUf17a/8jFr2LBhne5rV2jZsqXuu+8+rV27Vh988IHS09N1ww03aOPGja4uzaUIN2do9OjRevzxx5WVlaUuXbooPj5eK1asUElJiVO/gIAA5eTkOLWdOHFCBw8eVEBAQLljBwQEqKioSIcOHXJqz87OdiwTEBCg7OzsMu+XvldZHx8fH8eHrav4+fnp6NGjKioqcrSV1l1ezRXtKz8/P7m7u1e6TG3tz5qoybhVOWdqs96DBw9Kklq0aFFhHz8/P6evb86F7Tp13TWpty73cW2rq2NWE2dr3FIHDx6s033tCocPH9b8+fM1YMAADR48WF27dtXrr7+u0NDQs75/6zPCzRlq3bq1HnnkEW3dulWpqany9PTUDTfcoODgYE2cONHxHXZUVJQOHTqkjIwMx7KlIahXr17ljh0eHi4PDw+lpaU52rZs2aJdu3Y5vu6KiorSjz/+6HQCf/rpp/Lx8VFoaKijz8ljlPYpHcOVwsLCJEk//fSTo61t27YKCAhwqjk/P1/ffvtthTV7enoqPDzcaZmSkhKlpaU5lqmt/VkTNRm3KudMVFSUVq9erePHjzuN27FjRzVr1qxaNW7cuFFt2rSRn59fhX169OjhdKzOhe06dd3VHbc2z4mNGzfKw8NDXbp0qdkG1EBdHbOaOFvjltq4caN69OhxxuPUN8XFxfroo4908803y9/fX9OmTdPAgQO1fft2paWlacSIEfL09Dzr+7dec/WMZis6duyYeeedd0xMTIxxd3d3zGa/8sorTY8ePcy3335rvvzyS9OhQwenW/L27NljOnbs6PRsljFjxpjzzz/frFixwnz//fcmKirKREVFOd4vva3ziiuuMOvXrzepqammRYsW5d4K/sADD5iff/7ZzJ49u8yt4IcPHzbr1q0z69atM5LM9OnTzbp160xmZubZ3FXGGGN69uxpZs6c6dQ2bdo007RpU/PBBx+YDRs2mGuvvbbMreADBgxwWm7hwoXGbreb1157zfz0009m9OjRpmnTpk53hdTG/jTGOPZVeHi4ufnmm826devMpk2bKtzGqoz77bffmo4dO5o9e/Y42k53zhw6dMj4+/ub4cOHm40bN5qFCxeaRo0aOd3aXFhY6Ki3VatWZsKECWbdunXml19+caoxLi7utM8F2bBhg2nQoIE5ePDgObNdJ6vKuEuXLnW6e6o2z4nExEQzYMCASvdxbaurY2aMMZs2bTLr1q0zgwcPNv3793fsk8rU5HNx3759Zt26debll182kszq1avNunXrnG77LigoMA0bNjSrV6+u0X6rz6ZOnWp8fX3N6NGjzVdffVVp37O1f+s7ws1ZtnfvXpOXl2eM+fNhSsOGDTPe3t7Gx8fHxMfHOz1MaceOHUaSWblypaOt9KFzzZo1M40aNTLXX3+92bdvn9M6du7caa666irTsGFD4+fnZ+6///5yH+IXFhZmPD09zQUXXFDmIX6lt/yd+oqLi6vV/VGeOXPmmIsvvtiprfQhfv7+/sZut5uBAweaLVu2OPUJDg42iYmJTm0zZ840559/vvH09DSRkZHmm2++cXq/tvZnefsqODjY8X7p/tyxY0eVxy1vmdOdM8Y4P5QuMDDQTJs2zen90vPq1Fe/fv2c9ouvr6/jlvjKREZGmpSUlHNiu+bPn29O/Tfc6cYtb5naOCeMMaZjx46VPs7gbKmrY1b6QMVTX6XK+4yryediYmJiues5+XPt7bffrvQW/3PZjh07Kn3m18nO1v6t7wg3cLmjR4+aoKAg8/XXX7u6lFozb9480759e1NUVOTqUqpkzpw55vLLL69S3w8//NB07tzZFBcXn+WqztzkyZOdwo4rLV++3HTu3LnKD1+rTfXlmK1YscI0bdrUcRXpbOrVq5d56623zvp6UD81qNXvuIAaaNiwod544w3l5ua6upRas3z5cj311FPy8PBwdSlV4uHhoZkzZ1ap76BBg/TLL79o7969CgoKOsuVnZmPPvpIs2bNcnUZkqSCggLNnz9fDRrU/cdufTlmy5cv10MPPXRG86aqIjc3VzfccIOGDRt2VteD+stmjDGuLgIAAKC2cLcUAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwFMINAACwlP8HqxZJdW5x16EAAAAASUVORK5CYII=", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], diff --git a/tutorials/qnn_research/Expressibility_CN.ipynb b/tutorials/qnn_research/Expressibility_CN.ipynb index 1619a99..d18b820 100644 --- a/tutorials/qnn_research/Expressibility_CN.ipynb +++ b/tutorials/qnn_research/Expressibility_CN.ipynb @@ -84,10 +84,25 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "id": "e05a5803", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/openfermion/hamiltonians/hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import numpy as np\n", "import paddle\n", @@ -106,12 +121,22 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "id": "04344561", "metadata": { "scrolled": false }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " elif dtype == np.bool:\n" + ] + } + ], "source": [ "num_qubit = 1 # 设定量子比特数\n", "num_sample = 2000 # 设定采样次数\n", @@ -149,7 +174,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "id": "0530af37", "metadata": {}, "outputs": [], @@ -250,13 +275,13 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 4, "id": "b9dbeb68", "metadata": {}, "outputs": [ { "data": { - "image/png": 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\n", 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", 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\n", 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", 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    " ] @@ -350,7 +375,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 5, "id": "2af57d70", "metadata": { "scrolled": false @@ -358,7 +383,7 @@ "outputs": [ { "data": { - "image/png": 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SQjfWEGmPqrqsff7unvbfAIfP8Jq7gX17lv8GeOow65QkTW/kE+uSpPnDEJEkdWaISJI6M0QkSZ0ZIpKkzgwRSVJnc+Y8EUlaqGY6+xxg+fJdWLXqzBFX1D9DRJLGbKazz5t1B424mvvG4SxJUmeGiCSpM0NEktSZISJJ6swQkSR1ZohIkjozRCRJnRkikqTOPNlwTGY6Q3Wun50qSb0MkTGZ6QzVuX52qiT1MkQkaQ5bt+6H7LXXll8u1637MUuXjqGgKQwRSZrD7rmHaUctvv/9PcdQzZYMEUkTzfnF8TJEJE005xfHyxAZopnGMpt1049nzvQav1VJmosMkSGaaSwTZh7PnOk1fquSNBd5sqEkqTNDRJLUmSEiSerMOZEJ5+GNksbJEJlwHt4oaZwczpIkdWaISJI6czhrntraiY7Ol0galJGHSJLdgHOARwIFrKyqj0zZJsBHgAOBu4GXV9XVSfYAPgtsD7y6qr6ZZBHwVeDgqrp7hLsyp23tREfnSyQNyjh6IvcCJ7ah8GDgqiQXV9X3erZ5EfDE9vEs4BPtn68G3gSspwmZlwCvBc4zQOYnjz6T5raRh0hV3Qrc2j7/xyTXA0uB3hA5BDinqgq4IslOSR4NbAQWt4+NSXYCDgIOGOEuaIQ8+kya28Y6J5JkOfAM4Mopq5YCN/Usb2jbPkYzFLYDTa/kXcApVbVpG59zAnACwLJlywZRuqQ5zouZjsbYQiTJjsAXgDdX1S/7eU1V3Qjs077+CcCuwPVJzgXuD7yrqv5hmtetBFYCrFixogayA5LmNC9mOhpjCZEk29MEyGeqatU0m9wM7NazvGvb1uv9wMnAG4FP0cyTnAIcNeh6JQ2Wc13zxziOzgpwJnB9VZ0+w2argTck+TzNhPpd7VzK5vf4Y+CWqrohyWJgU/tYPNzqJQ2Cc13zxzh6Is8FjgG+k+Satu0dwDKAqjoDuJDm8N61NIf4vmLzi9sQOhk4om1aCXyGZl9eO/zyx2Om8d2Zbm4laXrOlQzWOI7O+lsg29imgNdvZd0LepavB/YaZI1z0UzjuzPd3ErS9JwrGSzPWNfAzTTeDX7bW2hm+l2wBz1/GCIauJnGu5t1fttbSGb6XbAHPX8YIguQY8KTayH38uZir8ajzAyRBckx4cm1kHt5c7FX41Fmhoj6MGnftiat3umM4lv3fPh7GqRRXPl6LvamZssQ0TZN2retSat3OqP41j0f/p4GaRRXvp6LvanZMkQ0UvNhPmYhz0uoPwvpvC5DRCM1H+ZjFvK8hPqzkM7rMkS04M3Us7jttg086lG7btG+tW+T86GnJd0XhogWvK2NUz/zmfft2+R86GlJ94UhogVjvo9TD6oXZG9qS/P9d2c2DBEtGPN9nHpQvSB7U1ua7787s2GI6HfG+W3Lb3qTbT6e/6D+GCL6nXF+2/Kb3mSbj+c/qD/3G3cBkqTJZYhIkjpzOEudzcU5lFF9/kI0ir9zf66TxxBRZ3NxDmVUn78QjeLv3J/r5DFEpBGY6Rt2l7PipbnEEJFGYGu9tvt6Vrw0lxgi0jznOTgaJkNEmuc8B0fD5CG+kqTODBFJUmeGiCSpM0NEktSZISJJ6swQkSR1ZohIkjozRCRJnRkikqTODBFJUmdjCZEkByT5QZK1SU6aZv0OSc5v11+ZZHnb/twk1yZZk+SJbdtOSb6WxECUpBEb+X+8SbYDPga8CNgTeGmSqRfxOR74eVU9AfgQcGrbfiJwIPBm4DVt28nAKVW1acilS5KmGMe3938FrK2qdVV1D/B54JAp2xwCnN0+vwDYL0mAjcDi9rExyeOB3arqspFULkn6Pamq0X5gchhwQFW9sl0+BnhWVb2hZ5vr2m02tMs/BJ4F7AqcAfwaOAY4DXhXVd2wjc88ATihXdwD+EHH8ncGftrxtZPKfV4YFto+L7T9hdnv82OrasnUxom6FHxVXQPsDZDkecCtzdOcT9NLObGqfjLN61YCK2f7+UnWVNWK2b7PJHGfF4aFts8LbX9hePs8juGsm4HdepZ3bdum3SbJIuChwM82r2yHtk4G3ge8B3gb8EngjUOrWpK0hXGEyLeAJybZPcn9gSOB1VO2WQ0c1z4/DLi0fn/c7Vjgwqq6k2Z+ZFP7WDzUyiVJv2fkw1lVdW+SNwAXAdsBZ1XVd5O8F1hTVauBM4Fzk6wF7qQJGgCSLAZeDuzfNp0OXAjcA7xsyOXPekhsArnPC8NC2+eFtr8wpH0e+cS6JGn+8AQ9SVJnhogkqTNDZBpdL8syqfrY33+f5HvtJWcuSfLYcdQ5SNva557tXpKkkkz84aD97HOSf9f+rL+b5LOjrnHQ+vjdXpbk60m+3f5+HziOOgclyVlJbm/PtZtufZJ8tP37uDbJXrP+0Kry0fOgmez/IfA44P7A3wN7TtnmdcAZ7fMjgfPHXfeQ93dfYHH7/LWTvL/97nO73YOBy4ErgBXjrnsEP+cnAt8GHtYu7zLuukewzyuB17bP9wTWj7vuWe7z84C9gOtmWH8g8BUgNOfcXTnbz7QnsqXZXJZlEm1zf6vq61V1d7t4Bc25PZOsn58xNOchnQr8ZpTFDUk/+/wq4GNV9XOAqrp9xDUOWj/7XMBD2ucPBW4ZYX0DV1WX0xzROpNDgHOqcQWwU5JHz+YzDZEtLQVu6lne0LZNu01V3QvcBTxiJNUNXj/72+t4mm8yk2yb+9x283erqv81ysKGqJ+f85OAJyX5RpIrkhwwsuqGo599/k/A0Uk20Jwq8KejKW1s7uu/922aqMueaLySHA2sAP543LUMU3tbgdNpzkdaSBbRDGntQ9PbvDzJU6vqF+MsasheCny6qj6Y5Nk056c9pbwqeN/siWxp1pdlmTD97C9Jng+8Ezi4qv55RLUNy7b2+cHAU4DLkqynGTtePeGT6/38nDcAq6tqY1X9CPgHmlCZVP3s8/HAXwNU1TeBB9BcqHC+6uvf+31hiGxpEJdlmSTb3N8kzwD+G02ATPo4OWxjn6vqrqrauaqWV9Vymnmgg6tqzXjKHYh+fq+/RNMLIcnONMNb60ZY46D1s883AvsBJPkDmhC5Y6RVjtZq4Nj2KK29gbuq6tbZvKHDWVPULC/LMmn63N+/AHYE/nt7/MCNVXXw2IqepT73eV7pc58vAvZP8j3gt8B/qKpJ7WH3u88nAp9M8haaSfaXT/AXQpJ8juaLwM7tPM97gO0BquoMmnmfA4G1wN3AK2b9mRP89yVJGjOHsyRJnRkikqTODBFJUmeGiCSpM0NEktSZISINQJLfJrmm57E8yf+dYdtPJzlsG+/3u22SfCrJnu3zdwy+eqk7zxORBuPXVfX0KW3PGcQbV9UrexbfAZwyiPeVBsEQkYYkyT9V1Y7tFZ7/EngBzcXv7unZ5pk01+naEfgpzclut055n8uAt9JcHeGBSa4BvktzmfM7q+rD7XbvB26vqo8Md8+k/8/hLGkwHtgzlPXFKev+LbAHzf0qjqXtoSTZniZcDquqZwJnAe+f6QOq6iTaHk9VHdVuf2z7XvejuXLCeYPdLWnr7IlIgzHdcNZmzwM+V1W/BW5JcmnbvgfNhR4vbi8nsx3Q93WMqmp9kp+11zZ7JPDtSb5MiSaTISKNT4DvVtWzZ/Een6K5ZP2jaHom0kg5nCUN3+XAEUm2a+8it2/b/gNgSXsfC5Jsn+RfbOO9NrbDYJt9ETgA+Jc0FxqURsqeiDR8XwT+NfA9mkuPfxOgqu5pD+P9aJKH0vx7/DDNpPlMVgLXJrm6qo5q3+PrwC/a4TJppLyKrzTB2gn1q4HDq+qGcdejhcfhLGlCtScgrgUuMUA0LvZEJEmd2RORJHVmiEiSOjNEJEmdGSKSpM4MEUlSZ/8P3P8TD53nHzcAAAAASUVORK5CYII=\n", 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", 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\n", 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", 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\n", 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", 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    " ] @@ -444,7 +469,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 6, "id": "1d73cffe", "metadata": {}, "outputs": [ @@ -452,7 +477,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Ry,Ry-Rz,和 Ry-Rz-Rz 神经网络的表达能力分别为 0.24,0.03,和 0.01。\n" + "Ry,Ry-Rz,和 Ry-Rz-Rz 神经网络的表达能力分别为 0.19,0.05,和 0.02。\n" ] } ], @@ -483,7 +508,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 7, "id": "c557d91a", "metadata": { "scrolled": false @@ -498,7 +523,7 @@ }, { "data": { - "image/png": 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\n", 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", 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\n", 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", 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\n", 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", 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\n", 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", 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    " ] @@ -587,12 +612,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "深度为 1,2,3 的神经网络的表达能力分别为 [0.2949 0.0234 0.0077]\n" + "深度为 1,2,3 的神经网络的表达能力分别为 [0.2429 0.011 0.01 ]\n" ] }, { "data": { - "image/png": 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fvbFOG+aJSJOoKCJYp7hoHrthDJMzBvDwW+u5+8UVHNKGeSJygrR1VoSLiY7i/gnD6Z0YzyNvb6CsqpqHc0eREBsddDQRaSc0ougAzIzvXXoW944fwhurt3PDk0so31cTdCwRaSdUFB3ITV8axG9zR7G8uJxJjy1ka/n+oCOJSDugouhgrhzen2e+kcmWPQeY8OhCPi2tDDqSiLRxKooOKPv0Xsy5fRw1dc6E6Yso3LQr6Egi0oapKDqoof2TeOGObHp2ieO6J5bw5qrtQUcSkTaqzReFmZ1mZk+a2bygs0Sa1J6dmTftXM7sk8jtzxYyt6A46Egi0ga1aFGY2VNmVmpmK464/jIzW2tmn5rZ/21oHu6+0d1vbsmcHdkpXePJu3UcX0rvxffnf8zv/rJeG+aJyBe09IjiGeCy+leYWTTwCPBVYAiQa2ZDzOwcM/vzEafkFs4nQJf4GJ64MYNrRqXwi9fXce9LK6mtU1mISEiLbnDn7u+Z2cAjrs4CPnX3jQBmNhu4yt3/G7iyqY9lZrcBtwGkpaU1dTYdVlxMFL+cNILeifHMfG8jO6sO8qspI4iP0YZ5Ih1dEOsoUoD6C8NLwtcdlZmdYmYzgFFm9h/Hup+7z3T3DHfP6N27d/Ol7UCiooy7Lz+bH15+Ni9/spWvPZVPxQFtmCfS0bX5ldnuXubu09z99PCoQ1rYreefxm+mjGTp57uZ8thiSisOBB1JRAIURFFsBlLrXR4Qvk7akKtHpfDUTZlsKtvLtdMXsnFHVdCRRCQgQRRFAXCGmQ0yszggB3gpgBxyHOef2Zu8W8ex/2AtE2csYnnxnqAjiUgAWvrnsXnAImCwmZWY2c3ufgj4JvAasBqY6+4rWzKHNN2I1O7MuyObLvHR5D6+mHfX7Qg6koi0Mouk38yb2XhgfHp6+q3r168POk5EKa08wE1PFbBueyUPThrONaMGBB1JRJqRmRW6e8bRbmvzK7NPhLsvcPfbkpKSgo4ScZITE5hz+ziyBvXkO3OWM/O9DUFHEpFWElFFIS0rMSGWp7+eyRXD+/GzV9bw0z+vok4b5olEPB3hTk5IfEw0v80ZRe+u8Tzx/mfsrKrmgYkjiIvRdw6RSKWikBMWFWXcM34Iyd3ieeDVtZTtPcj068fQNV5vJ5FIpK+B0iRmxp0XpPPgxOEs3FBG7szF7KyqDjqWiLSAiCoKMxtvZjPLy8uDjtJhTMpI5fEbx7C+tJKJ0xdSVLYv6Egi0swiqij0q6dgXHRWH2bdOo49+2u4dvpCVmxWUYtEkogqCgnO6LQezJt2LvExUeTMXMzCT3cGHUlEmomKQppNenIi8+/IJqV7J772dD4Llm8JOpKINAMVhTSrvkkJzJ12LqNSe3DX7A95+oPPgo4kIidJRSHNLqlTLH+4OYuvDOnDjxes4v5X1+jwqiLtmIpCWkRCbDSPXjeGqWPTmP7OBr4372NqauuCjiUiTRBRW0jV2ylg0FEEiI4y7rt6GH0SE/j1m+soq6rmketG0zkuot52IhEvokYU+nls22NmfOuSM7jvmmG8u24HUx9fwu69B4OOJSInIKKKQtqu68aeyvTrx7BqawUTZiykZLc2zBNpL1QU0mouHdqXZ28ey87KaiZMX8iabRVBRxKRRlBRSKvKGtST56dlYxiTZixiycayoCOJyHGoKKTVDe6byPw7s0lOjOeGp/J5dcW2oCOJSANUFBKIlO6dmDctm6H9u3Hnc4U8u3hT0JFE5BhUFBKYHl3imHXLOC4cnMyP/rSCX7+xThvmibRBKgoJVKe4aB67YQyTMwbw0FvrufvFFdTq8KoibUpEbfmkDe7ap5joKO6fMJzeifE88vYGyqqqeTh3FAmx0UFHExEibEShDe7aLzPje5eexb3jh/DG6u3c8OQSyvfVBB1LRIiwopD276YvDeK3uaNYXlzO5McWsbV8f9CRRDq8JheFmc1sziAih105vD/PfCOTzXv2M+HRhXxaWhl0JJEO7bhFYWbRZvado9z0WAvkEQEg+/RezLl9HDV1zsQZiyjctDvoSCId1nGLwt1rgdyjXF/YIolEwob2T+KFO7Lp0TmO655YzFurtwcdSaRDauyipw/M7Hdmdp6ZjT58atFkIkBqz87Mm3YuZ/ZJ5LY/FjK3oDjoSCIdTmN/Hjsy/O9P6l3nwEXNmkbkKE7pGk/ereO447llfH/+x+yoqubOC07HzIKOJtIhNKoo3P3Clg4i0pAu8TE8cWMGP5j/MQ++tpbSigP81/ihREepLERaWqOKwsxOAe4B/onQSOJ94Cfu3qZ2/akN7iJbXEwUv5w0gt6J8cx8byM7qw7yqykjiI/RhnkiLamx6yhmAzuACcDE8Pk5LRWqqbTBXeSLijLuvvxsfnj52bz8yVZueqqAigPaME+kJTW2KPq5+/9z98/Cp58CfVoymEhDbj3/NH4zZSQFn+9iymOLKa04EHQkkYjV2KJ43cxyzCwqfJoMvNaSwUSO5+pRKTx1UyabyvZy7fSFbNxRFXQkkYjU2KK4FZgFVIdPs4HbzazSzHQ8SwnM+Wf2Ju/Wcew/WMvEGYtYXrwn6EgiEadRReHuie4e5e6x4VNU+LpEd+/W0iFFGjIitTvz7simS3w0uY8v5t11O4KOJBJRGlUUZnbzEZejzeyelokkcuIG9erC/DuyGXhKF25+poAXPywJOpJIxGjsoqeLzewVM+tnZsOAxUBiC+YSOWHJiQnMuX0cWYN68p05y5n53oagI4lEhMZucDfVzKYAnwB7ganu/kGLJhNpgsSEWJ7+eibfnbucn72yhtKKau6+/GyitGGeSJM1doO7M4BvAfOBs4EbzOxDd9/XkuFEmiI+Jprf5oyid9d4nnj/M3ZWVfPAxBHExejwKyJN0dh9PS0A/tXd37LQDna+CxQAQ1ssmchJiIoy7hk/hN6J8Tz42lrK9h5k+vVj6BofUUf/FWkVjf2KleXubwF4yC+Ba1oulsjJMzP+9cJ0Hpw4nIUbypj6+GJ2VlUHHUuk3WmwKMzs+wDuXmFmk464+aaWCtVUZjbezGaWl5cHHUXakEkZqTx+4xjWba9k4vSFFJVpianIiTjeiCKn3vn/OOK2y5o5y0nTvp7kWC46qw/P3TKOPftruHb6QlZs1pcJkcY6XlHYMc4f7bJImzbm1B7Mm3Yu8TFR5MxczMJPdwYdSaRdOF5R+DHOH+2ySJuXnpzI/DuySeneia89nc+C5VuCjiTS5h2vKEaYWYWZVQLDw+cPXz6nFfKJNLu+SQnMvf1cRqX24K7ZH/LMB58FHUmkTWuwKNw92t27hffpFBM+f/hybGuFFGluSZ1j+cPNWXxlSB/uXbCKB15dg7sGySJHoy2QpMNKiI3m0evGMHVsGo++s4HvzfuYmtq6oGOJtDna+kg6tOgo476rh5GcGM9v3lzPrr0HeWTqaDrF6fCqIodpRCEdnpnx7UvO5L5rhvHO2lKmPrGY3XsPBh1LpM1QUYiEXTf2VKZfP4aVWyqYMGMhJbu1YZ4IqChEvuDSoX159uax7KysZsL0hazZpgM4iqgoRI6QNagnz0/LxjAmzVjEko1lQUcSCZSKQuQoBvdNZP6d2SQnxnPDU/m8umJb0JFEAqOiEDmGlO6dmDctm6H9u3Hnc4U8u3hT0JFEAqGiEGlAjy5xzLplHBcOTuZHf1rBr99Ypw3zpMNRUYgcR6e4aB67YQyTxgzgobfWc/eLK6itU1lIxxFRG9yZ2XhgfHp6etBRJMLEREfxwMThJHeL55G3N1BWVc3DuaNIiNWGeRL5ImpEoeNRSEsyM7536VncO34Ib6zezo1P5lO+ryboWCItLqKKQqQ13PSlQfw2dxQfFe9h8mOL2Fq+P+hIIi1KRSHSBFcO788zX89k8579THh0IZ+WVgYdSaTFqChEmig7vRdzbh9HTZ0zccYiCjftDjqSSItQUYichKH9k3jhjmy6d4rluicW89bq7UFHEml2KgqRk5TaszPz7sjmzD6J3PbHQuYuLQ46kkizUlGININeXePJu3UcX0rvxffnfcwjb3+qDfMkYqgoRJpJl/gYnrgxg2tGpfDga2u596WV2jBPIkJEbXAnErS4mCh+OWkEvbrG8fhfP2Nn1UF+NWUE8THaME/aLxWFSDOLijJ+eMUQkhMTuO+V1ezae5DHbhxDt4TYoKOJNIkWPYm0kFvPP43fTBnJoo1lnP/A26zaUh50JJEmUVGItKCrR6UAsGdfDZc//D535S2jtOJAwKlEToyKQqQVvbR8K+P++y2+8UwB2/Zo1x/SPqgoRFpZncNf1pTyz794m9/9ZT3bNcKQNk4rs0VaUWy0EWVG5sAeHKip4xevr+PXb67norOSmZqVxvln9iY6yoKOKfIFKgqRVhAbbUSbMTEjlbsuTic5MQGAz3fuZXZBMfMKi3lj1Xb6JyUwOTOVyRmp9O/eKeDUIiEWiVuPZmRk+NKlS4OOIQLA5Q/9ldGn9vhCQRzp4KE63lq9nbyCYv66fgcGXDA4mZzMVC46K5mYaC0llpZlZoXunnHU21QUIm1L8a59zF1azJyCYkorq+nTLZ5JY1KZkplKas/OQceTCKWiEGmHDtXW8fbaHeTlF/HO2lIc+Kf0XkzNSuOSIX2I1ShDmpGKQqSd27JnP3OXFjO3oJgt5Qfo1TWOiWNSyclMZWCvLkHHkwigohCJELV1znvrQqOMt9aUUlvnZJ9+CjlZaVw6tI/2KSVN1mGKwszGA+PT09NvXb9+fdBxRFrU9ooDzCssIS+/iJLd++nROZYJoweQk5VGenLXoONJO9NhiuIwjSikI6mrcz7YsJO8/CJeX7mdQ3VO1sCe5I5N5avD+pEQq1GGHJ+KQqSD2FFZzfxlJczOL+Lzsn10S4jh2tEDyM1KY3DfxKDjSRumohDpYNydRRvLmJ1fzKsrtnGwto7Rad3JyUrjyuH96BynbW3li1QUIh3Yrr0HeWFZaF3Ghh17SYyP4apR/cnNSmNo/6Sg40kboaIQEdydpZt2k7ekiJc/2Ur1oTqGD0giNyuN8SP60zVeo4yOTEUhIl9Qvq+GFz8sYXZBMWu2VdI5Lpp/GREaZQwfkISZdkzY0agoROSo3J0Pi/cwO7+IBcu3sr+mliH9upGblcpVo1J0+NYOREUhIsdVcaCGlz7aQl5+ESu3VJAQG8WVw0OjjNFp3TXKiHAqChE5IZ+UlDMrv4iXPtrM3oO1nNmnKzmZaVw7OoXuneOCjictQEUhIk2yt/oQC5ZvIa+gmOXFe4iLieKKc/qRk5lK1qCeGmVEEBWFiJy0VVsqmF1QxIvLNlNZfYjTenchNzONCWMG0LOLRhntnYpCRJrN/oO1vPzJVvLyiyjctJu46Ci+MrQPuVlpnHvaKUTpUK7tkopCRFrEuu2V5OUX8cKyzZTvr+HUUzqTk5nGxDED6J0YH3Q8OQEqChFpUQdqanl1xTby8otY8tkuYqKMLw/pQ05WGuel99Ioox1QUYhIq9mwo4o5BcXMKyxh196DDOjRiSkZqUzKSKVv0tGPGS7BU1GISKurPlTLG6u2k5dfxAeflhFlcNFZfZg6NpV/PjOZaI0y2pSGikI7dxGRFhEfE82Vw/tz5fD+bCrby+yCYp5fWsKbq7fTLymByRmpTM5MJaV7p6CjynFoRCEiraamto63Vm8nL7+Y99bvAOCCM3uTk5XGRWclExsdFXDCjkuLnkSkzSnetY/nlxYzZ2kx2yuq6Z0Yz+SMAeRkppHas3PQ8TocFYWItFmHaut4Z+0O8vKLeHttKXUO553Ri9ysNC45uw9xMRpltAYVhYi0C1vL9zO3oIS5S4vZvGc/p3SJY2J4lDGoV5eg40U0FYWItCu1dc5763cwO7+IN1eXUlvnjDutJ7lZaVw6tC8JsdFBR4w4KgoRabdKKw7wfGEJswuKKN61n+6dY5kwegC5WamkJycGHS9iqChEpN2rq3MWbigjL7+I11dto6bWyRzYg5zMNK4Y3k+jjJOkohCRiLKzqpr5haFDuX62cy/dEmK4ZlQKuWPTOKtvt6DjtUsqChGJSO7O4o27mF1QxP9+so2DtXWMTO3O1Kw0rhzRj85x2qa4sVQUIhLxdu89yAsfbiYvv4hPS6voGh/DVSNDh3IdlpIUdLw2T0UhIh2Gu1O4aTez8ot4+eOtVB+q45yUJHKyUvmXEf1JTIgNOmKbpKIQkQ6pfF8Nf/ooNMpYs62SznHRjB/en9yxaYwYkKRDudajohCRDs3d+ah4D7Pzi3lp+Rb219RyVt9Epo5N46qRKSR10ihDRSEiElZ5oIaXlm8hL7+IFZsrSIiN4opz+pOblcqYU3t02FGGikJE5Cg+KSknr6CIlz7aQlX1Ic5I7kpOVhrXjkqhR5e4oOO1KhWFiEgD9lYf4s8fbyEvv5iPivcQFxPFV4f1JTcrjbGDenaIUUa7Lgozuxq4AugGPOnurx9vGhWFiDTV6q0VzM4v4oUPN1N54BCn9epCTlYqE0YP4JSu8UHHazGBFYWZPQVcCZS6+7B6118GPAREA0+4+88bMa8ewC/c/ebj3VdFISIna//BWl75ZCt5+UUs3bSb2GjjK0P7kpuZRvbppxAVYYdyDbIozgeqgD8cLgoziwbWAV8GSoACIJdQafz3EbP4hruXhqf7JfCcuy873uOqKESkOa3fXklefjEvfFjCnn01pPXszJTMVCZlDCA5MSHoeM0i0EVPZjYQ+HO9ojgXuNfdLw1f/g8Adz+yJA5Pb8DPgTfc/c3GPKaKQkRawoGaWl5buY28/CIWb9xFTJRx8dnJ5Galcd4ZvYlux6OMhooiiB2hpADF9S6XAGMbuP+/AZcASWaW7u4zjnYnM7sNuA0gLS2tmaKKiPxdQmw0V41M4aqRKWzcUcWcgmLmFZbw2srtpHTvxJTMVCZnpNI3KTJGGYcFMaKYCFzm7reEL98AjHX3bzbXY2pEISKt5eChOt5YtZ28/CLe/3QnUQYXnZVMTmYaFwzuTUx0+ziUa1sbUWwGUutdHhC+TkSk3YmLieKK4f24Yng/NpXtZU5BMc8XlvDm6qX07ZbA5IwBTM5MZUCPzkFHbbIgRhQxhFZmX0yoIAqAqe6+srkeUyMKEQlSTW0db60uZXZBEe+u2wHA+Wf0JjcrjYvPTia2DY4yAhtRmFkecAHQy8xKgHvc/Ukz+ybwGqFfOj3VnCUhIhK02OgoLhvWl8uG9aVk9z7mLi1hbkEx054tpHdiPJPGDCAnM420U9rHKKPNb3B3IsxsPDA+PT391vXr1wcdR0Tkbw7V1vHuuh3k5RfxlzWl1Dn8U3ovcrJS+cqQvsTFBDvKaNdbZjeFFj2JSFu2tXw/zy8tYU5BMZv37OeULnFMGDOAnMxUTuvdNZBMKgoRkTaots756/odzM4v5s3V2zlU54wd1JOpY9O4dGhfEmKjWy2LikJEpI0rrTzAvMISZucXU7RrH907x3LtqAHkZqVyRp/EFn98FYWISDtRV+cs2ljGrPwiXl+5jZpaJ+PUHuRkpXHFOf3oFNcyowwVhYhIO1RWVc38ZaFRxsade0lMiOGaUSnkZKYxpH+3Zn0sFYWISDvm7iz5bBez84t4ZcU2Dh6qY0Rqd6ZmpfL0B5+TcWoP7rr4DJK7NX3XIR2mKPTzWBGJdHv2HeSFZZvJyy9ifWkVAFEGMVFRTM4Y0OTC6DBFcZhGFCIS6dydZUW7mTB90Reuj4+JYtKYEy+Mhoqi7W1HLiIix2VmjDm15z9cX32ojufyi/hm3ofN9lhB7BRQRERaQGy0EW3GxIxU7ro4vdnmq6IQEWnnjiyI5j7qnopCRKQdG9KvG6NP7dEiBXGYikJEpB175VvntfhjRNTKbDMbb2Yzy8vLg44iIhIxIqoo3H2Bu9+WlJQUdBQRkYgRUUUhIiLNT0UhIiINUlGIiEiDInIXHma2A9jUxMl7ATubMY5IfXp/SUs6mffXqe7e+2g3RGRRnAwzW3qs/Z2InCy9v6QltdT7S4ueRESkQSoKERFpkIriH80MOoBENL2/pCW1yPtL6yhERKRBGlGIiEiDVBQiItIgFUWYmT1lZqVmtiLoLBJ5zCzVzN42s1VmttLMvhV0JokcZpZgZvlmtjz8/vpxs85f6yhCzOx8oAr4g7sPCzqPRBYz6wf0c/dlZpYIFAJXu/uqgKNJBDAzA7q4e5WZxQLvA99y98XNMX+NKMLc/T1gV9A5JDK5+1Z3XxY+XwmsBlKCTSWRwkOqwhdjw6dmGwWoKERamZkNBEYBSwKOIhHEzKLN7COgFHjD3Zvt/aWiEGlFZtYVmA98290rgs4jkcPda919JDAAyDKzZluErqIQaSXhZcfzgefc/YWg80hkcvc9wNvAZc01TxWFSCsIr2x8Eljt7r8KOo9EFjPrbWbdw+c7AV8G1jTX/FUUYWaWBywCBptZiZndHHQmiShfAm4ALjKzj8Kny4MOJRGjH/C2mX0MFBBaR/Hn5pq5fh4rIiIN0ohCREQapKIQEZEGqShERKRBKgoREWmQikJERBqkohBpBmZ2r5n9exOmG1n/Z7JNnY9IS1JRiARrJKDtKaRNU1GINJGZ/dDM1pnZ+8Dg8HWnm9mrZlZoZn81s7PC1z9jZjPMbGl4mivNLA74CTAlvAHelPCsh5jZO2a20czuCubZifxdTNABRNojMxsD5BAaEcQAywgdY2ImMM3d15vZWOBR4KLwZAOBLOB0QvviSQf+C8hw92+G53svcBZwIZAIrDWz6e5e0ypPTOQoVBQiTXMe8KK77wMws5eABCAbeD60aycA4utNM9fd64D1ZraRUCEczcvuXg1Um1kp0AcoaYHnINIoKgqR5hMF7Anv6vlojtxfzrH2n1Nd73wt+n8qAdM6CpGmeQ+42sw6hQ9tOh7YB3xmZpMgtMdYMxtRb5pJZhZlZqcDpwFrgUpCi5hE2iwVhUgThA9rOgdYDvwvoT12AlwH3Gxmy4GVwFX1JisC8sP3n+buBwitqxhyxMpskTZFe48VaQVm9gzwZ3efF3QWkROlEYWIiDRIIwoREWmQRhQiItIgFYWIiDRIRSEiIg1SUYiISINUFCIi0qD/D/8/b1yE5jC3AAAAAElFTkSuQmCC\n", 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", 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    " ] @@ -613,13 +638,13 @@ " print(\" 采样第 %d 个样本...\" % (2 * index))\n", " cir1 = Circuit(n)\n", " # 作用 complex_entangled_layer 层\n", - " cir1.complex_entangled_layer('full', n, d)\n", + " cir1.complex_entangled_layer('full', d)\n", " # 输出态的态矢量\n", " rho1 = cir1(pq.state.zero_state(n))\n", " \n", " cir2 = Circuit(n)\n", " # 作用 complex_entangled_layer 层\n", - " cir2.complex_entangled_layer('full', n, d)\n", + " cir2.complex_entangled_layer('full', d)\n", " # 输出态的态矢量\n", " rho2 = cir2(pq.state.zero_state(n))\n", " \n", diff --git a/tutorials/qnn_research/Expressibility_EN.ipynb b/tutorials/qnn_research/Expressibility_EN.ipynb index 8bcc83b..1193ce3 100644 --- a/tutorials/qnn_research/Expressibility_EN.ipynb +++ b/tutorials/qnn_research/Expressibility_EN.ipynb @@ -84,10 +84,25 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "id": "3810b843", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/openfermion/hamiltonians/hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import numpy as np\n", "import paddle\n", @@ -106,10 +121,20 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 2, "id": "8cc9cff3", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " elif dtype == np.bool:\n" + ] + } + ], "source": [ "num_qubit = 1 # the number of qubit\n", "num_sample = 2000 # the number of sample\n", @@ -147,7 +172,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "id": "c0330832", "metadata": {}, "outputs": [], @@ -248,13 +273,13 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 4, "id": "409b2dc8", "metadata": {}, "outputs": [ { "data": { - "image/png": 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+ "image/png": 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", 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\n", 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", 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    " ] @@ -348,7 +373,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 5, "id": "eeb57c55", "metadata": { "scrolled": false @@ -356,7 +381,7 @@ "outputs": [ { "data": { - "image/png": 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\n", 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", 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\n", 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", 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\n", 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", 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    " ] @@ -442,7 +467,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 6, "id": "cc1bb1b3", "metadata": {}, "outputs": [ @@ -450,7 +475,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The expressiblity of Ry, Ry-Rz, and Ry-Rz-Rz are 0.21, 0.05, and 0.02, respectively.\n" + "The expressiblity of Ry, Ry-Rz, and Ry-Rz-Rz are 0.21, 0.03, and 0.02, respectively.\n" ] } ], @@ -481,7 +506,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 7, "id": "17d5b27b", "metadata": { "scrolled": false @@ -496,7 +521,7 @@ }, { "data": { - "image/png": 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\n", 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", 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\n", 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", 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\n", 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", 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9gKVAAGt2dzvMzKyyWh6J7EJ2BtUXJD2RHiOB84E9JM0Adk/zSBom6WqAiFhINmD+aHqcncra/QA4NyKWkiWXfwaeBK6vYXvMzKxEzcZEIuIBPjiDqtRuZepPAY7OzY8DxlXY9im56XfIjlTMzKzOfMW6mZkVVvOzs3qCWbOeZ+jQfZYrb23dgAkTrmlARGZm9eEk0g0WL4aWltuXK29rWz6xmJmtStydZWZmhTmJmJlZYU4iZmZWmJOImZkV5iRiZmaFOYmYmVlhTiJmZlaYk4iZmRXmJGJmZoU5iZiZWWFOImZmVpiTiJmZFeYkYmZmhTmJmJlZYU4iZmZWmJOImZkV5iRiZmaFdZpEJD0m6QRJ69UjIDMzax7VHImMBjYGHpV0s6S9JKnGcZmZWRPoNIlExMyI+D6wFfBzYBzwgqT/kLR+rQM0M7OVV1VjIpK2Ay4EfgL8Evgq8CZwT+1CMzOzlV2fzipIegx4A7gGOC0i/pEWPSJplxrGZmZmK7lOkwjw1YiYVW5BROzfzfGYmVkTqaY762hJ67bPSFpP0g9rF5KZmTWLapLI3hHxRvtMRLwOjKxZRGZm1jSqSSK9Ja3ePiNpTWD1DuqbmVkPUc2YyI3A3ZL+O80fCVxXu5DMzKxZVHOdyI+Ac4Ft0uOciPhxZ+tJGidpgaSncmVnSZor6Yn0KNstJmmEpOckzZR0Wq78RknTJJ2XKztd0n6dxWNmZt2vmiMRIuIO4I4V3Pa1wE+B8SXlF0fEBZVWktQbuBzYA5hDdqX8xBTr3yNiO0mTJQ0A+gHDI8ID/WZmDVDNvbP2lzRD0iJJb0p6S9Kbna0XEfcDCwvEtBMwMyJmRcRi4GZgFPAusKakXkBf4D3gbODMAvswM7NuUM3A+o+BfSNiQESsExFrR8Q6XdjnialLalyFmzq2ALNz83OAloiYDrwCTAVuB7YAekXE1C7EYmZmXVBNEpmfPsC7wxXA5sD2wDyyW6lULSJOjojtI+JC4BzgDEnfl3SrpG9WWk/SGElTJE155ZVXuhC+mZnlVZNEpki6RdLBqWtrf0mFrlSPiPkR8V5ELAWuIuu6KjUXGJyb3ySVvU/SKOAxoD+weUQcCBwgqV+F/Y6NiGERMWzQoEFFQjczszKqGVhfB3gb2DNXFsCEFd2ZpI0iYl6a/TLwVJlqjwJbStqMLHkcBHwtt42+wMnAF4EtUywAvYHVUqxmZlYHnSaRiDiyyIYl3QTsCgyUNIdsAHxXSduTffC3AcekuhsDV0fEyIhYIulE4E6yxDAuIp7ObfoE4LqIeFvSNKCfpCeBSfkr683MrPaquYvvVmRjGRtGxMfTbeH37ey02og4uEzxNRXqvkTuVioRMQmYVKHuJbnpAMrtx8zM6qCa7qyrgO8CPwOIiGmSfg742oxOzJr1PEOH7lN2WWvrBkyYUDanmpk1jWqSSL+I+GPJL+IuqVE8q5TFi6Gl5fayy9rayicXM7NmUs3ZWa9K2pw0gC3pALLTc83MrIer5kjkBGAs8FFJc4G/AF+vaVRmZtYUqjk7axawu6S1yK4Qf6v2YZmZWTOo5uysH5TMAxARZ9coJjMzaxLVdGf9LTe9BvAloLtug2JmZk2smu6sZe5vJekCsgsBzcysh6vm7KxS/cjuZ2VmZj1cNWMiT7Ls/akGkf2Oh5mZ9XDVjIl8KTe9hOzW8L7Y0MzMqkoipaf0rpO/ej0iivx6oZmZrQKqSSJTyX7f43VAwLrAi2lZAB+pSWRmZrbSq2ZgfTKwT0QMjIgPkXVv3RURm0WEE4iZWQ9WTRLZOd2aHYCIuAP4dO1CMjOzZlFNd9ZLkk4HbkjzhwAv1S4kMzNrFtUciRxMdlrvbWQ/iTsI/xCUmZlR3RXrC4GTJK0VEX/rrL6ZmfUc1Vxs+GngaqA/METSJ4BjIuL4Wge3Kqv0q4f+xUMzaybVjIlcDOwFTASIiD9J+mxNo+oBKv3qoX/x0MyaSVX3zoqI2SVF79UgFjMzazLVHInMTl1aIakvcBK+FbyZmVHdkcixZD+R2wLMBbZP82Zm1sN1eCQiqTdwaUQcUqd4zMysiXR4JBIR7wGbSlqtTvGYmVkTqWZMZBbwoKSJ5H4qNyIuqllUZmbWFCoeiUi6Pk3uC/wm1V079zAzsx6uoyORHSVtTHbb9/+sUzxmZtZEOkoiVwJ3A5sBU3Llwr8jYmZmdNCdFRGXRcQ2wH9HxEdyD/+OiJmZAVVcJxIRxxXZsKRxkhZIeipXtr6kyZJmpL/rVVj38FRnhqTDU9nqkn4n6SlJx+fqjpU0tEiMZmbWNVXd9qSga4ERJWWnAXdHxJZkXWWnla4kaX3gTGA4sBNwZko2ewEPANsBh6a6nwB6R8TUGrXBzMw6ULMkEhH3AwtLikcB16Xp64D9yqy6FzA5IhZGxOtkP887AngX6Af0JRuXATgHOKN7Izczs2rV8kiknA0jYl6afhnYsEydFiB/w8c5qWwy0Ao8DFwmaV9gakT4VxbNzBqkmosNayIiQlKsQP0lwNcA0o0g7wRGSboIGAKMj4iJ5daVNAYYAzBkyJCuhm5mZkm9j0TmS9oIIP1dUKbOXGBwbn6TVJZ3PDAe2BlYBIwGTq2004gYGxHDImLYoEGDuhC+mZnl1TuJTAQOT9OHA78uU+dOYE9J66UB9T1TGQCp7EtkSaQfsJTsupU1axi3mZmVUbMkIukm4CFga0lzJB0FnA/sIWkGsHuaR9IwSVfD+7/pfg7waHqcncra/QA4NyKWkiWXfwaeBK7HzMzqqmZjIhFxcIVFu5WpOwU4Ojc/DhhXYbun5KbfITtSMTOzBqh3d5aZma1CnETMzKywhp3ia+XNmvU8Q4fus1x5a+sGTJhwTQMiMjOrzElkJbN4MbS03L5ceVvb8onFzKzR3J1lZmaFOYmYmVlhTiJmZlaYk4iZmRXmJGJmZoU5iZiZWWFOImZmVpiTiJmZFeYkYmZmhTmJmJlZYU4iZmZWmJOImZkV5iRiZmaFOYmYmVlhTiJmZlaYk4iZmRXmJGJmZoU5iZiZWWFOImZmVpiTiJmZFeYkYmZmhTmJmJlZYU4iZmZWmJOImZkV5iRiZmaFOYmYmVlhTiJmZlZYQ5KIpDZJT0p6QtKUMssl6TJJMyVNkzQ0lW8t6bFU9qlU1kfS7yX1q3c7zMx6uj4N3PfnI+LVCsv2BrZMj+HAFenvMcBJQBtwKfAV4Djghoh4u9YBN9KsWc8zdOg+y5W3tm7AhAnXNCAiM7PGJpGOjALGR0QAD0taV9JGwLtAv/R4V9K6wD7AiIZFWieLF0NLy+3Llbe1LZ9YzMzqpVFJJIC7JAXws4gYW7K8BZidm5+Tyi4HxgOrkx2VnAGcFxFLO9qZpDHAGIAhQ4Z0SwPMzKxxSeQzETFX0gbAZEnPRsT9na0UES8CuwJI2gLYBJgu6XpgNeCMiPhzmfXGAmMBhg0bFt3XjMar1M0F7uoys9prSBKJiLnp7wJJtwE7AfkkMhcYnJvfJJXlnQucDnwbuJpsnOQ84JDaRL1yqtTNBe7qMrPaq/vZWZLWkrR2+zSwJ/BUSbWJwGHpLK2dgUURMS+3jc8BL0XEDLLxkaXp4TO0zMzqqBFHIhsCt0lq3//PI+J3ko4FiIgrgUnASGAm8DZwZPvKylY8HRidisYCN6ZtHVenNpiZGQ1IIhExC/hEmfIrc9MBnFBh/QD2yM1PB4Z2f6RmZtYZX7FuZmaFOYmYmVlhTiJmZlaYk4iZmRXmJGJmZoU5iZiZWWFOImZmVpiTiJmZFeYkYmZmhTmJmJlZYU4iZmZWmJOImZkV5iRiZmaFray/sW7doNKvHvoXD82suziJrMIq/eqhf/HQzLqLu7PMzKwwJxEzMyvMScTMzApzEjEzs8I8sG7v23//o2hrW7Bcuc/mMrNKnETsfW1tC3w2l5mtEHdnmZlZYU4iZmZWmLuzeqBKV7LPmvUCLS0NCMjMmpaTSA9U6Ur2Z5/dtmx93z7FzCpxErFO+fYpZlaJx0TMzKwwJxEzMyvM3VlWE5UuXHz55Tl8+MObLFfu8RWz5uQkYjVR6cLFZ5/dlh139PiK2aqiIUlE0gjgUqA3cHVEnF+yfHVgPLAj8BowOiLaJO0CXAEsBg6OiBmS1gVuBUZExNI6NqPHq3TWVrZsxU4X9hlgZs2p7klEUm/gcmAPYA7wqKSJEfFMrtpRwOsRsYWkg4AfAaOBU4GRQCtwbJo/HTjPCaT+Kp21BZVPF17Rbd1zz7ZOLmYrsUYciewEzIyIWQCSbgZGAfkkMgo4K03/D/BTSQLeBfqlx7uSNgcGR8R99Qnd6m1Fkws4wZjVkyKivjuUDiDrejo6zR8KDI+IE3N1nkp15qT554HhwCbAlcDfgUOBC4AzImJGJ/scA4xJs1sDzxUMfyDwasF1m5Xb3DO4zau+rrZ304gYVFrYVAPrEfEEsDOApM8C87JJ3UJ2lHJqRMwvs95YYGxX9y9pSkQM6+p2monb3DO4zau+WrW3EdeJzAUG5+Y3SWVl60jqAwwgG2AnlYlsLOQc4EzgX4GrgG/XLGozM1tOI5LIo8CWkjaTtBpwEDCxpM5E4PA0fQBwTyzb73YYMCkiFpKNjyxNj341jdzMzJZR9+6siFgi6UTgTrJTfMdFxNOSzgamRMRE4BrgekkzgYVkiQYASf2AI4A9U9FFwCSy036/VuPwu9wl1oTc5p7BbV711aS9dR9YNzOzVYfvnWVmZoU5iZiZWWFOImVIGiHpOUkzJZ1WZvnqkm5Jyx+R1NqAMLtVFW3+F0nPSJom6W5JmzYizu7UWZtz9b4iKSQ19emg1bRX0oHpdX5a0s/rHWN3q+J9PUTSvZIeT+/tkY2IsztJGidpQbrertxySbosPSfTJA3t0g4jwo/cg2yw/3ngI8BqwJ+AbUvqHA9cmaYPAm5pdNx1aPPngX5p+rie0OZUb23gfuBhYFij467xa7wl8DiwXprfoNFx16HNY4Hj0vS2QFuj4+6Gdn8WGAo8VWH5SOAOQGTX3T3Slf35SGR579+WJSIWA+23ZckbBVyXpv8H2C1du9KsOm1zRNwbEW+n2YfJru9pZtW8zpBdi/Qj4J16BlcD1bT3m8DlEfE6QEQsfy//5lJNmwNYJ00PAF6qY3w1ERH3k53VWskoYHxkHgbWlbRR0f05iSyvBZidm5+TysrWiYglwCLgQ3WJrjaqaXPeUWTfZJpZp21Oh/mDI+K39QysRqp5jbcCtpL0oKSH0922m1k1bT4L+LqkOWSXCnyrPqE11Ir+v3eoqW57Yo0n6evAMOBzjY6lliT1IrsG6YgGh1JPfci6tHYlO9K8X9I/RcQbjQyqxg4Gro2ICyV9iuz6tI+H7wpeNR+JLK/Lt2VpQtW0GUm7A98H9o2If9QptlrprM1rAx8H7pPURtZ3PLGJB9ereY3nABMj4t2I+AvwZ7Kk0qyqafNRZL9HREQ8BKxBdqPCVVlV/+/VchJZXnfclqXZdNpmSTsAPyNLIM3eVw6dtDkiFkXEwIhojYhWsnGgfSNiSmPC7bJq3te/IjsKQdJAsu6tWXWMsbtV0+YXgd0AJG1DlkReqWuU9TcROCydpbUzsCgi5hXdmLuzSkQXb8vSjKps80+A/sAv0jkEL0bEvg0LuouqbPMqo8r23gnsKekZ4D3guxHRtEfYVbb5VOAqSaeQDbIf0eRfCJF0E9mXgYFprOdMoC9ARFxJNvYzEpgJvA0c2aX9NfnzZWZmDeTuLDMzK8xJxMzMCnMSMTOzwpxEzMysMCcRMzMrzEnErBtIek/SE7lHq6Q/VKh7raQDOtne+3UkXS1p2zT9ve6P3qw4Xydi1j3+HhHbl5R9ujs2HBFH52a/B5zXHds16w5OImY1IumvEdE/3eH5P4E9yG58tzhXZ0eye3T1B14lu9htXsl27gO+Q3Z3hDUlPQE8TXab84URcUmqdy6wICIurW3LzD7g7iyz7rFmrivrtpJlXwa2Jvu9isNIRyiS+pIllwMiYkdgHHBupR1ExGmkI56IOCTVPyxtqxfZnRNu6N5mmXXMRyJm3aNcd1a7zwI3RcR7wEuS7knlW5Pd5HFyupVMb6DqexhFRJuk19J9zTYEHm/m25RYc3ISMWscAU9HxKe6sI2ryW5X/2GyIxOzunJ3llnt3Q+MltQ7/YLc51P5c8Cg9DsWSOor6WOdbOvd1A3W7jZgBPBJshsNmtWVj0TMau824AvAM2S3Hn8IICIWp9N4L5M0gOz/8RKyQfNKxgLTJE2NiEPSNu4F3kjdZWZ15bv4mjWxNKA+FfhqRMxodDzW87g7y6xJpQsQZwJ3O4FYo/hIxMzMCvORiJmZFeYkYmZmhTmJmJlZYU4iZmZWmJOImZkV9v+eZ6RJMJqOGwAAAABJRU5ErkJggg==\n", 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", 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    " ] @@ -585,12 +610,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "The expressibility of depth 1, 2 and 3 is [0.2715 0.0152 0.0096]\n" + "The expressibility of depth 1, 2 and 3 is [0.3136 0.0122 0.0097]\n" ] }, { "data": { - "image/png": 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\n", 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", "text/plain": [ "
    " ] @@ -611,13 +636,13 @@ " print(\" sampling %d-th sample...\" % (2 * index))\n", " cir1 = Circuit(n)\n", " # add complex entangled layers\n", - " cir1.complex_entangled_layer('full', n, d)\n", + " cir1.complex_entangled_layer('full', d)\n", " # output a state vector\n", " rho1 = cir1(pq.state.zero_state(n))\n", " \n", " cir2 = Circuit(n)\n", " # add complex entangled layers\n", - " cir2.complex_entangled_layer('full', n, d)\n", + " cir2.complex_entangled_layer('full', d)\n", " # output another state vector\n", " rho2 = cir2(pq.state.zero_state(n))\n", " \n", diff --git a/tutorials/qnn_research/Fisher_CN.ipynb b/tutorials/qnn_research/Fisher_CN.ipynb index f7d6659..f8daf02 100644 --- a/tutorials/qnn_research/Fisher_CN.ipynb +++ b/tutorials/qnn_research/Fisher_CN.ipynb @@ -310,7 +310,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 16, "metadata": {}, "outputs": [], "source": [ @@ -323,14 +323,14 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "--Ry(0.826)----Rz(4.587)--\n", + "--Ry(2.574)----Rz(6.022)--\n", " \n" ] } @@ -349,76 +349,76 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The QFIM at [0. 4.58719969] is \n", + "The QFIM at [0. 6.02232647] is \n", " [[1. 0.]\n", " [0. 0.]].\n", - "The QFIM at [0.15707963 4.58719969] is \n", + "The QFIM at [0.15707963 6.02232647] is \n", + " [[1.00000000e+00 3.87542900e-08]\n", + " [3.87542900e-08 2.44718161e-02]].\n", + "The QFIM at [0.31415927 6.02232647] is \n", + " [[ 1.00000024e+00 -1.25257100e-08]\n", + " [-1.25257100e-08 9.54916961e-02]].\n", + "The QFIM at [0.4712389 6.02232647] is \n", + " [[ 1.00000000e+00 -9.98981000e-08]\n", + " [-9.98981000e-08 2.06107258e-01]].\n", + "The QFIM at [0.62831853 6.02232647] is \n", + " [[1.00000024 0. ]\n", + " [0. 0.34549158]].\n", + "The QFIM at [0.78539816 6.02232647] is \n", + " [[ 1.00000000e+00 -1.03238260e-07]\n", + " [-1.03238260e-07 5.00000059e-01]].\n", + "The QFIM at [0.9424778 6.02232647] is \n", + " [[ 1.00000024e+00 -5.11963400e-08]\n", + " [-5.11963400e-08 6.54508745e-01]].\n", + "The QFIM at [1.09955743 6.02232647] is \n", + " [[ 1.00000000e+00 -8.24729700e-08]\n", + " [-8.24729700e-08 7.93892649e-01]].\n", + "The QFIM at [1.25663706 6.02232647] is \n", + " [[1.00000024e+00 3.54160800e-08]\n", + " [3.54160800e-08 9.04508740e-01]].\n", + "The QFIM at [1.41371669 6.02232647] is \n", + " [[ 1.00000024e+00 -4.52859700e-08]\n", + " [-4.52859700e-08 9.75528458e-01]].\n", + "The QFIM at [1.57079633 6.02232647] is \n", + " [[1.00000e+00 8.42937e-08]\n", + " [8.42937e-08 1.00000e+00]].\n", + "The QFIM at [1.72787596 6.02232647] is \n", " [[1. 0. ]\n", - " [0. 0.02447182]].\n", - "The QFIM at [0.31415927 4.58719969] is \n", - " [[1. 0. ]\n", - " [0. 0.09549146]].\n", - "The QFIM at [0.4712389 4.58719969] is \n", - " [[1. 0. ]\n", - " [0. 0.20610736]].\n", - "The QFIM at [0.62831853 4.58719969] is \n", - " [[ 1.0000000e+00 -8.1719260e-08]\n", - " [-8.1719260e-08 3.4549149e-01]].\n", - "The QFIM at [0.78539816 4.58719969] is \n", - " [[ 1.00000000e+00 -1.49011600e-08]\n", - " [-1.49011600e-08 5.00000017e-01]].\n", - "The QFIM at [0.9424778 4.58719969] is \n", - " [[ 1.00000000e+00 -3.05229200e-08]\n", - " [-3.05229200e-08 6.54508507e-01]].\n", - "The QFIM at [1.09955743 4.58719969] is \n", - " [[1. 0. ]\n", - " [0. 0.79389268]].\n", - "The QFIM at [1.25663706 4.58719969] is \n", - " [[ 9.99999881e-01 -1.25257100e-08]\n", - " [-1.25257100e-08 9.04508410e-01]].\n", - "The QFIM at [1.41371669 4.58719969] is \n", - " [[1. 0. ]\n", - " [0. 0.97552822]].\n", - "The QFIM at [1.57079633 4.58719969] is \n", - " [[0.99999988 0. ]\n", - " [0. 0.99999988]].\n", - "The QFIM at [1.72787596 4.58719969] is \n", - " [[9.99999881e-01 5.18176500e-08]\n", - " [5.18176500e-08 9.75528170e-01]].\n", - "The QFIM at [1.88495559 4.58719969] is \n", - " [[1.00000024e+00 4.79417900e-08]\n", - " [4.79417900e-08 9.04508749e-01]].\n", - "The QFIM at [2.04203522 4.58719969] is \n", - " [[1.00000000e+00 6.73742000e-08]\n", - " [6.73742000e-08 7.93892595e-01]].\n", - "The QFIM at [2.19911486 4.58719969] is \n", - " [[1.00000000e+00 8.17192500e-08]\n", - " [8.17192500e-08 6.54508507e-01]].\n", - "The QFIM at [2.35619449 4.58719969] is \n", - " [[0.99999976 0. ]\n", - " [0. 0.49999986]].\n", - "The QFIM at [2.51327412 4.58719969] is \n", - " [[1.0000000e+00 8.1719250e-08]\n", - " [8.1719250e-08 3.4549149e-01]].\n", - "The QFIM at [2.67035376 4.58719969] is \n", - " [[0.99999988 0. ]\n", - " [0. 0.20610746]].\n", - "The QFIM at [2.82743339 4.58719969] is \n", - " [[ 1.00000000e+00 -3.54160700e-08]\n", - " [-3.54160700e-08 9.54916844e-02]].\n", - "The QFIM at [2.98451302 4.58719969] is \n", - " [[0.99999976 0. ]\n", - " [0. 0.02447181]].\n", - "The QFIM at [3.14159265 4.58719969] is \n", - " [[ 1.0000000e+00 -1.2644054e-07]\n", - " [-1.2644054e-07 0.0000000e+00]].\n" + " [0. 0.97552829]].\n", + "The QFIM at [1.88495559 6.02232647] is \n", + " [[1.00000024 0. ]\n", + " [0. 0.9045087 ]].\n", + "The QFIM at [2.04203522 6.02232647] is \n", + " [[ 1.00000000e+00 -1.74251400e-08]\n", + " [-1.74251400e-08 7.93892595e-01]].\n", + "The QFIM at [2.19911486 6.02232647] is \n", + " [[1.00000024 0. ]\n", + " [0. 0.65450875]].\n", + "The QFIM at [2.35619449 6.02232647] is \n", + " [[9.99999762e-01 1.18139420e-07]\n", + " [1.18139420e-07 4.99999863e-01]].\n", + "The QFIM at [2.51327412 6.02232647] is \n", + " [[1.00000024 0. ]\n", + " [0. 0.34549158]].\n", + "The QFIM at [2.67035376 6.02232647] is \n", + " [[1.00000000e+00 4.99490600e-08]\n", + " [4.99490600e-08 2.06107471e-01]].\n", + "The QFIM at [2.82743339 6.02232647] is \n", + " [[1.00000000e+00 3.54160700e-08]\n", + " [3.54160700e-08 9.54915711e-02]].\n", + "The QFIM at [2.98451302 6.02232647] is \n", + " [[9.99999881e-01 4.52859700e-08]\n", + " [4.52859700e-08 2.44718147e-02]].\n", + "The QFIM at [3.14159265 6.02232647] is \n", + " [[1.00000e+00 8.42937e-08]\n", + " [8.42937e-08 0.00000e+00]].\n" ] } ], @@ -447,19 +447,17 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 19, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -513,7 +511,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 20, "metadata": {}, "outputs": [], "source": [ @@ -528,16 +526,16 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "--Ry(3.322)----*----Ry(1.502)--\n", + "--Ry(2.591)----*----Ry(1.165)--\n", " | \n", - "--Ry(2.820)----x----Ry(6.056)--\n", + "--Ry(0.346)----x----Ry(3.989)--\n", " \n" ] } @@ -556,54 +554,54 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 22, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The QFI norm along [1, 1, 1, 1] at [0. 0. 1.50244081 6.05584192] is 6.00315457.\n", - "The QFI norm along [1, 1, 1, 1] at [0.31415927 0.31415927 1.50244081 6.05584192] is 5.91733027.\n", - "The QFI norm along [1, 1, 1, 1] at [0.62831853 0.62831853 1.50244081 6.05584192] is 5.83627391.\n", - "The QFI norm along [1, 1, 1, 1] at [0.9424778 0.9424778 1.50244081 6.05584192] is 5.83150589.\n", - "The QFI norm along [1, 1, 1, 1] at [1.25663706 1.25663706 1.50244081 6.05584192] is 5.92686631.\n", - "The QFI norm along [1, 1, 1, 1] at [1.57079633 1.57079633 1.50244081 6.05584192] is 6.00792258.\n", - "The QFI norm along [1, 1, 1, 1] at [1.88495559 1.88495559 1.50244081 6.05584192] is 5.85534601.\n", - "The QFI norm along [1, 1, 1, 1] at [2.19911486 2.19911486 1.50244081 6.05584192] is 5.38331038.\n", - "The QFI norm along [1, 1, 1, 1] at [2.51327412 2.51327412 1.50244081 6.05584192] is 4.49167993.\n", - "The QFI norm along [1, 1, 1, 1] at [2.82743339 2.82743339 1.50244081 6.05584192] is 3.27580421.\n", - "The QFI norm along [1, 1, 1, 1] at [3.14159265 3.14159265 1.50244081 6.05584192] is 1.98361799.\n", - "The QFI norm along [1, 1, 1, 1] at [3.45575192 3.45575192 1.50244081 6.05584192] is 0.86783892.\n", - "The QFI norm along [1, 1, 1, 1] at [3.76991118 3.76991118 1.50244081 6.05584192] is 0.24795494.\n", - "The QFI norm along [1, 1, 1, 1] at [4.08407045 4.08407045 1.50244081 6.05584192] is 0.26226001.\n", - "The QFI norm along [1, 1, 1, 1] at [4.39822972 4.39822972 1.50244081 6.05584192] is 0.90598547.\n", - "The QFI norm along [1, 1, 1, 1] at [4.71238898 4.71238898 1.50244081 6.05584192] is 2.02176400.\n", - "The QFI norm along [1, 1, 1, 1] at [5.02654825 5.02654825 1.50244081 6.05584192] is 3.31871778.\n", - "The QFI norm along [1, 1, 1, 1] at [5.34070751 5.34070751 1.50244081 6.05584192] is 4.53936095.\n", - "The QFI norm along [1, 1, 1, 1] at [5.65486678 5.65486678 1.50244081 6.05584192] is 5.40715063.\n", - "The QFI norm along [1, 1, 1, 1] at [5.96902604 5.96902604 1.50244081 6.05584192] is 5.87441809.\n", - "The QFI norm along [1, 1, 1, 1] at [6.28318531 6.28318531 1.50244081 6.05584192] is 6.00315457.\n", - "The QFI norm along [1, 1, 1, 1] at [6.59734457 6.59734457 1.50244081 6.05584192] is 5.92209829.\n", - "The QFI norm along [1, 1, 1, 1] at [6.91150384 6.91150384 1.50244081 6.05584192] is 5.83627391.\n", - "The QFI norm along [1, 1, 1, 1] at [7.2256631 7.2256631 1.50244081 6.05584192] is 5.83150589.\n", - "The QFI norm along [1, 1, 1, 1] at [7.53982237 7.53982237 1.50244081 6.05584192] is 5.92686631.\n", - "The QFI norm along [1, 1, 1, 1] at [7.85398163 7.85398163 1.50244081 6.05584192] is 6.00792258.\n", - "The QFI norm along [1, 1, 1, 1] at [8.1681409 8.1681409 1.50244081 6.05584192] is 5.87441809.\n", - "The QFI norm along [1, 1, 1, 1] at [8.48230016 8.48230016 1.50244081 6.05584192] is 5.38331038.\n", - "The QFI norm along [1, 1, 1, 1] at [8.79645943 8.79645943 1.50244081 6.05584192] is 4.48691182.\n", - "The QFI norm along [1, 1, 1, 1] at [9.1106187 9.1106187 1.50244081 6.05584192] is 3.28534056.\n", - "The QFI norm along [1, 1, 1, 1] at [9.42477796 9.42477796 1.50244081 6.05584192] is 1.97884973.\n", - "The QFI norm along [1, 1, 1, 1] at [9.73893723 9.73893723 1.50244081 6.05584192] is 0.87737556.\n", - "The QFI norm along [1, 1, 1, 1] at [10.05309649 10.05309649 1.50244081 6.05584192] is 0.24318658.\n", - "The QFI norm along [1, 1, 1, 1] at [10.36725576 10.36725576 1.50244081 6.05584192] is 0.26702836.\n", - "The QFI norm along [1, 1, 1, 1] at [10.68141502 10.68141502 1.50244081 6.05584192] is 0.90598547.\n", - "The QFI norm along [1, 1, 1, 1] at [10.99557429 10.99557429 1.50244081 6.05584192] is 2.01222750.\n", - "The QFI norm along [1, 1, 1, 1] at [11.30973355 11.30973355 1.50244081 6.05584192] is 3.32348596.\n", - "The QFI norm along [1, 1, 1, 1] at [11.62389282 11.62389282 1.50244081 6.05584192] is 4.52028855.\n", - "The QFI norm along [1, 1, 1, 1] at [11.93805208 11.93805208 1.50244081 6.05584192] is 5.39761453.\n", - "The QFI norm along [1, 1, 1, 1] at [12.25221135 12.25221135 1.50244081 6.05584192] is 5.86965007.\n", - "The QFI norm along [1, 1, 1, 1] at [12.56637061 12.56637061 1.50244081 6.05584192] is 5.99838655.\n" + "The QFI norm along [1, 1, 1, 1] at [0. 0. 1.16512394 3.98858905] is 6.00315457.\n", + "The QFI norm along [1, 1, 1, 1] at [0.31415927 0.31415927 1.16512394 3.98858905] is 5.92209829.\n", + "The QFI norm along [1, 1, 1, 1] at [0.62831853 0.62831853 1.16512394 3.98858905] is 5.83627391.\n", + "The QFI norm along [1, 1, 1, 1] at [0.9424778 0.9424778 1.16512394 3.98858905] is 5.84580996.\n", + "The QFI norm along [1, 1, 1, 1] at [1.25663706 1.25663706 1.16512394 3.98858905] is 5.94117037.\n", + "The QFI norm along [1, 1, 1, 1] at [1.57079633 1.57079633 1.16512394 3.98858905] is 6.00792258.\n", + "The QFI norm along [1, 1, 1, 1] at [1.88495559 1.88495559 1.16512394 3.98858905] is 5.86965007.\n", + "The QFI norm along [1, 1, 1, 1] at [2.19911486 2.19911486 1.16512394 3.98858905] is 5.38807843.\n", + "The QFI norm along [1, 1, 1, 1] at [2.51327412 2.51327412 1.16512394 3.98858905] is 4.49644803.\n", + "The QFI norm along [1, 1, 1, 1] at [2.82743339 2.82743339 1.16512394 3.98858905] is 3.27580421.\n", + "The QFI norm along [1, 1, 1, 1] at [3.14159265 3.14159265 1.16512394 3.98858905] is 1.98838624.\n", + "The QFI norm along [1, 1, 1, 1] at [3.45575192 3.45575192 1.16512394 3.98858905] is 0.86783892.\n", + "The QFI norm along [1, 1, 1, 1] at [3.76991118 3.76991118 1.16512394 3.98858905] is 0.25272329.\n", + "The QFI norm along [1, 1, 1, 1] at [4.08407045 4.08407045 1.16512394 3.98858905] is 0.26702836.\n", + "The QFI norm along [1, 1, 1, 1] at [4.39822972 4.39822972 1.16512394 3.98858905] is 0.90598547.\n", + "The QFI norm along [1, 1, 1, 1] at [4.71238898 4.71238898 1.16512394 3.98858905] is 2.02653225.\n", + "The QFI norm along [1, 1, 1, 1] at [5.02654825 5.02654825 1.16512394 3.98858905] is 3.33302230.\n", + "The QFI norm along [1, 1, 1, 1] at [5.34070751 5.34070751 1.16512394 3.98858905] is 4.52505665.\n", + "The QFI norm along [1, 1, 1, 1] at [5.65486678 5.65486678 1.16512394 3.98858905] is 5.40715063.\n", + "The QFI norm along [1, 1, 1, 1] at [5.96902604 5.96902604 1.16512394 3.98858905] is 5.86965007.\n", + "The QFI norm along [1, 1, 1, 1] at [6.28318531 6.28318531 1.16512394 3.98858905] is 6.00315457.\n", + "The QFI norm along [1, 1, 1, 1] at [6.59734457 6.59734457 1.16512394 3.98858905] is 5.92686631.\n", + "The QFI norm along [1, 1, 1, 1] at [6.91150384 6.91150384 1.16512394 3.98858905] is 5.84580996.\n", + "The QFI norm along [1, 1, 1, 1] at [7.2256631 7.2256631 1.16512394 3.98858905] is 5.85057798.\n", + "The QFI norm along [1, 1, 1, 1] at [7.53982237 7.53982237 1.16512394 3.98858905] is 5.93163433.\n", + "The QFI norm along [1, 1, 1, 1] at [7.85398163 7.85398163 1.16512394 3.98858905] is 6.00315457.\n", + "The QFI norm along [1, 1, 1, 1] at [8.1681409 8.1681409 1.16512394 3.98858905] is 5.87441809.\n", + "The QFI norm along [1, 1, 1, 1] at [8.48230016 8.48230016 1.16512394 3.98858905] is 5.37854233.\n", + "The QFI norm along [1, 1, 1, 1] at [8.79645943 8.79645943 1.16512394 3.98858905] is 4.49167993.\n", + "The QFI norm along [1, 1, 1, 1] at [9.1106187 9.1106187 1.16512394 3.98858905] is 3.29010873.\n", + "The QFI norm along [1, 1, 1, 1] at [9.42477796 9.42477796 1.16512394 3.98858905] is 1.98361799.\n", + "The QFI norm along [1, 1, 1, 1] at [9.73893723 9.73893723 1.16512394 3.98858905] is 0.88691220.\n", + "The QFI norm along [1, 1, 1, 1] at [10.05309649 10.05309649 1.16512394 3.98858905] is 0.25749165.\n", + "The QFI norm along [1, 1, 1, 1] at [10.36725576 10.36725576 1.16512394 3.98858905] is 0.27179672.\n", + "The QFI norm along [1, 1, 1, 1] at [10.68141502 10.68141502 1.16512394 3.98858905] is 0.90598547.\n", + "The QFI norm along [1, 1, 1, 1] at [10.99557429 10.99557429 1.16512394 3.98858905] is 2.02176400.\n", + "The QFI norm along [1, 1, 1, 1] at [11.30973355 11.30973355 1.16512394 3.98858905] is 3.32825413.\n", + "The QFI norm along [1, 1, 1, 1] at [11.62389282 11.62389282 1.16512394 3.98858905] is 4.51552044.\n", + "The QFI norm along [1, 1, 1, 1] at [11.93805208 11.93805208 1.16512394 3.98858905] is 5.39761453.\n", + "The QFI norm along [1, 1, 1, 1] at [12.25221135 12.25221135 1.16512394 3.98858905] is 5.87441809.\n", + "The QFI norm along [1, 1, 1, 1] at [12.56637061 12.56637061 1.16512394 3.98858905] is 6.00315457.\n" ] } ], @@ -629,19 +627,17 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 23, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -682,16 +678,16 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "--Ry(4.207)----*----Ry(2.825)--\n", + "--Ry(5.101)----*----Ry(1.234)--\n", " | \n", - "--Ry(1.769)----x----Ry(4.774)--\n", + "--Ry(5.941)----x----Ry(4.639)--\n", " \n", "The number of parameters is 4.\n", "The EQD is 3. \n", @@ -718,16 +714,16 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "--Ry(1.794)----Rx(3.255)----*----Ry(2.579)----Rx(4.742)--\n", + "--Ry(2.643)----Rx(4.541)----*----Ry(4.525)----Rx(2.093)--\n", " | \n", - "--Ry(1.964)----Rx(1.118)----x----Ry(1.707)----Rx(0.770)--\n", + "--Ry(6.033)----Rx(5.897)----x----Ry(3.874)----Rx(5.445)--\n", " \n", "The number of parameters is 8.\n", "The EQD is 6. \n", @@ -772,12 +768,14 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "import paddle.nn as nn\n", - "from paddle_quantum.gate import IQPEncoding, ComplexEntangledLayer, RX\n", + "from paddle_quantum.ansatz.layer import ComplexEntangledLayer\n", + "from paddle_quantum.gate import IQPEncoding, RX\n", + "from paddle_quantum.loss import ExpecVal\n", "from paddle_quantum.hamiltonian import Hamiltonian\n", "from paddle_quantum.state import zero_state\n", "\n", @@ -787,6 +785,7 @@ " self.num_qubits, self.encoding = num_qubits, encoding\n", " self.S = [[i, i + 1] for i in range(num_qubits - 1)]\n", " self.init_state = zero_state(num_qubits)\n", + " self.loss_func = ExpecVal(Hamiltonian([[1.0, 'z0']]))\n", " \n", " if encoding == 'IQP':\n", " self.complex_layer = nn.LayerList([ComplexEntangledLayer(num_qubits=num_qubits, depth=depth)])\n", @@ -810,7 +809,7 @@ " state = RX(j, param=x[j].item())(state)\n", " state = self.complex_layers[depth](state)\n", "\n", - " return state.expec_val(Hamiltonian([[1.0, 'z0']])) * 0.5 + 0.5" + " return self.loss_func(state) * 0.5 + 0.5" ] }, { @@ -822,14 +821,14 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "running in get_gradient: 100%|##################################| 1000/1000 [00:45<00:00, 22.07it/s]\n" + "running in get_gradient: 100%|##################################| 1000/1000 [00:29<00:00, 33.93it/s]\n" ] } ], @@ -865,7 +864,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -877,14 +876,12 @@ }, { "data": { - "image/png": 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", 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GnZ45AYC9e/fC09MTW7duxT///AO5XI6LFy+iW7dueOuttzBnzhyhUxMREVEzodhupaxm9Wj1o2Inc023W7UxM67QSFC9k3kbM263ImroBK+cVFRQUIAHDx5AIpEIOgRP5bhyQkRETYliu9XtR6scik7mihWQ29kFuJNbBJkG+61MjfRVznUoOpm3e5SE2EhMYGLI7VZEDVWdrpxERETA0dERHTp0AAC0aNECLVq0UBmTmpqKmzdvYvDgwUI+goiIiBq4whLZ40Plik7mFX6/nV2IghLZU+cx0BM9aiZYsY+H6nkPiYkBRCKuehA1dYKSE09PT6xcuRIrVqyocsy3336LFStWqPQ+ISIiosZBViZHZm7h43K6jw6aVzzvcT+/+rYCCm3MjFSrWj3RybyNmTH0ud2KiCAwOdFkJ1hZWRn/hoOIiKgBksvlkBaUqHUvv10h8cjIKdRou1XLitutVBoJlv/e1pzbrYhIc4IPxD/N9evXK+3YTkRERHWrsERWoY+H6nkPxQrIw2LNtlvZSJ5sJKjayVzSgtutiEh7NE5OXn31VZXXhw4dQlJSkto4mUyG1NRUREREYMSIEbUOkIiIiB6TlclxN7eowvaqio0Ey/9vlobbrSxNjZTVrJQHzZX9PVrASsztVkRUvzSu1qWnp/f4TSJRtVu7RCIR+vbti++//x6dO3eufZTNBKt1ERE1b3K5HDkFpRUOlFdsJFh+3uNOTiFKa7DdSlFG98lO5rbcbkVE9Ujr1bpu3rwJoPz/cTo5OeHtt9/GggUL1Mbp6+ujVatWMDU1FRA2ERFR01VYIkPGE93Ln+xknq/Bdit9PRHaSkyq7WRu3sKQ262IqNHRODlxcHBQ/r5792706tVL5RoREVFzVlYmx928ItU+HlLVMx/38jTbbtXa1Eile3m7JxIPa7EJt1sRUZMk6ED8jBkzVF7fv38f+fn5sLe310pQREREDYlcLkdOYalKZav0J1Y9MqSabbdqYaivUlJXcdDc7tFWK1vzFmhhxO1WRNQ8Ca7WJZVKsWLFCuzfvx/37t2DSCRCaWkpAOD8+fNYvXo1PvzwQzz33HNaC5aIiKguFJWWb7e6pVjlUK56PD5onldU+tR5FNutbJWNBFXPe9hZtOB2KyKiaghKTu7fv4+BAwfi2rVr6N27N6ysrBAXF6e87+bmhsjISPzwww9MToiIqMG4n1+M8GuZuJKWU2HbVSHu5RVp9P5WLQ3V+nhU7GRuLTaGgb7e0yciIqJKCUpOVq1ahWvXrmH//v2YPHkyVq9ejTVr1ijvt2jRAh4eHjh16pTWAiUiIqopuVyOhDu5OBmXiVPxmbic8gBV7bwyMdSr0L1cvZN5O263IiKqc4KSkyNHjmD06NGYPHlylWMcHR1x9uxZwYEREREJUVgiw7kbWTj1KCG5lV2gcr+brQQDO1miQ+uWKqV2LVpyuxURka4JSk7S09Ph5+dX7RhjY2Pk5+cLCoqIiKgmMqSFCEvIxMm4TET+ew8FJY/L8Rob6GFQ5zbwcrGGp4s17Cxa6DBSIiKqjqDkxNLSEqmpqdWOiY+Ph62traCgiIiIqlNWJsfft6Q4FXcHJ+MzcfV2jsr9thITeHWzhreLNQZ2asPtWEREjYSg5GTw4ME4fPgw0tLS0L59e7X7sbGx+P333zFz5sxaB0hERAQAeUWlOHP9Lk7GZSIs4a7KIXaRCOhlbwHvR6sj3W0l3KJFRNQICUpO3n//fRw+fBiDBg1CQEAA7t27BwCIi4vD2bNn8f7778PY2BjvvPOOVoMlIqLmJTkrH6fiy8+ORN3IQons8Wl2M2MDDO7SBl4uNhjS1QptzIx1GCkREWmDSC6XP71jVCWOHDmCadOmIS8vD0B5RRSRSAS5XA6xWIx9+/Zh5MiRWg22qcvJyYG5uTmkUikkEomuwyEiqnclsjJcSn6gTEj+zcxTue9o2RJeLjbw7maNvo6tYWTAsr1ERI2Bps+5gpswjhkzBjdv3kRQUBDOnz+P+/fvQyKRoH///pg5cybatGkjdGoiImpGHuQXI/zaXZyMz0R4QiZyCh83OzTQE6GvY2t4d7OGl4s1nKzMdBgpERHVNcErJ6R9XDkhouZALpfjembeo94jd3ApWbX3SKuWhvDsag2vbtZ4wdkK5i0MdRcsERFpRZ2vnBAREWmqsESGqBtZyu1aaQ9Ue4+4tBXDy8Ua3t2s0cu+FfT1eJidiKg5qlVyEhMTg7/++gu3b99GSUmJ2n2RSITly5fX5iOIiKiRupNTiLD4TJyMz8SZ66q9R4wM9DCokyW8utnAi71HiIjoEUHbujIzMzF16lSEhYUBKF+ir3RykQgymazSe6SO27qIqDErK5Pjn9vSR9u1MnHlllTlvo3EuPwwu4s1Bna2REsjLt4TETUXdbqt6//+7/9w6tQpjBw5En5+frC1tYWBAf8jQ0TU3OQXleKP6/dwKv4OTsWr9h4BgJ6Peo94uVijRzv2HiEiouoJyiiOHTsGT09PHD16VNvxEBFRA5eS9RCn4ss7s5+/cR/FsjLlPVMjfQzuYgUvF2sM6WoNKzF7jxARkeYEJSeGhoZ47rnntB0LERE1QKWyMvyZko2T8XdwKi4T15/oPdKhdUt4d7OGt4sN+nZsBWMDfR1FSkREjZ2g5OSFF15ATEyMlkMhIqKGIvthee+RU/GZOJ1wF9KCx0VP9PVE6OPQ6lHvERt0sjLldi0iItIKQcnJunXrMGjQIGzduhVvvPGGtmMiIqJ6JpfL8W9mHk7GZ+JUXCYuJt9X6T1ioeg94mKNwc5WMG/J3iNERKR9gpswXr16FS+88ALatGkDNze3Sk/di0Qi7Ny5s9ZBNhes1kVE9amoVIbzN+7jVHwmTsbfQep91d4jXW3E8OpmDW8Xazzbgb1HiIhIOE2fcwUlJzdv3sTw4cORmJhY7TiWEq4ZJidEVNcycwoRllBe6veP6/fwsFi198gAJ0t4d7OGZ1dr2LduqcNIiYioKanTUsJvvvkmEhMTMW/ePLz88sssJUxE1ECVlclx9XZO+WH2+Ez8nabae8RabKw8OzKIvUeIiEjHBP1XKCIiAr6+vvjiiy+0HQ8REdVSflEpIv+9h1Px5SskmblP9B5pb17eDLGbNbrbSqDH7VpERNRACEpOjI2N0aVLF23HQkREAqXef/jo7Egmom5kobj0ce+Rlkb6eMG5DbxdbDDExQrWYhMdRkpERFQ1QcnJsGHDcPbsWW3HQkREGiqVleFyajZOxmXiVPwdXLuj2nvEvnULeLvYwMvFGv2dWrP3CBERNQp6Qt60YcMGpKen45133kFhYaG2YwIAREdHY+TIkbCwsICpqSnc3d1x4MCBGs+TmZmJhQsXwtnZGSYmJrC0tMSAAQOwfft2tbGFhYX48MMP0b17d5iYmKBVq1YYMWIEIiMjK53b398fIpGoyh8iIm2SPizBkb9u4+39l9Fn7QlM+vIcvgxPxLU7edDXE6Ffx9ZYOsIFJxYNRsQ7nlg1pgcGd7FiYkJERI2GoJWTV155Bebm5ti0aRO+/vprODs7V1lK+OTJkzWePywsDD4+PjAxMYGfnx/EYjFCQkIwZcoUpKamYvHixRrNExMTg+HDh+PBgwcYNWoUJk6ciLy8PMTFxeHnn3/GvHnzlGMLCwvh7e2Ns2fPws3NDfPmzUN2djZCQkLg4eGBkJAQjB07ttLPWbBgASwsLGr8PYmIqiOXy5F4N+/R6kgmLiY/gKxC8xHzFoYY0tUKXi7W8OhiBYuWRjqMloiIqPYElRLW09NswUVIKeHS0lK4uLggLS0NUVFR6NWrFwBAKpWiX79+SEpKwrVr1+Dg4FDtPDk5OXB1dUVBQQFOnDgBNzc3tc+pWGFsw4YNeOeddzBp0iTs27cP+vrlf9OYmJiI3r17w9jYGImJiRCLxcr3+Pv7IygoCDdv3oSjo2ONvmdVMbOUMFHzVlQqw4Wb95UJScr9hyr3u9iYKQ+zP2tvAQN9QQvgRERE9apOSwmXlZU9fZBAp06dQmJiImbOnKlMTADA3Nwcy5YtUyYEK1asqHaebdu2ISUlBTt37lRLTAColT4+fPgwAGDVqlXKxAQAOnXqhFdffRWfffYZDh48iJkzZ9bi2xERqbubW1TeeyQuE39cv4v8ir1H9PXg3skS3i7l3dnZe4SIiJqyBlfQ/vTp0wCA4cOHq93z8fEBAISHhz91nuDgYIhEIkyYMAEJCQkIDQ1FQUEBXFxc8OKLL8LISHX7Q0ZGBgCgY8eOanMprp06darS5OTo0aPIzc2FsbExunXrBm9vb7X5iYgU5PLy3iOK6lp/pWar3LcSG8OrqzW8ulnj+c5tYGrc4P5fNRERUZ1ocP/Fu379OgDA2dlZ7V7btm1hZmamHFOV4uJiXLlyBVZWVtiyZQtWrlypstrj5OSEQ4cOwdXVVXmtTZs2+Pfff3Hz5k10795dZb6bN28CAK5du1bp57355psqr21tbbF7925lMlWVoqIiFBU97j+Qk5NT7XgiarweFpci8t8snHrUDPFOjmrvEbf25vBysYa3iw16tGPvESIiap5qlZykpaUhLCwMt2/fVnnIVhCJRFi+fHmN5pRKy7sXm5ubV3pfIpEox1Tl/v37kMlkyMrKwpo1a7B+/XpMmzYNJSUl+Oqrr/DRRx/B19cX8fHxMDEpr/c/YsQIREVFYc2aNfjhhx+UW7tu3ryJ3bt3AwCys7NVPmfw4MEYNWoU3N3dYWVlhbS0NOzbtw/r1q3DmDFjEBkZiT59+lQZ57p167B69WqN/lyIqPFJe/AQYY9WR84mqvceeb5zG3h3s4ZnV2tYS9h7hIiISNCBeAB45513sHnzZpUD73K5XFlCV/F7TQ/EDx8+HMePH8f169fRuXNntft2dnbIy8urNkG5ffs27OzsAJRX0vrss89U7k+ZMgUHDhzAd999h1deeQUAkJubC3d3d8TGxqJnz57w8vJSVutydHTE33//DRcXF8TFxT31O+zatQuzZs2Cr68vjhw5UuW4ylZO7O3teSCeqJGSlclxOeWBsjN7fEauyv32rVqUnx3pZoP+HVvDxJAlfomIqHmo0wPx33zzDTZu3Ihhw4Zh7ty5mDBhAvz9/eHj44OIiAjs2LED48aNw/z582s8t2LFpKrkIycnB61atdJoDgAYM2aM2v0xY8bgwIEDuHjxojI5EYvFiIyMxJo1a/DTTz9h69atsLa2xty5czF69GgMHjwY1tbWGn2HGTNm4P/+7/+q7I+iYGxsDGNjY43mJKKGSVpQgohrd3EqPhOnEzLx4GGJ8p6eCOjj0Bpe3coPsztbm7EHEhERUTUEJSdff/01HB0d8dtvvynLCjs6OmLKlCmYMmUKJk+ejGHDhmHSpEk1nltx1uT69et47rnnVO5lZGQgLy8P/fr1q3YOU1NT2NnZ4datW5X2H1FcKygoULu+adMmbNq0SeX6nj17AKDaLVoV6evrw8LCAg8ePNBoPBE1HnK5HDfu5eNUXCZOxt9BdJJq7xGJiQGGdLWGdzf2HiEiIqopQclJfHw8pk2bptLvpLS0VPm7h4cHRo0ahQ0bNmDixIk1mtvDwwPr1q1DaGgo/Pz8VO4dO3ZMOeZpvLy88N133yE2Nha9e/dWuRcbGwsAGvcm+eGHHwBALZ6qpKSkICMjA127dtVoPBE1bMWlZeW9R+LvICw+E0lZqr1HOlubKUv9PufQir1HiIiIBBJ8IL7iioSpqSmysrJU7nft2hUnTpyo8bze3t5wcnLC3r178dZbb6k0YQwICICRkRGmT5+uHJ+eng6pVApbW1uV7Vxz587Fd999h8DAQIwePVoZb0ZGBjZv3gw9PT1MmDBB5bNzcnLU9sB9+umnOHHiBMaPH4++ffsqr2dkZEAmkynPtihkZ2fD398fADB16tQaf38iahju5RUh7NHZkT+u30Ne0eO/gDHS10N/p9aPEhIbdLBk7xEiIiJtEJSc2NnZIS0tTfm6U6dOOH/+vMqYf/75B6ampjUPyMAAO3bsgI+PDwYPHgw/Pz+IxWKEhIQgOTkZGzZsUFnxWLp0KYKCgrB7925lUgAAAwcOxKJFi7Bp0ya4ubnB19cXJSUlOHz4MDIzMxEQEIAuXbqofS9PT084OztDJBLh9OnTuHTpEvr06YOdO3eqjI2Pj8ewYcMwcOBAODs7w8rKCqmpqfj999+RlZUFLy8vLFmypMbfn4h0Qy6XIzY959F2rUz8lZaNiuVC2pgZw8vFCl4uNnjeuQ3M2HuEiIhI6wT913XQoEH4448/lK/Hjh2Ljz76CHPmzMGYMWNw5swZ/Pbbb2orE5ry9PTEmTNnsHLlSgQHB6OkpASurq74+OOPMWXKFI3n2bhxI1xdXfHFF19gz549EIlEePbZZ/Hll19i/PjxauNfeeUVhIWF4eTJkxCJROjSpQs++eQTvPnmm2oH1zt16gR/f39ER0fj0KFDkEqlMDMzg5ubG6ZOnYrZs2erdJonooanoFiGs4n3cDK+vDt7Rk6hyv1n7CTwcrGBt4s1XO3M2XuEiIiojgkqJXz69Gl8/PHH+PLLL+Hg4IC8vDx4eHjg8uXLEIlEkMvlcHR0RFhYGBwcHOoi7iZJ0xJrRCTcreyC8lK/cXdwNjELRRV6j7Qw1Mfzzm3g7WINTxdr2LD3CBERkVZo+pwruM/JkxRbphITE+Hg4ABfX19B27qaMyYnRNonK5MjJjUbp+Lv4GSceu8RO4sW8H5U6tfdyZK9R4iIiOpAnfY5iYiIgEQiUR5WBwBDQ8MaV+YiIqoLOYUVe4/cxf38YuU9PRHQu0MreHWzhreLDbrYsPcIERFRQyEoOfH09MScOXOwbds2bcdDRCTIjbt5OBWfiZNxmYhOuo/SCr1HxIreIy7lvUdambL3CBERUUMkKDmxtraGiQn3YhOR7hSXluFi0v3yw+zxmbh5L1/lficrU3h3s1H2HjFk7xEiIqIGT1ByMmzYMJw+fRpyuZzbIYio3mTlFeF0Qvl2rYhrd5FbofeIob4I/TtawutRM0THNjzzRkRE1NgIOhB/+/ZtDBgwAMOHD8fHH3+M1q1b10VszQ4PxBOpksvliEvPLT/MHp+JmNQne48YwbOrNby7WeN5Zyv2HiEiImqg6rRal5eXF7KysvDPP//AyMgIHTt2hI2NjdoqikgkwsmTJ2sefTPF5IQIKCx51Hskrny7VrpUtfdIj3aS8s7s3Wzgxt4jREREjUKdJid6eprt3RaJRJDJZDWdvtlickLNVbpU0XskE5GJ91BY8rj3iImhHp7v3AZeLuXnR9qa87wbERFRY1OnpYTLysqePoiIqAqyMjn+SsvGqbhMnIzPRFx6jsp9O4sW5WdHulljAHuPEBERNRvcoE1E9SK3sAR/XC/frnU6IRNZFXqPiBS9R1zKz490tRGz2AYREVEzxOSEiOpM0r38R6V+7+D8jSd6jxgbYHBXK3i7WGNIV2u0Zu8RIiKiZq9WyUlaWhrCwsJw+/ZtFBUVqd0XiURYvnx5bT6CiBqRElkZopPu49Sjw+w3nug94mRlWn6Y3cUGfRzZe4SIiIhUCToQDwDvvPMONm/erHLgvWLfE8XvPBCvOR6Ip8bofn4xTieUnx2JSFDtPWKgJ0J/p9bKw+wd2XuEiIioWarTA/HffPMNNm7ciGHDhmHu3LmYMGEC/P394ePjg4iICOzYsQPjxo3D/PnzBX8BImqY5HI54jNyy6trxWfiz5QHKr1HLE2NMETZe6QNJCaGuguWiIiIGhVBycnXX38NR0dH/Pbbb8qywo6OjpgyZQqmTJmCyZMnY9iwYZg0aZJWgyUi3SgskeFcYhZOxt/BqbhM3H6i90h3Wwm8u5V3Zu/Z3oK9R4iIiEgQQclJfHw8pk2bptLvpLT08VYODw8PjBo1Chs2bMDEiRNrHyUR1bsMaeGj1ZE7OPOvau8RY4NHvUe6WcOzqzXaWbTQYaRERETUVAg+EG9hYaH83dTUFFlZWSr3u3btihMnTggOjIjqV9mj3iNh8eXnR67eVu090s7cBJ6PSv0OcGqDFkbsPUJERETaJSg5sbOzQ1pamvJ1p06dcP78eZUx//zzD0xNefiVqCHLLSzBmev3cDK+vPfIvTzV3iPP2lvAu1v5YXaXtuw9QkRERHVLUHIyaNAg/PHHH8rXY8eOxUcffYQ5c+ZgzJgxOHPmDH777TdMmDBBa4ESkfak3n+Itb/E4WT8HZTInug90sUKXi7WGNLVCpZmxjqMkoiIiJobQaWET58+jY8//hhffvklHBwckJeXBw8PD1y+fBkikQhyuRyOjo4ICwuDg4NDXcTdJLGUMNW1ElkZdp65ic9OXFOeIenYxrS8M7uLNfo4toaRAXuPEBERkXZp+pwruM/Jk0pKSnD48GEkJibCwcEBvr6+3NZVQ0xOqC79mfIAy368gviMXABA/46tsWpMD3Sz5b9rREREVLfqtM9JZQwNDVmZi6gByikswSe/J+D788mQywGLloZ4f2Q3THyuPc+QEBERUYNS6+QkKysLf/31F6RSKczNzdGzZ09YWlpqIzYiqgW5XI7f/snAqiNXkZlbBACY0Ls9lo104VkSIiIiapAEJydJSUlYsGABfvnlF1TcGSYSiTB69Gh89tlncHR01EaMRFRDqfcfYuWRqzgVnwmg/FzJ2nHPYGDnNjqOjIiIiKhqgpKTxMREDBo0CJmZmXB2dsagQYNgY2ODO3fu4OzZszhy5AiioqJw9uxZODk5aTtmIqpCqawMuyJv4tPj11FQIoOhvgjzhnTG/CGdYGLIviRERETUsAlKTt59913cvXsXX375JV577TWVfetyuRxff/015s+fj3fffRf/+9//tBYsEVUtJjUbS3+8grj08uaJ/Tq2RsD4Z9DZWqzjyIiIiIg0I6haV6tWrTBkyBD89NNPVY4ZO3YsIiIi8ODBg1oF2JywWhcJkVtYgg3HEvBt1OMD78tGlB9419PjgXciIiLSvTqt1iWTydCjR49qxzzzzDMICwsTMj0RaUAul+P3fzKw6ueruJNTfuD9pWft8P6objzwTkRERI2SoOSkd+/euHr1arVjrl69ij59+ggKioiqdyu7ACsP/4MTceUH3h0tW2LteFcM4oF3IiIiasQEJSdr166Ft7c3duzYgdmzZ6vd//rrr3Hs2DGcPHmy1gES0WOlsjLsOZuETcev4WHxowPvHp0w37MzD7wTERFRoyfozMmaNWtw7tw5hIaGokuXLirVuiIjI3Ht2jX4+PjA3d1d9cNEIixfvlxrwTc1PHNC1fnr0YH32EcH3vs6tkLAeFc42/DAOxERETVsmj7nCkpO9PT0BAUlEokgk8kEvbc5YHJClcktLMHG0GsIOpcEuRwwb2GIZSNdMOk5ex54JyIiokahTg/E86A7Ud2Ty+U4dvUOVh25ioycQgDAuF7t8MHo7mjDA+9ERETUBAlKTjw8PLQdBxFVUH7g/SpOxN0BADhYtsRH457BC85WOo6MiIiIqO4ISk6IqG5UduB9zuBOeMOLB96JiIio6WNyQtRAXEmTYulPf+OfW+UH3vs4tELAS67owgPvRERE1EwwOSHSsbyiUmwMTUDQ2SSUyQGJiQGWjeyGyX144J2IiIiaF2Flt+pBdHQ0Ro4cCQsLC5iamsLd3R0HDhyo8TyZmZlYuHAhnJ2dYWJiAktLSwwYMADbt29XG1tYWIgPP/wQ3bt3h4mJCVq1aoURI0YgMjKyyvnT09Mxa9Ys2NrawsTEBF27dsXatWtRUlJS41ip+Qm9moFhm8KxO7I8MRnbqx1OLh4Cv34dmJgQERFRsyOolHBdCwsLg4+PD0xMTODn5wexWIyQkBAkJydjw4YNWLx4sUbzxMTEYPjw4Xjw4AFGjRqFbt26IS8vD3FxcTAyMsKvv/6qHFtYWAhvb2+cPXsWbm5u8PLyQnZ2NkJCQvDw4UOEhIRg7NixKvNnZGSgX79+SEtLw/jx4+Hs7Izw8HBERUVhzJgxOHToEEQizR8wWUq4+SgqlWHJwb9xOOY2AKBD6/ID74O78MA7ERERNT1a7XOSk5MDExMTGBkZaTXIypSWlsLFxQVpaWmIiopCr169AABSqRT9+vVDUlISrl27BgcHh6fG7OrqioKCApw4cQJubm5qn2Ng8HhX24YNG/DOO+9g0qRJ2LdvH/T1yw8fJyYmonfv3jA2NkZiYiLE4sf7/2fMmIFvv/0W27dvx9y5cwGUl3+dOnUq9u/fj7179+Lll1/W+LszOWkeHhaXYs53l/DH9Xsw0BPh9cFOeMvbmQfeiYiIqMnS9DlXo21drVq1wscff6x8/eqrr+LIkSO1j7ISp06dQmJiIqZOnapMTADA3Nwcy5YtQ3FxMYKCgp46z7Zt25CSkoLAwEC1xASASmICAIcPHwYArFq1SpmYAECnTp3w6quv4u7duzh48KDyem5uLoKDg+Hk5IQ5c+Yor4tEIgQGBgIAvvnmG82+NDUbOYUlmL7zAv64fg8tDPWxZ2Y/LHnRhYkJERERETRMTkQiEcrKypSv9+zZg5iYmDoJ6PTp0wCA4cOHq93z8fEBAISHhz91nuDgYIhEIkyYMAEJCQnYsmUL1q9fjyNHjqC4uFhtfEZGBgCgY8eOavcU106dOqW8du7cORQVFWHYsGFqW7ccHBzQtWtXREZGQiaTPTVWah6y8orw8tdRuJj8ABITA3w/uz+ed26j67CIiIiIGgyNqnW1a9cO//77b13HAgC4fv06AMDZ2VntXtu2bWFmZqYcU5Xi4mJcuXIFVlZW2LJlC1auXKmSXDk5OeHQoUNwdXVVXmvTpg3+/fdf3Lx5E927d1eZ7+bNmwCAa9euaRSn4npCQgKSk5Ph5ORU6ZiioiIUFRUpX+fk5FT7vajxSpcW4JUd55F4Nx+Wpkb4dlY/9GhnruuwiIiIiBoUjZITT09P/PDDD7h37x5sbW0BAIcOHUJSUlK17xOJRNi5c2eNApJKpQDKt3FVRiKRKMdU5f79+5DJZMjKysKaNWuwfv16TJs2DSUlJfjqq6/w0UcfwdfXF/Hx8TAxMQEAjBgxAlFRUVizZg1++OEH5daumzdvYvfu3QCA7OzsGsVZcVxl1q1bh9WrV1f7XajxS87Kx392nEfagwLYmpvg+9n90cnKTNdhERERETU4GiUn69evx507d3D8+HGUlZVBJBIhJibmqVu7hCQn2qBYJZHJZHjjjTdUqnutWbMGCQkJOHDgAA4ePIhXXnkFALBw4UIEBwcjODgY8fHxKtW6HB0d8ffff0NPT7uVl5cuXYpFixYpX+fk5MDe3l6rn0G6lZCRi2k7zyMztwiOli3x/ez+aN+qpa7DIiIiImqQNHratrGxwe+//46CggIkJSVBLpfj7bffxs2bN6v9uXHjRo0DUqxEVLXioDjpr8kcADBmzBi1+4prFy9eVF4Ti8WIjIzEwoULIZVKsXXrVoSGhmLu3LnYunUrAMDa2rpGcT4Zy5OMjY0hkUhUfqjp+Cs1G1O+PofM3CK4tBXjwNwBTEyIiIiIqlGjDvGGhobo0KEDPDw80KtXr6eW8xVCcYbj+vXreO6551TuZWRkIC8vD/369at2DlNTU9jZ2eHWrVuwsLBQu6+4VlBQoHZ906ZN2LRpk8r1PXv2AAD69OlTaZyVuX79OoyMjNChQ4dqY6Wm6VxiFmYHRSO/WIZe9hbYM7MvLFrWfSluIiIiosZM0D6lsLAwTJ8+XduxAAA8PDwAAKGhoWr3jh07pjKmOl5eXgCA2NhYtXuKa46OjhrF9MMPPwAA/Pz8lNfc3d1hZGSE48eP48lWMcnJyUhISMCgQYPUShZT03cq/g78d19AfrEMAztZ4vvZ/ZmYEBEREWmgVoco8vPz8cMPP+Cdd97BnDlz8M477+CHH35Afn6+4Dm9vb3h5OSEvXv3qpxpkUqlCAgIgJGRkUpilJ6ejvj4eLXtVYqmiIGBgSoH2TMyMrB582bo6elhwoQJKu+prFrWp59+ihMnTmD8+PHo27ev8rpEIoGfnx9u3LiBr776SnldLpdj6dKlAIDXXnut5n8A1Kj9/NdtvP7tJRSVlmFoN2vs8u8LM2MmqERERESa0KhDfGVCQkLw+uuvIzs7W2XlQCQSwcLCAt988w1eeuklQUGFhYXBx8cHJiYm8PPzg1gsRkhICJKTk7FhwwaVA+7+/v4ICgrC7t274e/vrzLP4sWLsWnTJtjb28PX1xclJSU4fPgwMjMzERAQoEwiFMRiMTw9PeHs7AyRSITTp0/j0qVL6NOnD0JDQ9GqVSuV8enp6ejfvz/S0tLw0ksvoXPnzggPD0dUVBR8fX1x+PBhtR4o1WGH+MZt/4UULP3pCuRyYGyvdtgwqScM9bVbRIGIiIioMdL0OVdQcnL27Fl4eHhAX18fM2bMgKenJ2xtbZGRkYGwsDAEBQVBJpMhPDwcAwYMEPQFLly4gJUrV+Ls2bMoKSmBq6srFi1ahClTpqiMqy45AcrPi3zxxReIjY2FSCTCs88+i0WLFmH8+PFqY+fNm4ewsDCkpqZCJBKhS5cumDp1Kt58800YGxtXGmd6ejo++OAD/PLLL3jw4AEcHBwwffp0LFmyBEZGNdvKw+Sk8drxxw189EscAGBq/w74cOwz0NfTPDElIiIiasrqNDkZPXo0Tp8+jcjISPTs2VPt/t9//42BAwfC09MTP//8c02nb7aYnDQ+crkcn564js9PlhdGmOPhhPdedKnRihkRERFRU6fpc66gPSfnzp3DlClTKk1MAMDNzQ2TJ0/G2bNnhUxP1CiUlcmx5misMjF5x6crExMiIiKiWhB0Uvfhw4ewsbGpdoyNjQ0ePnwoKCiihk5WJsd7IX/jf5fSAACrx/TAjIGOug2KiIiIqJETtHLi6OiI48ePVzvm5MmTGpfqJWpMikvL8Na+y/jfpTToiYCNk3oyMSEiIiLSAkHJyeTJk3Hp0iXMmDEDt2/fVrmXnp4Of39/XLp0Se3wOlFjV1Asw+vfXcQvV9JhqC/Ctv/0xoTn2us6LCIiIqImQdCB+IcPH8LT0xPR0dEwMjJC586dYWNjgzt37uDff/9FcXEx+vXrh7CwMLRo0aIu4m6SeCC+YcstLMGsPRdxIek+TAz18PW0PhjcxUrXYRERERE1eHV6IL5ly5aIiIjAqlWr0L59e8TGxiIsLAyxsbFo3749Vq9ejfDwcCYm1GTczy/G1G/O40LSfYiNDfD9rP5MTIiIiIi0THATxopyc3ORk5MDiUQCsVisjbiaJa6cNEwZ0kJM23ke1zPz0NrUCN++2g/P2JnrOiwiIiKiRkPT51xB1bqeJBaLmZRQk5SS9RD/2RmF1PsFaCsxwfez+6OztZmuwyIiIiJqkrSSnBA1Rdfv5OI/O84jM7cIDpYt8f2s/rBv3VLXYRERERE1WUxOiCpxJU2K6bvO48HDEnS1EeO7Wf1gLTHRdVhERERETRqTE6InnL+RhVlBF5FXVIqe7c0R9Go/WLQ00nVYRERERE0ekxOiCsISMjH3u0soKi1D/46tsdO/L8yM+T8TIiIiovrApy6iR375Ox1vB19GiUwOLxdrbPtPb5gY6us6LCIiIqJmQ1Cfk2+//RbHjh3TdixEOnMgOhVv7vsTJTI5fHu2w1fTnmNiQkRERFTPBCUns2bNwu+//67tWIh0YueZm1gS8jfK5MDL/ezx2ZReMNQX9D8NIiIiIqoFQdu6bG1tUVpaqu1YiOqVXC7H5yf/xacnrgEAXh/shKUjXCASiXQcGREREVHzJCg5GTNmDI4fP46ioiIYGxtrOyaielExMVk8rAve8OrMxISIiIhIhwTtXVm7di1MTU3x0ksv4erVq9qOiajOXb0txeenrgMAVozujje9nZmYEBEREemYoJWTZ599FkVFRYiJicHvv/8OExMTWFtbqz3ciUQiJCYmaiVQIm2Rlcmx7Kd/ICuTY5SrLV59vqOuQyIiIiIiCExOysrKYGRkhA4dOqhcl8vl1b4magj2XkjBX6nZEBsbYIVvd12HQ0RERESPCEpOkpKStBwGUf3IzC3E+t/jAQD/9ekKG4mJjiMiIiIiIgXWS6Vm5cOjccgtLIVbe3O84u6g63CIiIiIqIJad4iPjY1FfHw88vPzMW3aNG3ERFQnIq7dxc9/3YaeCAgY7wp9PR6AJyIiImpIBK+cREdHo1evXnB1dcWkSZPg7++vvBcREYGWLVviyJEj2oiRqNYKS2RYfvgfAMCMgY54xs5cxxERERER0ZMEJSdXr16Fl5cXbt68iYULF2LEiBEq91944QW0adMG//vf/7QSJFFtfRH2L5KzHqKtxASLh3fVdThEREREVAlBycnKlSsBAJcuXcKGDRvQt29flfsikQgDBgxAdHR07SMkqqV/M3PxZXh5SeuVvt1hZlzr3YxEREREVAcEJSfh4eGYMGECOnfuXOWYDh06ID09XXBgRNogl8vx/k//oEQmh5eLNV58pq2uQyIiIiKiKghKTnJzc2FtbV3tmIKCAshkMkFBEWlLyJ+3cP7mfZgY6mH1mB7sAk9ERETUgAlKTuzt7XHlypVqx/z555/o1KmToKCItOFBfjECfo0DALw9tAvsW7fUcUREREREVB1Bycno0aMRGhqKEydOVHr/wIEDiIqKwrhx42oTG1GtrPstDvfzi9HVRoxZz3fUdThERERE9BSCTgYvW7YMBw8exMiRIzFjxgxkZGQAALZt24Zz585h3759cHR0xKJFi7QaLJGmLty8jwMX0wAAAS89A0N99hslIiIiaugEJSdWVlYIDw/HtGnTsHPnTuX1N954AwDQv39/7Nu3D+bm7CVB9a+4tAzv/1S+7fDlfvZ4zqG1jiMiIiIiIk0Irqnq5OSEyMhIxMTEICoqCvfv34dEIkH//v3VSgsT1adv/riB65l5sDQ1wrsvuug6HCIiIiLSUK0bPvTq1Qu9evXSQihEtZeS9RCfn7wOAHh/VDdYtDTScUREREREpKlaJydZWVn466+/IJVKYW5ujp49e8LS0lIbsRHViFwux/LD/6CotAwDO1li/LN2ug6JiIiIiGpAcHKSlJSEBQsW4JdffoFcLldeF4lEGD16ND777DM4OjpqI0Yijfx6JQPh1+7CSF8PH457hj1NiIiIiBoZQclJYmIiBg0ahMzMTDg7O2PQoEGwsbHBnTt3cPbsWRw5cgRRUVE4e/YsnJyctB0zkZqcwhKs/vkqAGDekE7oZGWm44iIiIiIqKYE1Vd99913cffuXXz55ZeIj4/Hrl27sG7dOuzatQtxcXHYvn077t69i3fffVdwYNHR0Rg5ciQsLCxgamoKd3d3HDhwoMbzZGZmYuHChXB2doaJiQksLS0xYMAAbN++XW1saWkpdu3ahQEDBsDKygpisRjdu3fHkiVLlOWSK/L394dIJKryh+rPxmMJyMwtQsc2ppg3hM0/iYiIiBojQSsnJ0+exJgxY/D666+r3ROJRJgzZw5+/fXXKps0Pk1YWBh8fHxgYmICPz8/iMVihISEYMqUKUhNTcXixYs1micmJgbDhw/HgwcPMGrUKEycOBF5eXmIi4vDzz//jHnz5qmMnzJlCn788Ud07twZfn5+MDY2RlRUFD755BN8//33+PPPP9G2bVu1z1mwYAEsLCwEfVeqvb9Ss/FtVDIA4MOxz8DEUF/HERERERGREIKSE5lMhh49elQ75plnnkFYWFiN5y4tLcVrr70GPT09REREKCuBrVixAv369cOyZcswceJEODg4VDtPTk4Oxo4dCwC4dOkS3Nzc1D6nogsXLuDHH39Ev379cObMGRgaGirvLViwAJ9//jm+/vprrFixQu2z3n77bZ6v0ZFSWRmW/XQFcjkwrlc7PO/cRtchEREREZFAgrZ19e7dG1evXq12zNWrV9GnT58az33q1CkkJiZi6tSpKiWKzc3NsWzZMhQXFyMoKOip82zbtg0pKSkIDAxUS0wAwMBANS+7ceMGAGDo0KEqiQkAjB49GgBw9+7dmn4dqmPfnkvG1ds5kJgY4P1R3XUdDhERERHVgqCVk7Vr18Lb2xs7duzA7Nmz1e5//fXXOHbsGE6ePFnjuU+fPg0AGD58uNo9Hx8fAEB4ePhT5wkODoZIJMKECROQkJCA0NBQFBQUwMXFBS+++CKMjFT7XyhWgk6cOIFVq1apJChHjx4FAHh7e1f6WUePHkVubi6MjY3RrVs3eHt7q81P2pcuLcDG0AQAwLsjXGAlNtZxRERERERUGxolJ2vWrFG75unpiTlz5mDjxo0q1boiIyNx7do1+Pj44OTJkxg4cGCNArp+vbyBnrOzs9q9tm3bwszMTDmmKsXFxbhy5QqsrKywZcsWrFy5EmVlZcr7Tk5OOHToEFxdXZXXXF1dsWDBAmzevBndu3fHiBEjYGxsjHPnzuHSpUtYvXo1xo0bV+nnvfnmmyqvbW1tsXv3bmUyVZWioiIUFRUpX+fk5FQ7nlStPhKL/GIZenewwMt9O+g6HCIiIiKqJZG8YpOSKujpCdr9BZFIBJlMVqP3DB8+HMePH8f169fRuXNntft2dnbIy8uDVCqtco6MjAzY2tpCX18fenp6WLduHaZNm4aSkhJ89dVX+Oijj9ChQwfEx8fDxMRE5b2bN2/GO++8g5KSEuU1X19fBAQE4JlnnlEZu2vXLojFYri7u8PKygppaWnYt28f1q1bB5lMhsjIyGq3tq1atQqrV69Wuy6VSiGRSKp8HwEn4+5gVtBF6OuJcPTN59HNln9eRERERA1VTk4OzM3Nn/qcq1Fyosk2qqp4eHjUaLw2kpPbt2/Dzq68O/iCBQvw2WefqdyfMmUKDhw4gO+++w6vvPIKAKCsrAxz587Fvn37sGHDBowdOxYtW7ZEZGQk3nrrLaSnpyMsLAx9+/Z96nfYtWsXZs2aBV9fXxw5cqTKcZWtnNjb2zM5eYqHxaUYtikCt7ILMGewE5aO7KbrkIiIiIioGpomJxpt66ppglEb5ubmAFBl8pGTk4NWrVppNAcAjBkzRu3+mDFjcODAAVy8eFGZnOzatQvffPMNNm/ejDlz5ijHjhgxAgcPHkSvXr2wbNkyHD9+/KnfYcaMGfi///s/REZGVjvO2NgYxsY8J1FTm09ex63sAthZtMCCoerb/4iIiIiocRK2X6sOKc6aVHauJCMjA3l5eZWeR6nI1NRUuXJSWf8RxbWCggLltd9++w1A+VmaJ/Xs2ROtWrXC5cuXNfoO+vr6sLCwQH5+vkbjSXPxGTnY+cdNAMDqMT3Q0khQTQciIiIiaoBq9WR39+5dxMbG4vbt2ypnNCqaPn16jeb08PDAunXrEBoaCj8/P5V7x44dU455Gi8vL3z33XeIjY1F7969Ve7FxsYCgEpvkuLiYgCVlwsuKipCbm4urK2tNfoOKSkpyMjIQNeuXTUaT5opK5Pj/Z/+QWmZHD49bDC0u42uQyIiIiIiLRKUnBQUFODNN9/Ed999p9bMUEEul0MkEtU4OfH29oaTkxP27t2Lt956S9nrRCqVIiAgAEZGRipzpqenQyqVwtbWVmU719y5c/Hdd98hMDAQo0ePVq6WZGRkYPPmzdDT08OECROU4wcNGoSjR48iICAAgwYNUtlutWrVKpSWlqqsqmRkZEAmkylXaBSys7Ph7+8PAJg6dWqNvjtVL/hiKi4lP4CpkT5Wjam+CSgRERERNT6CkpO33noLu3btgpubGyZOnAhbW1u1poaCAzIwwI4dO+Dj44PBgwfDz88PYrEYISEhSE5OxoYNG1RWPJYuXYqgoCDs3r1bmRQAwMCBA7Fo0SJs2rQJbm5u8PX1RUlJCQ4fPozMzEwEBASgS5cuyvHz589HUFAQTp48qeyF0qJFC0RGRuLChQuwsrJSKakcHx+PYcOGYeDAgXB2doaVlRVSU1Px+++/IysrC15eXliyZIlW/kwIuJdXhMDf4gEAC4d1ga15Cx1HRERERETaJiijCAkJQZ8+fXDu3Dno6+trOyZ4enrizJkzWLlyJYKDg1FSUgJXV1d8/PHHmDJlisbzbNy4Ea6urvjiiy+wZ88eiEQiPPvss/jyyy8xfvx4lbESiQRRUVH4+OOPcfjwYezZswcymQzt27fH3Llz8f7776N9+/bK8Z06dYK/vz+io6Nx6NAhSKVSmJmZwc3NDVOnTsXs2bPr5M+muVr7SxykBSXobiuB/0BHXYdDRERERHVAo1LCTzI3N8ecOXOwfv36uoip2dK0xFpzc/bfe5i64zxEIuCn+YPQy95C1yERERERUQ1o+pwrqFpX3759n9qlnUgbikpl+ODQPwCAae4OTEyIiIiImjBBycmHH36I0NBQHD16VNvxEKnYfjoRN+7lw0psjP/6sPoZERERUVMm6MzJgAEDEBoaijFjxqB3797o2bNnpcszIpEIy5cvr3WQ1DzduJuHbWGJAIAVo7tDYmKo44iIiIiIqC4JOnOSlZWF8ePH48yZM9VPLhJBJpMJDq654ZmTx+RyOf6z4zzOJmZhcBcrBM3sC5FIpOuwiIiIiEgATZ9zBa2cvPnmmzhz5gxGjhwJPz8/rZYSJgKAwzG3cTYxC8YGevhwbA8mJkRERETNgKCM4vfff8eQIUN45oTqRE5hCT76JRYA8KZXZzhYmuo4IiIiIiKqD4IOxMvlcvTp00fbsRABAA5fvoV7ecVwamOK1wd30nU4RERERFRPBCUngwYNwl9//aXtWIgAAD9evgUAmNq/A4wMBP0rSkRERESNkKAnvw0bNiA6Ohpbt27VdjzUzCXdy8fllGzoiYAxPdvpOhwiIiIiqkeCzpysX78ebm5uWLBgAT7//HO4ublVWUp4586dtQ6Smo+fHq2aPO9sBWuJiY6jISIiIqL6JKiUsJ6eZgsuLCVcM829lLBcLseQDaeRnPUQn03phXHP2uk6JCIiIiLSgjotJXzz5k3BgRFV5c+UbCRnPURLI30M72Gj63CIiIiIqJ4JSk4cHBy0HQcRfrqcBgB4sUdbtDRi3xwiIiKi5oalkKhBKC4tw9G/0wGA27mIiIiImilBfz397bffajx2+vTpQj6CmpnTCZnIflgCK7ExBnVuo+twiIiIiEgHBCUn/v7+EIlE1Y6Ry+UQiURMTkgjh2LKq3SN7dkO+nrV/7tFRERERE2ToORk9+7dlV6XSqX4888/sXfvXowZMwa+vr61Co6aB2lBCU7EZQIAxvfmli4iIiKi5kpQcjJjxoxq78+ZMwdeXl6YN2+eoKCoefntSjqKS8vQ1UaM7rbNr4QyEREREZWrkwPxAwYMwJgxY7BixYq6mJ6amB8fNV4c96zdU7cLEhEREVHTVWfVuhwcHPDXX3/V1fTURKQ9eIgLN+9DJALG9mqn63CIiIiISIfqJDmRy+WIiIhAixYt6mJ6akIOx9wGALh3tEQ7C/77QkRERNScCTpzEhERUen10tJS3Lp1C99++y2io6NZqYuqJZfL8eOf5Y0XeRCeiIiIiAQlJ0OGDKn2bIBcLsegQYOwadMmwYFR0/fPrRwk3s2HsYEeRjzTVtfhEBEREZGOCUpOVqxYUWlyoqenh1atWqFv377o379/rYOjpu3Hy+WrJsO620BsYqjjaIiIiIhI1wQlJ6tWrdJyGNTclMrK8PNf5edNxj/LLV1EREREVIfVuoiq88e/93AvrxiWpkYY3MVK1+EQERERUQMgaOVEobS0FAkJCcjOzoZMJqt0zODBg2vzEdREHXrU28S3ZzsY6jNHJiIiIiKByYlcLseKFSuwZcsW5ObmVju2qqSFmq+8olIcu5oBoLzxIhERERERIDA5+fDDD7F27VpYWFhg+vTpaN++PQwMarUIQ83I7/9koLCkDE5tTNGzvbmuwyEiIiKiBkJQRrFr1y44ODjg4sWLsLS01HZM1MQptnSNe9au2pLURERERNS8CNrsn5GRgXHjxjExoRrLkBYiMvEeAGBcL27pIiIiIqLHBCUnHTt2RE5OjrZjoWbgyF+3IJcDfRxaoYNlS12HQ0REREQNiKDkZN68eTh69CgyMzO1HQ81cT/+Wb6la3xvrpoQERERkSpBZ07Gjh2LP/74AwMHDsSKFSvQu3dvSCSSSsd26NChVgFS0xGXnoP4jFwY6ethlKutrsMhIiIiogZGUHLSsWNHiEQiyOVyzJw5s8pxIpEIpaWlgoOjpkVxEN7TxQoWLY10HA0RERERNTSCkpPp06ezyhLViKxMjkMxj7Z0Pdtex9EQERERUUMkKDnZs2ePlsOgpi7qRhbu5BTBvIUhPF2sdB0OERERETVAgg7E14fo6GiMHDkSFhYWMDU1hbu7Ow4cOFDjeTIzM7Fw4UI4OzvDxMQElpaWGDBgALZv3642trS0FLt27cKAAQNgZWUFsViM7t27Y8mSJcjIyKh0/vT0dMyaNQu2trYwMTFB165dsXbtWpSUlNQ41qZMcRB+lJstjA30dRwNERERETVEIrlcLtd1EE8KCwuDj48PTExM4OfnB7FYjJCQECQnJ2PDhg1YvHixRvPExMRg+PDhePDgAUaNGoVu3bohLy8PcXFxMDIywq+//qoyfsKECfjxxx/RuXNnvPjiizA2NkZUVBQiIyNha2uLP//8E23btlWOz8jIQL9+/ZCWlobx48fD2dkZ4eHhiIqKwpgxY3Do0KEabX/LycmBubk5pFJplQUGGqOCYhn6fHQc+cUy/G/uAPR1bK3rkIiIiIioHmn6nNvgkpPS0lK4uLggLS0NUVFR6NWrFwBAKpWiX79+SEpKwrVr1+Dg4FDtPDk5OXB1dUVBQQFOnDgBNzc3tc8xMHi8q+3ChQvo378/+vXrhzNnzsDQ0FB5b8GCBfj888+xevVqrFixQnl9xowZ+Pbbb7F9+3bMnTsXACCXyzF16lTs378fe/fuxcsvv6zxd2+qycnhmFtYsD8G7Vu1wB9LPHleiYiIiKiZ0fQ5t8Ft6zp16hQSExMxdepUZWICAObm5li2bBmKi4sRFBT01Hm2bduGlJQUBAYGqiUmAFQSEwC4ceMGAGDo0KEqiQkAjB49GgBw9+5d5bXc3FwEBwfDyckJc+bMUV4XiUQIDAwEAHzzzTdPjbM5UFTpGv+sHRMTIiIiIqpSg0tOTp8+DQAYPny42j0fHx8AQHh4+FPnCQ4OhkgkwoQJE5CQkIAtW7Zg/fr1OHLkCIqLi9XG9+jRAwBw4sQJtfMiR48eBQB4e3srr507dw5FRUUYNmyY2gO3g4MDunbtisjISMhksqfG2pQVlsjwx/V7AICxvdh4kYiIiIiqJqhaV126fv06AMDZ2VntXtu2bWFmZqYcU5Xi4mJcuXIFVlZW2LJlC1auXImysjLlfScnJxw6dAiurq7Ka66urliwYAE2b96M7t27Y8SIETA2Nsa5c+dw6dIlrF69GuPGjdMoTsX1hIQEJCcnw8nJqdIxRUVFKCoqUr7Oycmp9ns1RmkPHqK0TA5TI310sjLVdThERERE1IBpvHISGxtbl3EoSaVSAOXbuCojkUiUY6py//59yGQyZGVlYc2aNVi/fj3u3LmDtLQ0LF++HDdv3oSvry8KCwtV3vfZZ5/hs88+Q3JyMrZs2YINGzYgMjISw4YNw0svvVTjOCuOq8y6detgbm6u/LG3t6/2ezVGN+89BAA4tjHlli4iIiIiqpbGyckzzzyDLl26YMmSJThz5gwa2Dl6FYpVEplMhvnz52Px4sWwtraGnZ0d1qxZg0mTJiE5ORkHDx5Uec/rr7+ODz74AFu2bEF6ejqkUil+/fVXxMXFwd3dHdHR0VqNc+nSpZBKpcqf1NRUrc7fECRn5QMAHC25akJERERE1dM4OVm/fj3atm2LTZs2wcPDA23btsXs2bPx888/q61A1IZiJaKqFQfFSX9N5gCAMWPGqN1XXLt48aLy2q5du/DNN99g7dq1mDNnDtq2bQuJRIIRI0bg4MGDyM/Px7Jly2oU55OxPMnY2BgSiUTlp6m5ee9RctKmpY4jISIiIqKGTuPk5L///S8iIiKQkZGBHTt2wN3dHfv27cO4cePQpk0bjB8/HkFBQbh3716tAlKc4ajsXElGRgby8vKqPOehYGpqCju78sPXFhYWavcV1woKCpTXfvvtNwCAp6en2viePXuiVatWuHz5skZxKq4bGRmhQ4cO1cba1CU9Wjlx4MoJERERET1Fjat1tWnTBjNnzsThw4dx7949/Pjjj5g8eTLOnj2LmTNnwtbWFoMHD8amTZuQmJhY44A8PDwAAKGhoWr3jh07pjKmOl5eXgAqPyujuObo6Ki8pqjgVbFcsEJRURFyc3NhbGysvObu7g4jIyMcP35cbYtbcnIyEhISMGjQILWSxc1N0qMzJx3bMDkhIiIiourVqpRwixYtMHbsWOzatQvp6ekIDw/HggULkJGRgf/+97/o0qULnnnmGXzwwQcaz+nt7Q0nJyfs3bsXMTExyutSqRQBAQEwMjLC9OnTldfT09MRHx+vtr1K0RQxMDAQ2dnZyusZGRnYvHkz9PT0MGHCBOX1QYMGAQACAgJUKmgBwKpVq1BaWqqyqiKRSODn54cbN27gq6++Ul6Xy+VYunQpAOC1117T+Hs3RYUlMtyWlq9OOVhyWxcRERERVa/OOsTHxsbi0KFDOHz4MC5duoTS0lKN3xsWFgYfHx+YmJjAz88PYrEYISEhSE5OxoYNG7B48WLlWH9/fwQFBWH37t3w9/dXmWfx4sXYtGkT7O3t4evri5KSEhw+fBiZmZkICAhQJhFA+RmR/v37Iz4+Ho6OjnjxxRfRokULREZG4sKFC7CyskJUVJRKWeD09HT0798faWlpeOmll9C5c2eEh4cjKioKvr6+OHz4cI0qVDW1DvH/ZuZi6KYImBrp45/VPqzWRURERNRM6bxDfPfu3bFs2TKcP38eaWlpNXqvp6cnzpw5g0GDBiE4OBjbt2+HjY0N9u/fr5KYPM3GjRuxe/du2NjYYM+ePdi7dy+6dOmCH3/8USUxAcpXQqKiorB06VK0bNkSe/bswdatW3H37l3MnTsXf/75p1q/EltbW5w/fx4zZ87EmTNn8OmnnyIrKwsffvghDh482OwfxllGmIiIiIhqos5WTqjmmtrKyY4/buCjX+IwytUWX/ynt67DISIiIiId0fnKCRHLCBMRERFRTTA5oTqTnFW+rYtlhImIiIhIE0xOqM4oVk5YRpiIiIiINMHkhOpEUSnLCBMRERFRzTA5oTqRev8h5HLA1EgfVmbGT38DERERETV7TE6oTig6wztYsowwEREREWnGQOgbY2NjsXXrVkRHRyM7OxsymUxtjEgkQmJiYq0CpMYpKYvnTYiIiIioZgQlJ+Hh4XjxxRdRVFQEAwMD2NjYwMBAfSq2UGm+FMkJz5sQERERkaYEJSfvvfceSktLsWPHDsyYMQP6+vrajosauaQK3eGJiIiIiDQhKDn566+/4Ofnh1dffVXb8VAToWzAyB4nRERERKQhQQfiTU1NYW1tre1YqImoWEaY3eGJiIiISFOCkpORI0fijz/+0HYs1ESwjDARERERCSEoOfnkk0+QnZ2Nt956Cw8fPtR2TNTIsYwwEREREQkh6MyJn58fzMzM8MUXX2DPnj3o0qULJBKJ2jiRSISTJ0/WOkhqXFhGmIiIiIiEEJScnD59Wvl7Xl4e/vzzz0rH8W/NmyeWESYiIiIiIQQlJ2VlZdqOg5oQlhEmIiIiIiEEnTkhqo5i5YRlhImIiIioJrSSnOTn5yM9PR35+fnamI4asaJSGW5ns4wwEREREdWc4OSkuLgYa9euhbOzMyQSCdq3bw+JRAJnZ2cEBASguLhYm3FSI5F6vwBlLCNMRERERAIIOnNSUFAAb29vnD9/Hvr6+nB2doatrS0yMjKQmJiI5cuX4+jRozh58iRatGih7ZipAUu6pzgMzzLCRERERFQzglZOPv74Y0RFRWHy5MlITExEfHw8wsLCEBcXhxs3bmDKlCmIiorC+vXrtR0vNXDK8ybc0kVERERENSQoOQkODkbv3r2xb98+2Nvbq9xr37499u7di+eeew779+/XSpDUePAwPBEREREJJSg5SUpKwvDhw6sdM3ToUCQlJQmZnhqx5CyWESYiIiIiYQQlJy1btsTdu3erHXP37l20bMmtPc3NzXtcOSEiIiIiYQQlJ+7u7ti/fz+uXr1a6f3Y2FgEBwdjwIABtQqOGheWESYiIiKi2hBUrWvZsmUIDQ1F3759MWvWLHh4eMDGxgZ37tzB6dOnsXv3bpSUlGDp0qXajpcaMJYRJiIiIqLaEJScDBo0CHv37sVrr72GL774Atu2bVPek8vlMDc3R1BQEAYNGqS1QKnhYxlhIiIiIqoNQckJAEyaNAkvvvgiDh8+jMuXLyMnJwcSiQTPPvssxo4dC7FYrM04qRFgGWEiIiIiqg3ByQkAiMVivPLKK3jllVe0FQ81YiwjTERERES1IehAPFFllGWEmZwQERERkQAarZx8++23AIDx48dDLBYrX2ti+vTpwiKjRkdZRpg9ToiIiIhIAJFcLpc/bZCenh5EIhHi4uLQpUsX5evqyOVyiEQiyGQyrQXb1OXk5MDc3BxSqRQSiUTX4dRIUakM3Zb/jjI5cGGZN6wlJroOiYiIiIgaCE2fczVaOdm1axdEIhFsbW0BALt379ZOlNRkKMoItzTSh5WYZYSJiIiIqOY0Sk78/f1VXs+YMaMuYqFGLDmLZYSJiIiIqHZ4IJ60QnHepCPLCBMRERGRQIKSk9TUVJw6dQoPHz5UXisrK8PHH3+MQYMGYejQofjll1+0FiQ1fKzURURERES1JajPyfLly/Hzzz8jIyNDeW3t2rVYuXKl8nV4eDjOnj2Lvn371j5KavDY44SIiIiIakvQyklkZCSGDh0KQ0NDAOWVubZu3QoXFxekpKTgwoULMDU1xSeffCI4sOjoaIwcORIWFhYwNTWFu7s7Dhw4UON5MjMzsXDhQjg7O8PExASWlpYYMGAAtm/frjJu1apVEIlE1f7MmjVL5T3+/v7Vjm9OHneHZ3JCRERERMIIWjnJzMyEg4OD8nVMTAzu3r2LVatWoX379mjfvj3GjRuH8PBwQUGFhYXBx8cHJiYm8PPzg1gsRkhICKZMmYLU1FQsXrxYo3liYmIwfPhwPHjwAKNGjcLEiRORl5eHuLg4/Pzzz5g3b55y7JAhQ6qcZ8eOHbh16xZ8fHwqvb9gwQJYWFjU5Cs2KcWlZbj1oAAA4GjJMydEREREJIyg5KSsrAxlZWXK16dPn4ZIJIKXl5fymp2dncq2L02Vlpbitddeg56eHiIiItCrVy8AwIoVK9CvXz8sW7YMEydOVEmOKpOTk4OxY8cCAC5dugQ3Nze1z6loyJAhlSYod+7cwdq1a2FpaYlx48ZV+llvv/02HB0dNfp+TVHK/YcsI0xEREREtSZoW1eHDh1w4cIF5etDhw7B1tYWXbt2VV7LyMgQtJpw6tQpJCYmYurUqcrEBADMzc2xbNkyFBcXIygo6KnzbNu2DSkpKQgMDFRLTADAwECzvCwoKAilpaWYNm0ajIyMNP4ezQnLCBMRERGRNghaOZkwYQLWrl2LiRMnwsTEBGfOnMEbb7yhMiY2NhZOTk41nvv06dMAgOHDh6vdU2yr0mS7WHBwMEQiESZMmICEhASEhoaioKAALi4uePHFFzVONHbu3AkAmD17dpVjjh49itzcXBgbG6Nbt27w9vZuVokMywgTERERkTYISk7++9//IjQ0FD/++CMAwM3NDatWrVLeT05OxoULF/Dee+/VeO7r168DAJydndXutW3bFmZmZsoxVSkuLsaVK1dgZWWFLVu2YOXKlSrb0JycnHDo0CG4urpWO88ff/yBa9euwd3dHT169Khy3Jtvvqny2tbWFrt3767yjIpCUVERioqKlK9zcnKqHd9QKcoIO7BSFxERERHVgqBtXRKJBFFRUfj777/x999/49KlS2jVqpXKmB9//BHz58+v8dxSqRRA+Tauqj5bMaYq9+/fh0wmQ1ZWFtasWYP169fjzp07SEtLw/Lly3Hz5k34+vqisLCw2nmetmoyePBgHDhwACkpKSgoKMD169exZs0aZGdnY8yYMbh48WK1869btw7m5ubKH3t7+2rHN1SKSl0dmZwQERERUS2I5HK5XNdBVDR8+HAcP34c169fR+fOndXu29nZIS8vr9oE5fbt27CzswNQXknrs88+U7k/ZcoUHDhwAN999x1eeeWVSufIycmBra0t9PT0kJ6eDjMzM42/w65duzBr1iz4+vriyJEjVY6rbOXE3t4eUqkUEolE48/TtRfWn0Lq/QIEv+6O/k6Wug6HiIiIiBqYnJwcmJubP/U5V9DKSV1SrJhUlXwovpgmcwDAmDFj1O4rrlW3srF//348fPgQU6ZMqVFiAgAzZsyAiYkJIiMjqx1nbGwMiUSi8tPYVCwj3JE9ToiIiIioFgQnJydOnMDIkSNhZWUFQ0ND6Ovrq/1oWhGrIsVZk8rOlWRkZCAvL6/S8ygVmZqaKldOKqsYprhWUFBQ5Rw7duwAUP1B+Kro6+vDwsIC+fn5NX5vY5P6gGWEiYiIiEg7BB2IVzRELCsrg4ODA1xcXAQlIpXx8PDAunXrEBoaCj8/P5V7x44dU455Gi8vL3z33XeIjY1F7969Ve7FxsYCQJW9Sa5cuYLo6Gj06NED7u7uNf4OKSkpyMjIUCmt3FQl3WMZYSIiIiLSDkEZxZo1a9CiRQscPnxYpfGiNnh7e8PJyQl79+7FW2+9pex1IpVKERAQACMjI0yfPl05Pj09HVKpFLa2tirbuebOnYvvvvsOgYGBGD16tHK1JCMjA5s3b4aenh4mTJhQaQyKg/CzZs2qMs6MjAzIZDLlCo1CdnY2/P39AQBTp06t6ddvdJIeVepiGWEiIiIiqi1ByUlCQgKmTZum9cQEKG+OuGPHDvj4+GDw4MHw8/ODWCxGSEgIkpOTsWHDBpUVj6VLlyIoKAi7d+9WJgUAMHDgQCxatAibNm2Cm5sbfH19UVJSgsOHDyMzMxMBAQHo0qWL2ucXFxfj+++/V0uCnhQfH49hw4Zh4MCBcHZ2hpWVFVJTU/H7778jKysLXl5eWLJkiTb/aBqkiisnRERERES1ISg5sbS0RMuWdfc35Z6enjhz5gxWrlyJ4OBglJSUwNXVFR9//DGmTJmi8TwbN26Eq6srvvjiC+zZswcikQjPPvssvvzyS4wfP77S9xw6dAhZWVmYPHkyLC2rrjzVqVMn+Pv7Izo6GocOHYJUKoWZmRnc3NwwdepUzJ49G/r6+jX+7o0NywgTERERkbYIKiW8YMECnDhxAn/99ZfWzpqQ5iXWGhKWESYiIiKip6nTUsIBAQGwsLDAlClTkJKSIjhIatxYRpiIiIiItEnQsoerqytKSkoQFRWFQ4cOwcLCotLeIyKRCImJibUOkhomlhEmIiIiIm0SlJyUlZXBwMAAHTp0UF6rbHdYA2s+T1qWnMUywkRERESkPYKSk6SkJC2HQY3RzXvlZYQdLVlGmIiIiIhqT3CHeCJFGWFHnjchIiIiIi2odamt2NhYxMfHIz8/H9OmTdNGTNRIKMoIc+WEiIiIiLRB8MpJdHQ0evXqBVdXV0yaNEmlAWJERARatmyJI0eOaCNGaqAeJydcOSEiIiKi2hOUnFy9ehVeXl64efMmFi5ciBEjRqjcf+GFF9CmTRv873//00qQ1PBULCPMbV1EREREpA2CkpOVK1cCAC5duoQNGzagb9++KvdFIhEGDBiA6Ojo2kdIDVLFMsLWLCNMRERERFogKDkJDw/HhAkT0Llz5yrHdOjQAenp6YIDo4aNZYSJiIiISNsEJSe5ubmwtraudkxBQQFkMpmgoKjhYxlhIiIiItI2QcmJvb09rly5Uu2YP//8E506dRIUFDV8ipUTnjchIiIiIm0RlJyMHj0aoaGhOHHiRKX3Dxw4gKioKIwbN642sVEDdvMeywgTERERkXYJ6nOybNkyHDx4ECNHjsSMGTOQkZEBANi2bRvOnTuHffv2wdHREYsWLdJqsNRwJGcptnVx5YSIiIiItENQcmJlZYXw8HBMmzYNO3fuVF5/4403AAD9+/fHvn37YG5urp0oqUEpLi1D2oNHyQm3dRERERGRlgjuEO/k5ITIyEjExMQgKioK9+/fh0QiQf/+/dVKC1PTkvaojHALQ5YRJiIiIiLtEZycKPTq1Qu9evXSQijUWCQpywi3ZBlhIiIiItIaQQfiqXlLelRGuCO3dBERERGRFgleOcnNzcXOnTvx119/4fbt2ygpKVEbIxKJcPLkyVoFSA1PUoUGjERERERE2iIoOYmOjsaIESPw4MEDyOXyKsdxy0/TpCgj3LENywgTERERkfYI2ta1YMECZGdnIzAwECkpKSgpKUFZWZnaDzvEN00sI0xEREREdUHQysnly5fh5+eHd955R9vxUAPHMsJEREREVFcErZy0bt0aVlZW2o6FGgGWESYiIiKiuiIoORk3bhxOnTqFsrIybcdDDRzLCBMRERFRXRGUnKxbtw6Ghob4z3/+g1u3bmk7JmrAWEaYiIiIiOqKoDMnEokEX3/9NYYOHYoDBw6gVatWkEgkauNEIhESExNrHSQ1HCwjTERERER1RdDKycmTJ/H8888jOzsbBgYGaNGiBeRyudoPt301PUlZipUTlhEmIiIiIu0StHLy7rvvQi6XIzg4GBMnTuTZg2Yk6R5XToiIiIiobghKTmJjY/HKK69g0qRJ2o6HGrCKZYR55oSIiIiItE3Qti4rKyu0aNFC27FQA8cywkRERERUlwQlJ//5z3/w22+/oaCgQNvxUAOm6AzPMsJEREREVBcEJSerVq3CM888gxdffBGRkZHIy8vTdlzUAN18dN7EkedNiIiIiKgOCDpzotjSJZfLMXjw4CrHiUQilJaWCouMGpzkR2WEHXnehIiIiIjqgKDk5IUXXuC2nmboJssIExEREVEdEpScnD59WsthUGPAMsJEREREVJcEnTmh5odlhImIiIiorjE5IY2wjDARERER1TWNtnW9+uqrEIlECAgIgI2NDV599VWNJheJRNi5c6egwKKjo7Fy5UqcPXsWJSUlcHV1xaJFizB58uQazZOZmYl169bh6NGjSE1NhampKbp06YLp06dj3rx5ynGrVq3C6tWrq53r1VdfVfs+6enp+OCDD/Drr7/iwYMHcHBwwPTp07FkyRIYGhrWKNaGjGWEiYiIiKiuaZSc7NmzByKRCO+++y5sbGywZ88ejSYXmpyEhYXBx8cHJiYm8PPzg1gsRkhICKZMmYLU1FQsXrxYo3liYmIwfPhwPHjwAKNGjcLEiRORl5eHuLg4/PzzzyrJyZAhQ6qcZ8eOHbh16xZ8fHxUrmdkZKB///5IS0vD+PHj4ezsjPDwcHzwwQe4cOECDh061GQe5FlGmIiIiIjqmkgul8ufNig5ORkAYGdnBwMDA+VrTTg4ONQooNLSUri4uCAtLQ1RUVHo1asXAEAqlaJfv35ISkrCtWvXnjpvTk4OXF1dUVBQgBMnTsDNzU3tcwwMnp6b3blzB+3bt4e5uTlu374NIyMj5b0ZM2bg22+/xfbt2zF37lwA5eWVp06div3792Pv3r14+eWXNf7uOTk5MDc3h1QqhUQi0fh99WHl4X8QdC4Zcz064b0RLroOh4iIiIgaEU2fczU6c+Lg4AAHBwflw7zitSY/NXXq1CkkJiZi6tSpysQEAMzNzbFs2TIUFxcjKCjoqfNs27YNKSkpCAwMVEtMAGiUmABAUFAQSktLMW3aNJXEJDc3F8HBwXBycsKcOXOU10UiEQIDAwEA33zzjUaf0Rgoygg7WrKMMBERERHVDUGlhOuSokzx8OHD1e4ptlWFh4c/dZ7g4GCIRCJMmDABCQkJCA0NRUFBAVxcXPDiiy+qJBrVUWxLmz17tsr1c+fOoaioCMOGDVPbuuXg4ICuXbsiMjISMpkM+vr6Gn1WQ8YGjERERERU1zRKTiIiIgR/QHUd5Ctz/fp1AICzs7PavbZt28LMzEw5pirFxcW4cuUKrKyssGXLFqxcuRJlZWXK+05OTjh06BBcXV2rneePP/7AtWvX4O7ujh49emgcp+J6QkICkpOT4eTkVOmYoqIiFBUVKV/n5ORUG4+ulMjKkPagAADPnBARERFR3dEoORkyZIjgg90ymaxG46VSKYDybVyVkUgkyjFVuX//PmQyGbKysrBmzRqsX78e06ZNQ0lJCb766it89NFH8PX1RXx8PExMTKqcp6pVE03jrDiuMuvWrXtqhbCGIO1BAWRlcpgY6sFGwjLCRERERFQ3NEpOVqxYoZacREVF4dixY3B2dsagQYNgY2ODO3fu4OzZs7h27Rp8fHzg7u5eJ0E/jWKVRCaT4Y033lCp7rVmzRokJCTgwIEDOHjwIF555ZVK58jJycH//vc/mJmZYcqUKXUS59KlS7Fo0SKVz7S3t6+Tz6qNpAqVuppK9TEiIiIiang0Sk5WrVql8vqPP/7AunXr8PXXX2PWrFkqD6xyuRzffPMNFixYgPfff7/GASlWIqpaccjJyUGrVq00mgMAxowZo3Z/zJgxOHDgAC5evFhlcrJ//348fPgQs2bNgpmZmaA4n4zlScbGxjA2bvgrEUlZLCNMRERERHVPUIf45cuXY9SoUZg9e7ba36SLRCK8/vrrGDFiBJYvX17juRVnOCo7V5KRkYG8vLwqz3komJqaws7ODgBgYWGhdl9xraCgoMo5duzYAaDyLV1Pi1Nx3cjICB06dKg21sZAuXLCw/BEREREVIcEJSeXLl1Ct27dqh3TrVs3XLx4scZze3h4AABCQ0PV7h07dkxlTHW8vLwAALGxsWr3FNccHR0rfe+VK1cQHR2NHj16VLk1zd3dHUZGRjh+/DiebBWTnJyMhIQEDBo0SOOSxQ1ZEssIExEREVE9EJScGBkZ4fLly9WOuXz5ssbleivy9vaGk5MT9u7di5iYGOV1qVSKgIAAGBkZYfr06crr6enpiI+PV9tepWiKGBgYiOzsbOX1jIwMbN68GXp6epgwYUKlMSgOws+aNavKOCUSCfz8/HDjxg189dVXyutyuRxLly4FALz22muafekGLollhImIiIioHghKToYPH47ff/8dgYGBKC4uVrlXXFyMdevW4dixY8q+JDVhYGCAHTt2oKysDIMHD8brr7+OxYsXo2fPnrh27RoCAgJUVjyWLl2Kbt264aefflKZZ+DAgVi0aBGuXr0KNzc3/N///R9ef/119OzZE7du3cJHH32ELl26qH1+cXExvv/+e7UkqDKBgYGwt7fH/PnzMXHiRLz33nsYOHAg9u3bB19fX/j5+dX4+zc0LCNMRERERPVF0J6jTz75BH/88Qfef/99bN68GX369IG1tTUyMzNx8eJFZGZmol27dli/fr2goDw9PXHmzBmsXLkSwcHBKCkpgaurKz7++OMaVc7auHEjXF1d8cUXX2DPnj0QiUR49tln8eWXX2L8+PGVvufQoUPIysrC5MmTYWlpWe38tra2OH/+PD744AP88ssv+Pnnn+Hg4IAPP/wQS5YsaRKVrVhGmIiIiIjqi0j+5IEJDWVkZOC9997DgQMHUFhYqLxuYmKCyZMnIzAwEG3bttVaoM1BTk4OzM3NIZVKlX1SdC0sPhMz90TDpa0Yv79ds4aaRERERESA5s+5gk9rt23bFnv27ME333yDhIQESKVSmJubo0uXLoLOmlDDxDLCRERERFRfal1KytDQEM8884w2YqEGSFFG2KENK3URERERUd0SdCCemg9FGeGOXDkhIiIiojrG5ISqpdjW5cDkhIiIiIjqGJMTqlLFMsId2eOEiIiIiOoYkxOqEssIExEREVF9YnJCVapYqasp9GwhIiIiooaNyQlVSVGpi2WEiYiIiKg+1LqUcGxsLOLj45Gfn49p06ZpIyZqIJIfVepiGWEiIiIiqg+CV06io6PRq1cvuLq6YtKkSfD391fei4iIQMuWLXHkyBFtxEg6cvPRygnLCBMRERFRfRCUnFy9ehVeXl64efMmFi5ciBEjRqjcf+GFF9CmTRv873//00qQpBvJLCNMRERERPVIUHKycuVKAMClS5ewYcMG9O3bV+W+SCTCgAEDEB0dXfsISSdKZGVIZRlhIiIiIqpHgpKT8PBwTJgwAZ07d65yTIcOHZCeni44MNKtWxXKCFuLWUaYiIiIiOqeoOQkNzcX1tbW1Y4pKCiATCYTFBTp3s0KZYT19FhGmIiIiIjqnqDkxN7eHleuXKl2zJ9//olOnToJCop0T1FG2MGSlbqIiIiIqH4ISk5Gjx6N0NBQnDhxotL7Bw4cQFRUFMaNG1eb2EiHFGWEHXnehIiIiIjqiaA+J8uWLcPBgwcxcuRIzJgxAxkZGQCAbdu24dy5c9i3bx8cHR2xaNEirQZL9ecmGzASERERUT0TlJxYWVkhPDwc06ZNw86dO5XX33jjDQBA//79sW/fPpibm2snSqp3yVlMToiIiIiofgnuEO/k5ITIyEjExMQgKioK9+/fh0QiQf/+/dVKC1PjwjLCRERERKQLgpMThV69eqFXr15aCIUaigxpIWRlchgZsIwwEREREdUfQQfip02bhuPHj0Mul2s7HmoAcgpLAADmLQxZRpiIiIiI6o2g5OSHH37Aiy++iPbt2+O///0vYmJitBwW6VJuYSkAQGxS64U1IiIiIiKNCUpOLl26hLfeegtlZWXYtGkTnnvuObi6uuKTTz7BrVu3tB0j1bM8ZXJiqONIiIiIiKg5EZScPPvss/j0009x69Yt/PLLL/Dz88PNmzfx7rvvwsHBAUOHDkVQUBDy8vK0HS/Vg9yi8m1dYmOunBARERFR/RGUnCjfrKeHESNG4IcffsCdO3ewe/dueHp64vTp03j11VfRtm1bbcVJ9YjbuoiIiIhIF2qVnFRkamqKGTNm4KeffsKaNWtgYGCAgoICbU1P9YjJCRERERHpglaePsvKynDs2DF8//33OHz4MAoKCiASiTB06FBtTE/1TFGti2dOiIiIiKg+1So5uXjxIr7//nvs378fd+/ehVwuh6urK6ZNm4apU6eiXbt22oqT6lEeV06IiIiISAcEPX1+9NFH+OGHH3Dt2jXI5XLY2tpi0aJFmDZtGtzc3LQdI9WzXFbrIiIiIiIdEJScrFixAqampvjPf/6DadOmwdvbG3p6Wju+QjqWW8hqXURERERU/wQ9fX777bd46aWX0LJlS23HQw0AD8QTERERkS4Ievp85ZVXtB0HNSDc1kVEREREusC9WKQmr4grJ0RERERU/zRKTvT09GBgYIBr164pX+vr6z/1x8CAD7eN0eNSwvznR0RERET1R6Onz8GDB0MkEinPmCheU9NTViZXrpyYMTkhIiIionqk0dPn6dOnq31NTUd+cSnk8vLfJTxzQkRERET1iGdOSIVi1cRQXwRjA/7rQURERET1R9DTp5OTEz7//PNqx3zxxRdwcnISFBQAREdHY+TIkbCwsICpqSnc3d1x4MCBGs+TmZmJhQsXwtnZGSYmJrC0tMSAAQOwffv2SseXlZVh165deP7552FhYYGWLVuiS5cumDlzJnJzc1XG+vv7QyQSVfnTGFWs1NVYvwMRERERNU6CDhUkJSUhOzu72jHZ2dlITk4WMj3CwsLg4+MDExMT+Pn5QSwWIyQkBFOmTEFqaioWL16s0TwxMTEYPnw4Hjx4gFGjRmHixInIy8tDXFwcfv75Z8ybN09lfFFRESZOnIijR4/Czc0N/v7+MDY2RkpKCn799Vd8+OGHEIvFap+zYMECWFhYCPquDU0uD8MTERERkY7U2ROoVCqFsbFxjd9XWlqK1157DXp6eoiIiECvXr0AlHel79evH5YtW4aJEyfCwcGh2nlycnIwduxYAMClS5fg5uam9jlPeu+993D06FEEBgbi3XffVblXVlZW5We9/fbbcHR01ODbNXw5j1ZOzNgdnoiIiIjqmcZPoBERESqvk5KS1K4BgEwmQ2pqKn744Qd06dKlxgGdOnUKiYmJmDlzpjIxAQBzc3MsW7YM/v7+CAoKwooVK6qdZ9u2bUhJScHOnTvVEhMAamWOb926ha1bt+KFF15QS0yA8vLJzQG7wxMRERGRrmj8BDpkyBDlGQSRSISgoCAEBQVVOlYul0MkEiEwMLDGASkqgQ0fPlztno+PDwAgPDz8qfMEBwdDJBJhwoQJSEhIQGhoKAoKCuDi4oIXX3wRRkZGKuMPHjyI0tJSTJo0Cbm5uThy5AhSUlJgY2MDHx8f2NnZVflZR48eRW5uLoyNjdGtWzd4e3urzd9Y5ClXTlipi4iIiIjql8bJyYoVKyASiSCXy7FmzRp4eHhgyJAhauP09fXRunVreHp6olu3bjUO6Pr16wAAZ2dntXtt27aFmZmZckxViouLceXKFVhZWWHLli1YuXKlyrYsJycnHDp0CK6ursprly5dAlB+VqZr165IT09X3jMyMkJgYCAWLlxY6ee9+eabKq9tbW2xe/duZTJVlaKiIhQVFSlf5+TkVDu+PjwsLk9OTI31dRwJERERETU3Gicnq1atUv4eHh6OmTNnYvr06VoPSCqVAijfxlUZiUSiHFOV+/fvQyaTISsrC2vWrMH69esxbdo0lJSU4KuvvsJHH30EX19fxMfHw8TEBEB5VS8AWL16NYYNG4YTJ07A3t4eEREReP3117Fo0SK4uLhgxIgRys8ZPHgwRo0aBXd3d1hZWSEtLQ379u3DunXrMGbMGERGRqJPnz5Vxrlu3TqsXr26Rn8+da2gWAYAaGnE5ISIiIiI6peggxRhYWF1kphoi2KVRCaTYf78+Vi8eDGsra1hZ2eHNWvWYNKkSUhOTsbBgwfV3mNtbY2QkBB0794dYrEYo0aNwo4dOwAAGzduVPmcV199FZMmTYK9vT1MTEzQuXNnLF++HFu3bkVxcTHWrFlTbZxLly6FVCpV/qSmpmrzj0GQ/EfJSQtDnjkhIiIiovolKDk5e/YsFi1ahIyMjErvp6enY9GiRYiKiqrx3IoVk6pWR3JycqpcVXlyDgAYM2aM2n3FtYsXL6q9Z+jQoWjZsqXKeB8fHxgbG6uMr86MGTNgYmKCyMjIascZGxtDIpGo/OhaAbd1EREREZGOCEpONm7ciJ9//hlt27at9L6trS2OHj2KTz/9tMZzK86aVHauJCMjA3l5eZWeR6nI1NRUeYC9sv4jimsFBQXKa127dq1yvJ6eHsRiscr46ujr68PCwgL5+fkajW9IHipWTriti4iIiIjqmaDkJDo6Gs8//3y1YwYPHixo5cTDwwMAEBoaqnbv2LFjKmOq4+XlBQCIjY1Vu6e4VrE3SXXj7969i3v37mncyyQlJQUZGRmNsvfJw5JHZ04MmZwQERERUf0SlJxkZmZWW1oXKK+spThkXhPe3t5wcnLC3r17ERMTo7wulUoREBAAIyMjlfMu6enpiI+PV9sGNnfuXABAYGCgSjf7jIwMbN68GXp6epgwYYLyuoeHB7p164aTJ0/i+PHjyutyuRzLli0DAEyePFllnlu3bqnFn52dDX9/fwDA1KlTa/z9de3xgXieOSEiIiKi+iXoCdTCwgIpKSnVjklOToaZmVnNAzIwwI4dO+Dj44PBgwfDz88PYrEYISEhSE5OxoYNG1RWJJYuXYqgoCDs3r1bmRQAwMCBA7Fo0SJs2rQJbm5u8PX1RUlJCQ4fPozMzEwEBASoNInU19fH7t274eXlhZEjR+Kll15C+/btcebMGVy4cAG9e/fGe++9pxwfHx+PYcOGYeDAgXB2doaVlRVSU1Px+++/IysrC15eXliyZEmNv7+uKUoJc1sXEREREdU3QcmJu7s7fvrpJ6SmpsLe3l7tfkpKCg4dOqTcKlVTnp6eOHPmDFauXIng4GCUlJTA1dUVH3/8MaZMmaLxPBs3boSrqyu++OIL7NmzByKRCM8++yy+/PJLjB8/Xm18//79ceHCBaxcuRInT55ETk4OOnTogKVLl2LZsmUwNTVVju3UqRP8/f0RHR2NQ4cOQSqVwszMDG5ubpg6dSpmz54Nff3G94DPUsJEREREpCsiuVwur+mbIiIi4OnpCTs7O3z00UcYNmwYbG1tkZ6ejtDQUHzwwQdIT0/HqVOnMHjw4LqIu0lSVCKTSqU6q9w1bFM4rmfmYe9r/TGwUxudxEBERERETYumz7mCVk4GDx6MTZs2YfHixZg5cyYAKLvHA+XVrTZv3szEpBF6yDMnRERERKQjgp9AFyxYAE9PT3z55ZeIjo6GVCqFhYUF+vXrh7lz5+KZZ57RZpxUTwpKuK2LiIiIiHSjVn897ubmhm3btmkrFmoAlAfiWUqYiIiIiOqZoFLC1DSVlclRWFIGgCsnRERERFT/BCcnpaWl+PTTT9GvXz9IJBIYGDxehImJicH8+fNx7do1rQRJ9UOxpQvgmRMiIiIiqn+CnkALCgowfPhwnD17Fm3atIFEIkF+fr7yfseOHbF79260bt0aH330kdaCpbqlOAwvEgEmhlxUIyIiIqL6JegJNCAgAJGRkVi3bh0yMjIwe/Zslfvm5ubw8PDAsWPHtBIk1Q/FeZOWhvoQiUQ6joaIiIiImhtByUlwcDA8PT2xZMkSiESiSh9knZycntpFnhoWxcpJC27pIiIiIiIdEJScpKSkoE+fPtWOEYvFkEqlgoIi3XjI7vBEREREpEOCkhOxWIzMzMxqxyQmJsLKykpQUKQbBUxOiIiIiEiHBCUn7u7u+Pnnn5GdnV3p/dTUVPz666/sEN/IKHucMDkhIiIiIh0QlJy88847ePDgAby9vREZGYnS0vKH2ocPH+LkyZPw8fFBaWkpFi1apNVgqW6xOzwRERER6ZKgk8+DBw/G1q1bsWDBApXVEbFYDADQ19fHtm3b8Nxzz2knSqoXygPxhjwQT0RERET1T/BT6Lx58zBkyBB8+eWXOH/+PO7fvw+JRIL+/ftj/vz56NGjhzbjpHrAA/FEREREpEsaJSdHjhyBi4sLunTponK9W7du2Lx5c50ERvWvQNHnhMkJEREREemARmdOxo8fj/379ytfOzk54fPPP6+zoEg3Hvc5YXJCRERERPVPo+TE0NAQJSUlytdJSUlVVuqixovbuoiIiIhIlzRKTjp06IAzZ85AJpMpr1XWFZ4at8d9TnggnoiIiIjqn0ZPoVOnTsWaNWvQunVrWFpaAgA+/fRT7N69u9r3iUQiJCYm1j5KqhcPSxTVurhyQkRERET1T6Pk5IMPPoCJiQl++eUX3L59GyKRCHK5HHK5vNr3Pe0+NSw8EE9EREREuqRRcmJgYID33nsP7733HgBAT08PCxcuxIoVK+o0OKpf+UWPtnUZc1sXEREREdU/jc6cHDlyBNeuXVO+XrlyJYYMGVJXMZGOKLZ1teS2LiIiIiLSAUGlhIOCghATE1NXMZGOcFsXEREREekSSwmTEvucEBEREZEusZQwKbGUMBERERHpEksJkxKbMBIRERGRLrGUMAEAysrkKCjhti4iIiIi0h2WEiYAQGHp4y17XDkhIiIiIl3Q6MzJk1hKuOlRbOkCABMDJidEREREVP8EnXxeuXKltuMgHVMchm9hqA89PRY7ICIiIqL6J2jlBABKS0vx6aefol+/fpBIJDAweJznxMTEYP78+SqNG6lh42F4IiIiItI1QSsnBQUFGD58OM6ePYs2bdpAIpEgPz9feb9jx47YvXs3WrdujY8++khrwVLdefioASMPwxMRERGRrghaOQkICEBkZCTWrVuHjIwMzJ49W+W+ubk5PDw8cOzYMa0ESXWvgCsnRERERKRjgpKT4OBgeHp6YsmSJRCJRJU2ZHRyckJKSkqtA6T68ZANGImIiIhIxwQlJykpKejTp0+1Y8RiMaRSqaCgqP6ZmRigX8fW6NFOoutQiIiIiKiZEvTX5GKxGJmZmdWOSUxMhJWVlaCgqP65O1niwJwBug6DiIiIiJoxQSsn7u7u+Pnnn5GdnV3p/dTUVPz6668YPHhwbWIjIiIiIqJmRFBy8s477+DBgwfw9vZGZGQkSkvLKz09fPgQJ0+ehI+PD0pLS7Fo0SLBgUVHR2PkyJGwsLCAqakp3N3dceDAgRrPk5mZiYULF8LZ2RkmJiawtLTEgAEDsH379krHl5WVYdeuXXj++edhYWGBli1bokuXLpg5cyZyc3PVxqenp2PWrFmwtbWFiYkJunbtirVr16KkpKTGsRIRERERNWciuVwuF/LG7du3Y8GCBZDJZGr39PX1sW3bNrUqXpoKCwuDj48PTExM4OfnB7FYjJCQECQnJ2PDhg1YvHixRvPExMRg+PDhePDgAUaNGoVu3bohLy8PcXFxMDIywq+//qoyvqioCBMnTsTRo0fh5uYGT09PGBsbIyUlBadOncKlS5fQvn175fiMjAz069cPaWlpGD9+PJydnREeHo6oqCiMGTMGhw4dqrRYQFVycnJgbm4OqVQKiYRnP4iIiIioadD0OVdwcgIAcXFx+PLLL3H+/Hncv38fEokE/fv3x/z589GjRw9Bc5aWlsLFxQVpaWmIiopCr169AABSqRT9+vVDUlISrl27BgcHh2rnycnJgaurKwoKCnDixAm4ubmpfU7FxpEAsHDhQnz22WcIDAzEu+++q3KvrKwMAKCn93ixacaMGfj222+xfft2zJ07FwAgl8sxdepU7N+/H3v37sXLL7+s8XdnckJERERETVG9JCd1ITQ0FD4+Ppg5cyZ27dqlci8oKAj+/v5YvXo1VqxYUe08gYGBWLp0KXbu3IlXX331qZ9769YtODo6YsCAAYiIiHjq+NzcXFhZWcHOzg7//vuvygpJcnIyHB0d4enpiVOnTj11LgUmJ0RERETUFGn6nNvgmlqcPn0aADB8+HC1ez4+PgCA8PDwp84THBwMkUiECRMmICEhAaGhoSgoKICLiwtefPFFGBkZqYw/ePAgSktLMWnSJOTm5uLIkSNISUmBjY0NfHx8YGdnpzL+3LlzKCoqwrBhw9S2bjk4OKBr166IjIyETCaDvj4bGxIRERERPU2DS06uX78OAHB2dla717ZtW5iZmSnHVKW4uBhXrlyBlZUVtmzZgpUrVyq3ZQHlDSIPHToEV1dX5bVLly4BALKzs9G1a1ekp6cr7xkZGSEwMBALFy7UKE7F9YSEBCQnJ8PJyanSMUVFRSgqKlK+zsnJqfZ7ERERERE1ZYKqddUlReNGc3PzSu9LJJKnNne8f/8+ZDIZsrKysGbNGqxfvx537txBWloali9fjps3b8LX1xeFhYXK9yj6tqxevRo9e/bE1atXkZOTg6NHj6JNmzZYtGgRfvvttxrFWXFcZdatWwdzc3Plj729fbXfi4iIiIioKWtwyYk2KFZJZDIZ5s+fj8WLF8Pa2hp2dnZYs2YNJk2ahOTkZBw8eFDtPdbW1ggJCUH37t0hFosxatQo7NixAwCwceNGrca5dOlSSKVS5U9qaqpW5yciIiIiakwaXHKiWImoasVBcZhGkzkAYMyYMWr3FdcuXryo9p6hQ4eiZcuWKuN9fHxgbGxc6fjq4nwylicZGxtDIpGo/BARERERNVcNLjlRnOGo7FxJRkYG8vLyqjznoWBqaqo8wG5hYaF2X3GtoKBAea1r165VjtfT04NYLFYZX12ciutGRkbo0KFDtbESEREREVG5BpeceHh4ACgvKfykY8eOqYypjpeXFwAgNjZW7Z7imqOjo0bj7969i3v37qmMd3d3h5GREY4fP44nqzEnJycjISEBgwYNUuulQkRERERElWtwyYm3tzecnJywd+9exMTEKK9LpVIEBATAyMgI06dPV15PT09HfHy82vYqRVPEwMBAZGdnK69nZGRg8+bN0NPTw4QJE5TXPTw80K1bN5w8eRLHjx9XXpfL5Vi2bBkAYPLkycrrEokEfn5+uHHjBr766iuV8UuXLgUAvPbaa7X4kyAiIiIial4aXBNGAAgLC4OPjw9MTEzg5+cHsViMkJAQJCcnY8OGDVi8eLFyrL+/P4KCgrB79274+/urzLN48WJs2rQJ9vb28PX1RUlJCQ4fPozMzEwEBAQokwiF8+fPw8vLC8XFxXjppZfQvn17nDlzBhcuXEDv3r0REREBU1NT5fj09HT0798faWlpeOmll9C5c2eEh4cjKioKvr6+OHz4sFoPlOqwCSMRERERNUWaPuc2uJUTAPD09MSZM2cwaNAgBAcHY/v27bCxscH+/ftVEpOn2bhxI3bv3g0bGxvs2bMHe/fuRZcuXfDjjz+qJSYA0L9/f1y4cAFjx47FyZMnsWXLFmRlZWHp0qUIDw9XSUwAwNbWFufPn8fMmTNx5swZfPrpp8jKysKHH36IgwcP1igxISIiIiJq7hrkyklzxZUTIiIiImqKGvXKCRERERERNT9MToiIiIiIqEFgndsGRLHDTtHAkYiIiIioKVA83z7tRAmTkwYkNzcXAGBvb6/jSIiIiIiItC83Nxfm5uZV3ueB+AakrKwMt2/fhlgsrrdKXzk5ObC3t0dqaioP4Tcz/Gf//+3de1SUdf4H8PdwVYab3ER0BUE084KaGoQ3EgUvZCu4rlaCgHm31VzynFpRN3N1ca2wqPUEZJ3VMpUNL6CbYEYisWubrjcUok1UTEAEFBA+vz9+Z2adZrjJMzDp+3XOnCPf7zPf+XyfjzPzfOa5PbqY+0cb8//oYu4fbZ2dfxHB7du34eHhATOzps8s4Z4TE2JmZoZevXp1ymvb29vzg+oRxdw/upj7Rxvz/+hi7h9tnZn/5vaYaPCEeCIiIiIiMgksToiIiIiIyCSwOHnEWVtbIz4+HtbW1p0dCnUw5v7Rxdw/2pj/Rxdz/2j7peSfJ8QTEREREZFJ4J4TIiIiIiIyCSxOiIiIiIjIJLA4ISIiIiIik8DihIiIiIiITAKLk4fMN998gylTpsDR0RFqtRr+/v749NNP2zRGbW0t1q9fD19fX3Tp0gUeHh548cUXUVpaaqSoSSntyb+I4NChQ1i0aBGGDBkCBwcH2NjYwM/PD2+88Qbu3r1r5OipPZR479+vvLwcPXv2hEqlQmhoqIKRkjEolf/S0lKsWLFC+/nv7OyMgIAAJCUlGSFqUoISuS8pKcFLL72Exx9/HGq1Gt27d8fo0aPx0UcfoaGhwUiRU3t9/PHHWLBgAUaMGAFra2uoVCqkpqa2eZzGxkYkJiZi8ODB6Nq1K1xdXTF79mwUFhYqH3RrCD00jh49KpaWlmJnZyfz58+XlStXiqenpwCQhISEVo3R0NAgISEhAkD8/f3llVdekRkzZohKpRJvb28pLS018izoQbU3/3fu3BEAYm1tLSEhIbJq1SpZunSp+Pr6CgAZOXKkVFdXd8BMqK2UeO//3Jw5c0StVgsACQkJUThiUpJS+T916pS4urqKhYWFTJ8+XVavXi1Lly6VCRMmyOTJk404A3pQSuT+8uXL4uLiIiqVSkJDQyUuLk4WLlwo7u7uAkCioqKMPAt6UJpcu7i4aP+dkpLS5nFiY2MFgAwcOFDi4uLk+eefFysrK3FycpKLFy8qH3gLWJw8JOrr68XHx0esra3l1KlT2vaKigrp16+fWFlZyffff9/iOMnJyQJAZs+eLY2Njdr2pKQkASAvvviiMcKndlIi/3V1dfL6669LWVmZXntYWJgAkM2bNxsjfGoHpd779/vss88EgGzbto3FiYlTKv+3bt2S3r17i6urq/z73/82+DpkWpTK/aJFiwSAvPnmmzrt5eXl0rt3bwHQ5s8Q6hhHjhzR5mbjxo0PVJwcPXpUAMjYsWOltrZW237w4EEBIJMmTVIy5FZhcfKQyMzMFAAyb948vb7U1FQBIOvWrWtxnICAAIMfRI2NjeLt7S1qtVpqamoUi5uUoVT+m/L1118LAJk6dWp7wiQjUDr3paWl4urqKi+88IIUFRWxODFxSuVfs2HzwQcfGCNMMgKlcq85WsLQL+Rz5swRAJKfn69IzGQ8D1qczJ49WwDIsWPH9PrGjx8vAKS4uFihKFuH55w8JLKzswEAkyZN0usLCQkBABw7dqzZMe7evYuTJ0+if//+8PT01OlTqVSYOHEiqqurkZ+fr0zQpBgl8t8cS0tLAICFhcUDj0HGoXTuFy5cCHNzc7z11luKxEfGpVT+P/nkE6hUKoSHh+PChQtITEzE5s2b8fnnn6Ourk7RmEkZSuV+0KBBAICDBw/qtFdUVCAnJwfu7u54/PHH2xktmars7Gyo1WoEBgbq9Smx/fAguKXxkCgoKAAA+Pr66vW5u7vD1tZWu0xTLl++jMbGRoNj3D92QUEBxowZ086ISUlK5L85ycnJAAx/CVLnUjL3H3/8Mfbu3Yu0tDR069YNt27dUjRWUp4S+a+rq8Pp06fh6uqKxMRExMfHo7GxUdvv7e2NtLQ0DB48WNngqV2Ueu///ve/R3p6OlasWIGMjAwMGTIElZWVSEtLg42NDfbt24euXbsqHj91vurqaly9ehWDBg2Cubm5Xv/9230diXtOHhKajQgHBweD/fb29i1uaLRmjPuXI9OhRP6bcujQIbz//vsYMGAAYmJiHjhGMg6lcl9SUoLly5dj9uzZmD59uqIxkvEokf+ysjI0NDTg5s2bWL9+PTZv3ozr16/jxx9/xB/+8AcUFRUhLCyMV+wzMUq997t3744TJ04gNDQUGRkZ2Lx5M9577z3cunULc+fOhZ+fn6Jxk+kw1e0+FidE1KRvvvkGs2bNgoODA3bv3g1ra+vODomMJDY2FpaWlnj77bc7OxTqYJq9JA0NDVi8eDFefvlluLm5oWfPnli/fj1mzpyJ4uJifPbZZ50cKRnDpUuXEBgYiBs3buD48eO4ffs2/vvf/2LNmjX44x//iAkTJvBywtShWJw8JDRVb1PVbWVlZZOVcVvGuH85Mh1K5P/n8vPzMWnSJJiZmSEzMxMDBw5sd5ykPCVy/+GHH+LQoUN455134OLioniMZDxKfvYDwDPPPKPXr2nj+YamRanP/aioKBQXFyM9PR2jR4+Gra0tevXqhdWrV2PZsmU4ceIEdu3apWjsZBpMdbuPxclDornjAq9du4aqqqomzyXR8Pb2hpmZWZPHFjZ3fCt1LiXyf7/8/HxMnDgRjY2NyMzMxMiRIxWLlZSlRO5PnToFAJg5cyZUKpX20adPHwBAZmYmVCoVhg4dqmzw1G5K5F+tVqNnz54AAEdHR71+TdudO3faFywpSonc3759Gzk5ORgwYADc3d31+oOCggD87zOCHi5qtRo9evRAUVGRwb1jnbXdx+LkITFu3DgAwOHDh/X6MjMzdZZpSteuXTFq1ChcuHABxcXFOn0igiNHjkCtVmPEiBEKRU1KUSL/GprCpKGhARkZGXjyySeVC5QUp0TuAwICEBMTo/eYNWsWAKBXr16IiYnBjBkzFI6e2kup9/7TTz8NADh79qxen6bNy8vrQcMkI1Ai95orsf30008G+2/cuAEAPKT3ITZu3DhUV1cjJydHr0/z/2js2LEdG1SHXriYjKa+vl68vb2bvRlTUVGRtr2kpETOnTsnFRUVOuPwJoy/TErlPz8/XxwdHcXW1la++uqrDoqe2kOp3BvC+5yYPqXyn5OTo71DdHl5ubb96tWr0rNnTzEzM5MLFy4YeTbUFkrlvn///gJAtm/frtNeXl4ujz32mACQI0eOGHMqpICW7nNy48YNOXfunNy4cUOnnTdhJKM6evSoWFpaip2dncyfP19Wrlwpnp6eAkASEhJ0lo2MjDT4n7ihoUF7QyZ/f3955ZVXJDw8XFQqlfTp00dKS0s7cEbUFu3N/82bN6Vbt24CQEJDQyU+Pl7vsXXr1o6dFLWKEu99Q1ic/DIolf+VK1cKAPnVr34lixcvlvnz54ubm5sAkDfeeKODZkNtoUTuDx48KBYWFgJAJkyYIKtWrZKYmBhxdXUVABIeHt6BM6K22L59u0RGRkpkZKQMHz5cAEhgYKC27f6CMz4+XgBIfHy83jixsbHaHyfi4uLkhRdeECsrK3FycuqUHyVYnDxkTp48KaGhoWJvby9du3aVUaNGya5du/SWa+4L6u7du7J27Vrx8fERKysrcXd3l9jYWLl27VoHzIDaoz3512yINvfw9PTsuMlQmyjx3v85Fie/HErlPyUlRUaMGCE2NjaiVqtl9OjRsnfvXiNHT+2hRO7z8vJk5syZ0qNHD7GwsBBbW1sZOXKkJCYmyr179zpgFvQgNDlt6hEZGaldtrnipKGhQd566y0ZOHCgWFtbi7Ozs8yaNUsuXbrUcZO5j0pEROEjxYiIiIiIiNqMJ8QTEREREZFJYHFCREREREQmgcUJERERERGZBBYnRERERERkElicEBERERGRSWBxQkREREREJoHFCRERERERmQQWJ0REREREZBJYnBAR0SPFy8sLXl5enR0GVCoVxo8f39lhEBEBAL788kuEhYXBw8MDKpUKaWlpbR5DRJCQkIB+/frB2toaPXv2xIYNG9o0hkWbX5WIiIiIiB4q1dXV8PPzQ3R0NGbMmPFAY7z00ks4fPgwEhISMHjwYJSVlaGsrKxNY7A4ISIi6gTnzp2DjY1NZ4dBRAQAmDx5MiZPntxkf21tLV599VXs3LkTFRUVGDRoEDZt2qTdA3zu3DkkJSXhzJkz6N+/PwCgT58+bY6Dh3URERF1gsceewy9e/fu7DCIiFpl6dKlOHHiBHbt2oXvvvsOM2fORGhoKAoKCgAA6enp8Pb2xv79+9GnTx94eXkhNja2zXtOWJwQEVGT9uzZg3HjxsHNzQ1dunSBh4cHgoODsWfPHp3lkpOTMX36dHh5eaFLly5wcnJCSEgIsrKy9MbMzs6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"text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], diff --git a/tutorials/qnn_research/Fisher_EN.ipynb b/tutorials/qnn_research/Fisher_EN.ipynb index 871b91c..a6250df 100644 --- a/tutorials/qnn_research/Fisher_EN.ipynb +++ b/tutorials/qnn_research/Fisher_EN.ipynb @@ -272,9 +272,22 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import paddle\n", "from paddle_quantum.ansatz import Circuit\n", @@ -309,7 +322,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -322,14 +335,14 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "--Ry(2.384)----Rz(5.641)--\n", + "--Ry(0.754)----Rz(6.117)--\n", " \n" ] } @@ -348,76 +361,76 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The QFIM at [0. 5.64109135] is \n", - " [[ 9.99999881e-01 0.00000000e+00]\n", - " [ 0.00000000e+00 -5.96046400e-08]].\n", - "The QFIM at [0.15707963 5.64109135] is \n", - " [[1.00000000e+00 6.53168000e-09]\n", - " [6.53168000e-09 2.44715806e-02]].\n", - "The QFIM at [0.31415927 5.64109135] is \n", - " [[1.0000000e+00 6.0467490e-08]\n", - " [6.0467490e-08 9.5491401e-02]].\n", - "The QFIM at [0.4712389 5.64109135] is \n", + "The QFIM at [0. 6.11720181] is \n", + " [[1.00000024e+00 0.00000000e+00]\n", + " [0.00000000e+00 2.38418590e-07]].\n", + "The QFIM at [0.15707963 6.11720181] is \n", + " [[1.00000024e+00 4.52859700e-08]\n", + " [4.52859700e-08 2.44718779e-02]].\n", + "The QFIM at [0.31415927 6.11720181] is \n", + " [[1.00000024e+00 4.79417900e-08]\n", + " [4.79417900e-08 9.54915827e-02]].\n", + "The QFIM at [0.4712389 6.11720181] is \n", + " [[1.00000000e+00 4.99490500e-08]\n", + " [4.99490500e-08 2.06107258e-01]].\n", + "The QFIM at [0.62831853 6.11720181] is \n", + " [[1.00000024 0. ]\n", + " [0. 0.34549158]].\n", + "The QFIM at [0.78539816 6.11720181] is \n", + " [[ 1.00000024e+00 -6.65203000e-08]\n", + " [-6.65203000e-08 5.00000213e-01]].\n", + "The QFIM at [0.9424778 6.11720181] is \n", + " [[1.00000024 0. ]\n", + " [0. 0.65450871]].\n", + "The QFIM at [1.09955743 6.11720181] is \n", " [[1.00000000e+00 3.25239200e-08]\n", - " [3.25239200e-08 2.06107365e-01]].\n", - "The QFIM at [0.62831853 5.64109135] is \n", - " [[0.99999988 0. ]\n", - " [0. 0.34549142]].\n", - "The QFIM at [0.78539816 5.64109135] is \n", - " [[ 9.99999881e-01 -3.67179700e-08]\n", - " [-3.67179700e-08 4.99999940e-01]].\n", - "The QFIM at [0.9424778 5.64109135] is \n", + " [3.25239200e-08 7.93892663e-01]].\n", + "The QFIM at [1.25663706 6.11720181] is \n", " [[1. 0. ]\n", - " [0. 0.65450851]].\n", - "The QFIM at [1.09955743 5.64109135] is \n", - " [[0.99999976 0. ]\n", - " [0. 0.79389244]].\n", - "The QFIM at [1.25663706 5.64109135] is \n", - " [[0.99999988 0. ]\n", - " [0. 0.90450845]].\n", - "The QFIM at [1.41371669 5.64109135] is \n", - " [[ 1.00000000e+00 -4.52859700e-08]\n", - " [-4.52859700e-08 9.75528206e-01]].\n", - "The QFIM at [1.57079633 5.64109135] is \n", - " [[1.000000e+00 4.214685e-08]\n", - " [4.214685e-08 1.000000e+00]].\n", - "The QFIM at [1.72787596 5.64109135] is \n", + " [0. 0.90450854]].\n", + "The QFIM at [1.41371669 6.11720181] is \n", + " [[1.0000000e+00 4.5285970e-08]\n", + " [4.5285970e-08 9.7552822e-01]].\n", + "The QFIM at [1.57079633 6.11720181] is \n", + " [[ 1.000000e+00 -4.214685e-08]\n", + " [-4.214685e-08 1.000000e+00]].\n", + "The QFIM at [1.72787596 6.11720181] is \n", " [[1. 0. ]\n", - " [0. 0.97552827]].\n", - "The QFIM at [1.88495559 5.64109135] is \n", - " [[ 1.00000000e+00 -3.54160800e-08]\n", - " [-3.54160800e-08 9.04508529e-01]].\n", - "The QFIM at [2.04203522 5.64109135] is \n", - " [[ 9.99999881e-01 -8.24729700e-08]\n", - " [-8.24729700e-08 7.93892489e-01]].\n", - "The QFIM at [2.19911486 5.64109135] is \n", - " [[ 1.00000000e+00 -1.02392670e-07]\n", - " [-1.02392670e-07 6.54508507e-01]].\n", - "The QFIM at [2.35619449 5.64109135] is \n", - " [[9.99999762e-01 3.67179700e-08]\n", - " [3.67179700e-08 4.99999905e-01]].\n", - "The QFIM at [2.51327412 5.64109135] is \n", - " [[ 9.99999881e-01 -3.05229200e-08]\n", - " [-3.05229200e-08 3.45491419e-01]].\n", - "The QFIM at [2.67035376 5.64109135] is \n", - " [[1.0000000e+00 3.2523910e-08]\n", - " [3.2523910e-08 2.0610763e-01]].\n", - "The QFIM at [2.82743339 5.64109135] is \n", - " [[9.99999881e-01 4.79417900e-08]\n", - " [4.79417900e-08 9.54914519e-02]].\n", - "The QFIM at [2.98451302 5.64109135] is \n", + " [0. 0.97552828]].\n", + "The QFIM at [1.88495559 6.11720181] is \n", + " [[1.00000024e+00 3.54160800e-08]\n", + " [3.54160800e-08 9.04508740e-01]].\n", + "The QFIM at [2.04203522 6.11720181] is \n", + " [[ 1.00000024e+00 -9.98981200e-08]\n", + " [-9.98981200e-08 7.93892820e-01]].\n", + "The QFIM at [2.19911486 6.11720181] is \n", + " [[ 1.00000024e+00 -5.11963400e-08]\n", + " [-5.11963400e-08 6.54508710e-01]].\n", + "The QFIM at [2.35619449 6.11720181] is \n", + " [[1.00000024e+00 6.65203000e-08]\n", + " [6.65203000e-08 5.00000256e-01]].\n", + "The QFIM at [2.51327412 6.11720181] is \n", + " [[1.00000024e+00 3.05229200e-08]\n", + " [3.05229200e-08 3.45491583e-01]].\n", + "The QFIM at [2.67035376 6.11720181] is \n", + " [[1.00000024e+00 3.25239100e-08]\n", + " [3.25239100e-08 2.06107816e-01]].\n", + "The QFIM at [2.82743339 6.11720181] is \n", + " [[ 1.00000024e+00 -1.25257200e-08]\n", + " [-1.25257200e-08 9.54918095e-02]].\n", + "The QFIM at [2.98451302 6.11720181] is \n", " [[1. 0. ]\n", - " [0. 0.02447182]].\n", - "The QFIM at [3.14159265 5.64109135] is \n", - " [[ 9.99999881e-01 8.42936900e-08]\n", - " [ 8.42936900e-08 -5.96046400e-08]].\n" + " [0. 0.02447176]].\n", + "The QFIM at [3.14159265 6.11720181] is \n", + " [[1.00000024e+00 4.21468500e-08]\n", + " [4.21468500e-08 2.38418590e-07]].\n" ] } ], @@ -446,19 +459,17 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -512,7 +523,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 6, "metadata": {}, "outputs": [], "source": [ @@ -527,16 +538,16 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "--Ry(0.069)----*----Ry(5.656)--\n", + "--Ry(5.330)----*----Ry(2.760)--\n", " | \n", - "--Ry(0.001)----x----Ry(5.061)--\n", + "--Ry(4.243)----x----Ry(1.829)--\n", " \n" ] } @@ -555,54 +566,54 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The QFI norm along [1, 1, 1, 1] at [0. 0. 5.65593147 5.06090069] is 6.00792258.\n", - "The QFI norm along [1, 1, 1, 1] at [0.31415927 0.31415927 5.65593147 5.06090069] is 5.93163433.\n", - "The QFI norm along [1, 1, 1, 1] at [0.62831853 0.62831853 5.65593147 5.06090069] is 5.85534601.\n", - "The QFI norm along [1, 1, 1, 1] at [0.9424778 0.9424778 5.65593147 5.06090069] is 5.83627391.\n", - "The QFI norm along [1, 1, 1, 1] at [1.25663706 1.25663706 5.65593147 5.06090069] is 5.93163433.\n", - "The QFI norm along [1, 1, 1, 1] at [1.57079633 1.57079633 5.65593147 5.06090069] is 6.01269060.\n", - "The QFI norm along [1, 1, 1, 1] at [1.88495559 1.88495559 5.65593147 5.06090069] is 5.87441809.\n", - "The QFI norm along [1, 1, 1, 1] at [2.19911486 2.19911486 5.65593147 5.06090069] is 5.37854233.\n", - "The QFI norm along [1, 1, 1, 1] at [2.51327412 2.51327412 5.65593147 5.06090069] is 4.49644803.\n", - "The QFI norm along [1, 1, 1, 1] at [2.82743339 2.82743339 5.65593147 5.06090069] is 3.28057238.\n", - "The QFI norm along [1, 1, 1, 1] at [3.14159265 3.14159265 5.65593147 5.06090069] is 1.98361799.\n", - "The QFI norm along [1, 1, 1, 1] at [3.45575192 3.45575192 5.65593147 5.06090069] is 0.87260724.\n", - "The QFI norm along [1, 1, 1, 1] at [3.76991118 3.76991118 5.65593147 5.06090069] is 0.25749165.\n", - "The QFI norm along [1, 1, 1, 1] at [4.08407045 4.08407045 5.65593147 5.06090069] is 0.26702836.\n", - "The QFI norm along [1, 1, 1, 1] at [4.39822972 4.39822972 5.65593147 5.06090069] is 0.91552211.\n", - "The QFI norm along [1, 1, 1, 1] at [4.71238898 4.71238898 5.65593147 5.06090069] is 2.04083701.\n", - "The QFI norm along [1, 1, 1, 1] at [5.02654825 5.02654825 5.65593147 5.06090069] is 3.32825413.\n", - "The QFI norm along [1, 1, 1, 1] at [5.34070751 5.34070751 5.65593147 5.06090069] is 4.54412905.\n", - "The QFI norm along [1, 1, 1, 1] at [5.65486678 5.65486678 5.65593147 5.06090069] is 5.40715063.\n", - "The QFI norm along [1, 1, 1, 1] at [5.96902604 5.96902604 5.65593147 5.06090069] is 5.89349018.\n", - "The QFI norm along [1, 1, 1, 1] at [6.28318531 6.28318531 5.65593147 5.06090069] is 6.01269060.\n", - "The QFI norm along [1, 1, 1, 1] at [6.59734457 6.59734457 5.65593147 5.06090069] is 5.94117037.\n", - "The QFI norm along [1, 1, 1, 1] at [6.91150384 6.91150384 5.65593147 5.06090069] is 5.85057798.\n", - "The QFI norm along [1, 1, 1, 1] at [7.2256631 7.2256631 5.65593147 5.06090069] is 5.83150589.\n", - "The QFI norm along [1, 1, 1, 1] at [7.53982237 7.53982237 5.65593147 5.06090069] is 5.93163433.\n", - "The QFI norm along [1, 1, 1, 1] at [7.85398163 7.85398163 5.65593147 5.06090069] is 6.00315457.\n", - "The QFI norm along [1, 1, 1, 1] at [8.1681409 8.1681409 5.65593147 5.06090069] is 5.87918611.\n", - "The QFI norm along [1, 1, 1, 1] at [8.48230016 8.48230016 5.65593147 5.06090069] is 5.38331038.\n", - "The QFI norm along [1, 1, 1, 1] at [8.79645943 8.79645943 5.65593147 5.06090069] is 4.49167993.\n", - "The QFI norm along [1, 1, 1, 1] at [9.1106187 9.1106187 5.65593147 5.06090069] is 3.29487691.\n", - "The QFI norm along [1, 1, 1, 1] at [9.42477796 9.42477796 5.65593147 5.06090069] is 1.98361799.\n", - "The QFI norm along [1, 1, 1, 1] at [9.73893723 9.73893723 5.65593147 5.06090069] is 0.88691220.\n", - "The QFI norm along [1, 1, 1, 1] at [10.05309649 10.05309649 5.65593147 5.06090069] is 0.24795494.\n", - "The QFI norm along [1, 1, 1, 1] at [10.36725576 10.36725576 5.65593147 5.06090069] is 0.26702836.\n", - "The QFI norm along [1, 1, 1, 1] at [10.68141502 10.68141502 5.65593147 5.06090069] is 0.90598547.\n", - "The QFI norm along [1, 1, 1, 1] at [10.99557429 10.99557429 5.65593147 5.06090069] is 2.02176400.\n", - "The QFI norm along [1, 1, 1, 1] at [11.30973355 11.30973355 5.65593147 5.06090069] is 3.32825413.\n", - "The QFI norm along [1, 1, 1, 1] at [11.62389282 11.62389282 5.65593147 5.06090069] is 4.52982475.\n", - "The QFI norm along [1, 1, 1, 1] at [11.93805208 11.93805208 5.65593147 5.06090069] is 5.40715063.\n", - "The QFI norm along [1, 1, 1, 1] at [12.25221135 12.25221135 5.65593147 5.06090069] is 5.88395414.\n", - "The QFI norm along [1, 1, 1, 1] at [12.56637061 12.56637061 5.65593147 5.06090069] is 6.00792258.\n" + "The QFI norm along [1, 1, 1, 1] at [0. 0. 2.75956345 1.82911766] is 5.99838655.\n", + "The QFI norm along [1, 1, 1, 1] at [0.31415927 0.31415927 2.75956345 1.82911766] is 5.91733027.\n", + "The QFI norm along [1, 1, 1, 1] at [0.62831853 0.62831853 2.75956345 1.82911766] is 5.83150589.\n", + "The QFI norm along [1, 1, 1, 1] at [0.9424778 0.9424778 2.75956345 1.82911766] is 5.83627391.\n", + "The QFI norm along [1, 1, 1, 1] at [1.25663706 1.25663706 2.75956345 1.82911766] is 5.93163433.\n", + "The QFI norm along [1, 1, 1, 1] at [1.57079633 1.57079633 2.75956345 1.82911766] is 6.00792258.\n", + "The QFI norm along [1, 1, 1, 1] at [1.88495559 1.88495559 2.75956345 1.82911766] is 5.85534601.\n", + "The QFI norm along [1, 1, 1, 1] at [2.19911486 2.19911486 2.75956345 1.82911766] is 5.38331038.\n", + "The QFI norm along [1, 1, 1, 1] at [2.51327412 2.51327412 2.75956345 1.82911766] is 4.49167993.\n", + "The QFI norm along [1, 1, 1, 1] at [2.82743339 2.82743339 2.75956345 1.82911766] is 3.28057238.\n", + "The QFI norm along [1, 1, 1, 1] at [3.14159265 3.14159265 2.75956345 1.82911766] is 1.98361799.\n", + "The QFI norm along [1, 1, 1, 1] at [3.45575192 3.45575192 2.75956345 1.82911766] is 0.87737556.\n", + "The QFI norm along [1, 1, 1, 1] at [3.76991118 3.76991118 2.75956345 1.82911766] is 0.25272329.\n", + "The QFI norm along [1, 1, 1, 1] at [4.08407045 4.08407045 2.75956345 1.82911766] is 0.26702836.\n", + "The QFI norm along [1, 1, 1, 1] at [4.39822972 4.39822972 2.75956345 1.82911766] is 0.91552211.\n", + "The QFI norm along [1, 1, 1, 1] at [4.71238898 4.71238898 2.75956345 1.82911766] is 2.03130050.\n", + "The QFI norm along [1, 1, 1, 1] at [5.02654825 5.02654825 2.75956345 1.82911766] is 3.31871778.\n", + "The QFI norm along [1, 1, 1, 1] at [5.34070751 5.34070751 2.75956345 1.82911766] is 4.53459285.\n", + "The QFI norm along [1, 1, 1, 1] at [5.65486678 5.65486678 2.75956345 1.82911766] is 5.40715063.\n", + "The QFI norm along [1, 1, 1, 1] at [5.96902604 5.96902604 2.75956345 1.82911766] is 5.87441809.\n", + "The QFI norm along [1, 1, 1, 1] at [6.28318531 6.28318531 2.75956345 1.82911766] is 5.99838655.\n", + "The QFI norm along [1, 1, 1, 1] at [6.59734457 6.59734457 2.75956345 1.82911766] is 5.92209829.\n", + "The QFI norm along [1, 1, 1, 1] at [6.91150384 6.91150384 2.75956345 1.82911766] is 5.83627391.\n", + "The QFI norm along [1, 1, 1, 1] at [7.2256631 7.2256631 2.75956345 1.82911766] is 5.83627391.\n", + "The QFI norm along [1, 1, 1, 1] at [7.53982237 7.53982237 2.75956345 1.82911766] is 5.93640235.\n", + "The QFI norm along [1, 1, 1, 1] at [7.85398163 7.85398163 2.75956345 1.82911766] is 5.99838655.\n", + "The QFI norm along [1, 1, 1, 1] at [8.1681409 8.1681409 2.75956345 1.82911766] is 5.86965007.\n", + "The QFI norm along [1, 1, 1, 1] at [8.48230016 8.48230016 2.75956345 1.82911766] is 5.37854233.\n", + "The QFI norm along [1, 1, 1, 1] at [8.79645943 8.79645943 2.75956345 1.82911766] is 4.49644803.\n", + "The QFI norm along [1, 1, 1, 1] at [9.1106187 9.1106187 2.75956345 1.82911766] is 3.29010873.\n", + "The QFI norm along [1, 1, 1, 1] at [9.42477796 9.42477796 2.75956345 1.82911766] is 1.98361799.\n", + "The QFI norm along [1, 1, 1, 1] at [9.73893723 9.73893723 2.75956345 1.82911766] is 0.87737556.\n", + "The QFI norm along [1, 1, 1, 1] at [10.05309649 10.05309649 2.75956345 1.82911766] is 0.24795494.\n", + "The QFI norm along [1, 1, 1, 1] at [10.36725576 10.36725576 2.75956345 1.82911766] is 0.26702836.\n", + "The QFI norm along [1, 1, 1, 1] at [10.68141502 10.68141502 2.75956345 1.82911766] is 0.90598547.\n", + "The QFI norm along [1, 1, 1, 1] at [10.99557429 10.99557429 2.75956345 1.82911766] is 2.02653225.\n", + "The QFI norm along [1, 1, 1, 1] at [11.30973355 11.30973355 2.75956345 1.82911766] is 3.32348596.\n", + "The QFI norm along [1, 1, 1, 1] at [11.62389282 11.62389282 2.75956345 1.82911766] is 4.52505665.\n", + "The QFI norm along [1, 1, 1, 1] at [11.93805208 11.93805208 2.75956345 1.82911766] is 5.40238258.\n", + "The QFI norm along [1, 1, 1, 1] at [12.25221135 12.25221135 2.75956345 1.82911766] is 5.87441809.\n", + "The QFI norm along [1, 1, 1, 1] at [12.56637061 12.56637061 2.75956345 1.82911766] is 5.98885053.\n" ] } ], @@ -628,19 +639,17 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -681,16 +690,16 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "--Ry(3.567)----*----Ry(2.500)--\n", + "--Ry(5.171)----*----Ry(3.574)--\n", " | \n", - "--Ry(2.784)----x----Ry(2.298)--\n", + "--Ry(5.103)----x----Ry(1.247)--\n", " \n", "The number of parameters is 4.\n", "The EQD is 3. \n", @@ -717,16 +726,16 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "--Ry(2.514)----Rx(3.037)----*----Ry(5.264)----Rx(0.932)--\n", + "--Ry(4.515)----Rx(5.898)----*----Ry(1.415)----Rx(2.717)--\n", " | \n", - "--Ry(5.648)----Rx(5.991)----x----Ry(4.027)----Rx(2.537)--\n", + "--Ry(1.522)----Rx(2.778)----x----Ry(3.684)----Rx(0.956)--\n", " \n", "The number of parameters is 8.\n", "The EQD is 6. \n", @@ -771,12 +780,14 @@ }, { "cell_type": "code", - "execution_count": 27, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "import paddle.nn as nn\n", - "from paddle_quantum.gate import IQPEncoding, ComplexEntangledLayer, RX\n", + "from paddle_quantum.ansatz.layer import ComplexEntangledLayer\n", + "from paddle_quantum.gate import IQPEncoding, RX\n", + "from paddle_quantum.loss import ExpecVal\n", "from paddle_quantum.hamiltonian import Hamiltonian\n", "from paddle_quantum.state import zero_state\n", "\n", @@ -786,6 +797,7 @@ " self.num_qubits, self.encoding = num_qubits, encoding\n", " self.S = [[i, i + 1] for i in range(num_qubits - 1)]\n", " self.init_state = zero_state(num_qubits)\n", + " self.loss_func = ExpecVal(Hamiltonian([[1.0, 'z0']]))\n", " \n", " if encoding == 'IQP':\n", " self.complex_layer = nn.LayerList([ComplexEntangledLayer(num_qubits=num_qubits, depth=depth)])\n", @@ -809,7 +821,7 @@ " state = RX(j, param=x[j].item())(state)\n", " state = self.complex_layers[depth](state)\n", "\n", - " return state.expec_val(Hamiltonian([[1.0, 'z0']])) * 0.5 + 0.5" + " return self.loss_func(state) * 0.5 + 0.5" ] }, { @@ -821,14 +833,14 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "running in get_gradient: 100%|##################################| 1000/1000 [00:47<00:00, 20.99it/s]\n" + "running in get_gradient: 100%|##################################| 1000/1000 [00:26<00:00, 37.54it/s]\n" ] } ], @@ -864,26 +876,24 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "the number of parameters:24\n" + "the number of parameters: 24\n" ] }, { "data": { - "image/png": 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", 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", 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    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], diff --git a/tutorials/qnn_research/Noise_CN.ipynb b/tutorials/qnn_research/Noise_CN.ipynb index f3eb5b4..dc5e971 100644 --- a/tutorials/qnn_research/Noise_CN.ipynb +++ b/tutorials/qnn_research/Noise_CN.ipynb @@ -89,7 +89,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "id": "scheduled-attraction", "metadata": { "ExecuteTime": { @@ -98,9 +98,18 @@ } }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " elif dtype == np.bool:\n" + ] + }, { "data": { - "image/png": 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    " ] @@ -116,7 +125,7 @@ "{'0': 1.0, '1': 0.0}" ] }, - "execution_count": 5, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -153,7 +162,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "id": "fiscal-literature", "metadata": { "ExecuteTime": { @@ -165,7 +174,7 @@ "outputs": [ { "data": { - "image/png": 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", "text/plain": [ "
    " ] @@ -329,7 +338,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "id": "mobile-death", "metadata": { "ExecuteTime": { @@ -372,7 +381,7 @@ "cir = Circuit(num_qubits)\n", "\n", "# 添加自定义噪声,其输入为 Kraus 算符的列表\n", - "cir.kraus_repr(Kraus_ops, 0)\n", + "cir.kraus_channel(Kraus_ops, 0)\n", "\n", "# 执行电路\n", "fin_state = cir(init_state)\n", @@ -407,7 +416,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "id": "spread-monkey", "metadata": { "ExecuteTime": { @@ -421,8 +430,8 @@ "output_type": "stream", "text": [ "初态和贝尔态之间的保真度为 1\n", - "经过了传输(去极化信道)之后的纠缠对和贝尔态的保真度为 0.81333\n", - "又经过了存储(振幅阻尼信道)之后的纠缠对和贝尔态的保真度为 0.66752\n" + "经过了传输(去极化信道)之后的纠缠对和贝尔态的保真度为 0.85750\n", + "又经过了存储(振幅阻尼信道)之后的纠缠对和贝尔态的保真度为 0.73556\n" ] } ], @@ -495,7 +504,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 8, "id": "unavailable-october", "metadata": { "ExecuteTime": { @@ -528,7 +537,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 9, "id": "protected-difficulty", "metadata": { "ExecuteTime": { @@ -542,30 +551,45 @@ "output_type": "stream", "text": [ "========== Training Noisy VQE ==========\n", - "iter: 0 loss: -0.3881\n", - "iter: 10 loss: -0.6246\n", - "iter: 20 loss: -0.6454\n", - "iter: 30 loss: -0.6611\n", - "iter: 40 loss: -0.6608\n", - "iter: 50 loss: -0.6616\n", - "iter: 60 loss: -0.6620\n", - "iter: 70 loss: -0.6621\n", + "iter: 0 loss: -0.1625\n", + "iter: 10 loss: -0.6263\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "iter: 20 loss: -0.6325\n", + "iter: 30 loss: -0.6562\n", + "iter: 40 loss: -0.6611\n", + "iter: 50 loss: -0.6615\n", + "iter: 60 loss: -0.6617\n", + "iter: 70 loss: -0.6620\n", "iter: 80 loss: -0.6621\n", - "iter: 90 loss: -0.6622\n", + "iter: 90 loss: -0.6621\n", "========== Training Noise Free VQE ==========\n", - "iter: 0 loss: 0.0636\n", - "iter: 10 loss: -0.6282\n", - "iter: 20 loss: -0.7518\n", - "iter: 30 loss: -0.8124\n", - "iter: 40 loss: -0.8229\n", - "iter: 50 loss: -0.8208\n", - "iter: 60 loss: -0.8243\n", - "iter: 70 loss: -0.8242\n", + "iter: 0 loss: 0.1523\n", + "iter: 10 loss: -0.7000\n", + "iter: 20 loss: -0.8147\n", + "iter: 30 loss: -0.8196\n", + "iter: 40 loss: -0.8192\n", + "iter: 50 loss: -0.8224\n", + "iter: 60 loss: -0.8242\n", + "iter: 70 loss: -0.8243\n", "iter: 80 loss: -0.8246\n", "iter: 90 loss: -0.8246\n", "\n", - "含噪电路计算得到的基态能量是: -0.6621563 Ha\n", - "不含噪电路计算得到的基态能量是: -0.82461804 Ha\n", + "含噪电路计算得到的基态能量是: -0.66215205 Ha\n", + "不含噪电路计算得到的基态能量是: -0.8246203 Ha\n", "真实的基态能量为: -0.82462114 Ha\n" ] } diff --git a/tutorials/qnn_research/Noise_EN.ipynb b/tutorials/qnn_research/Noise_EN.ipynb index bda786f..a78a219 100644 --- a/tutorials/qnn_research/Noise_EN.ipynb +++ b/tutorials/qnn_research/Noise_EN.ipynb @@ -84,7 +84,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2021-04-09T02:32:24.919291Z", @@ -92,9 +92,26 @@ } }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/openfermion/hamiltonians/hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " elif dtype == np.bool:\n" + ] + }, { "data": { - "image/png": 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"text/plain": [ "
    " ] @@ -110,7 +127,7 @@ "{'0': 1.0, '1': 0.0}" ] }, - "execution_count": 2, + "execution_count": 1, "metadata": {}, "output_type": "execute_result" } @@ -145,7 +162,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2021-04-09T02:32:25.168455Z", @@ -156,7 +173,7 @@ "outputs": [ { "data": { - "image/png": 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"text/plain": [ "
    " ] @@ -315,7 +332,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2021-04-09T02:54:20.758898Z", @@ -357,7 +374,7 @@ "cir = Circuit(num_qubits)\n", "\n", "# Add customized channel, input is a list of Kraus operators\n", - "cir.kraus_repr(Kraus_ops, 0)\n", + "cir.kraus_channel(Kraus_ops, 0)\n", "\n", "# Execute the circuit\n", "fin_state = cir(init_state)\n", @@ -382,7 +399,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": { "ExecuteTime": { "end_time": "2021-04-09T02:58:30.352039Z", @@ -395,8 +412,8 @@ "output_type": "stream", "text": [ "Fidelity between the initial state and the Bell state 1\n", - "after transmission (depolarizing channel), the fidelity between the entangled state and Bell state 0.81333\n", - "after preservation (amplitude damping channel), the fidelity between the entangled state and Bell state 0.66752\n" + "after transmission (depolarizing channel), the fidelity between the entangled state and Bell state 0.85750\n", + "after preservation (amplitude damping channel), the fidelity between the entangled state and Bell state 0.73556\n" ] } ], @@ -466,7 +483,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-04-09T03:06:13.534545Z", @@ -498,7 +515,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-04-09T03:06:36.986422Z", @@ -511,30 +528,30 @@ "output_type": "stream", "text": [ "========== Training Noisy VQE ==========\n", - "iter: 0 loss: -0.2139\n", - "iter: 10 loss: -0.6206\n", - "iter: 20 loss: -0.6481\n", - "iter: 30 loss: -0.6588\n", - "iter: 40 loss: -0.6599\n", - "iter: 50 loss: -0.6607\n", - "iter: 60 loss: -0.6618\n", - "iter: 70 loss: -0.6621\n", + "iter: 0 loss: -0.2233\n", + "iter: 10 loss: -0.6082\n", + "iter: 20 loss: -0.6373\n", + "iter: 30 loss: -0.6554\n", + "iter: 40 loss: -0.6618\n", + "iter: 50 loss: -0.6614\n", + "iter: 60 loss: -0.6621\n", + "iter: 70 loss: -0.6620\n", "iter: 80 loss: -0.6621\n", "iter: 90 loss: -0.6621\n", "========== Training Noise Free VQE ==========\n", - "iter: 0 loss: -0.0799\n", - "iter: 10 loss: -0.7243\n", - "iter: 20 loss: -0.8103\n", - "iter: 30 loss: -0.8180\n", - "iter: 40 loss: -0.8230\n", - "iter: 50 loss: -0.8240\n", - "iter: 60 loss: -0.8243\n", + "iter: 0 loss: -0.1235\n", + "iter: 10 loss: -0.7679\n", + "iter: 20 loss: -0.7933\n", + "iter: 30 loss: -0.8177\n", + "iter: 40 loss: -0.8219\n", + "iter: 50 loss: -0.8239\n", + "iter: 60 loss: -0.8244\n", "iter: 70 loss: -0.8245\n", - "iter: 80 loss: -0.8246\n", + "iter: 80 loss: -0.8245\n", "iter: 90 loss: -0.8246\n", "\n", - "Ground state energy from noisy circuit: -0.66215336 Ha\n", - "Ground state energy from noiseless circuit: -0.82461333 Ha\n", + "Ground state energy from noisy circuit: -0.6621509 Ha\n", + "Ground state energy from noiseless circuit: -0.82461375 Ha\n", "Actual ground state energy: -0.82462114 Ha\n" ] } diff --git a/tutorials/qnn_research/VAns_CN.ipynb b/tutorials/qnn_research/VAns_CN.ipynb index 91b2ca9..f3f343f 100644 --- a/tutorials/qnn_research/VAns_CN.ipynb +++ b/tutorials/qnn_research/VAns_CN.ipynb @@ -45,11 +45,11 @@ "1. 准备一个简单的初始电路,使用经典优化器对电路参数进行调整,最小化目标损失函数,记录最优值。\n", "2. 从一个集合中随机选择量子门模块(如下图所示,各量子门模块仅由 $R_y$ 门、$R_z$ 门,和 $CNOT$ 门组成),随机选择插入模块所作用的量子比特,并将模块添加到电路末尾。添加模块中的量子门的参数都初始化为 $0$ ,这样添加的模块一开始等同于 $I$。\n", "\n", - "![Inserting Blocks](blocks.png)\n", + "![Inserting Blocks](figures/vans-fig-blocks.png)\n", "\n", "3. 根据下图中的规则化简电路,对化简后的电路进行优化,更新其参数,获得损失函数的当前最优值。比较当前损失函数最优值与上一个记录的最优值,根据设定的阈值决定是否接受新电路。若接受新电路,则继续遍历电路中的量子门,并删除不会降低损失的门,将精简过的电路记为当前电路,并记录其最优损失。若拒绝则直接回到第2步。\n", "\n", - "![Simplification rules](rules.png)\n", + "![Simplification rules](figures/vans-fig-rules.png)\n", "\n", "4. 重复步骤2-3,达到设定的迭代次数后停止,输出电路和最优损失。" ] @@ -70,9 +70,33 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, + "id": "5b479722", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "import paddle\n", "import paddle_quantum\n", @@ -80,7 +104,7 @@ "import numpy as np\n", "from paddle_quantum.ansatz import Circuit\n", "from paddle_quantum.ansatz.vans import Inserter, Simplifier, VAns, cir_decompose\n", - "from paddle_quantum.hamiltonian import Hamiltonian\n", + "from paddle_quantum.loss import ExpecVal\n", "\n", "np.random.seed(11)\n", "paddle.seed(11)" @@ -88,6 +112,7 @@ }, { "cell_type": "markdown", + "id": "0fbb44b3", "metadata": {}, "source": [ "我们首先需要构造氢分子的哈密顿量,具体的说明可见[变分量子本征求解器(VQE)](https://qml.baidu.com/tutorials/quantum-simulation/variational-quantum-eigensolver.html)。" @@ -95,34 +120,40 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, + "id": "b9092685", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "converged SCF energy = -1.11675930739643\n" + ] + } + ], "source": [ - "geo = qchem.geometry(structure=[[\"H\", [-0.0, 0.0, 0.0]], [\"H\", [-0.0, 0.0, 0.74]]])\n", - "# 将分子信息存储在 molecule 里,包括单体积分(one-body integrations),双体积分(two-body integrations),分子的哈密顿量等\n", - "molecule = qchem.get_molecular_data(\n", - " geometry=geo,\n", + "# `driver` 用来计算分子中的各种积分\n", + "driver = qchem.PySCFDriver()\n", + "\n", + "# 通过氢分子的性质构造一个 Molecule 类,注:长度单位为埃\n", + "mol = qchem.Molecule(\n", + " geometry=[(\"H\", [0.0, 0.0, 0.0]), (\"H\", [0.0, 0.0, 0.74])],\n", " basis=\"sto-3g\",\n", - " charge=0,\n", - " multiplicity=1,\n", - " method=\"fci\",\n", - " if_save=True,\n", - " if_print=True,\n", + " multiplicity=1, \n", + " driver=driver\n", ")\n", + "\n", "# 提取哈密顿量\n", - "molecular_hamiltonian = qchem.spin_hamiltonian(\n", - " molecule=molecule,\n", - " filename=None,\n", - " multiplicity=1,\n", - " mapping_method=\"jordan_wigner\",\n", - ")\n", + "molecular_hamiltonian = mol.get_molecular_hamiltonian()\n", + "\n", "# n 为量子比特数\n", "n = molecular_hamiltonian.n_qubits" ] }, { "cell_type": "markdown", + "id": "a293c9ef", "metadata": {}, "source": [ "接下来我们需要定义损失函数,也就是电路输出量子态关于该哈密顿量的期望值。" @@ -131,16 +162,20 @@ { "cell_type": "code", "execution_count": 3, + "id": "e3b2a6f1", "metadata": {}, "outputs": [], "source": [ "# 定义损失函数\n", - "def loss_func(cir: Circuit, H: Hamiltonian) -> paddle.Tensor:\n", - " return cir().expec_val(H)" + "expec_val = ExpecVal(molecular_hamiltonian)\n", + "\n", + "def loss_func(cir: Circuit) -> paddle.Tensor:\n", + " return expec_val(cir())" ] }, { "cell_type": "markdown", + "id": "03f731ca", "metadata": {}, "source": [ "在训练前,我们还需要设定一些有关 VAns 算法和优化器的参数。读者可以自行调整这些参数来观察 VAns 算法的变化。" @@ -149,6 +184,7 @@ { "cell_type": "code", "execution_count": 4, + "id": "9a67f6ed", "metadata": {}, "outputs": [], "source": [ @@ -167,11 +203,12 @@ { "cell_type": "code", "execution_count": 5, + "id": "f36f9933", "metadata": {}, "outputs": [], "source": [ "# 初始化一个 VAns 的模块对象\n", - "vans = VAns(n, loss_func, molecular_hamiltonian,\n", + "vans = VAns(n, loss_func,\n", " epsilon=EPSI,\n", " insert_rate=IR,\n", " iter=ITERI,\n", @@ -184,6 +221,7 @@ }, { "cell_type": "markdown", + "id": "ccbb7a5d", "metadata": {}, "source": [ "### 初始电路" @@ -191,6 +229,7 @@ }, { "cell_type": "markdown", + "id": "c414477f", "metadata": {}, "source": [ "我们给出了一个简单的初始电路,其参数是从均匀分布中随机选取的。对于这个初始电路,我们运行优化过程使损失函数最小化。优化过程和普通的 VQE 算法相同,参数 **iter** 和 **LR** 分别决定了优化器迭代次数和学习率。记录优化后的参数化电路以及损失,将其作为结构优化的起始点。" @@ -199,32 +238,30 @@ { "cell_type": "code", "execution_count": 6, + "id": "7f6a5748", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "c:\\Users\\v_zhanglei48\\Anaconda3\\envs\\pq_new\\lib\\site-packages\\paddle\\fluid\\framework.py:744: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", - " elif dtype == np.bool:\n", - "c:\\Users\\v_zhanglei48\\Anaconda3\\envs\\pq_new\\lib\\site-packages\\paddle\\tensor\\creation.py:130: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", - "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", - " if data.dtype == np.object:\n" + " elif dtype == np.bool:\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "iter: 20 loss: [-0.9960856]\n", - "iter: 40 loss: [-1.0926806]\n", - "iter: 60 loss: [-1.11364]\n", - "iter: 80 loss: [-1.1163325]\n", - "iter: 100 loss: [-1.1167175]\n", - "iter: 120 loss: [-1.1167548]\n", + "iter: 20 loss: [-0.99608564]\n", + "iter: 40 loss: [-1.0926807]\n", + "iter: 60 loss: [-1.1136395]\n", + "iter: 80 loss: [-1.116332]\n", + "iter: 100 loss: [-1.1167176]\n", + "iter: 120 loss: [-1.1167545]\n", "当前电路:\n", - "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(3.039)-------------------------------------------------------------x--\n", + "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(1.375)-------------------------------------------------------------x--\n", " | | \n", "----------------------------x----Rx(4.249)----Rz(3.141)----Rx(4.246)----Rz(5.477)----*------------------------------|--\n", " | | \n", @@ -248,6 +285,7 @@ }, { "cell_type": "markdown", + "id": "cd46de5a", "metadata": {}, "source": [ "### 插入量子门模块" @@ -255,6 +293,7 @@ }, { "cell_type": "markdown", + "id": "deae6f90", "metadata": {}, "source": [ "现在我们从量子门模块集合中随机选取模块,随机选取插入模块所作用的量子比特,并将模块插入到当前电路中。注意新插入模块中的量子门的参数都被设置为 $0$,这样添加模块前后的电路实际上是相同的,也就是说更新后的电路可以继承之前电路的损失。下面的代码展示了如何在电路中插入模块。一次插入模块的数量由参数 **insert_rate** 决定。另一个参数 **epsilon** 是用来设定插入模块初始参数与 $0$ 之间的差别。" @@ -263,6 +302,7 @@ { "cell_type": "code", "execution_count": 7, + "id": "5b9e2fb9", "metadata": {}, "outputs": [ { @@ -270,7 +310,7 @@ "output_type": "stream", "text": [ "添加过后的电路:\n", - "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(3.039)----------------------------------------------------------------------------------------------------x--\n", + "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(1.375)----------------------------------------------------------------------------------------------------x--\n", " | | \n", "----------------------------x----Rz(0.000)----Rx(0.000)----Rz(-0.00)----Rx(4.249)----Rz(3.141)----Rx(4.246)----Rz(5.477)----*------------------------------|--\n", " | | \n", @@ -292,6 +332,7 @@ }, { "cell_type": "markdown", + "id": "1cc6aa81", "metadata": {}, "source": [ "### 简化电路" @@ -299,6 +340,7 @@ }, { "cell_type": "markdown", + "id": "34b6e391", "metadata": {}, "source": [ "接下来我们需要化简当前的量子电路。化简电路的规则十分简单:\n", @@ -313,13 +355,14 @@ { "cell_type": "code", "execution_count": 8, + "id": "f6055682", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ - "c:\\Users\\v_zhanglei48\\Anaconda3\\envs\\pq_new\\lib\\site-packages\\paddle\\fluid\\dygraph\\math_op_patch.py:251: UserWarning: The dtype of left and right variables are not the same, left dtype is paddle.float64, but right dtype is paddle.float32, the right dtype will convert to paddle.float64\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/dygraph/math_op_patch.py:276: UserWarning: The dtype of left and right variables are not the same, left dtype is paddle.float64, but right dtype is paddle.float32, the right dtype will convert to paddle.float64\n", " warnings.warn(\n" ] }, @@ -327,7 +370,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(3.039)------------------------------------------------x--\n", + "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(1.375)------------------------------------------------x--\n", " | | \n", "----------------------------x----Rz(5.962)----Rx(5.858)----Rz(9.426)----*------------------------------|--\n", " | | \n", @@ -335,8 +378,8 @@ " | | \n", "----------------------------x----Rz(3.604)----Rx(5.126)----Rz(4.462)-----------------------------------*--\n", " \n", - "iter: 20 loss: [-1.1040964]\n", - "iter: 40 loss: [-1.1159219]\n", + "iter: 20 loss: [-1.104097]\n", + "iter: 40 loss: [-1.1159214]\n", "iter: 60 loss: [-1.1165943]\n", "iter: 80 loss: [-1.116723]\n", "iter: 100 loss: [-1.1167536]\n", @@ -391,6 +434,7 @@ }, { "cell_type": "markdown", + "id": "9f38888b", "metadata": {}, "source": [ "简化后的电路如下所示。" @@ -399,6 +443,7 @@ { "cell_type": "code", "execution_count": 9, + "id": "84da6b93", "metadata": {}, "outputs": [ { @@ -426,6 +471,7 @@ }, { "cell_type": "markdown", + "id": "c690bbd8", "metadata": {}, "source": [ "我们将上述的插入量子门模块和简化电路的步骤一起作为电路结构优化的一次迭代,总的迭代次数由参数 **iter_out** 决定。" @@ -433,6 +479,7 @@ }, { "cell_type": "markdown", + "id": "c6f114ba", "metadata": {}, "source": [ "### 简化版本" @@ -440,6 +487,7 @@ }, { "cell_type": "markdown", + "id": "bcc99140", "metadata": {}, "source": [ "上述过程清晰明了地展示了 VAns 的运行步骤和原理,包括了量子门模块添加以及电路简化的过程,然而实际在量桨中使用 VAns 可以不必了解这些繁杂的步骤,因为量桨提供了一个经过封装的 VAns 算法,以便用户进行调用。下面的一行代码可以完成所有的电路结构优化以及参数训练过程。" @@ -448,6 +496,7 @@ { "cell_type": "code", "execution_count": 10, + "id": "49a180b9", "metadata": {}, "outputs": [ { @@ -455,13 +504,13 @@ "output_type": "stream", "text": [ "Out iteration 1 for structure optimization:\n", - "iter: 20 loss: [-1.1167214]\n", - "iter: 40 loss: [-1.1166948]\n", + "iter: 20 loss: [-1.1167216]\n", + "iter: 40 loss: [-1.1166946]\n", "iter: 60 loss: [-1.1167494]\n", - "iter: 80 loss: [-1.116759]\n", + "iter: 80 loss: [-1.1167588]\n", "iter: 100 loss: [-1.1167591]\n", - "iter: 120 loss: [-1.1167595]\n", - " Current loss: [-1.1167595]\n", + "iter: 120 loss: [-1.1167594]\n", + " Current loss: [-1.1167594]\n", " Current cir:\n", "--Rx(3.141)----*----------------------x--\n", " | | \n", @@ -473,136 +522,144 @@ " \n", "\n", "Out iteration 2 for structure optimization:\n", - "iter: 20 loss: [-1.008932]\n", - "iter: 40 loss: [-1.1085335]\n", - "iter: 60 loss: [-1.133744]\n", - "iter: 80 loss: [-1.1368372]\n", - "iter: 100 loss: [-1.1372123]\n", - "iter: 120 loss: [-1.1372803]\n", + "iter: 20 loss: [-1.1363345]\n", + "iter: 40 loss: [-1.1367742]\n", + "iter: 60 loss: [-1.137219]\n", + "iter: 80 loss: [-1.1372814]\n", + "iter: 100 loss: [-1.1372831]\n", + "iter: 120 loss: [-1.1372838]\n", " accpet the new circuit!\n", " start deleting gates\n", " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: reject deletion\n", - " Deletion: reject deletion\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", " Deletion: reject deletion\n", - " 3 gates are deleted!\n", - " Current loss: -1.1331816911697388\n", + " Deletion: accept deletion with acceptable loss\n", + " 10 gates are deleted!\n", + " Current loss: -1.126142144203186\n", " Current cir:\n", - "--Rx(3.143)----*------------------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.223)----Rz(2.485)----*--------*---------------------|--\n", - " | | | | \n", - "--------------------|------------------------------|--------x--------Rx(3.142)----|--\n", - " | | | \n", - "--------------------x------------------------------x----Rz(0.458)-----------------*--\n", - " \n", + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.226)----*----*--------x--------Rz(-0.81)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n", "\n", "Out iteration 3 for structure optimization:\n", - "iter: 20 loss: [-0.37809896]\n", - "iter: 40 loss: [-1.0471339]\n", - "iter: 60 loss: [-1.1262195]\n", - "iter: 80 loss: [-1.1365637]\n", - "iter: 100 loss: [-1.1371676]\n", - "iter: 120 loss: [-1.1372685]\n", + "iter: 20 loss: [-1.1365268]\n", + "iter: 40 loss: [-1.1370414]\n", + "iter: 60 loss: [-1.1372557]\n", + "iter: 80 loss: [-1.1372817]\n", + "iter: 100 loss: [-1.1372832]\n", + "iter: 120 loss: [-1.1372838]\n", " accpet the new circuit!\n", " start deleting gates\n", " Deletion: reject deletion\n", " Deletion: reject deletion\n", - " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", - " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", - " 4 gates are deleted!\n", - " Current loss: -1.1282802820205688\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: reject deletion\n", + " Deletion: reject deletion\n", + " 6 gates are deleted!\n", + " Current loss: -1.1340010166168213\n", " Current cir:\n", - "--Rx(3.143)----*----------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.224)----Rz(2.252)----*----*-----------------|--\n", - " | | | | \n", - "--------------------|------------------------------|----x----Rx(3.146)----|--\n", - " | | | \n", - "--------------------x------------------------------x----------------------*--\n", - " \n", + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.225)----*----*--------x--------Rz(-1.16)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n", "\n", "Out iteration 4 for structure optimization:\n", - "iter: 20 loss: [-0.5603936]\n", - "iter: 40 loss: [-1.0798837]\n", - "iter: 60 loss: [-1.1325867]\n", - "iter: 80 loss: [-1.1360469]\n", - "iter: 100 loss: [-1.1370715]\n", - "iter: 120 loss: [-1.1372685]\n", + "iter: 20 loss: [-1.1371578]\n", + "iter: 40 loss: [-1.1371865]\n", + "iter: 60 loss: [-1.1372653]\n", + "iter: 80 loss: [-1.1372821]\n", + "iter: 100 loss: [-1.1372833]\n", + "iter: 120 loss: [-1.137284]\n", " accpet the new circuit!\n", " start deleting gates\n", " Deletion: reject deletion\n", " Deletion: reject deletion\n", " Deletion: reject deletion\n", - " Deletion: accept deletion with acceptable loss\n", - " Deletion: accept deletion with acceptable loss\n", - " Deletion: accept deletion with acceptable loss\n", - " Deletion: accept deletion with acceptable loss\n", - " Deletion: accept deletion with acceptable loss\n", - " Deletion: accept deletion with acceptable loss\n", " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", - " 9 gates are deleted!\n", - " Current loss: -1.1321836709976196\n", + " 3 gates are deleted!\n", + " Current loss: -1.135810136795044\n", " Current cir:\n", - "--Rx(3.145)----*----------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.228)----Rz(2.075)----*----*-----------------|--\n", - " | | | | \n", - "--------------------|------------------------------|----x----Rx(3.143)----|--\n", - " | | | \n", - "--------------------x------------------------------x----------------------*--\n", - " \n", + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.225)----*----*--------x--------Rz(-1.30)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n", "\n", "Out iteration 5 for structure optimization:\n", - "iter: 20 loss: [-1.136969]\n", - "iter: 40 loss: [-1.1371931]\n", - "iter: 60 loss: [-1.137272]\n", - "iter: 80 loss: [-1.1372828]\n", - "iter: 100 loss: [-1.1372837]\n", - "iter: 120 loss: [-1.1372838]\n", + "iter: 20 loss: [-1.1363769]\n", + "iter: 40 loss: [-1.1369352]\n", + "iter: 60 loss: [-1.1372398]\n", + "iter: 80 loss: [-1.137279]\n", + "iter: 100 loss: [-1.1372832]\n", + "iter: 120 loss: [-1.1372834]\n", " accpet the new circuit!\n", " start deleting gates\n", " Deletion: reject deletion\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: reject deletion\n", " Deletion: reject deletion\n", " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", - " Deletion: reject deletion\n", - " 2 gates are deleted!\n", - " Current loss: -1.1372729539871216\n", + " Deletion: accept deletion with acceptable loss\n", + " 8 gates are deleted!\n", + " Current loss: -1.135881781578064\n", " Current cir:\n", - "--Rx(3.142)----*----------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.226)----Rz(1.571)----*----*-----------------|--\n", - " | | | | \n", - "--------------------|------------------------------|----x----Rx(3.149)----|--\n", - " | | | \n", - "--------------------x------------------------------x----------------------*--\n", - " \n", + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.226)----*----*--------x--------Rz(-1.30)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n", "\n", "\n", "\n", - "The final loss: -1.1372729539871216\n", + "The final loss: -1.135881781578064\n", "The final circuit:\n", - "--Rx(3.142)----*----------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.226)----Rz(1.571)----*----*-----------------|--\n", - " | | | | \n", - "--------------------|------------------------------|----x----Rx(3.149)----|--\n", - " | | | \n", - "--------------------x------------------------------x----------------------*--\n", - " \n" + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.226)----*----*--------x--------Rz(-1.30)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n" ] } ], @@ -613,6 +670,7 @@ }, { "cell_type": "markdown", + "id": "ef7dab92", "metadata": {}, "source": [ "最终 VAns 算法给出的电路如下:" @@ -621,6 +679,7 @@ { "cell_type": "code", "execution_count": 11, + "id": "871f0334", "metadata": {}, "outputs": [ { @@ -628,16 +687,16 @@ "output_type": "stream", "text": [ "最终电路:\n", - "--Rx(3.142)----*----------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.226)----Rz(1.571)----*----*-----------------|--\n", - " | | | | \n", - "--------------------|------------------------------|----x----Rx(3.149)----|--\n", - " | | | \n", - "--------------------x------------------------------x----------------------*--\n", - " \n", + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.226)----*----*--------x--------Rz(-1.30)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n", "最终损失:\n", - "-1.1372729539871216\n" + "-1.135881781578064\n" ] } ], diff --git a/tutorials/qnn_research/VAns_EN.ipynb b/tutorials/qnn_research/VAns_EN.ipynb index 5fb6736..75e37cf 100644 --- a/tutorials/qnn_research/VAns_EN.ipynb +++ b/tutorials/qnn_research/VAns_EN.ipynb @@ -38,6 +38,7 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ @@ -45,11 +46,11 @@ "1. Start with an initial circuit. Run the inner optimization, which is just the original VQE process, and get the optimal value. \n", "2. Randomly choose a block from the 'pool' (As the following figure shows, each block only consists of $R_y$, $R_z$, and $CNOT$ gates), and insert the block at the end of circuit. Qubits that the block is applied on are also uniformly sampled. The parameters of the inserted gates are initialized to $0$ so that the inserted circuit is equivalent to identity. \n", "\n", - "![Inserting Blocks](blocks.png)\n", + "![Inserting Blocks](figures/vans-fig-blocks.png)\n", "\n", "3. Simplify the circuit according to the following rules. Run the optimization process, and get the optimal value of loss function. Compare the loss value to the previously stored one, decide whether to accept the new circuit or not according to a pre-defined threshold. If the circuit is accepted, remove gates that do not lower the loss, set the circuit as the current circuit and store the corresponding loss value.\n", "\n", - "![Simplification rules](rules.png)\n", + "![Simplification rules](figures/vans-fig-rules.png)\n", "\n", "4. Repeat steps 2-3 for chosen number of iterations, output the resulting circuit and the optimal loss value.\n" ] @@ -70,9 +71,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + }, + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 1, + "metadata": {}, + "output_type": "execute_result" + } + ], "source": [ "import paddle\n", "import paddle_quantum\n", @@ -80,7 +104,7 @@ "import numpy as np\n", "from paddle_quantum.ansatz import Circuit\n", "from paddle_quantum.ansatz.vans import Inserter, Simplifier, VAns, cir_decompose\n", - "from paddle_quantum.hamiltonian import Hamiltonian\n", + "from paddle_quantum.loss import ExpecVal\n", "\n", "np.random.seed(11)\n", "paddle.seed(11)" @@ -95,28 +119,32 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "converged SCF energy = -1.11675930739643\n" + ] + } + ], "source": [ - "geo = qchem.geometry(structure=[[\"H\", [-0.0, 0.0, 0.0]], [\"H\", [-0.0, 0.0, 0.74]]])\n", - "# Save molecule information in to variable molecule, including one-body integrations, molecular and Hamiltonian\n", - "molecule = qchem.get_molecular_data(\n", - " geometry=geo,\n", + "# `driver` is used to calculate various molecular integrals.\n", + "driver = qchem.PySCFDriver()\n", + "\n", + "# Build a Molecule class based on its properties, note, the length unit is Angstrom.\n", + "mol = qchem.Molecule(\n", + " geometry=[(\"H\", [0.0, 0.0, 0.0]), (\"H\", [0.0, 0.0, 0.74])],\n", " basis=\"sto-3g\",\n", - " charge=0,\n", - " multiplicity=1,\n", - " method=\"fci\",\n", - " if_save=True,\n", - " if_print=True,\n", + " multiplicity=1, \n", + " driver=driver\n", ")\n", + "\n", "# Recall Hamiltonian\n", - "molecular_hamiltonian = qchem.spin_hamiltonian(\n", - " molecule=molecule,\n", - " filename=None,\n", - " multiplicity=1,\n", - " mapping_method=\"jordan_wigner\",\n", - ")\n", + "molecular_hamiltonian = mol.get_molecular_hamiltonian()\n", + "\n", "# n is the number of qubits\n", "n = molecular_hamiltonian.n_qubits" ] @@ -135,8 +163,10 @@ "outputs": [], "source": [ "# Define the loss function\n", - "def loss_func(cir: Circuit, H: Hamiltonian) -> paddle.Tensor:\n", - " return cir().expec_val(H)" + "expec_val = ExpecVal(molecular_hamiltonian)\n", + "\n", + "def loss_func(cir: Circuit) -> paddle.Tensor:\n", + " return expec_val(cir())" ] }, { @@ -171,7 +201,7 @@ "outputs": [], "source": [ "# initialize the framework\n", - "vans = VAns(n, loss_func, molecular_hamiltonian,\n", + "vans = VAns(n, loss_func,\n", " epsilon=EPSI,\n", " insert_rate=IR,\n", " iter=ITERI,\n", @@ -205,26 +235,23 @@ "name": "stderr", "output_type": "stream", "text": [ - "c:\\Users\\v_zhanglei48\\Anaconda3\\envs\\pq_new\\lib\\site-packages\\paddle\\fluid\\framework.py:744: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", - " elif dtype == np.bool:\n", - "c:\\Users\\v_zhanglei48\\Anaconda3\\envs\\pq_new\\lib\\site-packages\\paddle\\tensor\\creation.py:130: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", - "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", - " if data.dtype == np.object:\n" + " elif dtype == np.bool:\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ - "iter: 20 loss: [-0.9960856]\n", - "iter: 40 loss: [-1.0926806]\n", - "iter: 60 loss: [-1.11364]\n", - "iter: 80 loss: [-1.1163325]\n", - "iter: 100 loss: [-1.1167175]\n", - "iter: 120 loss: [-1.1167548]\n", + "iter: 20 loss: [-0.99608564]\n", + "iter: 40 loss: [-1.0926807]\n", + "iter: 60 loss: [-1.1136395]\n", + "iter: 80 loss: [-1.116332]\n", + "iter: 100 loss: [-1.1167176]\n", + "iter: 120 loss: [-1.1167545]\n", "Current circuit is:\n", - "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(3.039)-------------------------------------------------------------x--\n", + "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(1.375)-------------------------------------------------------------x--\n", " | | \n", "----------------------------x----Rx(4.249)----Rz(3.141)----Rx(4.246)----Rz(5.477)----*------------------------------|--\n", " | | \n", @@ -270,7 +297,7 @@ "output_type": "stream", "text": [ "Circuit after insertion:\n", - "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(3.039)----------------------------------------------------------------------------------------------------x--\n", + "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(1.375)----------------------------------------------------------------------------------------------------x--\n", " | | \n", "----------------------------x----Rz(0.000)----Rx(0.000)----Rz(-0.00)----Rx(4.249)----Rz(3.141)----Rx(4.246)----Rz(5.477)----*------------------------------|--\n", " | | \n", @@ -320,7 +347,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "c:\\Users\\v_zhanglei48\\Anaconda3\\envs\\pq_new\\lib\\site-packages\\paddle\\fluid\\dygraph\\math_op_patch.py:251: UserWarning: The dtype of left and right variables are not the same, left dtype is paddle.float64, but right dtype is paddle.float32, the right dtype will convert to paddle.float64\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/dygraph/math_op_patch.py:276: UserWarning: The dtype of left and right variables are not the same, left dtype is paddle.float64, but right dtype is paddle.float32, the right dtype will convert to paddle.float64\n", " warnings.warn(\n" ] }, @@ -328,7 +355,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(3.039)------------------------------------------------x--\n", + "--Rx(3.144)----Rz(3.512)----*----Rx(6.286)----Rz(1.375)------------------------------------------------x--\n", " | | \n", "----------------------------x----Rz(5.962)----Rx(5.858)----Rz(9.426)----*------------------------------|--\n", " | | \n", @@ -336,8 +363,8 @@ " | | \n", "----------------------------x----Rz(3.604)----Rx(5.126)----Rz(4.462)-----------------------------------*--\n", " \n", - "iter: 20 loss: [-1.1040964]\n", - "iter: 40 loss: [-1.1159219]\n", + "iter: 20 loss: [-1.104097]\n", + "iter: 40 loss: [-1.1159214]\n", "iter: 60 loss: [-1.1165943]\n", "iter: 80 loss: [-1.116723]\n", "iter: 100 loss: [-1.1167536]\n", @@ -456,13 +483,13 @@ "output_type": "stream", "text": [ "Out iteration 1 for structure optimization:\n", - "iter: 20 loss: [-1.1167214]\n", - "iter: 40 loss: [-1.1166948]\n", + "iter: 20 loss: [-1.1167216]\n", + "iter: 40 loss: [-1.1166946]\n", "iter: 60 loss: [-1.1167494]\n", - "iter: 80 loss: [-1.116759]\n", + "iter: 80 loss: [-1.1167588]\n", "iter: 100 loss: [-1.1167591]\n", - "iter: 120 loss: [-1.1167595]\n", - " Current loss: [-1.1167595]\n", + "iter: 120 loss: [-1.1167594]\n", + " Current loss: [-1.1167594]\n", " Current cir:\n", "--Rx(3.141)----*----------------------x--\n", " | | \n", @@ -474,136 +501,144 @@ " \n", "\n", "Out iteration 2 for structure optimization:\n", - "iter: 20 loss: [-1.008932]\n", - "iter: 40 loss: [-1.1085335]\n", - "iter: 60 loss: [-1.133744]\n", - "iter: 80 loss: [-1.1368372]\n", - "iter: 100 loss: [-1.1372123]\n", - "iter: 120 loss: [-1.1372803]\n", + "iter: 20 loss: [-1.1363345]\n", + "iter: 40 loss: [-1.1367742]\n", + "iter: 60 loss: [-1.137219]\n", + "iter: 80 loss: [-1.1372814]\n", + "iter: 100 loss: [-1.1372831]\n", + "iter: 120 loss: [-1.1372838]\n", " accpet the new circuit!\n", " start deleting gates\n", " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: reject deletion\n", - " Deletion: reject deletion\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", " Deletion: reject deletion\n", - " 3 gates are deleted!\n", - " Current loss: -1.1331816911697388\n", + " Deletion: accept deletion with acceptable loss\n", + " 10 gates are deleted!\n", + " Current loss: -1.126142144203186\n", " Current cir:\n", - "--Rx(3.143)----*------------------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.223)----Rz(2.485)----*--------*---------------------|--\n", - " | | | | \n", - "--------------------|------------------------------|--------x--------Rx(3.142)----|--\n", - " | | | \n", - "--------------------x------------------------------x----Rz(0.458)-----------------*--\n", - " \n", + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.226)----*----*--------x--------Rz(-0.81)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n", "\n", "Out iteration 3 for structure optimization:\n", - "iter: 20 loss: [-0.37809896]\n", - "iter: 40 loss: [-1.0471339]\n", - "iter: 60 loss: [-1.1262195]\n", - "iter: 80 loss: [-1.1365637]\n", - "iter: 100 loss: [-1.1371676]\n", - "iter: 120 loss: [-1.1372685]\n", + "iter: 20 loss: [-1.1365268]\n", + "iter: 40 loss: [-1.1370414]\n", + "iter: 60 loss: [-1.1372557]\n", + "iter: 80 loss: [-1.1372817]\n", + "iter: 100 loss: [-1.1372832]\n", + "iter: 120 loss: [-1.1372838]\n", " accpet the new circuit!\n", " start deleting gates\n", " Deletion: reject deletion\n", " Deletion: reject deletion\n", - " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", - " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", - " 4 gates are deleted!\n", - " Current loss: -1.1282802820205688\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: reject deletion\n", + " Deletion: reject deletion\n", + " 6 gates are deleted!\n", + " Current loss: -1.1340010166168213\n", " Current cir:\n", - "--Rx(3.143)----*----------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.224)----Rz(2.252)----*----*-----------------|--\n", - " | | | | \n", - "--------------------|------------------------------|----x----Rx(3.146)----|--\n", - " | | | \n", - "--------------------x------------------------------x----------------------*--\n", - " \n", + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.225)----*----*--------x--------Rz(-1.16)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n", "\n", "Out iteration 4 for structure optimization:\n", - "iter: 20 loss: [-0.5603936]\n", - "iter: 40 loss: [-1.0798837]\n", - "iter: 60 loss: [-1.1325867]\n", - "iter: 80 loss: [-1.1360469]\n", - "iter: 100 loss: [-1.1370715]\n", - "iter: 120 loss: [-1.1372685]\n", + "iter: 20 loss: [-1.1371578]\n", + "iter: 40 loss: [-1.1371865]\n", + "iter: 60 loss: [-1.1372653]\n", + "iter: 80 loss: [-1.1372821]\n", + "iter: 100 loss: [-1.1372833]\n", + "iter: 120 loss: [-1.137284]\n", " accpet the new circuit!\n", " start deleting gates\n", " Deletion: reject deletion\n", " Deletion: reject deletion\n", " Deletion: reject deletion\n", - " Deletion: accept deletion with acceptable loss\n", - " Deletion: accept deletion with acceptable loss\n", - " Deletion: accept deletion with acceptable loss\n", - " Deletion: accept deletion with acceptable loss\n", - " Deletion: accept deletion with acceptable loss\n", - " Deletion: accept deletion with acceptable loss\n", " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", - " 9 gates are deleted!\n", - " Current loss: -1.1321836709976196\n", + " 3 gates are deleted!\n", + " Current loss: -1.135810136795044\n", " Current cir:\n", - "--Rx(3.145)----*----------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.228)----Rz(2.075)----*----*-----------------|--\n", - " | | | | \n", - "--------------------|------------------------------|----x----Rx(3.143)----|--\n", - " | | | \n", - "--------------------x------------------------------x----------------------*--\n", - " \n", + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.225)----*----*--------x--------Rz(-1.30)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n", "\n", "Out iteration 5 for structure optimization:\n", - "iter: 20 loss: [-1.136969]\n", - "iter: 40 loss: [-1.1371931]\n", - "iter: 60 loss: [-1.137272]\n", - "iter: 80 loss: [-1.1372828]\n", - "iter: 100 loss: [-1.1372837]\n", - "iter: 120 loss: [-1.1372838]\n", + "iter: 20 loss: [-1.1363769]\n", + "iter: 40 loss: [-1.1369352]\n", + "iter: 60 loss: [-1.1372398]\n", + "iter: 80 loss: [-1.137279]\n", + "iter: 100 loss: [-1.1372832]\n", + "iter: 120 loss: [-1.1372834]\n", " accpet the new circuit!\n", " start deleting gates\n", " Deletion: reject deletion\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: accept deletion with acceptable loss\n", + " Deletion: reject deletion\n", " Deletion: reject deletion\n", " Deletion: reject deletion\n", " Deletion: accept deletion with acceptable loss\n", " Deletion: accept deletion with acceptable loss\n", - " Deletion: reject deletion\n", - " 2 gates are deleted!\n", - " Current loss: -1.1372729539871216\n", + " Deletion: accept deletion with acceptable loss\n", + " 8 gates are deleted!\n", + " Current loss: -1.135881781578064\n", " Current cir:\n", - "--Rx(3.142)----*----------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.226)----Rz(1.571)----*----*-----------------|--\n", - " | | | | \n", - "--------------------|------------------------------|----x----Rx(3.149)----|--\n", - " | | | \n", - "--------------------x------------------------------x----------------------*--\n", - " \n", + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.226)----*----*--------x--------Rz(-1.30)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n", "\n", "\n", "\n", - "The final loss: -1.1372729539871216\n", + "The final loss: -1.135881781578064\n", "The final circuit:\n", - "--Rx(3.142)----*----------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.226)----Rz(1.571)----*----*-----------------|--\n", - " | | | | \n", - "--------------------|------------------------------|----x----Rx(3.149)----|--\n", - " | | | \n", - "--------------------x------------------------------x----------------------*--\n", - " \n" + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.226)----*----*--------x--------Rz(-1.30)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n" ] } ], @@ -629,16 +664,16 @@ "output_type": "stream", "text": [ "Final circuit:\n", - "--Rx(3.142)----*----------------------------------------------------------x--\n", - " | | \n", - "---------------x----*----Rx(0.226)----Rz(1.571)----*----*-----------------|--\n", - " | | | | \n", - "--------------------|------------------------------|----x----Rx(3.149)----|--\n", - " | | | \n", - "--------------------x------------------------------x----------------------*--\n", - " \n", + "--Rx(3.141)----*------------------------------------*---------------------*----x--\n", + " | | | | \n", + "---------------x----*----Rx(0.226)----*----*--------x--------Rz(-1.30)----x----|--\n", + " | | | | \n", + "--------------------|-----------------|----x----Rx(3.141)----------------------|--\n", + " | | | \n", + "--------------------x-----------------x----------------------------------------*--\n", + " \n", "Final loss:\n", - "-1.1372729539871216\n" + "-1.135881781578064\n" ] } ], diff --git a/tutorials/qnn_research/VQCC_CN.ipynb b/tutorials/qnn_research/VQCC_CN.ipynb index a9baa89..809039e 100644 --- a/tutorials/qnn_research/VQCC_CN.ipynb +++ b/tutorials/qnn_research/VQCC_CN.ipynb @@ -75,7 +75,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 17, "id": "ae8f2fdb", "metadata": {}, "outputs": [], @@ -98,7 +98,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 18, "id": "4663732b", "metadata": { "scrolled": true @@ -131,7 +131,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 19, "id": "4e400e2e", "metadata": {}, "outputs": [], @@ -141,7 +141,7 @@ " # 初始化 n 个量子比特的量子电路\n", " cir = Circuit(n)\n", " # 内置的包含 U3 门和 CNOT 门的强纠缠电路模板\n", - " cir.complex_entangled_layer('full', n, D)\n", + " cir.complex_entangled_layer('full', D)\n", "\n", " return cir" ] @@ -158,7 +158,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 20, "id": "29c9ed4a", "metadata": {}, "outputs": [], @@ -185,7 +185,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 21, "id": "4046e5b0", "metadata": {}, "outputs": [], @@ -205,7 +205,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 22, "id": "7103bf1c", "metadata": {}, "outputs": [ @@ -213,8 +213,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 30 loss: 0.0318\n", - "iter: 60 loss: 0.0018\n", + "iter: 30 loss: 0.0230\n", + "iter: 60 loss: 0.0006\n", "iter: 90 loss: 0.0001\n", "iter: 120 loss: 0.0000\n", "iter: 150 loss: -0.0000\n", @@ -227,25 +227,29 @@ "--U---------x----*----U---------x----*----U---------x----*----U---------x----*----U---------x----*--\n", " \n", "优化后的参数 theta:\n", - " [[[[ 4.712 6.283 3.927]\n", - " [ 3.142 3.713 4.499]\n", - " [ 5.498 4.712 4.712]]\n", + " [[[[1.571 4.712 0.313]\n", + " [0. 4.596 4.043]\n", + " [6.283 1.43 1.599]]]\n", "\n", - " [[ 1.571 1.571 4.712]\n", - " [ 4.712 4.712 4.712]\n", - " [ 3.142 2.022 3.593]]\n", "\n", - " [[-0.785 4.713 1.571]\n", - " [ 0.785 1.571 6.283]\n", - " [ 6.283 0.48 0.305]]\n", + " [[[4.712 1.571 4.825]\n", + " [1.571 1.571 3.142]\n", + " [3.141 6.437 6.437]]]\n", "\n", - " [[ 4.712 0.785 6.283]\n", - " [ 1.571 -0. 3.142]\n", - " [ 3.142 3.844 3.844]]\n", "\n", - " [[ 6.283 0.987 3.725]\n", - " [ 4.712 4.712 6.284]\n", - " [ 6.283 1.993 4.29 ]]]]\n" + " [[[1.571 3.927 0. ]\n", + " [1.571 3.927 3.141]\n", + " [0. 2.73 4.338]]]\n", + "\n", + "\n", + " [[[1.571 1.571 3.927]\n", + " [4.713 4.712 2.356]\n", + " [3.142 5.064 5.537]]]\n", + "\n", + "\n", + " [[[4.712 4.825 3.141]\n", + " [0. 0.609 3.991]\n", + " [3.142 0.438 5.15 ]]]]\n" ] } ], @@ -291,7 +295,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 23, "id": "12678dff", "metadata": {}, "outputs": [ @@ -300,25 +304,25 @@ "output_type": "stream", "text": [ "sample: 1 :\n", - " trace distance is 0.00023\n", + " trace distance is 0.00017\n", "sample: 2 :\n", - " trace distance is 0.00027\n", + " trace distance is 0.00018\n", "sample: 3 :\n", - " trace distance is 0.00026\n", + " trace distance is 0.00017\n", "sample: 4 :\n", - " trace distance is 0.00027\n", + " trace distance is 0.00013\n", "sample: 5 :\n", - " trace distance is 0.00024\n", + " trace distance is 0.00022\n", "sample: 6 :\n", - " trace distance is 0.00024\n", + " trace distance is 0.00013\n", "sample: 7 :\n", - " trace distance is 0.00025\n", + " trace distance is 0.00015\n", "sample: 8 :\n", - " trace distance is 0.00024\n", + " trace distance is 0.00014\n", "sample: 9 :\n", - " trace distance is 0.00024\n", + " trace distance is 0.00014\n", "sample: 10 :\n", - " trace distance is 0.00027\n" + " trace distance is 0.00013\n" ] } ], @@ -387,7 +391,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 24, "id": "d6852694", "metadata": {}, "outputs": [], @@ -407,7 +411,7 @@ " cir.toffoli([0, 1, 2])\n", " \n", " # 构建 QNN\n", - " cir.complex_entangled_layer([3, 4, 5], n, D)\n", + " cir.complex_entangled_layer([3, 4, 5], D)\n", "\n", " for l in range(n):\n", " cir.cnot([n - 1 - l, 2 * n - 1 - l])\n", @@ -428,7 +432,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 25, "id": "7ee10c61", "metadata": {}, "outputs": [], @@ -457,7 +461,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 26, "id": "280e2858", "metadata": {}, "outputs": [], @@ -479,17 +483,26 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 27, "id": "77919a34", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "iter: 20 loss: 0.0720\n", - "iter: 40 loss: 0.0127\n", - "iter: 60 loss: 0.0013\n", + "iter: 20 loss: 0.1251\n", + "iter: 40 loss: 0.0174\n", + "iter: 60 loss: 0.0019\n", "iter: 80 loss: 0.0002\n", "iter: 100 loss: 0.0000\n", "iter: 120 loss: 0.0000\n", @@ -531,13 +544,13 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 28, "id": "df546ac5", "metadata": {}, "outputs": [], "source": [ "# 存储优化后的参数\n", - "theta_opt = cir.parameters()[0]" + "theta_opt = cir.parameters()" ] }, { @@ -560,7 +573,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 30, "id": "0c339ca3", "metadata": {}, "outputs": [ @@ -569,25 +582,25 @@ "output_type": "stream", "text": [ "sample 1 :\n", - " trace distance is 0.00159\n", + " trace distance is 0.20668\n", "sample 2 :\n", - " trace distance is 0.00153\n", + " trace distance is 0.18735\n", "sample 3 :\n", - " trace distance is 0.00149\n", + " trace distance is 0.24465\n", "sample 4 :\n", - " trace distance is 0.00153\n", + " trace distance is 0.1156\n", "sample 5 :\n", - " trace distance is 0.00142\n", + " trace distance is 0.27939\n", "sample 6 :\n", - " trace distance is 0.00167\n", + " trace distance is 0.18128\n", "sample 7 :\n", - " trace distance is 0.00158\n", + " trace distance is 0.22863\n", "sample 8 :\n", - " trace distance is 0.0016\n", + " trace distance is 0.25865\n", "sample 9 :\n", - " trace distance is 0.00153\n", + " trace distance is 0.33706\n", "sample 10 :\n", - " trace distance is 0.00152\n" + " trace distance is 0.16921\n" ] } ], @@ -606,7 +619,7 @@ " # 构造近似酉算子对应的电路\n", " cir_2 = Circuit(3)\n", " for j in range(D):\n", - " cir_2.u3(qubits_idx='full', num_qubits=3, param=theta_opt[j])\n", + " cir_2.u3(qubits_idx='full', param=theta_opt[j])\n", " cir_2.cnot(qubits_idx='cycle')\n", " # sampled 经过近似酉算子演化后的结果\n", " simulated_output = paddle.matmul(paddle.matmul(cir_2.unitary_matrix(), sampled.data), dagger(cir_2.unitary_matrix()))\n", @@ -673,7 +686,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.13" } }, "nbformat": 4, diff --git a/tutorials/qnn_research/VQCC_EN.ipynb b/tutorials/qnn_research/VQCC_EN.ipynb index 308fccd..a1fdcba 100644 --- a/tutorials/qnn_research/VQCC_EN.ipynb +++ b/tutorials/qnn_research/VQCC_EN.ipynb @@ -75,10 +75,25 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "id": "ae8f2fdb", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/openfermion/hamiltonians/hartree_fock.py:11: DeprecationWarning: Please use `OptimizeResult` from the `scipy.optimize` namespace, the `scipy.optimize.optimize` namespace is deprecated.\n", + " from scipy.optimize.optimize import OptimizeResult\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import numpy as np\n", "import paddle\n", @@ -98,7 +113,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "id": "4663732b", "metadata": {}, "outputs": [], @@ -129,7 +144,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "id": "4e400e2e", "metadata": {}, "outputs": [], @@ -139,7 +154,7 @@ " # Initialize the circuit\n", " cir = Circuit(n)\n", " # Call the built-in QNN template\n", - " cir.complex_entangled_layer('full', n, D)\n", + " cir.complex_entangled_layer('full', D)\n", "\n", " return cir" ] @@ -157,7 +172,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "id": "29c9ed4a", "metadata": {}, "outputs": [], @@ -184,7 +199,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "id": "4046e5b0", "metadata": {}, "outputs": [], @@ -204,19 +219,28 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 6, "id": "7103bf1c", "metadata": {}, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/home/zl/miniconda3/envs/pq/lib/python3.8/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " elif dtype == np.bool:\n" + ] + }, { "name": "stdout", "output_type": "stream", "text": [ - "iter: 30 loss: 0.0563\n", - "iter: 60 loss: 0.0029\n", - "iter: 90 loss: 0.0001\n", - "iter: 120 loss: 0.0000\n", - "iter: 150 loss: 0.0000\n", + "iter: 30 loss: 0.1692\n", + "iter: 60 loss: 0.1476\n", + "iter: 90 loss: 0.1465\n", + "iter: 120 loss: 0.1464\n", + "iter: 150 loss: 0.1464\n", "\n", "The trained circuit:\n", "--U----*---------x----U----*---------x----U----*---------x----U----*---------x----U----*---------x--\n", @@ -226,25 +250,29 @@ "--U---------x----*----U---------x----*----U---------x----*----U---------x----*----U---------x----*--\n", " \n", "The trained parameter theta:\n", - " [[[[ 1.571 -0. 4.776]\n", - " [ 3.141 1.091 1.877]\n", - " [ 1.571 0.785 3.814]]\n", + " [[[[ 3.142e+00 2.169e+00 1.385e+00]\n", + " [-1.571e+00 1.569e+00 2.356e+00]\n", + " [ 3.141e+00 5.280e+00 -1.279e+00]]]\n", + "\n", "\n", - " [[ 4.712 0. 3.927]\n", - " [ 3.142 3.404 1.833]\n", - " [ 1.57 3.141 6.283]]\n", + " [[[ 4.712e+00 1.570e+00 3.141e+00]\n", + " [ 3.927e+00 3.138e+00 3.139e+00]\n", + " [ 4.713e+00 4.712e+00 6.283e+00]]]\n", "\n", - " [[ 0.786 0. 6.283]\n", - " [ 3.142 3.352 1.782]\n", - " [ 1.571 6.283 4.712]]\n", "\n", - " [[ 6.283 1.919 3.579]\n", - " [ 3.927 5.946 4.712]\n", - " [ 4.712 3.863 1.571]]\n", + " [[[ 3.142e+00 2.963e+00 1.393e+00]\n", + " [ 3.142e+00 -3.700e-01 1.201e+00]\n", + " [ 2.356e+00 3.144e+00 6.283e+00]]]\n", "\n", - " [[ 0. 1.603 5.914]\n", - " [ 3.142 5.805 5.469]\n", - " [ 3.142 -1.259 5.361]]]]\n" + "\n", + " [[[ 3.142e+00 4.092e+00 9.500e-01]\n", + " [ 3.280e+00 1.572e+00 7.860e-01]\n", + " [ 3.927e+00 1.571e+00 6.281e+00]]]\n", + "\n", + "\n", + " [[[-1.570e+00 3.279e+00 -4.000e-03]\n", + " [ 4.712e+00 -1.380e-01 6.284e+00]\n", + " [ 1.571e+00 6.421e+00 6.283e+00]]]]\n" ] } ], @@ -290,7 +318,7 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 7, "id": "12678dff", "metadata": {}, "outputs": [ @@ -299,25 +327,25 @@ "output_type": "stream", "text": [ "sample 1 :\n", - " trace distance is 0.00041\n", + " trace distance is 0.19792\n", "sample 2 :\n", - " trace distance is 0.0004\n", + " trace distance is 0.2463\n", "sample 3 :\n", - " trace distance is 0.00042\n", + " trace distance is 0.2343\n", "sample 4 :\n", - " trace distance is 0.00045\n", + " trace distance is 0.18177\n", "sample 5 :\n", - " trace distance is 0.00037\n", + " trace distance is 0.18689\n", "sample 6 :\n", - " trace distance is 0.00041\n", + " trace distance is 0.18345\n", "sample 7 :\n", - " trace distance is 0.00042\n", + " trace distance is 0.22967\n", "sample 8 :\n", - " trace distance is 0.00039\n", + " trace distance is 0.22579\n", "sample 9 :\n", - " trace distance is 0.00043\n", + " trace distance is 0.21692\n", "sample 10 :\n", - " trace distance is 0.00041\n" + " trace distance is 0.25945\n" ] } ], @@ -387,7 +415,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 8, "id": "d6852694", "metadata": {}, "outputs": [], @@ -407,7 +435,7 @@ " cir.toffoli([0, 1, 2])\n", "\n", " # Construct QNN\n", - " cir.complex_entangled_layer([3, 4, 5], n, D)\n", + " cir.complex_entangled_layer([3, 4, 5], D)\n", " \n", " for l in range(n):\n", " cir.cnot([n - 1 - l, 2 * n - 1 - l])\n", @@ -428,7 +456,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 9, "id": "7ee10c61", "metadata": {}, "outputs": [], @@ -457,7 +485,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 10, "id": "280e2858", "metadata": {}, "outputs": [], @@ -479,7 +507,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 11, "id": "77919a34", "metadata": {}, "outputs": [ @@ -487,12 +515,12 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 20 loss: 0.3032\n", - "iter: 40 loss: 0.0080\n", - "iter: 60 loss: 0.0011\n", - "iter: 80 loss: 0.0002\n", - "iter: 100 loss: 0.0001\n", - "iter: 120 loss: 0.0000\n", + "iter: 20 loss: 0.4525\n", + "iter: 40 loss: 0.1755\n", + "iter: 60 loss: 0.0066\n", + "iter: 80 loss: 0.0021\n", + "iter: 100 loss: 0.0005\n", + "iter: 120 loss: 0.0001\n", "\n", "The trained circuit:\n", "Approximate circuit of U with circuit form input:\n", @@ -533,13 +561,13 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 12, "id": "777ca58e", "metadata": {}, "outputs": [], "source": [ "# Storage optimized parameters\n", - "theta_opt = cir.parameters()[0]" + "theta_opt = cir.parameters()" ] }, { @@ -562,7 +590,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 13, "id": "0c339ca3", "metadata": { "scrolled": false @@ -573,25 +601,25 @@ "output_type": "stream", "text": [ "sample 1 :\n", - " trace distance is 0.00245\n", + " trace distance is 0.20575\n", "sample 2 :\n", - " trace distance is 0.00239\n", + " trace distance is 0.2397\n", "sample 3 :\n", - " trace distance is 0.00236\n", + " trace distance is 0.23174\n", "sample 4 :\n", - " trace distance is 0.00222\n", + " trace distance is 0.15452\n", "sample 5 :\n", - " trace distance is 0.00235\n", + " trace distance is 0.2846\n", "sample 6 :\n", - " trace distance is 0.00251\n", + " trace distance is 0.2477\n", "sample 7 :\n", - " trace distance is 0.00241\n", + " trace distance is 0.21579\n", "sample 8 :\n", - " trace distance is 0.00248\n", + " trace distance is 0.1746\n", "sample 9 :\n", - " trace distance is 0.00228\n", + " trace distance is 0.18502\n", "sample 10 :\n", - " trace distance is 0.00242\n" + " trace distance is 0.32651\n" ] } ], @@ -610,7 +638,7 @@ " # Construct the circuit of approximate unitary\n", " cir_2 = Circuit(3)\n", " for j in range(D):\n", - " cir_2.u3(qubits_idx='full', num_qubits=3, param=theta_opt[j])\n", + " cir_2.u3(qubits_idx='full', param=theta_opt[j])\n", " cir_2.cnot(qubits_idx='cycle')\n", " # sampled after approximate unitary evolution\n", " simulated_output = paddle.matmul(paddle.matmul(cir_2.unitary_matrix(), sampled.data), dagger(cir_2.unitary_matrix()))\n", @@ -677,7 +705,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.13" } }, "nbformat": 4, diff --git a/tutorials/quantum_simulation/ClassicalShadow_Application_CN.ipynb b/tutorials/quantum_simulation/ClassicalShadow_Application_CN.ipynb index a3f9da9..8d8f0d3 100644 --- a/tutorials/quantum_simulation/ClassicalShadow_Application_CN.ipynb +++ b/tutorials/quantum_simulation/ClassicalShadow_Application_CN.ipynb @@ -539,7 +539,7 @@ "ave_LiH_energy_traditional = np.mean(estimator_traditional)\n", "end = time.time() \n", "\n", - "print(\"LiH ground state energy = \", LiH_energy.numpy()[0])\n", + "print(\"LiH ground state energy = \", LiH_energy)\n", "print(\"ave LiH ground state energy CS = \", ave_LiH_energy_CS)\n", "print(\"ave LiH ground state energy LBCS = \", ave_LiH_energy_LBCS)\n", "print(\"ave LiH ground state energy APS = \", ave_LiH_energy_APS)\n", @@ -664,7 +664,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.13" + "version": "3.8.16" } }, "nbformat": 4, diff --git a/tutorials/quantum_simulation/ClassicalShadow_Application_EN.ipynb b/tutorials/quantum_simulation/ClassicalShadow_Application_EN.ipynb index 623f467..a478b39 100644 --- a/tutorials/quantum_simulation/ClassicalShadow_Application_EN.ipynb +++ b/tutorials/quantum_simulation/ClassicalShadow_Application_EN.ipynb @@ -533,7 +533,7 @@ "ave_LiH_energy_traditional = np.mean(estimator_traditional)\n", "end = time.time() \n", "\n", - "print(\"LiH ground state energy = \", LiH_energy.numpy()[0])\n", + "print(\"LiH ground state energy = \", LiH_energy)\n", "print(\"ave LiH ground state energy CS = \", ave_LiH_energy_CS)\n", "print(\"ave LiH ground state energy LBCS = \", ave_LiH_energy_LBCS)\n", "print(\"ave LiH ground state energy APS = \", ave_LiH_energy_APS)\n", diff --git a/tutorials/quantum_simulation/DistributedVQE_CN.ipynb b/tutorials/quantum_simulation/DistributedVQE_CN.ipynb index 6a49c72..1a58bc7 100644 --- a/tutorials/quantum_simulation/DistributedVQE_CN.ipynb +++ b/tutorials/quantum_simulation/DistributedVQE_CN.ipynb @@ -133,10 +133,23 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 1, "id": "bb7c0db4", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import time\n", "import numpy as np\n", @@ -145,6 +158,9 @@ "import paddle\n", "import paddle_quantum\n", "from paddle_quantum.ansatz import Circuit\n", + "from paddle_quantum.hamiltonian import Hamiltonian\n", + "from paddle_quantum.loss import ExpecVal\n", + "from paddle_quantum.state import State\n", "from paddle_quantum.qinfo import pauli_str_to_matrix, schmidt_decompose\n", "import warnings\n", "\n", @@ -166,7 +182,7 @@ "metadata": {}, "outputs": [], "source": [ - "N = 10 # 量子比特数\n", + "N = 10 # 量子比特数\n", "SEED = 16 # 固定随机种子\n", "ITR = 100 # 设置迭代次数\n", "LR = 0.1 # 设置学习率\n", @@ -183,7 +199,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 3, "id": "32b310ed", "metadata": {}, "outputs": [], @@ -214,7 +230,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 4, "id": "6149b4d4", "metadata": {}, "outputs": [ @@ -223,7 +239,7 @@ "output_type": "stream", "text": [ "The ground state energy is -0.99783 Ha.\n", - "Schmidt rank of the ground state is 3.\n" + "Schmidt rank of the ground state is 32.\n" ] } ], @@ -238,7 +254,8 @@ "pauli_str_B = ['x0,y1,y2,x3,x4', 'x0,z1,z2,y3,x4'] # 子系统 B 的泡利字符串\n", "\n", "# 把相关对象转换为张量形式\n", - "H_mtr = paddle.to_tensor(pauli_str_to_matrix(zip(coefs, pauli_str), n=N))\n", + "H = Hamiltonian(list(zip(coefs, pauli_str)))\n", + "H_mtr = paddle.to_tensor(H.construct_h_matrix())\n", "coefs = paddle.to_tensor(coefs)\n", "H_A = [pauli_str_to_matrix([[1., pstr]], n=N//2) for pstr in pauli_str_A]\n", "H_A = paddle.to_tensor(np.stack(H_A))\n", @@ -259,16 +276,15 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 5, "id": "32cacc67", "metadata": {}, "outputs": [], "source": [ "# 构造参数化量子电路\n", "def U_cir(N, D):\n", - " \n", " cir = Circuit(N) # 初始化一个宽度为 N 量子比特的电路\n", - " cir.complex_entangled_layer('full', N, D) # 添加量子门\n", + " cir.complex_entangled_layer(depth=D) # 添加量子门\n", " return cir \n", "\n", "# 把参数化电路作用在计算基底上\n", @@ -296,7 +312,7 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 6, "id": "6ebf5159", "metadata": {}, "outputs": [], @@ -339,7 +355,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 7, "id": "066f5e72", "metadata": {}, "outputs": [], @@ -385,7 +401,7 @@ }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 8, "id": "78b46dcc", "metadata": {}, "outputs": [ @@ -399,19 +415,17 @@ "iter: 80, loss: -0.9977 Ha\n", "iter: 100, loss: -0.9978 Ha\n", "Ground truth is -0.9978 Ha\n", - "Training took 11.81s\n" + "Training took 11.03s\n" ] }, { "data": { - "image/png": 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+ "image/png": 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", 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    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -432,7 +446,7 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 9, "id": "2fff9166", "metadata": {}, "outputs": [], @@ -441,13 +455,12 @@ " def __init__(self, N, D, S):\n", " super().__init__()\n", " paddle.seed(SEED)\n", - " self.N = N\n", - " self.S = S\n", - " self.cir = [U_cir(N, D)]\n", + " self.cir = U_cir(N, D)\n", + " self.loss_fcn = ExpecVal(H)\n", " \n", " def forward(self):\n", - " vec = output_states(self.S, self.N, self.cir[0])\n", - " loss = vec.conj().t() @ H_mtr @ vec\n", + " output_state = self.cir()\n", + " loss = self.loss_fcn(output_state)\n", " return loss.cast('float64').flatten()" ] }, @@ -461,7 +474,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 10, "id": "a35f3eb4", "metadata": {}, "outputs": [ @@ -475,19 +488,17 @@ "iter: 80, loss: -0.9975 Ha\n", "iter: 100, loss: -0.9978 Ha\n", "Ground truth is -0.9978 Ha\n", - "Training took 2252.27s\n" + "Training took 6.84s\n" ] }, { "data": { - "image/png": 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", + "image/png": 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/pZ5fbYGBgdizZ4/RMhsbmzxDHoVp0aIF1q9fj6ysLBw/fhwbNmzA559/jueeew7Hjh3L90s8t/T0dMyePRvLli3DrVu3jMbG8+varlGjhtHv+kmX+qCnf76P74Xj5eWVZ4KmTqfDggUL8NVXX+HKlSvQarWG2/Lr6g0ICDD6vaDHApBvAGrcuDEaNmyIn3/+2TDev2rVKlSuXBldu3Y1tNOHlseDyeNSUlLyDCOqVKoS7Wl27do1+Pr65glMQUFBhttze/x1AKTXojiBe8WKFZg3bx7Onj2L7Oxsw/LHt29pODg4FDi8k5GRYfhiSk1NRWpqquE2lUoFLy8vk95HpqpTp06eOTL16tUDAFy9erVEn/OCVK5cOd/3Q357+pT2s6gP8H5+fnmWm+MfMb1r164ZhuFzy/1ezT2MXdTfjIJs3rwZM2fOxLFjx5CZmWlYnt/8ptJ8HioK9rxUcO3bt8elS5fw/fffo2HDhvj222/RvHlzo91bx40bh/Pnz2P27Nmwt7fHlClTEBQUZBjHt6TcvRGmsLOzQ4sWLfDRRx/h66+/RnZ2NtauXVvk/caMGYNZs2ZhwIAB+OWXX7Bjxw5ER0fD09Mz310XC9rlVzw2IbA4PvroI4wfPx7t27fHTz/9hO3btyM6OhoNGjTI97GLM1G0KC+88ALOnz+PQ4cOIS4uDrt27cKAAQOMvkz0ge/ff/8tcD3Xrl2DRqMx6ukrSyV9HX766ScMHToUtWvXxnfffYdt27YhOjoaTz31lFl3VfXx8YFWq82z11tWVhbu379vmM80d+5c+Pj4GC4tWrQw+bEKOtZM7jBsDcz1WcxveUk+n+ZSkvfqP//8g169esHe3h5fffUVtmzZgujoaDz//PP53s+cf5esFXterJCXlxccHR1x7ty5PLedPXsWSqXS6L8RDw8PDBs2DMOGDUNqairat2+P6dOnGx0DpHbt2pgwYQImTJiACxcuoGnTppg3bx5++uknk2qrWbMmAODcuXN46qmnjG47d+6c4XZz0k+SvHPnjmFZQX/g161bhyFDhmDevHmGZRkZGSU+MrD++Vy4cMHoi/3u3bt5/gtat24dOnXqhO+++85oeVJSEipXrmzSYz0uv/cCAAwaNAjvvPMOVq1ahZo1a0Kr1ebZo6tu3bqoX78+Nm7ciAULFuQ7fPTDDz8AAPr3719kncVRs2ZN/PHHH0hJSTF6vLNnzxpuN4d169ahVq1ahgP36U2bNs0s69fTT/w9dOgQevToYVh+6NAh6HQ6w+2DBw82Gn7QB1RT3kf6/+STkpKMJr8/3luld/HiRQghjJ6/fpfvwvYgKuqAfKVl7s9iaRX0fGvWrFng31r97aX166+/wt7eHtu3b4darTYsX7ZsWanXXVGx58UKqVQqdOnSBb/99pvRboXx8fFYtWoV2rZta9jT4/79+0b3dXZ2Rp06dQzdkmlpacjIyDBqU7t2bbi4uBh1XRZXaGgoqlSpgsWLFxvdf+vWrThz5kyeWfOm2LVrV77/WWzZsgWA8VCVk5NTvn8EVSpVnnUsWrSoxP+1RkREwNbWFosWLTJab35HJs3vsdeuXZtnF/KC+Pj4oGnTplixYoVRt3p0dHSecXe9GjVqoF27dlizZg1++uknBAQEoHXr1nnaTZs2DQ8ePMCrr76aZ1scPnwYc+bMQbNmzdC9e/di1VqUHj16QKvV4osvvjBa/vnnn0OhUJjtcfT/oebe7gcOHEBMTIxZ1q/31FNPwcPDA19//bXR8q+//hqOjo6G932tWrUQERFhuLRp0waAae8j/VyH3bt3G5bpDw2Qn9u3bxvtTq/RaPDDDz+gadOmhQ4ZOTk55Tt8Yy7m/iyWVkF/M3r06IHY2Fij98zDhw+xdOlS+Pv7FzlUXRwqlQoKhcLouV+9evWJPUp4cbDnpRz7/vvv8913/4033sDMmTMRHR2Ntm3b4vXXX4eNjQ2WLFmCzMxMfPLJJ4a2wcHB6NixI0JCQuDh4YFDhw5h3bp1GD16NADpP7DOnTtjwIABCA4Oho2NDTZs2ID4+Hijo68Wl62tLebMmYNhw4ahQ4cOGDRokGFXaX9/f7z55psl3h5jxoxBWloa+vbti8DAQGRlZWHfvn1Ys2YN/P39MWzYMEPbkJAQ/PHHH/jss8/g6+uLgIAAhIWFoWfPnvjxxx/h5uaG4OBgxMTE4I8//ijx7oVeXl6YOHEiZs+ejZ49e6JHjx44evQotm7dmqc3pWfPnvjwww8xbNgwtG7dGidOnMDKlStNGoqZPXs2IiMj0bZtW7z00ktITEzEokWL0KBBA6O5FLm98MILGDlyJG7fvm3YDfRxgwYNwqFDh/DZZ5/h9OnTiIqKQqVKlXDkyBF8//338PLywrp16/LMXcjJySmwd65v374FHnDwmWeeQadOnfDee+/h6tWraNKkCXbs2IHffvsN48aNM5qMWBo9e/bE+vXr0bdvX0RGRuLKlStYvHgxgoODC9xeuV27dg0//vgjABhO1zFz5kwA0n/cL774IgCpB2XGjBkYNWoU+vfvj65du+Kff/7BTz/9hFmzZsHDw6PQxzHlfdSlSxfUqFEDw4cPx6RJk6BSqQyv0fXr1/Osu169ehg+fDgOHjyIqlWr4vvvv0d8fHyR/9WHhIRgzZo1GD9+PFq0aAFnZ2c888wzRW6z4jL3Z7G0QkJC8PXXX2PmzJmoU6cOqlSpgqeeegqTJ0/Gzz//jO7du2Ps2LHw8PDAihUrcOXKFfz6668lGvZ+XGRkJD777DN069YNzz//PBISEvDll1+iTp06hQ7nPtHKevcmKpp+N76CLjdu3BBCCHHkyBHRtWtX4ezsLBwdHUWnTp3Evn37jNY1c+ZM0bJlS+Hu7i4cHBxEYGCgmDVrlmH34nv37olRo0aJwMBA4eTkJNzc3ERYWJj45Zdfil1nfrt0r1mzRjRr1kyo1Wrh4eEhoqKixM2bN43aDBkyRDg5ORV7u2zdulW89NJLIjAwUDg7Ows7OztRp04dMWbMGBEfH2/U9uzZs6J9+/bCwcHBaFfTBw8eiGHDhonKlSsLZ2dn0bVrV3H27FlRs2ZNo91RC3pu+e1SqtVqxQcffCB8fHyEg4OD6Nixozh58mSedWZkZIgJEyYY2rVp00bExMSIDh06GO2iqX+M3LuV5vbrr7+KoKAgoVarRXBwsFi/fn2+u17qJSYmCrVaLQCI06dPF7qNN23aJCIiIoS7u7vh/dagQQORnJycp21hu0rjsd1Q85OSkiLefPNN4evrK2xtbUXdunXFp59+arQ7rBDSrqGjRo3Kc//Ht29+dDqd+Oijj0TNmjWFWq0WzZo1E5s3by50e+Wmfy3yu+S3W+3SpUtF/fr1hZ2dnahdu7b4/PPP8zyfghT3fSSEEIcPHxZhYWHCzs5O1KhRQ3z22WcF7iodGRkptm/fLho3bizUarUIDAzM897K732dmpoqnn/+ecN7oajtpX+s/OT3ni7tZ1G/y/jdu3eNluf3dwXF2FU6Li5OREZGChcXlzyv76VLl8Rzzz0n3N3dhb29vWjZsqXYvHlzkc9RCOlwCADEsmXLjGp8fHt+9913om7duobXaNmyZfnuFl+az0NFohDiCZrhQ0Qmefnll/Hdd9/hm2++KfA8SWRZ/v7+6NixI08aSJQLh42IqEBLlixBfHw8XnvtNfj6+hpNRiUikgvDCxEVSKVS4f/+7//kLoOIyAj3NiIiIiKrwjkvREREZFXY80JERERWheGFiIiIrEqFm7Cr0+lw+/ZtuLi4WPzw1kRERGQeQgikpKTA19e3yIP/Vbjwcvv27TxnGSUiIiLrcOPGDVSvXr3QNhUuvOhP8nbjxg3D+X2IiIiofNNoNPDz88v35LCPq3DhRT9U5OrqyvBCRERkZYoz5YMTdomIiMiqMLwQERGRVWF4ISIiIqtS4ea8EBGRvLRaLbKzs+Uug8ohW1tbqFSqUq+H4YWIiMwmNTUVN2/eBM88Q/lRKBSoXr06nJ2dS7UehhciIjILrVaLmzdvwtHREV5eXjxQKBkRQuDu3bu4efMm6tatW6oeGIYXIiIyi+zsbAgh4OXlBQcHB7nLoXLIy8sLV69eRXZ2dqnCCyfsEhGRWbHHhQpirvcGwwsRERFZlTIJL19++SX8/f1hb2+PsLAwxMbGFtp+7dq1CAwMhL29PRo1aoQtW7aURZlERERkBSweXtasWYPx48dj2rRpOHLkCJo0aYKuXbsiISEh3/b79u3DoEGDMHz4cBw9ehR9+vRBnz59cPLkSUuXSkRET6COHTti3LhxcpdBJrB4ePnss88wYsQIDBs2DMHBwVi8eDEcHR3x/fff59t+wYIF6NatGyZNmoSgoCDMmDEDzZs3xxdffGHpUomIiMgKWDS8ZGVl4fDhw4iIiHj0gEolIiIiEBMTk+99YmJijNoDQNeuXQtsn5mZCY1GY3SxiPh44MMPgXfescz6iYiIqFgsGl7u3bsHrVaLqlWrGi2vWrUq4uLi8r1PXFycSe1nz54NNzc3w8XPz888xT/u0iVg2jRg/nzgwQPLPAYRUUUiBPDwoTyXEh4k78GDBxg8eDAqVaoER0dHdO/eHRcuXDDcfu3aNTzzzDOoVKkSnJyc0KBBA8O8zAcPHiAqKsqwq3jdunWxbNkys2xKMmb1x3l55513MH78eMPvGo3GMgEmPBxo1Ag4cQL48Udg7FjzPwYRUUWSlgaU8kiqJZaaCjg5mXy3oUOH4sKFC9i0aRNcXV3x9ttvo0ePHjh9+jRsbW0xatQoZGVlYffu3XBycsLp06cNR4udMmUKTp8+ja1bt6Jy5cq4ePEi0tPTzf3MCBYOL5UrV4ZKpUJ8fLzR8vj4eHh7e+d7H29vb5Paq9VqqNVq8xRcGIUCePVVYNQoYPFiYMwYaRkREVUI+tCyd+9etG7dGgCwcuVK+Pn5YePGjejfvz+uX7+Ofv36oVGjRgCAWrVqGe5//fp1NGvWDKGhoQAAf3//Mn8OTwqLDhvZ2dkhJCQEO3fuNCzT6XTYuXMnwsPD871PeHi4UXsAiI6OLrB9mYqKAhwdgTNngH/+kbsaIqLyzdFR6gGR4+LoaHK5Z86cgY2NDcLCwgzLPD09Ub9+fZw5cwYAMHbsWMycORNt2rTBtGnT8O+//xravvbaa1i9ejWaNm2Kt956C/v27Sv9NqR8WXxvo/Hjx+Obb77BihUrcObMGbz22mt4+PAhhg0bBgAYPHgw3sk1CfaNN97Atm3bMG/ePJw9exbTp0/HoUOHMHr0aEuXWjQ3N+D556XrS5bIWwsRUXmnUEhDN3JcLNQz/vLLL+Py5ct48cUXceLECYSGhmLRokUAgO7du+PatWt48803cfv2bXTu3BkTJ060SB1PPFEGFi1aJGrUqCHs7OxEy5Ytxf79+w23dejQQQwZMsSo/S+//CLq1asn7OzsRIMGDcTvv/9e7MdKTk4WAERycrK5yjd26JAQgBB2dkIkJFjmMYiIrFB6ero4ffq0SE9Pl7sUk3To0EG88cYb4vz58wKA2Lt3r+G2e/fuCQcHB7F27dp87zt58mTRqFGjfG9bvHixcHFxsUjN1qqw94gp399lMmF39OjRBfac/PXXX3mW9e/fH/3797dwVSUUEgKEhgKHDgHLlwOTJsldERERmUHdunXRu3dvjBgxAkuWLIGLiwsmT56MatWqoXfv3gCAcePGoXv37qhXrx4ePHiAXbt2ISgoCAAwdepUhISEoEGDBsjMzMTmzZsNt5F58dxGJfHKK9LPpUsBnU7eWoiIyGyWLVuGkJAQ9OzZE+Hh4RBCYMuWLbC1tQUAaLVajBo1CkFBQejWrRvq1auHr776CoA0z/Odd95B48aN0b59e6hUKqxevVrOp1NhKYQo4c7w5ZRGo4GbmxuSk5Ph6upqmQdJTQWqVQM0GiA6GnjsoHpERE+ijIwMXLlyBQEBAbC3t5e7HCqHCnuPmPL9zZ6XknB2Bl58Ubq+eLG8tRARET1hGF5KSj909NtvwJ078tZCRET0BGF4KalGjYDWrYGcHGDNGrmrISIiemIwvJRGZKT0c/9+eesgIiJ6gjC8lIb+KIwHDshbBxER0ROE4aU0QkOlozhevQokJMhdDRER0ROB4aU03NyAwEDpemysvLUQERE9IRheSqtlS+knh46IiIjKBMNLaennvbDnhYiIqEwwvJRW7vDCUwUQEVEZWL58Odzd3eUuA0OHDkWfPn3K/HEZXkqrUSPA3h5ISgIuXpS7GiIiIly9ehUKhQLHjh0rl+srLYaX0rK1BZo3l65z3gsR0RMhKytL7hLMwlqfB8OLOegn7XLeCxFRHmlZOUjLykHu8wBn5eiQlpWDzBxtvm11ukdts7VS24zs4rU1VUpKCqKiouDk5AQfHx98/vnn6NixI8aNG2do4+/vjxkzZmDw4MFwdXXFyJEjAQC//vorGjRoALVaDX9/f8ybN89o3QqFAhs3bjRa5u7ujuXLlwN41KOxfv16dOrUCY6OjmjSpAliYmKM7rN8+XLUqFEDjo6O6Nu3L+7fv1/ocwoICAAANGvWDAqFAh07dgTwaJhn1qxZ8PX1Rf369YtVZ0Hr05s7dy58fHzg6emJUaNGITs7u9D6SovhxRx4sDoiogIFT92O4Knbkfjw0X/5S3dfQvDU7Zj22ymjtiEz/kDw1O24lZRuWPZDzDUET92Ot3/916ht2zm7EDx1Oy7eTTUsW3f4psn1jR8/Hnv37sWmTZsQHR2Nf/75B0eOHMnTbu7cuWjSpAmOHj2KKVOm4PDhwxgwYAAGDhyIEydOYPr06ZgyZYrhC98U7733HiZOnIhjx46hXr16GDRoEHJycgAABw4cwPDhwzF69GgcO3YMnTp1wsyZMwtdX+x//0z/8ccfuHPnDtavX2+4befOnTh37hyio6OxefPmYtVX2Pp27dqFS5cuYdeuXVixYgWWL19eom1gChuLrv1JoQ8vx44BGRnSHBgiIir3UlJSsGLFCqxatQqdO3cGACxbtgy+vr552j711FOYMGGC4feoqCh07twZU6ZMAQDUq1cPp0+fxqeffoqhQ4eaVMfEiRMR+d8pZz744AM0aNAAFy9eRGBgIBYsWIBu3brhrbfeMjzOvn37sG3btgLX5+XlBQDw9PSEt7e30W1OTk749ttvYWdnV+z6CltfpUqV8MUXX0ClUiEwMBCRkZHYuXMnRowYUez1m4rhxRz8/YHKlYF794Djxx+FGSIiwukPuwIAHGxVhmUj29fGS20DoFIqjNoenhIBALC3edR2cHhNDGrpB6XCuO2etzvlaftcSHWTart8+TKys7PRUj/8D8DNzc0wnJJbaGio0e9nzpxB7969jZa1adMG8+fPh1arhUqlQnE1btzYcN3HxwcAkJCQgMDAQJw5cwZ9+/Y1ah8eHl5oeClMo0aNTAouRWnQoIHRc/Xx8cGJEyfMtv78cNjIHBQKDh0RERXA0c4GjnY2UOQKH3Y2Sjja2UBto8q3rTJXqLFVSW3tbYvX1lKcnJxMvo9CoTCa6wMg3/kgtra2RvcBAJ2FDr+R3/Mobp35yV27fl2Wql2P4cVceLA6IiKrU6tWLdja2uLgwYOGZcnJyTh//nyR9w0KCsLevXuNlu3duxf16tUz9ER4eXnhzp07htsvXLiAtLQ0k2oMCgrCgcf+Md6/f3+h99H3rGi12kLb6RVVp6nrszQOG5kLTxNARGR1XFxcMGTIEEyaNAkeHh6oUqUKpk2bBqVSadRTlJ8JEyagRYsWmDFjBv73v/8hJiYGX3zxBb766itDm6eeegpffPEFwsPDodVq8fbbb+fpqSjK2LFj0aZNG8ydOxe9e/fG9u3bixwyqlKlChwcHLBt2zZUr14d9vb2cHNzK7B9UXWauj5LY8+LubRoIf28eBFITJS3FiIiKrbPPvsM4eHh6NmzJyIiItCmTRsEBQXBvoidL5o3b45ffvkFq1evRsOGDTF16lR8+OGHRpN1582bBz8/P7Rr1w7PP/88Jk6cCEdHR5Pqa9WqFb755hssWLAATZo0wY4dO/D+++8Xeh8bGxssXLgQS5Ysga+vb565OY8rqk5T12dpCvH4IJeV02g0cHNzQ3JyMlxdXcv2wevVAy5cALZuBbp1K9vHJiKSWUZGBq5cuYKAgIAiv/jLs4cPH6JatWqYN28ehg8fLnc5FUph7xFTvr/Z82JOnLRLRGR1jh49ip9//hmXLl3CkSNHEBUVBQCy9y5QwRhezImTdomIrJL+AHQRERF4+PAh/vnnH1SuXFnusqgAnLBrTvpJu7lmrRMRUfnWrFkzHD58WO4yyATseTGnwEDp5927wMOH8tZCRERUQTG8mJOrK+DiIl2/dUveWoiIZFLB9gMhMzLXe4Phxdyq/3do6hs35K2DiKiM6Q/MlpWVVURLelLp3xumnDohP5zzYm5+fsCZM8BN089sSkRkzWxsbODo6Ii7d+/C1tYWSiX/P6ZHdDod7t69C0dHR9jYlC5+MLyYm77nheGFiJ4wCoUCPj4+uHLlCq5duyZ3OVQOKZVK1KhRo8ijFxeF4cXcOGxERE8wOzs71K1bl0NHlC87Ozuz9MgxvJibn5/0kz0vRPSEUiqVVn2EXSr/OCBpbhw2IiIisiiGF3PT97xw2IiIiMgiGF7MTd/zkpgIpKXJWwsREVEFxPBibq6ugLOzdJ0HqiMiIjI7hhdzUyg4dERERGRBDC+WwEm7REREFsPwYgkML0RERBbD8GIJHDYiIiKyGIYXS2DPCxERkcUwvFgCwwsREZHFMLxYAoeNiIiILIbhxRL0PS/37wPp6fLWQkREVMEwvFiCmxvg5CRd59ARERGRWTG8WELuA9UxvBAREZkVw4ulcNIuERGRRTC8WIo+vHDSLhERkVkxvFgKh42IiIgsguHFUjhsREREZBEML5bCYSMiIiKLYHixFA4bERERWQTDi6Xoe17u3QMyMuSthYiIqAJheLEUd3fA0VG6zt4XIiIis2F4sRQeqI6IiMgiGF4siXscERERmZ1Fw0tiYiKioqLg6uoKd3d3DB8+HKmpqYW2HzNmDOrXrw8HBwfUqFEDY8eORXJysiXLtByeXZqIiMjsLBpeoqKicOrUKURHR2Pz5s3YvXs3Ro4cWWD727dv4/bt25g7dy5OnjyJ5cuXY9u2bRg+fLgly7Qc9rwQERGZnUIIISyx4jNnziA4OBgHDx5EaGgoAGDbtm3o0aMHbt68CV9f32KtZ+3atXjhhRfw8OFD2NjY5Lk9MzMTmZmZht81Gg38/PyQnJwMV1dX8zyZklqyBHj1VaBXL+C33+SthYiIqBzTaDRwc3Mr1ve3xXpeYmJi4O7ubgguABAREQGlUokDBw4Uez36J5FfcAGA2bNnw83NzXDx0w/VlAccNiIiIjI7i4WXuLg4VKlSxWiZjY0NPDw8EBcXV6x13Lt3DzNmzCh0qOmdd95BcnKy4XKjPAUFDhsRERGZncnhZfLkyVAoFIVezp49W+rCNBoNIiMjERwcjOnTpxfYTq1Ww9XV1ehSbujDy927PFAdERGRmeQ/FlOICRMmYOjQoYW2qVWrFry9vZGQkGC0PCcnB4mJifD29i70/ikpKejWrRtcXFywYcMG2Nramlpm+VCpknSgurQ04NYtoHZtuSsiIiKyeiaHFy8vL3h5eRXZLjw8HElJSTh8+DBCQkIAAH/++Sd0Oh3CwsIKvJ9Go0HXrl2hVquxadMm2Nvbm1pi+aFQSL0v589LQ0cML0RERKVmsTkvQUFB6NatG0aMGIHY2Fjs3bsXo0ePxsCBAw17Gt26dQuBgYGIjY0FIAWXLl264OHDh/juu++g0WgQFxeHuLg4aLVaS5VqWZz3QkREZFYm97yYYuXKlRg9ejQ6d+4MpVKJfv36YeHChYbbs7Ozce7cOaSlpQEAjhw5YtgTqU6dOkbrunLlCvz9/S1ZrmXo9zi6fl3eOoiIiCoIi4YXDw8PrFq1qsDb/f39kfswMx07doSFDjsjH+4uTUREZFY8t5Gl1agh/WR4ISIiMguGF0vThxcOGxEREZkFw4ulMbwQERGZFcOLpennvCQlARqNrKUQERFVBAwvlubsDHh4SNc574WIiKjUGF7KAoeOiIiIzIbhpSzwWC9ERERmw/BSFtjzQkREZDYML2WBx3ohIiIyG4aXssCeFyIiIrNheCkLDC9ERERmw/BSFvTh5eZNwFrPjk1ERFROMLyUBR8fQKUCsrOB+Hi5qyEiIrJqDC9lQaUCqlWTrnPoiIiIqFQYXsoK570QERGZBcNLWeHu0kRERGbB8FJW2PNCRERkFgwvZYXhhYiIyCwYXsoKz29ERERkFgwvZYU9L0RERGbB8FJW9OHl3j0gLU3eWoiIiKwYw0tZcXMDXFyk69zjiIiIqMQYXsqKQsHdpYmIiMyA4aUscd4LERFRqTG8lCXucURERFRqDC9liT0vREREpcbwUpYYXoiIiEqN4aUsMbwQERGVGsNLWcodXoSQtxYiIiIrxfBSlqpVk3aZzswE7t6VuxoiIiKrxPBSluzsAB8f6TqP9UJERFQiDC9ljbtLExERlQrDS1njpF0iIqJSYXgpawwvREREpcLwUtYYXoiIiEqF4aWsMbwQERGVCsNLWWN4ISIiKhWGl7JWvbr0My4OyM6WtxYiIiIrxPBS1ipXBmxtpet37shbCxERkRVieClrSiXg6ytdv3VL3lqIiIisEMOLHPTh5fZteesgIiKyQgwvcqhWTfrJnhciIiKTMbzIgeGFiIioxBhe5KAPLxw2IiIiMhnDixw4YZeIiKjEGF7kwGEjIiKiEmN4kQOHjYiIiEqM4UUO+mGj1FRAo5G3FiIiIivD8CIHJyfAzU26zqEjIiIikzC8yIXzXoiIiEqE4UUuPMouERFRiTC8yIU9L0RERCXC8CIXhhciIqISYXiRC4eNiIiISoThRS7seSEiIioRhhe5MLwQERGViEXDS2JiIqKiouDq6gp3d3cMHz4cqampxbqvEALdu3eHQqHAxo0bLVmmPPTDRnFxgFYrby1ERERWxKLhJSoqCqdOnUJ0dDQ2b96M3bt3Y+TIkcW67/z586FQKCxZnryqVgWUSim4JCTIXQ0REZHVsFh4OXPmDLZt24Zvv/0WYWFhaNu2LRYtWoTVq1fjdhGTVI8dO4Z58+bh+++/t1R58rOxAby9pescOiIiIio2i4WXmJgYuLu7IzQ01LAsIiICSqUSBw4cKPB+aWlpeP755/Hll1/CW//lXojMzExoNBqji9XgCRqJiIhMZrHwEhcXhypVqhgts7GxgYeHB+Li4gq835tvvonWrVujd+/exXqc2bNnw83NzXDx8/MrVd1lSj/vhT0vRERExWZyeJk8eTIUCkWhl7Nnz5aomE2bNuHPP//E/Pnzi32fd955B8nJyYbLjRs3SvTYsuAeR0RERCazMfUOEyZMwNChQwttU6tWLXh7eyPhsYmoOTk5SExMLHA46M8//8SlS5fg7u5utLxfv35o164d/vrrrzz3UavVUKvVpjyF8oPDRkRERCYzObx4eXnBy8uryHbh4eFISkrC4cOHERISAkAKJzqdDmFhYfneZ/LkyXj55ZeNljVq1Aiff/45nnnmGVNLLf84bERERGQyk8NLcQUFBaFbt24YMWIEFi9ejOzsbIwePRoDBw6E739f2rdu3ULnzp3xww8/oGXLlvD29s63V6ZGjRoICAiwVKny4bARERGRySx6nJeVK1ciMDAQnTt3Ro8ePdC2bVssXbrUcHt2djbOnTuHtLQ0S5ZRfjG8EBERmUwhhBByF2FOGo0Gbm5uSE5Ohqurq9zlFC4pCahUSbr+8CHg6ChrOURERHIx5fub5zaSk5vbo8DCSbtERETFwvAiJ4WCQ0dEREQmYniRm36PI/a8EBERFQvDi9zY80JERGQShhe5MbwQERGZhOFFbhw2IiIiMgnDi9zY80JERGQShhe5MbwQERGZhOFFbrlPzlixjhdIRERkEQwvcvPxkX5mZQH378tbCxERkRVgeJGbnR2gP0s3h46IiIiKxPBSHnDeCxERUbExvJQH3F2aiIio2BheyoPq1aWfN27IWwcREZEVYHgpD2rWlH5euyZvHURERFaA4aU88PeXfjK8EBERFYnhpTzQh5erV+WsgoiIyCowvJQH+vBy4waQkyNrKUREROUdw0t54O0tHe9Fq+Xu0kREREVgeCkPlEqgRg3pOoeOiIiICsXwUl5w3gsREVGxMLyUFwwvRERExcLwUl5wd2kiIqJiYXgpL9jzQkREVCwML+WF/ii7DC9ERESFYngpL3isFyIiomJheCkvfHwAW1spuPDs0kRERAVieCkvVCoe64WIiKgYGF7KE+5xREREVCSGl/KEexwREREVieGlPOEeR0REREVieClP2PNCRERUJIaX8oThhYiIqEgML+WJPrxcvw5otbKWQkREVF4xvJQnvr6AjQ2P9UJERFQIhpfyJPexXri7NBERUb4YXsob7nFERERUKIaX8oaTdomIiArF8FLeMLwQEREViuGlvGF4ISIiKhTDS3nD8EJERFQohpfyJvexXnQ6WUshIiIqjxheyhtfX2mX6exs4M4duashIiIqdxheyhsbG8DPT7rOoSMiIqI8GF7KI857ISIiKhDDS3nE8EJERFQghpfyiOGFiIioQAwv5RHDCxERUYEYXsoj/fmNeHJGIiKiPBheyiN9z8u1a4BWK2spRERE5Q3DS3lUvTpgawtkZQE3b8pdDRERUbnC8FIe2dgAtWpJ1y9ckLcWIiKicobhpbyqW1f6yfBCRERkhOGlvGJ4ISIiyhfDS3nF8EJERJQvhpfyiuGFiIgoXxYLL4mJiYiKioKrqyvc3d0xfPhwpKamFnm/mJgYPPXUU3BycoKrqyvat2+P9PR0S5VZfunDy+XLQE6OvLUQERGVIxYLL1FRUTh16hSio6OxefNm7N69GyNHjiz0PjExMejWrRu6dOmC2NhYHDx4EKNHj4ZS+QR2EPn5AWo1kJ0NXL8udzVERETlhkIIIcy90jNnziA4OBgHDx5EaGgoAGDbtm3o0aMHbt68CV9f33zv16pVKzz99NOYMWNGiR9bo9HAzc0NycnJcHV1LfF6yoXgYODMGWD7dqBLF7mrISIishhTvr8t0qURExMDd3d3Q3ABgIiICCiVShw4cCDf+yQkJODAgQOoUqUKWrdujapVq6JDhw7Ys2dPoY+VmZkJjUZjdKkwOO+FiIgoD4uEl7i4OFSpUsVomY2NDTw8PBAXF5fvfS5fvgwAmD59OkaMGIFt27ahefPm6Ny5My4U8uU9e/ZsuLm5GS5+fn7meyJyY3ghIiLKw6TwMnnyZCgUikIvZ8+eLVEhOp0OAPDKK69g2LBhaNasGT7//HPUr18f33//fYH3e+edd5CcnGy43Lhxo0SPXy4xvBAREeVhY0rjCRMmYOjQoYW2qVWrFry9vZGQkGC0PCcnB4mJifD29s73fj4+PgCA4OBgo+VBQUG4XsiEVbVaDbVaXYzqrRDDCxERUR4mhRcvLy94eXkV2S48PBxJSUk4fPgwQkJCAAB//vkndDodwsLC8r2Pv78/fH19ce7cOaPl58+fR/fu3U0ps+LQh5crV6TdpW1MermIiIgqJIvMeQkKCkK3bt0wYsQIxMbGYu/evRg9ejQGDhxo2NPo1q1bCAwMRGxsLABAoVBg0qRJWLhwIdatW4eLFy9iypQpOHv2LIYPH26JMsu/atUAe3spuFy9Knc1RERE5YLF/pVfuXIlRo8ejc6dO0OpVKJfv35YuHCh4fbs7GycO3cOaWlphmXjxo1DRkYG3nzzTSQmJqJJkyaIjo5G7dq1LVVm+aZUAnXqACdPSkNHderIXREREZHsLHKcFzlVqOO8AMCzzwIbNgALFwJjxshdDRERkUXIfpwXMiNO2iUiIjLC8FLe6YeKGF6IiIgAMLyUf+x5ISIiMsLwUt7pw8vVq9JJGomIiJ5wDC/lna8v4OgIaLXS8V6IiIiecAwv5Z1CwXkvREREuTC8WAPOeyEiIjJgeLEG+vBy8aK8dRAREZUDDC/WgD0vREREBgwv1oDhhYiIyIDhxRroJ+xeuwZkZclbCxERkcwYXqyBtzfg7AzodMDly3JXQ0REJCuGF2vA3aWJiIgMGF6shX7ey/nz8tZBREQkM4YXa9GokfTzyBF56yAiIpIZw4u1aNVK+rl/v7x1EBERyYzhxVq0bCnNfbl8GUhIkLsaIiIi2TC8WAs3NyAoSLp+4IC8tRAREcmI4cWacOiIiIiI4cWqMLwQERExvFgVfXiJjQW0WnlrISIikgnDizUJDpaOtJuaCpw+LXc1REREsmB4sSYqlbTXEcChIyIiemIxvFgbznshIqInHMOLtWF4ISKiJxzDi7UJC5N+nj4NJCXJWgoREZEcGF6sTZUqQK1a0vWDB+WthYiISAYML9aIQ0dERPQEY3ixRvrwEhMjbx1EREQyYHixRuHh0s/9+wEh5K2FiIiojDG8WKPGjQF7e+DBA+DCBbmrISIiKlMML9bIzg4ICZGuc94LERE9YRherBUn7RIR0ROK4cVaMbwQEdETiuHFWunDy/HjwI0b8tZCRERUhhherFX16kCnToBOB8yfL3c1REREZYbhxZpNmiT9XLqUpwogIqInBsOLNevWDWjYEEhNBZYskbsaIiKiMsHwYs0UCmDCBOn6ggVAZqa89RAREZUBhhdr9/zzgK8vcOcOsGqV3NUQERFZHMOLtbOzA954Q7o+d640gZeIiKgCY3ipCF55BXBxAU6fBrZulbsaIiIii2J4qQjc3ICRI6Xrn34qby1EREQWxvBSUbzxBmBjA/z9N3DwoNzVEBERWQzDS0Xh5wcMGiRdnz1b3lqIiIgsiOGlIpk8Wdp9esMG4MQJuashIiKyCIaXiiQ4GOjXT7o+a5a8tRAREVkIw0tF8/770s9ffgHOnpW3FiIiIgtgeKlomjQBevUChAA++kjuaoiIiMyO4aUimjJF+rlqFXDpkry1EBERmRnDS0UUGiqdtFGrBT7+WO5qiIiIzIrhpaLS976sWAFcvy5vLURERGbE8FJRtW4NdOoEZGcDc+bIXQ0REZHZMLxUZPrel2+/lc57REREVAEwvFRkHTsCkZFAVhYwbBiQkyN3RURERKXG8FKRKRTA4sWAqysQGwt8/rncFREREZUaw0tFV736o9AyZQoPXEdERFbPYuElMTERUVFRcHV1hbu7O4YPH47U1NRC7xMXF4cXX3wR3t7ecHJyQvPmzfHrr79aqsQnx7BhQNeuQGYm8NJL0i7UREREVspi4SUqKgqnTp1CdHQ0Nm/ejN27d2PkyJGF3mfw4ME4d+4cNm3ahBMnTuDZZ5/FgAEDcPToUUuV+WRQKIClSwEXFyAmBli4UO6KiIiISkwhhBDmXumZM2cQHByMgwcPIjQ0FACwbds29OjRAzdv3oSvr2++93N2dsbXX3+NF1980bDM09MTc+bMwcsvv1ysx9ZoNHBzc0NycjJcXV1L/2QqkqVLgVdeARwcgOPHgbp15a6IiIgIgGnf3xbpeYmJiYG7u7shuABAREQElEolDhw4UOD9WrdujTVr1iAxMRE6nQ6rV69GRkYGOnbsWOB9MjMzodFojC5UgBEjgM6dgfR0aSiJw0dERGSFLBJe4uLiUKVKFaNlNjY28PDwQFxcXIH3++WXX5CdnQ1PT0+o1Wq88sor2LBhA+rUqVPgfWbPng03NzfDxc/Pz2zPo8JRKKRjvjg7A3v3cviIiIiskknhZfLkyVAoFIVezpZib5YpU6YgKSkJf/zxBw4dOoTx48djwIABOHHiRIH3eeedd5CcnGy43Lhxo8SP/0Tw9wfmzZOuv/sucO6crOUQERGZyqQ5L3fv3sX9+/cLbVOrVi389NNPmDBhAh48eGBYnpOTA3t7e6xduxZ9+/bNc79Lly6hTp06OHnyJBo0aGBYHhERgTp16mDx4sXFqpFzXopBCGnvo+hooFUrYM8eQKWSuyoiInqCmfL9bWPKir28vODl5VVku/DwcCQlJeHw4cMICQkBAPz555/Q6XQICwvL9z5paWkAAKXSuDNIpVJBp9OZUiYVRaEAvvsOaNgQ2L9f6ol56y25qyIiIioWi8x5CQoKQrdu3TBixAjExsZi7969GD16NAYOHGjY0+jWrVsIDAxEbGwsACAwMBB16tTBK6+8gtjYWFy6dAnz5s1DdHQ0+vTpY4kyn2x+fsD8+dL1KVN47iMiIrIaFjvOy8qVKxEYGIjOnTujR48eaNu2LZYuXWq4PTs7G+fOnTP0uNja2mLLli3w8vLCM888g8aNG+OHH37AihUr0KNHD0uV+WQbOhTo0UM699GQIdIZqImIiMo5ixznRU6c82KiW7ek4aOkJOC994CZM+WuiIiInkCyH+eFrEi1asCSJdL1jz4Cdu+Wtx4iIqIiMLwQMGCANIQkBPDCC1IvDBERUTnF8EKShQuB2rWBGzeAV1+VggwREVE5xPBCEhcXYNUqwMYGWLMG+PHHsntsIYCUFODyZeDAAWDzZuDIkbJ7fCIisioML/RIy5bABx9I10eNkk4hYEkJCcD48YC7O+DqKvX8tGoFPPMMEBICPPusFGiIiIhyYXghY2+/DbRvD6SmAm3bAq1bA7/8AuTkmO8x7t8HJk8GAgKAzz8H9CfTdHAAatQAmjaVjvi7YQMQFCS15Qk3iYjoPwwvZEylAtatkybw2tkBMTHA//4H1KoFzJolHcyuJPNh0tKAbduAceOk8yvNmSMta9EC2LJFCktpacC1a8DRo8Dx48DTT0vHoJkzB6hXD/j5Z87FISIiHueFChEXByxeDHz1FXD37qPldeoAvXpJl6ZNATe3vPdNSpJCyIED0jmU9uyRgohe06bAhx8CPXtKpyvIjxDS/Jfx44GLF6Vl/foBX38NFOM0FUREZD1M+f5meKGiZWQAq1dLw0c7dxqHEACoXFkKNHXqAJmZ0mTbS5fyrsfPD+jSBejdG4iMBJTF7PjLygJmz5YOoJeTIwWXxYulOTFERFQhMLwwvFhOSgqwYwfw229Sj0pcXMFt/f2libcdO0pDQPXqFdzLUhxHjkinMTh5Uvp90CDgiy8AD4+Sr5OIiMoFhheGl7KTkiL1sly8CFy4IM2Zad5culgiVGRmSntEzZkD6HSAry+wbJnUo0NERFaL4YXhpeI7cAAYPBg4f176fdQo4JNPAEdHeesiIqIS4bmNqOILC5MmBI8eLf3+5ZdAs2ZSqCEiogqN4YWsl6MjsGgRsH27dILJ8+el49JMnixNMiYiogqJ4YWsX5cuwIkTQFSUNA9mzhxpovChQ3JXRkREFsDwQhVDpUrATz9JR+WtUkU6mF6rVsD77+fdtZuIiKwawwtVLH36AKdOAQMHAlqtdFTgli2Bf/+VuzIiIjIThheqeCpXlk4lsHYt4OkpnWogNFQ60J05z9FERESyYHihiuu556RemF69gOxs4N13pZNN5nf0XyIishoML1SxVa0KbNwILF8OuLpKu1K3afPoKL1ERGR1GF6o4lMopNMKnDgBNG4MxMcDHToAhw/LXRkREZUAwws9OWrUAHbtkibwJiYCTz0lne2aiIisCsMLPVk8PIA//gDatwc0GqBrV+l3IiKyGgwv9ORxcQG2bpWCS1oa0LMnEBsrd1VERFRMDC/0ZHJ0BH77DYiMlM5U/eyzQFyc3FUREVExMLzQk0utBlatAgIDgVu3gP79eTReIiIrwPBCTzZXV2lXaldXafLum2/KXRERERWB4YWofn3pvEgA8NVXwPffy1sPEREViuGFCACeeQb44APp+muvcQIvEVE5xvBCpPf++9KJHbOygBdeANLT5a6IiIjywfBCpKdUAsuWAT4+wIULwIwZcldERET5YHghys3dXZr3AgCffCKdkZqIiMoVhheix/XpA/TrB2i1wPDhQE6O3BUREVEuDC9E+fniC6kX5vBhYMECuashIqJcGF6I8uPtDcydK12fMgW4fFneeoiIyIDhhaggL70EdOok7XX0yiuAEHJXREREYHghKphCASxdCtjbS2eeXrdO7oqIiAgML0SFq1MHmDxZuv7WW0BGhrz1EBERwwtRkSZOBKpVA65eBRYulLsaIqInHsMLUVGcnICPPpKuz5oFJCTIWw8R0ROO4YWoOF54AQgJATQaYNo0uashInqiMbwQFYdSCXz2mXR96VLg1Cl56yEieoIxvBAVV/v2wLPPAjqdNA+GiIhkwfBCZIo5cwBbW2DbNmDLFrmrISJ6IjG8EJmiTh1g7Fjp+qBBwJ498tZDRPQEYnghMtX06UC7dtLk3S5dgK1b5a6IiOiJwvBCZCpnZ2nYqEcP6dQBvXoBa9bIXRUR0RPDRu4CiKySoyOwcSMwZAjw88/SENLFi0CDBoBKJV1sbaXdqz085K6WiKhCYXghKilbW+DHHwE3N2DxYuD99/Nv06OHdJyYnj2l8yQREVGpKISoWKfK1Wg0cHNzQ3JyMlxdXeUuh54EQgDz5wMbNgA5OYBWK12Sk6XeGD1XV2lX62eeASIipN9L8lh370rrrlZN6gEiIqoATPn+ZnghsqSTJ4GVK4FVq4Dr1x8tt7WVJv326CHtweTsDLi4SD8BID4eiIuTLnfuAJcvA5cuSWEoNfXRejw8gBo1pEv37sDQoezdISKrxPDC8ELljU4n7Va9YQPw++/AhQslX5dCATg4AGlpeW/z9gbefBN49dWS9ewQEcmE4YXhhcq7CxekELNzJ3DvntSbkpoKpKRIQcfb+9GlalXA3x+oXVvqpfH3B9Rqaejoxg3pcvIk8MUX0nUAcHcHXnsNePlloFYtGZ8oEVHxMLwwvNCTKCtLGp6aMwc4e/bR8g4dpOGk5557NCxFRFTOMLwwvNCTTKeTduNevBj44w9pki8AODkBYWFAvXqPLrVrAz4+0hCTQlH4etPTgWvXpItOJ00WdnKSfnp4SL1EREQlxPDC8EIkuXFD2p17+fLC59mo1dLwVNWq0nwaheLRJT0duHpVmjxcGD8/oG1boE0b6WfDhtLxboiIiqFchJdZs2bh999/x7Fjx2BnZ4ekpKQi7yOEwLRp0/DNN98gKSkJbdq0wddff426desW+3EZXojyIQRw5Ig0N+b8+UeXK1ekeTbF5eIizbmxtZUmDOsviYlSb0xuzs5AixZAq1ZSj0/TplJPjZ2dFJZsbaVwpN+9PCfn0Tpyh6fUVODBA+OLRiPN+dFopItaDXh6ApUrS5cqVaT5QVWrFt2jRETlginf3xY7SF1WVhb69++P8PBwfPfdd8W6zyeffIKFCxdixYoVCAgIwJQpU9C1a1ecPn0a9uVk98+0rBwAgIOtCor//ihm5eiQo9NBpVRAbaPK09beRgWlUmqbrdUhW6uDUqGAvW3J2qZnaSEgoLZRQfVf2xytDlmlbJuRrYVOCNiplLBRSWeO0OoEMnO0JrVVQAEHu7xtbVVK2JagrU4nkJGjBQA42j16y2bmaKHVCdgolbCzMb2tEALp2doCX09T2hbntTfH+yS/17PYbUNCkNO0Wd7XPj0dGbfuQBefAPW9BKiyMgEhkKMTyNIKKNV2sA+oKYUWDw9k5OjyvvaaFGTuj4Vifwwc9v4DxMQAKSnI+GcvdHv2wS4nGzZCCiZahRKZNrZQCMAhJ/PRa6+yhU6phK02B7Y6aVvroECGrZ30emaXoK2rKzLrB0Fbvz5sfLxh5+oCuLpCuLgi3dEZsLWFo72tFKRsbJBpq4bW3h42jo6wc5GClnj4EOmaVOBhGhwyHkKRlgY8fIis1IfIeZgOVVYm1E4Ohl3d0xydARdXOFRyhcLNDXBzQ5adPXKEkF57lVIKkwoF0v57TxX52guBtIcZQHo67G0UhvO6ZGt1yFaooHRyhL29XaHvE/6N4N8Ic7z2udvKyWLh5YMPPgAALF++vFjthRCYP38+3n//ffTu3RsA8MMPP6Bq1arYuHEjBg4caKlSTRI8dTsA4PD7EfB0VgMAlu6+hLk7zmNgCz983K+xoW3IjD+Qnq3FP291gp+HdDCxH2KuYcbm0+jd1BcLBjYztG07ZxcSH2Zhx5vtUa+qCwBg3eGbeGf9CTwdXBXfDA41tI347G/cSkrHb6PaoImfOwBg8793MG7NMbStUxk/vRxmaNvriz24kJCKn0e0QnhtTwDAzrMJeOXHwwipWQm/vtba0HbAkhj8ezMZ3w8NxVOBVQEA+y7dw4vfxSLIxxVb32hnaDvk+1gcuJKIL59vjsjGPgCAo9cf4LnFMfD3dMRfkzoZ2r7202HsOncXnz7XGP1D/QAAZ+M0iFy4B1Vd1TjwboSh7fhfjmHLiTh82LsBBof7AwCuJaah09y/4GJvgxPTuxravrv+JH49chPvdA/EKx1qAwASUjLRavZO2CgVuPhRD0PbmZvP4Mf91/BG57p48+l6AABNRg6afLADAHBhVnfYqqQP5Nwd57B092WMbF8L7/YIAgDk6IThtT8+rQvcHGwBAF/uuogFOy/gxVY1MaNPQ8PjNZ6+Azk6gf3vdIa3mxS8l+29gtlbz6Jf8+qYN6CJoW3YRzuRkpGDXRM7IqCyEwDg59jrmPrbKfRo5I2vokIMbTvO3YV4TSZ+H9sWDXzdAAAbj97CpHX/olN9Lywb1tLQtvuC3bh6Pw3rXg1HqL90ioLtp+IxatURhAV4YM0r4VJDBwf0/f0WztzR4Mfh4WhX1wsAsPtsPF5afgiNq7th03OPaoj69gAOX3uAJS+GoGsDaZ5L7N0sDPozA3WrtEP09velnpQzZ/Dyr+exJ12N+Ud/Rp+dqwGtFier1kbvIZ+jWnI89i4ebljvmF5vIbpeOGZvW4RBx6VtfbGyH7oM/woe6Roc2fQuUKkSUKkS3q7fC7+51sGUrLMY7pQEZGbi1oN0tPPsBgdtFs6sGy/NzdFoMM2zJVZX64qJu3/A6JhfAACJDq4IGbsKAHB1TqShho87j8Cy0N4YtW8NJv3zIwAg3VaN4PG/AgBOf9bPEIwWtHsRX7b+H4Yd+g3Tdn5jWEfw25sB3MPhhV3gma4BACwNH4C57Qdj4PHt+HjbIkPbkPHrkG5rj39+HAO/jGRApcIPDbtgRstB6H0lFgt2L5V6th4+RNvXf0Cioxt2fPc66t2Tjhm0rklXvNNtDJ4+H4NvtsyV5h85OCDi2dm45eSJ3/5egCapdwCVCpt9m2Jc4/5oe/8Sfvp3JWBjA9jaoleTl3DBwRM/X9mE8NSbgE6HnS7+eKVWT4Sk3MKvJ1dKr6dOhwFNh+FfV198f2YdntJcBVQq7HOtiRfrPYugtLvYeu5n6YkpFBhSpy8OOFfHl1e2IjL1CqBU4qizL56r2Qv+WRr8dXOD1CumVOK1Kp2wy6EaPr27F/1TLgI6Hc7aVkJkzT6omvMQB648OnfYeO9O2OISgA/vxmCw5hygUOCarSs6+fWFiy4LJ27/CiiVgEKBd91b4lcHf7zz8CReybgIKBRIUDqglXsX2AgdLiZuklYqBGY6NcaPDrXxRuopvJl6GgCgUdiiSdU+AIALcetgq5Ce21ynRljqVA8j0y7g3bSTgEKBHCgQ7Cl9dx1/8DvcIAWZLx3qY4F9fbyYeQUz0k8ankdjt0jkKJTYn7QD3iIDALBMXRuzHRugX+Z1zEs/bmgb5tYNKQpb7ErZhQDdQwDAz3Y1MdWhEXpk38FXGUcN272jYyfEK+3xe9oeNNBJvaobVb6Y5NAEnXISsCz9kGG93Z064KrSCevSYhCqfQAA2G7jjVEOzRGWcx9r0g8Y2vat3gtnknPw4/CWhr8Rcio3pwe4cuUK4uLiEBHx6IvMzc0NYWFhiImJKTC8ZGZmIjPz0X9kGo3G4rUSURFUKmnOy/6HwMV7wMdzgGY/SV+CV+8D3xyU5sjcvSu1tbEB1p0Gzt0DvvwSaO4r9U7EpwBLDklDQVeuPFr/6qPAsdvSEYvbBkjLEtOAT3YB9g5S24wM6eB+Wy8CdwG0aQs0dJOGmR5mPVpXSIg0ZJWdDbhKgRD29tLwVlYW4JDrKMaBgYC9nTT8FVDnv2VBgNuz0vBb7gMIurkBmal5h9Ny0w/apz4ENInSdf0wXlpa0fOMcsvMlC4PHkjPB/hvrtJ/c52yKwGNAaRogNjYR/erMwBw8JR6y26ckJbVbQXU6ikNze3e/aht3f6AK6Thx8v/fQn6NwXq/ff8d+x41NajI+BcHTh+DDi3V1pWLQio2UvaTmvXPmr7XH2gdjWprpM7pWVVAoBhfYD0DGD9+kdte9cDAgOAo8eAo79Lyyr5AiP7Sq/XypWP2vbwABr5S+uN/W8dzp7AqC7S6/Ltt4/aPv0q0Lw2cOw4sFcKtlA7AeP6SNd//BH4r5cPHYcBYfWAE/8Cfy2TlilVwCQpvGDFD0CmFDLQ5nmgbX3g1Ckgesmjx5vYHVAppXpT70vLWj4LdGogDeluydX2jU6Ava10HrUHt6VlzSKBLo2kg1f+9tWjtq+3BFzspZPFJvz3mWnYGYhsIgX6dbnajmgKeDhJ2/fWGWlZ/TZAn+bA7dvAz7naTu8KoPzMYbP4hN3ly5dj3LhxRc552bdvH9q0aYPbt2/Dx8fHsHzAgAFQKBRYU8BZe6dPn27o5cnNUnNeOGxUdFt2CVeMLuGSvE8Kej1L+j4p6PUs7fsk9+tZaFshIIASvfYOtiooACAtDVnJGuToBFRKJdS2KqnHQadDWloGkJ0De2ih/G/OT3Z2DrJztFDqdNJQkKMj4OiINBs1YG8PezsbKP97ztk6geyMLCgz0mGfmW6Yg5SekQ2RkwO1yIHqvzlFhtdTJ2APrSGwpWdmQ2RnQ63TQmWjApRK5CiUyIICSpVKeu1V0vIMoYAuRws76GCjk06DoRVApk5AKQTslTDs3ZahA3QA7CBgAyG1zdEiUyug0GrhoNBJbYVAhlZAp1DCVgnp9VQooIUCmVBCAcBB+ehrKkMnoBMK2CoEbIW0Dp1OWgeEDo7QScFEp0OmVkArBGyEgB1ytVVIr5ejUhjmRGUqVNAqFLBRKGD337icEEC69CrCQeig+C9tZumAHCFgA0jr1bcV+rZaabVCIEtIvTIqCKgV4tGQoZCepz100I/CGNoK3aO2ANJ0UoPcbbOFAtlQQCl0sM/VNl0oIQCooYMK0mNlCwWyFUooIaS2/0kXSggh1fVfxzNyBJCFvG0z+vaDLijIosNGFpuwO3nyZMyZM6fQNmfOnEFgYKDhd0uHl/x6Xvz8/Dhhl4iIyIpYbMLuhAkTMHTo0ELb1Crh0Ty9/ztGRHx8vFF4iY+PR9OmTQu8n1qthlqtLtFjEhERkfUxKbx4eXnBy8syE3UCAgLg7e2NnTt3GsKKRqPBgQMH8Nprr1nkMYmIiMj6KItuUjLXr1/HsWPHcP36dWi1Whw7dgzHjh1Daq4JbYGBgdiwYQMAQKFQYNy4cZg5cyY2bdqEEydOYPDgwfD19UWfPn0sVSYRERFZGYvtbTR16lSsWLHC8HuzZtJuwbt27ULHjh0BAOfOnUNycrKhzVtvvYWHDx9i5MiRSEpKQtu2bbFt27Zyc4wXIiIikh9PD0BERESyM+X722LDRkRERESWwPBCREREVoXhhYiIiKwKwwsRERFZFYYXIiIisioML0RERGRVGF6IiIjIqjC8EBERkVWx2BF25aI/5p5Go5G5EiIiIiou/fd2cY6dW+HCS0pKCgDAz89P5kqIiIjIVCkpKXBzcyu0TYU7PYBOp8Pt27fh4uIChUJh1nVrNBr4+fnhxo0bPPWABXE7lw1u57LB7Vx2uK3LhqW2sxACKSkp8PX1hVJZ+KyWCtfzolQqUb16dYs+hqurKz8YZYDbuWxwO5cNbueyw21dNiyxnYvqcdHjhF0iIiKyKgwvREREZFUYXkygVqsxbdo0qNVquUup0Lidywa3c9ngdi473NZlozxs5wo3YZeIiIgqNva8EBERkVVheCEiIiKrwvBCREREVoXhhYiIiKwKwwsRERFZFYaXYvryyy/h7+8Pe3t7hIWFITY2Vu6SrNrs2bPRokULuLi4oEqVKujTpw/OnTtn1CYjIwOjRo2Cp6cnnJ2d0a9fP8THx8tUccXw8ccfQ6FQYNy4cYZl3M7mc+vWLbzwwgvw9PSEg4MDGjVqhEOHDhluF0Jg6tSp8PHxgYODAyIiInDhwgUZK7Y+Wq0WU6ZMQUBAABwcHFC7dm3MmDHD6GR+3M6m2717N5555hn4+vpCoVBg48aNRrcXZ5smJiYiKioKrq6ucHd3x/Dhw5GammqZggUVafXq1cLOzk58//334tSpU2LEiBHC3d1dxMfHy12a1eratatYtmyZOHnypDh27Jjo0aOHqFGjhkhNTTW0efXVV4Wfn5/YuXOnOHTokGjVqpVo3bq1jFVbt9jYWOHv7y8aN24s3njjDcNybmfzSExMFDVr1hRDhw4VBw4cEJcvXxbbt28XFy9eNLT5+OOPhZubm9i4caM4fvy46NWrlwgICBDp6ekyVm5dZs2aJTw9PcXmzZvFlStXxNq1a4Wzs7NYsGCBoQ23s+m2bNki3nvvPbF+/XoBQGzYsMHo9uJs027duokmTZqI/fv3i3/++UfUqVNHDBo0yCL1MrwUQ8uWLcWoUaMMv2u1WuHr6ytmz54tY1UVS0JCggAg/v77byGEEElJScLW1lasXbvW0ObMmTMCgIiJiZGrTKuVkpIi6tatK6Kjo0WHDh0M4YXb2Xzefvtt0bZt2wJv1+l0wtvbW3z66aeGZUlJSUKtVouff/65LEqsECIjI8VLL71ktOzZZ58VUVFRQghuZ3N4PLwUZ5uePn1aABAHDx40tNm6datQKBTi1q1bZq+Rw0ZFyMrKwuHDhxEREWFYplQqERERgZiYGBkrq1iSk5MBAB4eHgCAw4cPIzs722i7BwYGokaNGtzuJTBq1ChERkYabU+A29mcNm3ahNDQUPTv3x9VqlRBs2bN8M033xhuv3LlCuLi4oy2tZubG8LCwritTdC6dWvs3LkT58+fBwAcP34ce/bsQffu3QFwO1tCcbZpTEwM3N3dERoaamgTEREBpVKJAwcOmL2mCndWaXO7d+8etFotqlatarS8atWqOHv2rExVVSw6nQ7jxo1DmzZt0LBhQwBAXFwc7Ozs4O7ubtS2atWqiIuLk6FK67V69WocOXIEBw8ezHMbt7P5XL58GV9//TXGjx+Pd999FwcPHsTYsWNhZ2eHIUOGGLZnfn9LuK2Lb/LkydBoNAgMDIRKpYJWq8WsWbMQFRUFANzOFlCcbRoXF4cqVaoY3W5jYwMPDw+LbHeGF5LdqFGjcPLkSezZs0fuUiqcGzdu4I033kB0dDTs7e3lLqdC0+l0CA0NxUcffQQAaNasGU6ePInFixdjyJAhMldXcfzyyy9YuXIlVq1ahQYNGuDYsWMYN24cfH19uZ2fIBw2KkLlypWhUqny7H0RHx8Pb29vmaqqOEaPHo3Nmzdj165dqF69umG5t7c3srKykJSUZNSe2900hw8fRkJCApo3bw4bGxvY2Njg77//xsKFC2FjY4OqVatyO5uJj48PgoODjZYFBQXh+vXrAGDYnvxbUjqTJk3C5MmTMXDgQDRq1Agvvvgi3nzzTcyePRsAt7MlFGebent7IyEhwej2nJwcJCYmWmS7M7wUwc7ODiEhIdi5c6dhmU6nw86dOxEeHi5jZdZNCIHRo0djw4YN+PPPPxEQEGB0e0hICGxtbY22+7lz53D9+nVudxN07twZJ06cwLFjxwyX0NBQREVFGa5zO5tHmzZt8uzuf/78edSsWRMAEBAQAG9vb6NtrdFocODAAW5rE6SlpUGpNP7qUqlU0Ol0ALidLaE42zQ8PBxJSUk4fPiwoc2ff/4JnU6HsLAw8xdl9inAFdDq1auFWq0Wy5cvF6dPnxYjR44U7u7uIi4uTu7SrNZrr70m3NzcxF9//SXu3LljuKSlpRnavPrqq6JGjRrizz//FIcOHRLh4eEiPDxcxqorhtx7GwnB7WwusbGxwsbGRsyaNUtcuHBBrFy5Ujg6OoqffvrJ0Objjz8W7u7u4rfffhP//vuv6N27N3fhNdGQIUNEtWrVDLtKr1+/XlSuXFm89dZbhjbczqZLSUkRR48eFUePHhUAxGeffSaOHj0qrl27JoQo3jbt1q2baNasmThw4IDYs2ePqFu3LneVltuiRYtEjRo1hJ2dnWjZsqXYv3+/3CVZNQD5XpYtW2Zok56eLl5//XVRqVIl4ejoKPr27Svu3LkjX9EVxOPhhdvZfP7v//5PNGzYUKjVahEYGCiWLl1qdLtOpxNTpkwRVatWFWq1WnTu3FmcO3dOpmqtk0ajEW+88YaoUaOGsLe3F7Vq1RLvvfeeyMzMNLThdjbdrl278v2bPGTIECFE8bbp/fv3xaBBg4Szs7NwdXUVw4YNEykpKRapVyFErsMSEhEREZVznPNCREREVoXhhYiIiKwKwwsRERFZFYYXIiIisioML0RERGRVGF6IiIjIqjC8EBERkVVheCEiIiKrwvBCREREVoXhhYiIiKwKwwsRERFZlf8H2CVopAu341AAAAAASUVORK5CYII=", "text/plain": [ - "
    " + "
    " ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -497,11 +508,12 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "id": "5688a618", "metadata": {}, "source": [ - "有趣的是,通过比较两个模型的运行时间,我们发现,分布式 VQE 的运行速度比标准 VQE 快了一百多倍!事实上,这很容易理解:在分布式模型中,我们只需模拟两个 $N/2$ 量子比特的酉变换,这无论在时间还是空间上,都比标准 VQE 中模拟一个 $N$ 量子比特的酉变换高效得多。" + "有趣的是,在分布式模型中,我们只需模拟两个 $N/2$ 量子比特的酉变换,这无论在时间还是空间上,都比标准 VQE 中模拟一个 $N$ 量子比特的酉变换高效得多。" ] }, { @@ -566,7 +578,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.0" + "version": "3.8.13" } }, "nbformat": 4, diff --git a/tutorials/quantum_simulation/DistributedVQE_EN.ipynb b/tutorials/quantum_simulation/DistributedVQE_EN.ipynb index 7c4b2a4..b969271 100644 --- a/tutorials/quantum_simulation/DistributedVQE_EN.ipynb +++ b/tutorials/quantum_simulation/DistributedVQE_EN.ipynb @@ -136,6 +136,9 @@ "import paddle\n", "import paddle_quantum\n", "from paddle_quantum.ansatz import Circuit\n", + "from paddle_quantum.hamiltonian import Hamiltonian\n", + "from paddle_quantum.loss import ExpecVal\n", + "from paddle_quantum.state import State\n", "from paddle_quantum.qinfo import pauli_str_to_matrix, schmidt_decompose\n", "import warnings\n", "\n", @@ -223,7 +226,8 @@ "pauli_str_B = ['x0,y1,y2,x3,x4', 'x0,z1,z2,y3,x4'] # pauli substring for system B\n", "\n", "# Convert relavent object into Tensor form\n", - "H_mtr = paddle.to_tensor(pauli_str_to_matrix(zip(coefs, pauli_str), n=N))\n", + "H = Hamiltonian(list(zip(coefs, pauli_str)))\n", + "H_mtr = paddle.to_tensor(H.construct_h_matrix())\n", "coefs = paddle.to_tensor(coefs)\n", "H_A = [pauli_str_to_matrix([[1., pstr]], n=N//2) for pstr in pauli_str_A]\n", "H_A = paddle.to_tensor(np.stack(H_A))\n", @@ -416,13 +420,12 @@ " def __init__(self, N, D, S):\n", " super().__init__()\n", " paddle.seed(SEED)\n", - " self.N = N\n", - " self.S = S\n", - " self.cir = [U_cir(N, D)]\n", - "\n", + " self.cir = U_cir(N, D)\n", + " self.loss_fcn = ExpecVal(H)\n", + " \n", " def forward(self):\n", - " vec = output_states(self.S, self.N, self.cir[0])\n", - " loss = vec.conj().t() @ H_mtr @ vec\n", + " output_state = self.cir()\n", + " loss = self.loss_fcn(output_state)\n", " return loss.cast('float64').flatten()" ] }, @@ -470,10 +473,11 @@ ] }, { + "attachments": {}, "cell_type": "markdown", "metadata": {}, "source": [ - "Interestingly, by comparing the running time of the two models, we find that the distributed model runs 100 times faster than the standard VQE! In fact, this is easy to understand: in a distributed model, we only need to simulate two $N/2$-qubit unitary transformations, which is, of course, much more time- and space-efficient than simulating an $N$-qubit unitary transformation in the standard VQE." + "Interestingly, in a distributed model, we only need to simulate two $N/2$-qubit unitary transformations, which is, of course, much more time- and space-efficient than simulating an $N$-qubit unitary transformation in the standard VQE." ] }, { diff --git a/tutorials/quantum_simulation/QPP_CN.ipynb b/tutorials/quantum_simulation/QPP_CN.ipynb index cd049fe..450451c 100644 --- a/tutorials/quantum_simulation/QPP_CN.ipynb +++ b/tutorials/quantum_simulation/QPP_CN.ipynb @@ -34,9 +34,19 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", @@ -47,14 +57,13 @@ "\n", "# 量桨的通用函数\n", "import paddle_quantum as pq\n", - "from paddle_quantum.ansatz import Circuit\n", "from paddle_quantum.hamiltonian import Hamiltonian\n", - "from paddle_quantum.linalg import abs_norm, hermitian_random, unitary_random, block_enc_herm, herm_transform\n", + "from paddle_quantum.linalg import is_density_matrix, abs_norm, hermitian_random, unitary_random, block_enc_herm, herm_transform\n", "from paddle_quantum.qinfo import trace_distance, partial_trace_discontiguous\n", - "from paddle_quantum.state import is_density_matrix, random_state, zero_state, State\n", + "from paddle_quantum.state import random_state, zero_state, State\n", "\n", "# 量桨的 QPP 模块函数\n", - "from paddle_quantum.qpp import Q_generation, hamiltonian_laurent, qpp_angle_approximator, qpp_cir, qps, qubitize, purification_block_enc, simulation_cir\n", + "from paddle_quantum.qpp import Q_generation, hamiltonian_laurent, qpp_angle_approximator, qpp_cir, qps, purification_block_enc, simulation_cir\n", "\n", "# 设置计算精度和后端\n", "pq.set_dtype('complex128')" @@ -164,7 +173,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -194,16 +203,16 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Computations of angles for QPP are completed with mean error 1.692667280042757e-07\n", - "估计特征相位与输出态特征相位的匹配误差为 2.104050267612231e-11\n", - "输出态与输入态的 overlap 为 0.12645570235623324\n" + "Computations of angles for QPP are completed with mean error 2.3425470617139153e-07\n", + "估计本征相位与输出态本征相位的匹配误差为 1.7443920086179794e-08\n", + "输出态与输入态的 overlap 为 0.4704811537109915\n" ] } ], @@ -272,7 +281,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Computations of angles for QPP are completed with mean error 1.1413227206232605e-07\n" + "Computations of angles for QPP are completed with mean error 2.3203273480386816e-07\n" ] } ], @@ -298,8 +307,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "qubits [0, 1, 2, 3, 4] collapse to the state |00000> with probability 0.9999974132814917\n", - "输出态与期望态的迹距离为 4.903932274526325e-07\n" + "qubits [0, 1, 2, 3, 4] collapse to the state |00000> with probability 0.9999977632082053\n", + "输出态与期望态的迹距离为 3.6771539812188947e-07\n" ] } ], @@ -390,15 +399,15 @@ "name": "stdout", "output_type": "stream", "text": [ - "Computations of angles for QPP are completed with mean error 2.073248366556774e-07\n", - "模拟 Tr[rho * sigma^3.522308957539911] 的误差为 2.265239344059755e-05\n" + "Computations of angles for QPP are completed with mean error 8.796509127976865e-06\n", + "模拟 Tr[rho * sigma^1.4721306269945273] 的误差为 0.0028187969201126095\n" ] } ], "source": [ "# 估计 Tr[rho * sigma^(alpha - 1)]\n", "cir = simulation_cir(lambda x: (np.cos(x) ** 2) ** ((alpha - 1) / 2), U_sigma_hat)\n", - "val = cir(input_state).expec_val(H).item()\n", + "val = cir(input_state).expec_val(H)\n", "expect_val = paddle.trace(rho.data @ herm_transform(lambda x: x ** (alpha - 1), sigma)).real().item()\n", "print(f\"模拟 Tr[rho * sigma^{alpha - 1}] 的误差为 {np.abs(val - expect_val)}\")" ] diff --git a/tutorials/quantum_simulation/QPP_EN.ipynb b/tutorials/quantum_simulation/QPP_EN.ipynb index fddc2a8..9fe047d 100644 --- a/tutorials/quantum_simulation/QPP_EN.ipynb +++ b/tutorials/quantum_simulation/QPP_EN.ipynb @@ -34,9 +34,19 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/v_zhanglei48/opt/anaconda3/envs/pq/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import warnings\n", "warnings.filterwarnings(\"ignore\")\n", @@ -47,14 +57,13 @@ "\n", "# general functions in PaddleQuantum\n", "import paddle_quantum as pq\n", - "from paddle_quantum.ansatz import Circuit\n", "from paddle_quantum.hamiltonian import Hamiltonian\n", - "from paddle_quantum.linalg import abs_norm, hermitian_random, unitary_random, block_enc_herm, herm_transform\n", + "from paddle_quantum.linalg import abs_norm, hermitian_random, unitary_random, block_enc_herm, herm_transform, is_density_matrix\n", "from paddle_quantum.qinfo import trace_distance, partial_trace_discontiguous\n", - "from paddle_quantum.state import is_density_matrix, random_state, zero_state, State\n", + "from paddle_quantum.state import random_state, zero_state, State\n", "\n", "# functions in QPP module\n", - "from paddle_quantum.qpp import Q_generation, hamiltonian_laurent, qpp_angle_approximator, qpp_cir, qps, qubitize, purification_block_enc, simulation_cir\n", + "from paddle_quantum.qpp import Q_generation, hamiltonian_laurent, qpp_angle_approximator, qpp_cir, qps, purification_block_enc, simulation_cir\n", "\n", "# set the precision\n", "pq.set_dtype('complex128')" @@ -166,7 +175,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -196,16 +205,16 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Computations of angles for QPP are completed with mean error 1.3084730192565284e-07\n", - "The searching error for the QPS algorithm is 1.4529266689268915e-11\n", - "The overlap between input and output states is 0.6462206013583379\n" + "Computations of angles for QPP are completed with mean error 2.8162115647895675e-07\n", + "The searching error for the QPS algorithm is 4.606981463737032e-12\n", + "The overlap between input and output states is 0.37013326587541756\n" ] } ], @@ -274,7 +283,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Computations of angles for QPP are completed with mean error 3.6991674515121774e-07\n" + "Computations of angles for QPP are completed with mean error 2.477981491445382e-07\n" ] } ], @@ -301,8 +310,8 @@ "name": "stdout", "output_type": "stream", "text": [ - "qubits [0, 1, 2, 3, 4] collapse to the state |00000> with probability 0.9999982182557698\n", - "The trace distance between output and expected states is 5.304595279602356e-07\n" + "qubits [0, 1, 2, 3, 4] collapse to the state |00000> with probability 0.9999974886442893\n", + "The trace distance between output and expected states is 4.4205432295805146e-07\n" ] } ], @@ -394,15 +403,15 @@ "name": "stdout", "output_type": "stream", "text": [ - "Computations of angles for QPP are completed with mean error 4.448551001234416e-06\n", - "The estimation error for Tr[rho * sigma^1.4747437820674594] is 0.0022607517544651345\n" + "Computations of angles for QPP are completed with mean error 3.3321641726764387e-07\n", + "The estimation error for Tr[rho * sigma^2.0113183131522914] is 3.2651025185431726e-05\n" ] } ], "source": [ "# Estimate Tr[rho * sigma^(alpha - 1)]\n", "cir = simulation_cir(lambda x: (np.cos(x) ** 2) ** ((alpha - 1) / 2), U_sigma_hat)\n", - "val = cir(input_state).expec_val(H).item()\n", + "val = cir(input_state).expec_val(H)\n", "expect_val = paddle.trace(rho.data @ herm_transform(lambda x: x ** (alpha - 1), sigma)).real().item()\n", "print(f\"The estimation error for Tr[rho * sigma^{alpha - 1}] is {np.abs(val - expect_val)}\")" ] diff --git a/tutorials/quantum_simulation/VQE_CN.ipynb b/tutorials/quantum_simulation/VQE_CN.ipynb index 13bdf69..933cb0b 100644 --- a/tutorials/quantum_simulation/VQE_CN.ipynb +++ b/tutorials/quantum_simulation/VQE_CN.ipynb @@ -118,14 +118,27 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:13:45.528201Z", "start_time": "2021-04-30T09:13:43.385553Z" } }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import paddle\n", "import paddle_quantum.qchem as qchem\n", @@ -158,7 +171,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:13:45.545018Z", @@ -173,21 +186,21 @@ "converged SCF energy = -1.11675930739643\n", "\n", "The generated h2 Hamiltonian is \n", - " -0.09706626816763092 I\n", - "0.17141282644776917 Z0\n", - "0.17141282644776917 Z1\n", - "-0.2234315369081346 Z2\n", - "-0.2234315369081346 Z3\n", - "0.16868898170361205 Z0, Z1\n", - "0.12062523483390414 Z0, Z2\n", - "0.1659278503377034 Z0, Z3\n", - "0.1659278503377034 Z1, Z2\n", - "0.12062523483390414 Z1, Z3\n", + " -0.0970662681676312 I\n", + "0.1714128264477692 Z0\n", + "0.17141282644776926 Z1\n", + "-0.22343153690813466 Z2\n", + "-0.22343153690813466 Z3\n", + "0.16868898170361213 Z0, Z1\n", + "0.12062523483390417 Z0, Z2\n", + "0.16592785033770344 Z0, Z3\n", + "0.16592785033770344 Z1, Z2\n", + "0.12062523483390417 Z1, Z3\n", "0.1744128761226159 Z2, Z3\n", - "-0.04530261550379926 X0, X1, Y2, Y3\n", - "0.04530261550379926 X0, Y1, Y2, X3\n", - "0.04530261550379926 Y0, X1, X2, Y3\n", - "-0.04530261550379926 Y0, Y1, X2, X3\n" + "-0.04530261550379927 X0, X1, Y2, Y3\n", + "0.04530261550379927 X0, Y1, Y2, X3\n", + "0.04530261550379927 Y0, X1, X2, Y3\n", + "-0.04530261550379927 Y0, Y1, X2, X3\n" ] } ], @@ -235,7 +248,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -273,31 +286,12 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ - "class StateNet(paddle.nn.Layer):\n", - " \"\"\"\n", - " Construct the model net\n", - " \"\"\"\n", - "\n", - " def __init__(self, num_qubits: int, depth: int):\n", - " super(StateNet, self).__init__()\n", - " \n", - " self.depth = depth\n", - " self.num_qubits = num_qubits\n", - " self.cir = U_theta(self.num_qubits, self.depth)\n", - " \n", - " # 定义损失函数和前向传播机制\n", - " def forward(self):\n", - " \n", - " # 运行电路\n", - " state = self.cir(init_state)\n", - " # 计算损失函数\n", - " loss = loss_func(state) \n", - "\n", - " return loss, self.cir" + "# 定义损失函数\n", + "loss_func = ExpecVal(molecular_hamiltonian)" ] }, { @@ -311,7 +305,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:03.744957Z", @@ -337,48 +331,45 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "iter: 20 loss: -1.0784\n", - "iter: 20 Ground state energy: -1.0784 Ha\n", - "iter: 40 loss: -1.1300\n", - "iter: 40 Ground state energy: -1.1300 Ha\n", - "iter: 60 loss: -1.1366\n", - "iter: 60 Ground state energy: -1.1366 Ha\n", - "iter: 80 loss: -1.1372\n", - "iter: 80 Ground state energy: -1.1372 Ha\n", + "iter: 20 loss: -1.0310\n", + "iter: 20 Ground state energy: -1.0310 Ha\n", + "iter: 40 loss: -1.0969\n", + "iter: 40 Ground state energy: -1.0969 Ha\n", + "iter: 60 loss: -1.1149\n", + "iter: 60 Ground state energy: -1.1149 Ha\n", + "iter: 80 loss: -1.1165\n", + "iter: 80 Ground state energy: -1.1165 Ha\n", "\n", "训练后的电路:\n", - "--Ry(1.589)----*--------------x----Ry(4.701)----*--------------x----Ry(3.124)--\n", + "--Ry(1.583)----*--------------x----Ry(3.139)----*--------------x----Ry(4.707)--\n", " | | | | \n", - "--Ry(4.703)----x----*---------|----Ry(1.573)----x----*---------|----Ry(1.524)--\n", + "--Ry(4.721)----x----*---------|----Ry(3.134)----x----*---------|----Ry(7.874)--\n", " | | | | \n", - "--Ry(3.096)---------x----*----|----Ry(4.493)---------x----*----|----Ry(4.904)--\n", + "--Ry(4.715)---------x----*----|----Ry(6.283)---------x----*----|----Ry(1.578)--\n", " | | | | \n", - "--Ry(3.340)--------------x----*----Ry(1.555)--------------x----*----Ry(3.157)--\n", + "--Ry(1.555)--------------x----*----Ry(3.142)--------------x----*----Ry(1.558)--\n", " \n" ] } ], "source": [ "# 确定网络的参数维度\n", - "net = StateNet(N, D)\n", + "cir = U_theta(N, D)\n", "\n", "# 一般来说,我们利用Adam优化器来获得相对好的收敛,\n", "# 当然你可以改成SGD或者是RMS prop.\n", - "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())\n", + "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=cir.parameters())\n", "\n", "# 定义初始态\n", "init_state = zero_state(N)\n", "\n", - "# 定义损失函数\n", - "loss_func = ExpecVal(molecular_hamiltonian)\n", - "\n", "# 记录优化结果\n", "summary_iter, summary_loss = [], []\n", "\n", @@ -386,8 +377,9 @@ "for itr in range(1, ITR + 1):\n", "\n", " # 前向传播计算损失函数\n", - " loss, cir = net()\n", - "\n", + " state = cir(init_state)\n", + " loss = loss_func(state)\n", + " \n", " # 在动态图机制下,反向传播极小化损失函数\n", " loss.backward()\n", " opt.minimize(loss)\n", @@ -422,7 +414,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:21.341323Z", @@ -432,12 +424,14 @@ "outputs": [ { "data": { - "image/png": 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IMgrNSS4PzJ07F0OGDMHZs2cxbtw4bN68GVOmTMG0adMQFRWFl156CWPHjkV4eHjZKgNg1qxZWLx4MU6cOAErKyuMGzdO+9zGjRsxd+5cfPzxxzhx4gQ8PT3x9ddfl7i9hIQEPPvssxg3bhyio6Oxb98+PP300xBC4K233sLw4cPRp08fJCQkICEhAZ06dQIAODo6IiwsDOfPn8cXX3yBb7/9Fp999hkAYMSIEZg2bRpatGihXW/EiBEAgGHDhiEpKQnbt29HREQE2rdvj+DgYCQnJxdZv9zcXPTu3RuOjo44cOAADh06BAcHB/Tp0wc5BV7w8PBwxMbGIjw8HKtXr0ZYWJg2oAHA5MmTceTIEaxfvx5nzpzBsGHD0KdPH1y6dElbJjMzEwsXLsR3332Hc+fOoU6dOhg1ahRu3ryJffv24ddff8XKlSuRlJSkXefFF1/Ejh07kFDgkl9//PEHMjMztcdsEIIqLDU1VQAQqamplbPDDz4Qon9/IXbtqpz9EZFJun//vjh//ry4f/++zvL+/eUtJSV/2YYNctnSpbrbGDpULr91K3/Zli1y2aef6pZ97jm5/Nq1/GU7dpStzv/8848AIDZt2qSzvHbt2sLe3l7Y29uLt99+W7scgJg6dapO2U6dOokJEyboLBs2bJgICQkRQggRFxcnAIhTp05pn797964AIMLDw4UQQoSHhwsA4q+//tKW2bZtmwCg/X0GBQWJV199VWc/gYGBok2bNsUeX0REhAAgrl69WuTzo0ePFoMGDSp2fY1PP/1UBAQEaH+eM2dOof0eOHBAODk5iaysLJ3lDRs2FN98802R2/2///s/0bRpU6FWq7XLsrOzhZ2dndi5c6e2jj4+PiIvL09bZtiwYWLEiBFCCCGuXbsmLC0txY0bN3S2HRwcLGbOnCmEEGLVqlUCgIiMjNQ+Hx0dLQCI48ePa5ddunRJABCfffaZdlnz5s3FwoULtT8PGDBAjBkzpsjjEaL4/wMhSv/5zZYlU8QxS0RUzRw7dgyRkZFo0aIFsh+aY65Dhw46P0dHR6Nz5846yzp37ozo6Ogy77e15nqcADw9PQFA29IRHR2NwMBAnfJBQUHaxwcOHICDg4P2tnbtWrRp0wbBwcFo1aoVhg0bhm+//RZ37959ZD02bNiAzp07w8PDAw4ODnjvvfcQHx9f4jqnT59Geno6ateurVOPuLg4xMbGFrvO5cuX4ejoqC1fq1YtZGVl6azTokULWFpa6vxuNL+Xs2fPQqVSoUmTJjr73b9/v842bGxsdH6/MTExsLKyQvv27bXLGjVqhJo1a+rU8cUXX8SqVasAALdu3cL27dt1WvwMgQO8TRHHLBFRBfz8s7xXKvOXPf00MHAgUODzDwCwZk3hsv36Ab17Aw+PxdUMGSlYNji4bHVr1KgRFApFobFBfn5+AAC7ghPzPlBcd11xNIOIRYH+wtyH+x8fKDhYXNP9p1arS7WfDh066IyLcnd3h6WlJXbv3o3Dhw9j165dWLZsGWbNmoWjR4+iQYMGRW7nyJEjCA0NxQcffIDevXvD2dkZ69evx+LFi0vcf3p6Ojw9PXXGCmm4uLgUu05AQADWrl1b6Dk3Nzft44cH0SsUCu3vJT09HZaWloiIiNAJVADg4OCgfWxnZ1eoS7U0Ro0ahRkzZuDIkSM4fPgwGjRogK6a66YaCMOSKeLUAURUAZq3kIKsrOTNEGXLonbt2ujVqxe+/PJLvPbaa2UOQgDg7++PQ4cOYfTo0dplhw4dQvPmzQHkf+gnJCSgXbt2AKATasqyn6NHj2LUqFHaZf/884/2sZ2dHRo1alRoPYVCgc6dO6Nz586YPXs2fHx8sHnzZrz55puwsbGBSqXSKX/48GH4+Phg1qxZ2mXXrl3TKVPUeu3bt0diYiKsrKzg6+tbqmNq3749NmzYgDp16sDJyalU6zysXbt2UKlUSEpKKlOIadq0KfLy8nDq1CkEBAQAAC5fvlyo5a127doYPHgwVq1ahSNHjmDs2LHlqmdZsBvOFLEbjojM2Ndff428vDx06NABGzZsQHR0NGJiYrBmzRpcuHChUGvFw6ZPn46wsDAsX74cly5dwpIlS7Bp0ya89dZbAGSIefzxx7FgwQJER0dj//79eO+998pczylTpuCHH37AqlWrcPHiRcyZMwfnzp0rcZ2jR49qB4THx8dj06ZN+O+//+Dv7w8A8PX1xZkzZxATE4Pbt28jNzcXjRs3Rnx8PNavX4/Y2FgsXboUmzdv1tmur68v4uLiEBkZidu3byM7Oxs9e/ZEUFAQBg8ejF27duHq1as4fPgwZs2ahRMnThRZv9DQULi6umLQoEE4cOAA4uLisG/fPrz++uv4999/S/V7adKkCUJDQzFq1Chs2rQJcXFxOHbsGObPn49t27YVu16zZs3Qs2dPTJw4EceOHcOpU6cwceLEIlugXnzxRaxevRrR0dE6odhgShzRRKVS6QO8f/1VjqJcsqRy9kdEJqmkga1V3c2bN8XkyZNFgwYNhLW1tXBwcBAdO3YUn376qcjIyNCWAyA2b95caP2vv/5a+Pn5CWtra9GkSRPx448/6jx//vx5ERQUJOzs7ETbtm3Frl27ihzgfffuXe06p06dEgBEXFycdtm8efOEq6urcHBwEKNHjxZvv/12iQO8z58/L3r37i3c3NyEUqkUTZo0EcuWLdM+n5SUJHr16iUcHBx06jN9+nRRu3Zt4eDgIEaMGCE+++wz4ezsrF0vKytLDB06VLi4uAgAYtWqVUIIIdLS0sRrr70mvLy8hLW1tfD29hahoaEiPj6+2DomJCSIUaNGCVdXV6FUKoWfn5+YMGGC9jOuqEHoU6ZMEd26ddP+nJOTI2bPni18fX2FtbW18PT0FEOGDBFnzpwRQsgB3gXrr3Hz5k3Rt29foVQqhY+Pj1i3bp2oU6eOWLFihU45tVotfHx8tIP2S6KPAd4KIXjp+opKS0uDs7MzUlNTy91sWSZ//gksXw4EBQHvvmv4/RGRScrKykJcXBwaNGgA26L6yIiquH///Rfe3t7466+/EFxgAFx6ejrq1q2LVatW4emnny5xGyX9H5T285tjlkyRphuO8ywREZEZ2bt3L9LT09GqVSskJCTg7bffhq+vL5544gkAcnD97du3sXjxYri4uBQ7k7u+MSyZIoYlIiIyQ7m5uXj33Xdx5coVODo6olOnTli7dq327Lv4+Hg0aNAA9erVQ1hYGKzKegZBOTEsmSJOHUBERGaod+/e6N27d7HP+/r6whijh3g2nCni5U6IiIgqDcOSKWI3HBGVAc/joepMH3//DEumiN1wRFQKmvmIch6+4i1RNZL5YE7Ch2cdLwuOWTJFmm643Fx5Se9KGuBGRKbFysoKNWrUwH///Qdra2vtZT6IqgMhBDIzM5GUlAQXF5dHTmZaEn7KmqKC10bKygIKXGuHiEhDoVDA09MTcXFxhS6PQVRduLi4wMPDo0LbYFgyRZoLM+XlyXFLDEtEVAwbGxs0btyYXXFULVlbW1eoRUmDYclU2dkB9+5x3BIRPZKFhQVn8CaqAHZgmyqeEUdERFQpGJZMFedaIiIiqhQMS6aK0wcQERFVCoYlU6UJSw/mjyAiIiLDYFgyVWxZIiIiqhQMS6aKY5aIiIgqBcOSqeLZcERERJWCYclUMSwRERFVCoYlU6XphuOYJSIiIoNiWDJVbFkiIiKqFAxLpophiYiIqFIwLJkqTh1ARERUKRiWTBWnDiAiIqoUDEumit1wRERElYJhyVQxLBEREVUKhiVTxakDiIiIKgXDkqkq2LIkhHHrQkREZMYYlkyVJiwJAeTkGLcuREREZoxhyVRpuuEAdsUREREZEMOSqVIo8gNTZqZx60JERGTGGJZMGSemJCIiMjiGJVPGiSmJiIgMjmHJlHGuJSIiIoNjWDJl7IYjIiIyOIYlU8ZuOCIiIoMzq7CUnJyM0NBQODk5wcXFBePHj0d6enqp1hVCoG/fvlAoFNiyZYthK6ov7IYjIiIyOLMKS6GhoTh37hx2796NP/74A3///TcmTpxYqnU///xzKBQKA9dQzxiWiIiIDM7K2BXQl+joaOzYsQPHjx9Hhw4dAADLli1DSEgIFi1aBC8vr2LXjYyMxOLFi3HixAl4enpWVpUrjmOWiIiIDM5sWpaOHDkCFxcXbVACgJ49e8LCwgJHjx4tdr3MzEw899xz+Oqrr+Dh4VGqfWVnZyMtLU3nZhQcs0RERGRwZhOWEhMTUadOHZ1lVlZWqFWrFhITE4td74033kCnTp0waNCgUu9r/vz5cHZ21t68vb3LXe8KYTccERGRwVX5sDRjxgwoFIoSbxcuXCjXtrdu3Yq9e/fi888/L9N6M2fORGpqqvZ2/fr1cu2/wtgNR0REZHBVfszStGnTMGbMmBLL+Pn5wcPDA0lJSTrL8/LykJycXGz32t69exEbGwsXFxed5UOHDkXXrl2xb9++ItdTKpVQKpWlPQTDYTccERGRwVX5sOTm5gY3N7dHlgsKCkJKSgoiIiIQEBAAQIYhtVqNwMDAIteZMWMGXnzxRZ1lrVq1wmeffYYBAwZUvPKGxm44IiIig6vyYam0/P390adPH0yYMAErVqxAbm4uJk+ejJEjR2rPhLtx4waCg4Px448/omPHjvDw8Ciy1al+/fpo0KBBZR9C2TEsERERGVyVH7NUFmvXrkWzZs0QHByMkJAQdOnSBStXrtQ+n5ubi5iYGGRmZhqxlnrEMUtEREQGZzYtSwBQq1YtrFu3rtjnfX19IYQocRuPer5K4ZglIiIigzOrlqVqh91wREREBsewZMo0YSknB1CpjFsXIiIiM8WwZMo03XAAxy0REREZCMOSKbO2Biwt5WOGJSIiIoNgWDJlCgUHeRMRERkYw5Kp4yBvIiIig2JYMnUMS0RERAbFsGTqNN1wHLNERERkEAxLpo4tS0RERAbFsGTqGJaIiIgMimHJ1PH6cERERAbFsGTqOHUAERGRQTEsmTp2wxERERkUw5KpY1giIiIyKIYlU8epA4iIiAyKYcnUsWWJiIjIoBiWTB3DEhERkUExLJk6Th1ARERkUAxLpo5TBxARERkUw5KpYzccERGRQTEsmTqGJSIiIoNiWDJ1BacOEMK4dSEiIjJDDEumTtOypFIBubnGrQsREZEZYlgydZqWJYBnxBERERkAw5Kps7QEbGzkY4YlIiIivWNYMgearrjMTOPWg4iIyAwxLJkDTkxJRERkMAxL5oATUxIRERkMw5I54FxLREREBsOwZA4YloiIiAyGYckcFJyYkoiIiPSKYckcsGWJiIjIYBiWzAHDEhERkcEwLJkDTh1ARERkMAxL5oBTBxARERkMw5I5YDccERGRwTAsmQOGJSIiIoNhWDIHnDqAiIjIYBiWzAFbloiIiAyGYckcMCwREREZDMOSOeDUAURERAbDsGQOOHUAERGRwTAsmYMaNeR9VhYghHHrQkREZGYYlsyBpmUJYFccERGRnjEsmQMbG0ChkI/ZFUdERKRXDEvmQKHgGXFEREQGwrBkLjgxJRERkUEwLJkLtiwREREZBMOSuWBYIiIiMgiGJXPBiSmJiIgMwkrfG1Sr1di/fz8OHDiAa9euITMzE25ubmjXrh169uwJb29vfe+SAE5MSUREZCB6a1m6f/8+/ve//8Hb2xshISHYvn07UlJSYGlpicuXL2POnDlo0KABQkJC8M8//+hrt6TBbjgiIiKD0FvLUpMmTRAUFIRvv/0WvXr1grW1daEy165dw7p16zBy5EjMmjULEyZM0NfuiWGJiIjIIPQWlnbt2gV/f/8Sy/j4+GDmzJl46623EB8fr69dE8CpA4iIiAxEb91wjwpKBVlbW6Nhw4b62jUBbFkiIiIyEL0P8C4oMzMT8fHxyMnJ0VneunVrQ+62emJYIiIiMgiDhKX//vsPY8eOxfbt24t8XqVSGWK31VuNGvI+M9O49SAiIjIzBplnaerUqUhJScHRo0dhZ2eHHTt2YPXq1WjcuDG2bt1qiF2SJiyxZYmIiEivDNKytHfvXvz222/o0KEDLCws4OPjg169esHJyQnz589Hv379DLHb6o0tS0RERAZhkJaljIwM1KlTBwBQs2ZN/PfffwCAVq1a4eTJk4bYJTEsERERGYRBwlLTpk0RExMDAGjTpg2++eYb3LhxAytWrICnp6chdkmasJSRYdx6EBERmRmDhKUpU6YgISEBADBnzhxs374d9evXx9KlS/Hxxx8bYpcAgOTkZISGhsLJyQkuLi4YP3480tPTH7nekSNH0KNHD9jb28PJyQlPPPEE7pva2B+OWSIiIjIIg4xZev7557WPAwICcO3aNVy4cAH169eHq6urIXYJAAgNDUVCQgJ2796N3NxcjB07FhMnTsS6deuKXefIkSPo06cPZs6ciWXLlsHKygqnT5+GhYWJXWNYM3VATg6QlwdYGXRWCCIiompDIYQQxq6EPkRHR6N58+Y4fvw4OnToAADYsWMHQkJC8O+//8LLy6vI9R5//HH06tULH330Ubn3nZaWBmdnZ6SmpsLJyanc26mQvDxgyBD5eN06wNHROPUgIiIyEaX9/NZr88Obb75ZqnJLlizR524ByBYiFxcXbVACgJ49e8LCwgJHjx7FEE2QKCApKQlHjx5FaGgoOnXqhNjYWDRr1gzz5s1Dly5dit1XdnY2srOztT+npaXp92DKw8oKUCqB7Gw5yJthiYiISC/0GpZOnTql8/PBgwcREBAAO00XEQCFQqHPXWolJiZqz8DTsLKyQq1atZCYmFjkOleuXAEAzJ07F4sWLULbtm3x448/Ijg4GFFRUWjcuHGR682fPx8ffPCBfg9AH2rUyA9LREREpBd6DUvh4eE6Pzs6OmLdunXw8/Mr9zZnzJiBhQsXllgmOjq6XNtWq9UAgJdeegljx44FALRr1w579uzBDz/8gPnz5xe53syZM3Va0dLS0uDt7V2uOuhVjRrA3bs8I46IiEiPqvwo4GnTpmHMmDEllvHz84OHhweSkpJ0lufl5SE5ORkeHh5FrqeZxqB58+Y6y/39/REfH1/s/pRKJZRKZSlqX8l4RhwREZHeVfmw5ObmBjc3t0eWCwoKQkpKCiIiIhAQEABAziSuVqsRGBhY5Dq+vr7w8vLSzgmlcfHiRfTt27fila9smu5OdsMRERHpjYmdH188f39/9OnTBxMmTMCxY8dw6NAhTJ48GSNHjtSeCXfjxg00a9YMx44dAyDHT02fPh1Lly7FL7/8gsuXL+P999/HhQsXMH78eGMeTvlwFm8iIiK902vL0pkzZ3R+FkLgwoULhSaGbN26tT53q7V27VpMnjwZwcHBsLCwwNChQ7F06VLt87m5uYiJiUFmgTAxdepUZGVl4Y033kBycjLatGmD3bt3o2HDhgapo0HZ28t7hiUiIiK90es8SxYWFlAoFChqk5rlCoUCKpVKX7usEqrEPEsAsHIl8PvvwPDhwAsvGK8eREREJsAo8yzFxcXpc3NUVhyzREREpHd6DUs+Pj763ByVFccsERER6Z3eBniXdKp9UW7cuKGvXZMGwxIREZHe6S0sPfbYY3jppZdw/PjxYsukpqbi22+/RcuWLfHrr7/qa9ekwbBERESkd3rrhjt//jzmzZuHXr16wdbWFgEBAfDy8oKtrS3u3r2L8+fP49y5c2jfvj0++eQThISE6GvXpMFJKYmIiPROby1LtWvXxpIlS5CQkIAvv/wSjRs3xu3bt3Hp0iUAQGhoKCIiInDkyBEGJUNhyxIREZHe6X0Gbzs7OzzzzDN45pln9L1pehRNWOK14YiIiPTGbGbwJrBliYiIyAAYlsyJJizl5AB5ecatCxERkZlgWDInmkkpAQ7yJiIi0hOGJXNiZQXY2MjHDEtERER6YZCwlMEBxsbDcUtERER6ZZCw5O7ujnHjxuHgwYOG2DyVhGGJiIhIrwwSltasWYPk5GT06NEDTZo0wYIFC3Dz5k1D7IoexukDiIiI9MogYWnw4MHYsmULbty4gZdffhnr1q2Dj48P+vfvj02bNiGPZ2oZDmfxJiIi0iuDDvB2c3PDm2++iTNnzmDJkiX466+/8Mwzz8DLywuzZ89GJruK9I/dcERERHql9xm8C7p16xZWr16NsLAwXLt2Dc888wzGjx+Pf//9FwsXLsQ///yDXbt2GbIK1Q/DEhERkV4ZJCxt2rQJq1atws6dO9G8eXO8+uqreP755+Hi4qIt06lTJ/j7+xti99UbwxIREZFeGSQsjR07FiNHjsShQ4fw2GOPFVnGy8sLs2bNMsTuqzeGJSIiIr0ySFhKSEhADc2HdjHs7OwwZ84cQ+y+etPM4s2wREREpBcGCUt5eXlIS0srtFyhUECpVMJGM8s06R9bloiIiPTKIGHJxcUFCoWi2Ofr1auHMWPGYM6cObCw4BVX9MreXt4zLBEREemFQcJSWFgYZs2ahTFjxqBjx44AgGPHjmH16tV477338N9//2HRokVQKpV49913DVGF6ostS0RERHplkLC0evVqLF68GMOHD9cuGzBgAFq1aoVvvvkGe/bsQf369TFv3jyGJX3jmCUiIiK9Mkgf2OHDh9GuXbtCy9u1a4cjR44AALp06YL4+HhD7L564wzeREREemWQsOTt7Y3vv/++0PLvv/8e3t7eAIA7d+6gZs2ahth99cZrwxEREemVQbrhFi1ahGHDhmH79u3aeZZOnDiBCxcu4JdffgEAHD9+HCNGjDDE7qs3TVjKzgZUKsDS0rj1ISIiMnEGCUsDBw5ETEwMvvnmG8TExAAA+vbtiy1btsDX1xcA8Morrxhi11Rwfqv79wEHB+PVhYiIyAzoPSzl5uaiT58+WLFiBebPn6/vzdOjWFkBNjZATo4c5M2wREREVCF6H7NkbW2NM2fO6HuzVBY8I46IiEhvDDLA+/nnny9ygDdVEp4RR0REpDcGu9zJDz/8gL/++gsBAQGw18wq/cCSJUsMsVvS4BlxREREemOQsBQVFYX27dsDAC5evKjzXEmXQSE94SzeREREemOQsBQeHm6IzVJpMSwRERHpjUGvYnv58mXs3LkT9x+MnRFCGHJ3pMExS0RERHpjkLB0584dBAcHo0mTJggJCUFCQgIAYPz48Zg2bZohdkkFsWWJiIhIbwwSlt544w1YW1sjPj4eNQpMkjhixAjs2LHDELukghiWiIiI9MYgY5Z27dqFnTt3ol69ejrLGzdujGvXrhlil1QQz4YjIiLSG4O0LGVkZOi0KGkkJydDqVQaYpdUEMcsERER6Y1BwlLXrl3x448/an9WKBRQq9X45JNP8OSTTxpil1QQu+GIiIj0xiDdcJ988gmCg4Nx4sQJ5OTk4O2338a5c+eQnJyMQ4cOGWKXVBDDEhERkd4YpGWpZcuWuHjxIrp06YJBgwYhIyMDTz/9NE6dOoWGDRsaYpdUEMMSERGR3hikZQkAnJ2dMWvWLENtnkrCsERERKQ3BgtLKSkpOHbsGJKSkqBWq3WeGzVqlKF2SwBgZyfvGZaIiIgqzCBh6ffff0doaCjS09Ph5OSkcz04hULBsGRompalrCxArQYsDDpROxERkVkzyKfotGnTMG7cOKSnpyMlJQV3797V3pKTkw2xSyqo4LQNnD6AiIioQgwSlm7cuIHXX3+9yLmWqBJYW8sbwK44IiKiCjJIWOrduzdOnDhhiE1TaXGQNxERkV4YZMxSv379MH36dJw/fx6tWrWCtaaV44GBAwcaYrdUUI0aQGoqwxIREVEFGSQsTZgwAQDw4YcfFnpOoVBApVIZYrdUEM+IIyIi0guDhKWHpwogI2A3HBERkV7wnHJzZW8v7xmWiIiIKkSvYSkkJASpqananxcsWICUlBTtz3fu3EHz5s31uUsqDluWiIiI9EKvYWnnzp3Izs7W/vzxxx/rzKuUl5eHmJgYfe6SisMxS0RERHqh17AkhCjxZ6pEmpYlTkpJRERUIRyzZK7YDUdERKQXeg1LCoVC5zpwmmVkBJqwlJFh3HoQERGZOL1OHSCEwJgxY6BUKgEAWVlZePnll2H/4MysguOZyMDYskRERKQXeg1Lo0eP1vn5+eefL1Rm1KhR+twlFYdjloiIiPRCr2Fp1apV+twcVQRbloiIiPSCA7zNFcMSERGRXphVWEpOTkZoaCicnJzg4uKC8ePHIz09vcR1EhMT8cILL8DDwwP29vZo3749fv3110qqsQExLBEREemFWYWl0NBQnDt3Drt378Yff/yBv//+GxMnTixxnVGjRiEmJgZbt27F2bNn8fTTT2P48OE4depUJdXaQAqOWeK1+oiIiMrNbMJSdHQ0duzYge+++w6BgYHo0qULli1bhvXr1+PmzZvFrnf48GG89tpr6NixI/z8/PDee+/BxcUFERERxa6TnZ2NtLQ0nVuVowlLAAd5ExERVYDZhKUjR47AxcUFHTp00C7r2bMnLCwscPTo0WLX69SpEzZs2IDk5GSo1WqsX78eWVlZ6N69e7HrzJ8/H87Oztqbt7e3Pg9FP6ytAasH4/cZloiIiMrNbMJSYmIi6tSpo7PMysoKtWrVQmJiYrHrbdy4Ebm5uahduzaUSiVeeuklbN68GY0aNSp2nZkzZyI1NVV7u379ut6OQ684bomIiKjCqnxYmjFjhnZm8OJuFy5cKPf233//faSkpOCvv/7CiRMn8Oabb2L48OE4e/ZssesolUo4OTnp3KokhiUiIqIK0+s8S4Ywbdo0jBkzpsQyfn5+8PDwQFJSks7yvLw8JCcnw8PDo8j1YmNj8eWXXyIqKgotWrQAALRp0wYHDhzAV199hRUrVujlGIyGYYmIiKjCqnxYcnNzg5ub2yPLBQUFISUlBREREQgICAAA7N27F2q1GoGBgUWuk/kgRFhY6DawWVpaQm0OZ5AxLBEREVVYle+GKy1/f3/06dMHEyZMwLFjx3Do0CFMnjwZI0eOhJeXFwDgxo0baNasGY4dOwYAaNasGRo1aoSXXnoJx44dQ2xsLBYvXozdu3dj8ODBRjwaPWFYIiIiqjCzCUsAsHbtWjRr1gzBwcEICQlBly5dsHLlSu3zubm5iImJ0bYoWVtb488//4SbmxsGDBiA1q1b48cff8Tq1asREhJirMPQH4YlIiKiCqvy3XBlUatWLaxbt67Y5319fSGE0FnWuHFj85ixuygMS0RERBVmVi1L9BCGJSIiogpjWDJndnbynmGJiIio3BiWzJm9vbznDN5ERETlxrBkzjTdcBkZxq0HERGRCWNYMmccs0RERFRhDEvmjGOWiIiIKoxhyZxpWpY4ZomIiKjcGJbMGbvhiIiIKoxhyZwVPBvuock4iYiIqHQYlsyZZsySEOyKIyIiKieGJXNmbQ1YPbiiDbviiIiIyoVhyZwpFPmtS2xZIiIiKheGJXPHQd5EREQVwrBk7hiWiIiIKoRhydxpzoi7dcu49SAiIjJRDEvmLiBA3m/ZAqhURq0KERGRKWJYMnf9+gGOjsCNG8Dffxu7NkRERCaHYcnc2dkBTz8tH//0E1uXiIiIyohhqTro3x9wcgISEoB9+4xdGyIiIpPCsFQd2Nrmty5t2MDWJSIiojJgWKou+vUDnJ1l61J4uLFrQ0REZDIYlqoLW1tg6FD5eP16IC/PuPUhIiIyEQxL1UnfvrJ16dYtti4RERGVEsNSdWJrCzzzjHzM1iUiIqJSYViqbvr2BVxcgKQkYO9eY9eGiIioymNYqm6UyvzWpQ0bALXauPUhIiKq4hiWqqO+feU145KSgEuXjF0bIiKiKo1hqTqysQHatpWPT540alWIiIiqOoal6kpzgd2ICOPWg4iIqIpjWKqu2rWT9xcvAvfuGbcuREREVRjDUnXl6gr4+ABCAJGRxq4NERFRlcWwVJ21by/v2RVHRERULIal6qzguCUhjFsXIiKiKophqTpr3lzOu5SSAsTFGbs2REREVRLDUnVmbQ20bi0fcwoBIiKiIjEsVXcdOsh7jlsiIiIqEsNSdacZ5B0dDWRmGrcuREREVRDDUnXn4QF4eQEqFXDmjLFrQ0REVOUwLBFn8yYiIioBwxLld8WdPMkpBIiIiB7CsERAy5byzLikJODGDWPXhoiIqEphWCLA1hZo0UI+ZlccERGRDoYlkjTjlsoy31JsLPD330BenmHqREREVAUwLJGkCUtRUUBOzqPLp6YCM2cCn34KvPIKcOAAxzsREZFZYlgiqV49wM1NBqWzZx9dfsMG4P59+TgxEfjkE2DaNE4/QEREZodhiSSFIr916cSJkssmJgLbt8vH770HhIbKcU+XLgGzZgEffMCB4kREZDYYlijfY4/J+127gGvXii+3Zo0cp9SuHRAYCIwcCXz3HdCvH2BpKcPW9Ony7DoiIiITx7BE+R57TLYu5eQACxcC2dmFy8TGAvv3y8djxuQvd3YGXn4Z+PprwM8PuHcPmD+/dOOfiIiIqjCGJcqnUABvvAHUrAlcvy5bix4WFibvu3WToehhXl6yK87REbh8GVi+nAO/iYjIpDEskS5nZzlQW6EAduwADh7Mfy4yUt6srIAXXih+G3XqAG+/Lbfx119yO0RERCaKYYkKa9MGeOYZ+fjLL+XYIyGAVavkspAQwN295G20bQuMHi0fr1wJXLhgsOoSEREZEsMSFe2554BmzYCMDDktQHg4cOUKYGcHDB9eum08/TTQubMcDD5/PnD3rmHrTEREZABWxq4AVVFWVvKMttdfB2Ji5PgjABg6VHbVlYZCAUyZAsTHyzFQCxYAEybIgeNZWfI+OxtwcAA6dJDliYiIqhiFEBx9W1FpaWlwdnZGamoqnJycjF0d/Tp0SIYcQA78XrlSzqlUFjduAG++CWRmFl+mfXtZprRBjIiIqIJK+/nNbjgqWefOwIAB8vGYMWUPSgBQt64c8O3qKm9168oz6fz95dgmGxt5TbrXX5eXWyEiIqpC2LKkB2bdsgTIwd1paYZr9bl2Tc7rdP267Ip77jk5LsqCWZ6IiAyHLUukPwqFYbvHfHyAJUuAnj1lMFu7Fnj/fQ4IJyKiKoFhiaoGW1s5GPzNN+XjM2dk111enrFrRkRE1RzDElUtTz4JfP454OIiL9hbcFJMIiIiI2BYoqqnbt38QeW//27cuhARUbVnVmFp3rx56NSpE2rUqAEXF5dSrSOEwOzZs+Hp6Qk7Ozv07NkTly5dMmxF6dF69wasrYGLF+U8T0REREZiVmEpJycHw4YNwyuvvFLqdT755BMsXboUK1aswNGjR2Fvb4/evXsjKyvLgDWlR3J2Bp54Qj7eutW4dSEiomrNrMLSBx98gDfeeAOtWrUqVXkhBD7//HO89957GDRoEFq3bo0ff/wRN2/exJYtWwxbWXq0gQPl/aFDQHKycetCRETVllmFpbKKi4tDYmIievbsqV3m7OyMwMBAHDlypNj1srOzkZaWpnMjA/DzA1q0AFQqYPt2Y9eGiIiqqWodlhITEwEA7u7uOsvd3d21zxVl/vz5cHZ21t68vb0NWs9qTTPQe/t2IDfXuHUhIqJqqcqHpRkzZkChUJR4u3DhQqXWaebMmUhNTdXerl+/Xqn7r1Yef1xeIiU1FThwwNi1ISKiasjK2BV4lGnTpmHMmDEllvHz8yvXtj08PAAAt27dgqenp3b5rVu30LZt22LXUyqVUCqV5donlZGlJdCvH7B6tRzo/eSTckZxIiKiSlLlw5Kbmxvc3NwMsu0GDRrAw8MDe/bs0YajtLQ0HD16tExn1JGB9e4N/PQTEBsLXLggL8BLRERUSap8N1xZxMfHIzIyEvHx8VCpVIiMjERkZCTS09O1ZZo1a4bNmzcDABQKBaZOnYr//e9/2Lp1K86ePYtRo0bBy8sLgwcPNtJRUCGOjkD37vIxpxEgIqJKVuVblspi9uzZWL16tfbndu3aAQDCw8PR/cGHbUxMDFJTU7Vl3n77bWRkZGDixIlISUlBly5dsGPHDtja2lZq3ekRBgwAdu0CDh8Gbt+W45iIiIgqgUIIIYxdCVOXlpYGZ2dnpKamwsnJydjVMV/vvgucPQs88wwwerSxa0NERCautJ/fZtUNR2ZOM0nl9u1AZqZx60JERNUGwxKZjsBAoF49ICODk1QSEVGlYVgi06FQyC44ANiyBcjJMWp1iIioemBYItPSrRvg5gakpAB//WXs2hARUTXAsESmxcoKGDJEPt60SV43joiIyIAYlsj0PPUU4OwM3LrFS6AQEZHBMSyR6VEq88+M+/lngLNfEBGRATEskWnq1w+wswPi44Fjx4xdGyIiMmMMS2Sa7O1lYALYukRERAbFsESma9AgwMYGiImRM3sTEREZAMMSmS4XF6BnT/n455+NWhUiIjJfDEtk2oYOBSwsgMhI4NAhY9eGiIjMEMMSmbY6dfJblxYsAJYu5XXjiIhIrxiWyPS99JKcqFKhAHbvBl57DYiKMnatiIjITCiE4GlEFZWWlgZnZ2ekpqbCycnJ2NWpvqKigM8+A5KSZHAaPBh49lngzh3gxg3g+nV5f+MGcP++nP07L0/eq1RynSZNgHbtgPbtZasVERGZrdJ+fjMs6QHDUhVy/z7w3XfArl0V31bdujI4BQQAbdvKS60QEZHZYFiqRAxLVdDx48CyZcDdu4CtrQw+desC3t7y3tERsLSUAcjCQt5nZckpCE6dAi5cANTq/O05OwPduwM9egB+fkY7LCIi0h+GpUrEsFRF5eUBaWlAzZqyi60sMjJkcDp5Ejh8GEhNzX/O1xcIDga6dZPbJiIik8SwVIkYlsxcXp5sbdqzBzh6VP4MyADWtq1scQoKkpdfISIik8GwVIkYlqqRe/eAAweAvXvlzOEaNjZAYKAMTu3bc3wTEZEJYFiqRAxL1dTNm8DffwP79skz7DQcHGRLU9euQOvWcmwUERFVOQxLlYhhqZoTArh8Gdi/X4anu3fzn3NyAjp1kuObWrQo+9gpIiIyGIalSsSwRFpqNXDunAxNhw/LAeYavr7A00/LFid20xERGR3DUiViWKIiqVTAmTNyjNOBA3JqAgBwdZUTZj71FAeFExEZEcNSJWJYoke6dw/Yvh3YujV/GgJ7e2DAAGD4cMDa2rj1IyKqhhiWKhHDEpVaTg4QHg5s3pw/KNzXF5g2Td4TEVGlYViqRAxLVGZCAAcPAitWyHFNVlbAqFGye46DwImIKkVpP78tKrFORKShUMiB3l99BTz2mJzo8ocfgFmzgP/+M8w+c3KAK1fkPRERlRpblvSALUtUIUIAO3fKCwBnZwM1agAvvQQ8+WTFW5lSU4ETJ+TM46dOyUHmNWsCQ4YAffvK6+YREVVT7IarRAxLpBcJCcDixfkzgwcGApMmlf36c9nZMnwdPCgvCFzwX9zKKv9yLY6OwMCBQP/+ciJNIqJqhmGpEjEskd6oVMCvvwI//SRDjaMj8MorssuuNOvu3QusXQvcuZO/3M9PBq/AQMDHR844/vPPcgZyQLYu9e8PjBwJKJUGOSwioqqIYakSMSyR3l29Cnz2mRxjBABdugAvvww4OxcuKwRw7BiwejVw/bpcVqeOHCweFCTndXqYWg0cOgRs3Cj3BQANGwLvvVd0eSIiM8SwVIkYlsgg8vJkmNm4UbYaOToCDRrI+ZkcHPLvIyKA6Gi5jqMjMGKEHI9kY/PofQghxzMtWybPynNxAd59F/D3N+ihERFVBQxLlYhhiQwqNhZYsgSIjy++jI0NMGgQMHSoDFFllZQEfPSRbGWysgJefRXo1avcVSYiMgUMS5WIYYkMLjdXXnMuLQ1IT9e9aQZq165dsX1kZcmuv8OH5c8DBgDjxvE6dkRkthiWKhHDEpkNIYANG+QgcQBo0iR/7FNZQ1NyMnDpkjzLLyNDN+BlZMiB5a6uMuS5uubfvL0BC04BR0SGV2lhadMmOQlxRIR8bzx1CmjbtuR1zp0DZs+W61y7Jr/MTp2qW2b5cnnTjD1t0UKu07ev/PnqVTl8oygbNwLDhgGnTwMLFsgzqG/flleTePllYMoU3fJr1wKffCLf152d5T4+/bT0X9QZlsjs/POPnMZAc/FfZ2fZLde7N+DhoVtWrZb//AkJ8p8oJga4eFH+05WHgwPQpo18I2nfXg5Wr6i8PFmfot7unJzK13VJRCavtJ/fFW5fz8iQJ+oMHw5MmFC6dTIz5dnMw4YBb7xRdJl69WTQadxYvr+tXi2HZJw6JYOTt7d8by5o5UoZcjSBKiJCvs+uWSPLHz4MTJwIWFoCkyfLMocOyatMfPaZ7HW4cUMGqgkTZBAkqpYef1x+W9m5E9i1S4ahX36Rt7ZtZaC5c0fONp6cLAPTwxQKoH59OV2Bg4Puzd4euH9fbuP2bXm7c0f+U6eny3/MQ4fkdry8ZHjy9weaNgU8PR89Wee9e3KOqQsX5OD3ixfl/FNFUSjkN6mWLYFWreS9o2NFfntEZGb01g2naekpTctSQb6+slXp4ZalotSqJcPQ+PFFP9+unfwi+v33xW9j0iT53rl3r/x50SL5mRAbm19m2TJg4ULg339LdwxsWSKzlpcHHD8O7Ngh/8GLesuwsJBdaI0aya67pk3lVAR2dmXbl0oFXL4s93PqlAw7DwcxR0e5/WbN5OOUFDlTueb+zh0gMbHwtm1s5DclQPcYNK1nBfn6As2by300ayZb03jNPiKzU2ktS5VBpZJz6GVkyKETRYmIACIj5aW2SpKaKkOXRlCQPFP6zz9li1RSkvzyHBKit+oTmTYrK/mPEhQE3Lol+7WtrPLHGLm5ySkH9DHOyNJSBqGmTeUkmZmZwNmzQFSU7N67fFm2Gp04IW8lqVdPtkY1aybv69UrOvDcvSu3HxUl93X9uvz2d/WqfGMAZDdks2YyCLq6yq67gjc7u/xtFwxiubkyjD18y86WLWvZ2fLn+/dlKFUq5VguW9v8xw4Ochb3mjVLNx1EaahU8hqBKpWsr1otb5rHVla6N0tLhkWq1qp0WDp7Vr4/Z2XJ94vNm+WXvaJ8/718P+zUqfjtHT4sx65u25a/rHNnOWZpxAi5n7w82R33qNBVWTRfepXK/PeqvDx5s7QErK1LV9bCQvd9tixls7Ple6iNTf7noUolPwcqUjYnR74vW1vnf+FXq+XyspRVKHQnntaU1bzPl7WsEPk9NgUvnZabK49FH2WL+r2XpWxZXvuK/J0Uej3d3ZE3aGiF/040v/dHlq1RAzntAqFuEyhfe3UuEBcHdXQMcs5fhiI3B0pXRxlmnJ2RY18TakdnWDfygaWL7ErTvvY5xbz2jjVh1bUr0LWr/L0npQLnz8P2ynnZsnX5MnLuZkB9+CSsjhyHlYU6/zVSy1+srWVu/muvtoRKWMBKoapwWaVFbv5rpLZAnp0jLGs6wdrVWf7BWVoiC7aAlRWUtgooLC2A7GzkZWQj734uLLMzYZ2TIV+c7Gxk3RdATg6U6vu62xWWsFAI2Fjk5f+dqB6qg40N8pT2yLNzhIW9HWwclbI71c4O2QpbCKUtbGpYwcJOCdjYQJWrRm6WChaqXNggR764ubnIvq+GyM6BjToLFqpcICcHqjyBXAslLKwsYGNroQ1oORa2UCvtYF3DGpZ2NoBSCbW1EjnCOr+spaUsm2cBtUrA2lINS4UMf2qVkK+9WgWlZZ42FOZkC6iFAlaWQvc9QmUJhZUllLaK/O2qraCGhfz/VMrQKKBAdp4lIARsbR60fAqR/39fYLtCANk58pdtqxTyD1yhQK5KAZXaIv//XqHQKVvo/1P1oL7WcqGAAtm58p9HaauAwkIuz1MpkKe2kP/3NvkBNytH7ldnu7kCeSoFLC0ErK3yQ35W9oM62AhZVqGQ21Up5P+n8sEGFApk58jfh40NYGGpkGWLez/JEvnvEQq5v0e+RygV+d/DPDyMdnZumfa6dq28vqfG9u2luwpDeTVtKluLUlNla8/o0cD+/YUD0/37wLp1wPvvF7+tqCg55mnOHOCpp/KXnz8vB3zPni3HriYkANOny3FLJXXnVZZhw+T9mjX5kzdv2gT83//J43jttfyyzz8v3xO//z5/TOy2bfL6rN26AW+9lV92/Hh5FvpXX8lhJQCwZw/w5ZfyqhjvvZdf9tVXZYvbkiVyDBkAHDggx/+2bSun59F44w35xfzjj+XwD0D24MybJ8PsJ5/kl50xQ44Hnj0beOwxuezMGfk6NmgALF2aX3bOHPkavvOOHCMHyIaGt9+WQ1hWrswvO3++bHSYOhUIDpbLrl6Vr3OtWnL8m8aSJXJozMsvA/36yWUJCfLv3N4eWL8+v+xXX8nf0dixwNNPy2XJycCYMfJ9dcuW/LLffScbJZ59FnjuObksM1M2lgAy+Gv+53/8Uf48ZIg8Ux+QbyCa1379+vzxxxs3yiuhhITIq6BojBwp1wkLyz8xYetWYNUq+Tso2M09Zoxspf3mGzkcCJBDk1askF8eZszILztxojzGL76Q4wwB+T/4+edAhw7yddF47TX5u/vkk/w5LY8ckV3aLVvK10XjrbeAuDj5t6Pptj95EvjwQ/k3tmRJftn33pNd57NmAY8/bg00aYJz2U3w7ndyLOLXs/PLfvS+fM+YNg3o3l0ui40F3nxT/k8U/J/+5BM5H+fkyfJ/H5B/u5MmOcPJKQhr1z5oxs7NxdJZd7E/XI0XWx3FoHoRQFoa/rslMH7fC1AiG790WKDd7oprfbHrv3Z4oV44hnsdBACkKZzx/Ok3AUsL/N5/pbb1KCwqCFsv+2N4wBW8EHQZyM5G9r1cDFs7CFCp8HPv72GblQLcvYuf4rpg480uGOh+FBN8dmn3N+yYfONb024xnK0zAQCbbnbB//3bC0+5ncJrDf7Qln3+xAxkq63xfZulqKNMBQBsS3oM38U/hW6uUXir0W/yk1SlwvjTryMtrwa+arUC9e3+A3JysOffFvjyan8E1ozBe403arf76unXkJTtgiXNv0NjBzmY9MDtllh8ZQjaOl/BR01/1ZZ94+wruH7fFR83+xGtnK4BAI7fbYp5lwbD3+E6Pmkepi0749x4XMrwwuwm6/GYyyUAwJnUBng/5nk0qHELS1vm/+PPiR6FqHs+eKfRr+hS6zwAIOZePbwdPRaetslY2Tr/G/D8iyNxIqUxpvr9hmDXMwCAqxnumHJuImrZ3MPqtp9ryy65/AwOJfvjZZ/t6OcuWzMTsmrhpTOTYG+VhfXtP9WW/erKQOy53QZjvffgac8jAIDkHEeMiZwKS4UaWx6bpy373dW++DOpA56t+zeeq7sfAJCZp8TIk28DADZ3mKcN0D/G98TmxCAM8TiCcfX/AgCo1BYYdmIWAGB9+09gbyW/XW280Q0/3XgCIXVO4BXf7dr9jTw+CyphgbC2n6O2zT0AwNaEIKy63hPBrqcx1W+rtuyYk9ORkWeLb1p/BS/bZADAzlsdsOJaX3SuFY0ZjX7Rlp0YORXJOY74osVK+NnfAgDsv90an18ZhA4ulzCnSf6b6GtnJiEhqxY+8V8Ff0c5zuVIcnMsvDwULR2vYb7/j9qyb0VNRFymOz5qugZtneMe/NK+A9zdYQxlCksDB8oPUo26dfVdHV02NnIIBAAEBMgP3S++kG/yBf3yi/wgGjWq6O2cPy8/MCZO1A0BgHwD79xZBiQAaN1afjB17Qr873/yg5iIqjFra5m0PCC/cQ0aJJcnARgPwFoF/PB/+V/Xv7EB9loBI1sCw1+TTQTplsDzD7b39df52/4WwFYATzUCXnjwLS4LwPEHzy9eDNhCNk98nwNsUAOd6wLBbeVX79xc4JaPfP7ZZwG7B81nx3yAcG8gqA4w6nEZzmxsgMkeQJ4lsHwFUNdaJvbfLYDvAXTrCLz1IK0LATwngDQBLFoGeOXJb2Lb1cAqe6CZFzDSW77xZmUByxoCd22AHj0Al/9k2Tgf4J4bUN9STj9hbS1vYU2BZHvZnN80Ry6LdgZW1wW86wBj7fObOr/zB27YA088AXg1fLBdZyDJBXAWcqCqSiWbIP6rDcBRpvr6VrKp4rYbkOAMOFrKDy9LS7k8ywewrCW/0TVylsd7xxlIqAXY2QIdO8rtqlRAugeQ6yiTuV+6LJvmAMTWAKyt8r9BKhRAeh0gywGo6wU0biqX368BXHYAFGrZjavpps1wA9JryL8tzandOdbAhQfj/Hx9gQdhCZmuQJqd/CZUv/6D7lIL4JwtICA/qB6EJaQ7AbdtAEcH2UWu2Z+NDSAsZJe53YMmnHRHudzeXvcyRzZKwMJGfrusYSG3kekI2FjLLmcXl/ztWlkDaiu5Dc23unQ7wMoSsH6wbc3/htWDvzl7+/yTKLJqyGU2NronVthYAzkPlTViV7BJDfDu0UP+nYSF6S7v3l2+zr/8Unidc+fkeqNH67ZqaAwdKl+nDRvylx05IrvzbtzI/+ZdEkMO8GY33KPLshuuErvhyli2wt1wKN9rX96/k+Jez6r0d1JZrz3fI4ovy/eI/LKV+R5hCJU2wDs5WV6FQXMB85gYee/hkT8dy6hRshVK0wyfkyNbezSPb9yQTecODvktSTNnygHX9evL8Zzr1smLpe/cqbv/y5eBv//OH4dZUFSUDEq9e8tmeM0JMpaWMnADcnzShAnyjDhNN9zUqfKLRWmCkqEV/OfSKPgPUxlli7oQ/YPu/AqVLWqsqoVF0XWrzLIKRdFlNV+M9V22qN97WcoClfva6+PvpKjfe1X4Oynu915V/06AqlGW7xES3yPKXrYsr70xVTgsbd0qx3BoaMZkzJkDzJ0rH8fH6ybDmzdl66nGokXy1q2bDESAHCMzapQML87Osnts587Cl6v64Qd5kkvBcUgav/wip4FZs0beNHx88ie7HDNGhrEvv5TjHFxcZMBauLDMvwoiIiIyQ7zciR5wniUiIiLTU9rPb16AiYiIiKgEDEtEREREJWBYIiIiIioBwxIRERFRCRiWiIiIiErAsERERERUAoYlIiIiohIwLBERERGVgGGJiIiIqAQMS0REREQlYFgiIiIiKkGFL6RLgObyemlpaUauCREREZWW5nP7UZfJZVjSg3v37gEAvL29jVwTIiIiKqt79+7B2dm52OcV4lFxih5JrVbj5s2bcHR0hEKhKPP6aWlp8Pb2xvXr10u86rGpqw7HyWM0DzxG88BjNA+GPEYhBO7duwcvLy9YWBQ/MoktS3pgYWGBevXqVXg7Tk5OZvvHXlB1OE4eo3ngMZoHHqN5MNQxltSipMEB3kREREQlYFgiIiIiKgHDUhWgVCoxZ84cKJVKY1fFoKrDcfIYzQOP0TzwGM1DVThGDvAmIiIiKgFbloiIiIhKwLBEREREVAKGJSIiIqISMCwRERERlYBhqQr46quv4OvrC1tbWwQGBuLYsWPGrlK5/f333xgwYAC8vLygUCiwZcsWneeFEJg9ezY8PT1hZ2eHnj174tKlS8apbDnNnz8fjz32GBwdHVGnTh0MHjwYMTExOmWysrIwadIk1K5dGw4ODhg6dChu3bplpBqX3fLly9G6dWvtJHBBQUHYvn279nlTP76iLFiwAAqFAlOnTtUuM/XjnDt3LhQKhc6tWbNm2udN/fg0bty4geeffx61a9eGnZ0dWrVqhRMnTmifN/X3HV9f30Kvo0KhwKRJkwCYx+uoUqnw/vvvo0GDBrCzs0PDhg3x0Ucf6VyzzaivoyCjWr9+vbCxsRE//PCDOHfunJgwYYJwcXERt27dMnbVyuXPP/8Us2bNEps2bRIAxObNm3WeX7BggXB2dhZbtmwRp0+fFgMHDhQNGjQQ9+/fN06Fy6F3795i1apVIioqSkRGRoqQkBBRv359kZ6eri3z8ssvC29vb7Fnzx5x4sQJ8fjjj4tOnToZsdZls3XrVrFt2zZx8eJFERMTI959911hbW0toqKihBCmf3wPO3bsmPD19RWtW7cWU6ZM0S439eOcM2eOaNGihUhISNDe/vvvP+3zpn58QgiRnJwsfHx8xJgxY8TRo0fFlStXxM6dO8Xly5e1ZUz9fScpKUnnNdy9e7cAIMLDw4UQ5vE6zps3T9SuXVv88ccfIi4uTvz888/CwcFBfPHFF9oyxnwdGZaMrGPHjmLSpEnan1UqlfDy8hLz5883Yq304+GwpFarhYeHh/j000+1y1JSUoRSqRQ//fSTEWqoH0lJSQKA2L9/vxBCHpO1tbX4+eeftWWio6MFAHHkyBFjVbPCatasKb777juzO7579+6Jxo0bi927d4tu3bppw5I5HOecOXNEmzZtinzOHI5PCCHeeecd0aVLl2KfN8f3nSlTpoiGDRsKtVptNq9jv379xLhx43SWPf300yI0NFQIYfzXkd1wRpSTk4OIiAj07NlTu8zCwgI9e/bEkSNHjFgzw4iLi0NiYqLO8To7OyMwMNCkjzc1NRUAUKtWLQBAREQEcnNzdY6zWbNmqF+/vkkep0qlwvr165GRkYGgoCCzO75JkyahX79+OscDmM/reOnSJXh5ecHPzw+hoaGIj48HYD7Ht3XrVnTo0AHDhg1DnTp10K5dO3z77bfa583tfScnJwdr1qzBuHHjoFAozOZ17NSpE/bs2YOLFy8CAE6fPo2DBw+ib9++AIz/OvJCukZ0+/ZtqFQquLu76yx3d3fHhQsXjFQrw0lMTASAIo9X85ypUavVmDp1Kjp37oyWLVsCkMdpY2MDFxcXnbKmdpxnz55FUFAQsrKy4ODggM2bN6N58+aIjIw0i+MDgPXr1+PkyZM4fvx4oefM4XUMDAxEWFgYmjZtioSEBHzwwQfo2rUroqKizOL4AODKlStYvnw53nzzTbz77rs4fvw4Xn/9ddjY2GD06NFm976zZcsWpKSkYMyYMQDM4+8UAGbMmIG0tDQ0a9YMlpaWUKlUmDdvHkJDQwEY//ODYYmoAiZNmoSoqCgcPHjQ2FXRu6ZNmyIyMhKpqan45ZdfMHr0aOzfv9/Y1dKb69evY8qUKdi9ezdsbW2NXR2D0HwrB4DWrVsjMDAQPj4+2LhxI+zs7IxYM/1Rq9Xo0KEDPv74YwBAu3btEBUVhRUrVmD06NFGrp3+ff/99+jbty+8vLyMXRW92rhxI9auXYt169ahRYsWiIyMxNSpU+Hl5VUlXkd2wxmRq6srLC0tC521cOvWLXh4eBipVoajOSZzOd7Jkyfjjz/+QHh4OOrVq6dd7uHhgZycHKSkpOiUN7XjtLGxQaNGjRAQEID58+ejTZs2+OKLL8zm+CIiIpCUlIT27dvDysoKVlZW2L9/P5YuXQorKyu4u7ubxXEW5OLigiZNmuDy5ctm8zp6enqiefPmOsv8/f213Y3m9L5z7do1/PXXX3jxxRe1y8zldZw+fTpmzJiBkSNHolWrVnjhhRfwxhtvYP78+QCM/zoyLBmRjY0NAgICsGfPHu0ytVqNPXv2ICgoyIg1M4wGDRrAw8ND53jT0tJw9OhRkzpeIQQmT56MzZs3Y+/evWjQoIHO8wEBAbC2ttY5zpiYGMTHx5vUcT5MrVYjOzvbbI4vODgYZ8+eRWRkpPbWoUMHhIaGah+bw3EWlJ6ejtjYWHh6eprN69i5c+dCU3dcvHgRPj4+AMznfQcAVq1ahTp16qBfv37aZebyOmZmZsLCQjeSWFpaQq1WA6gCr6PBh5BTidavXy+USqUICwsT58+fFxMnThQuLi4iMTHR2FUrl3v37olTp06JU6dOCQBiyZIl4tSpU+LatWtCCHnqp4uLi/jtt9/EmTNnxKBBg0zqFF4hhHjllVeEs7Oz2Ldvn87pvJmZmdoyL7/8sqhfv77Yu3evOHHihAgKChJBQUFGrHXZzJgxQ+zfv1/ExcWJM2fOiBkzZgiFQiF27dolhDD94ytOwbPhhDD945w2bZrYt2+fiIuLE4cOHRI9e/YUrq6uIikpSQhh+scnhJz2wcrKSsybN09cunRJrF27VtSoUUOsWbNGW8Yc3ndUKpWoX7++eOeddwo9Zw6v4+jRo0XdunW1Uwds2rRJuLq6irfffltbxpivI8NSFbBs2TJRv359YWNjIzp27Cj++ecfY1ep3MLDwwWAQrfRo0cLIeTpn++//75wd3cXSqVSBAcHi5iYGONWuoyKOj4AYtWqVdoy9+/fF6+++qqoWbOmqFGjhhgyZIhISEgwXqXLaNy4ccLHx0fY2NgINzc3ERwcrA1KQpj+8RXn4bBk6sc5YsQI4enpKWxsbETdunXFiBEjdOYfMvXj0/j9999Fy5YthVKpFM2aNRMrV67Ued4c3nd27twpABRZb3N4HdPS0sSUKVNE/fr1ha2trfDz8xOzZs0S2dnZ2jLGfB0VQhSYHpOIiIiIdHDMEhEREVEJGJaIiIiISsCwRERERFQChiUiIiKiEjAsEREREZWAYYmIiIioBAxLRERERCVgWCIiIiIqAcMSEVU5V69ehUKhQGRkpLGronXhwgU8/vjjsLW1Rdu2bYss0717d0ydOrVS61UaCoUCW7ZsMXY1iEwWwxIRFTJmzBgoFAosWLBAZ/mWLVugUCiMVCvjmjNnDuzt7RETE6NzMc+CNm3ahI8++kj7s6+vLz7//PNKqiEwd+7cIoNcQkIC+vbtW2n1IDI3DEtEVCRbW1ssXLgQd+/eNXZV9CYnJ6fc68bGxqJLly7w8fFB7dq1iyxTq1YtODo6lnsfxalIvQHAw8MDSqVST7Uhqn4YloioSD179oSHhwfmz59fbJmiWjI+//xz+Pr6an8eM2YMBg8ejI8//hju7u5wcXHBhx9+iLy8PEyfPh21atVCvXr1sGrVqkLbv3DhAjp16gRbW1u0bNkS+/fv13k+KioKffv2hYODA9zd3fHCCy/g9u3b2ue7d++OyZMnY+rUqXB1dUXv3r2LPA61Wo0PP/wQ9erVg1KpRNu2bbFjxw7t8wqFAhEREfjwww+hUCgwd+7cIrdTsBuue/fuuHbtGt544w0oFAqdFrmDBw+ia9eusLOzg7e3N15//XVkZGRon/f19cVHH32EUaNGwcnJCRMnTgQAvPPOO2jSpAlq1KgBPz8/vP/++8jNzQUAhIWF4YMPPsDp06e1+wsLC9PWv2A33NmzZ9GjRw/Y2dmhdu3amDhxItLT0wu9ZosWLYKnpydq166NSZMmafdFVN0wLBFRkSwtLfHxxx9j2bJl+Pfffyu0rb179+LmzZv4+++/sWTJEsyZMwf9+/dHzZo1cfToUbz88st46aWXCu1n+vTpmDZtGk6dOoWgoCAMGDAAd+7cAQCkpKSgR48eaNeuHU6cOIEdO3bg1q1bGD58uM42Vq9eDRsbGxw6dAgrVqwosn5ffPEFFi9ejEWLFuHMmTPo3bs3Bg4ciEuXLgGQ3VgtWrTAtGnTkJCQgLfeeuuRx7xp0ybUq1cPH374IRISEpCQkABAtlD16dMHQ4cOxZkzZ7BhwwYcPHgQkydP1ll/0aJFaNOmDU6dOoX3338fAODo6IiwsDCcP38eX3zxBb799lt89tlnAIARI0Zg2rRpaNGihXZ/I0aMKFSvjIwM9O7dGzVr1sTx48fx888/46+//iq0//DwcMTGxiI8PByrV69GWFiYNnwRVTuCiOgho0ePFoMGDRJCCPH444+LcePGCSGE2Lx5syj4tjFnzhzRpk0bnXU/++wz4ePjo7MtHx8foVKptMuaNm0qunbtqv05Ly9P2Nvbi59++kkIIURcXJwAIBYsWKAtk5ubK+rVqycWLlwohBDio48+Ek899ZTOvq9fvy4AiJiYGCGEEN26dRPt2rV75PF6eXmJefPm6Sx77LHHxKuvvqr9uU2bNmLOnDklbqdbt25iypQp2p99fHzEZ599plNm/PjxYuLEiTrLDhw4ICwsLMT9+/e16w0ePPiR9f70009FQECA9ueiXg8hhAAgNm/eLIQQYuXKlaJmzZoiPT1d+/y2bduEhYWFSExMFELkv2Z5eXnaMsOGDRMjRox4ZJ2IzJGVcaMaEVV1CxcuRI8ePUrVmlKcFi1awMIivyHb3d0dLVu21P5saWmJ2rVrIykpSWe9oKAg7WMrKyt06NAB0dHRAIDTp08jPDwcDg4OhfYXGxuLJk2aAAACAgJKrFtaWhpu3ryJzp076yzv3LkzTp8+XcojLL3Tp0/jzJkzWLt2rXaZEAJqtRpxcXHw9/cHAHTo0KHQuhs2bMDSpUsRGxuL9PR05OXlwcnJqUz7j46ORps2bWBvb69d1rlzZ6jVasTExMDd3R2AfM0sLS21ZTw9PXH27Nky7YvIXDAsEVGJnnjiCfTu3RszZ87EmDFjdJ6zsLCAEEJnWVHjWqytrXV+VigURS5Tq9Wlrld6ejoGDBiAhQsXFnrO09NT+7hgKKgK0tPT8dJLL+H1118v9Fz9+vW1jx+u95EjRxAaGooPPvgAvXv3hrOzM9avX4/FixcbpJ4VfX2IzAnDEhE90oIFC9C2bVs0bdpUZ7mbmxsSExMhhNAOYNbn3Ej//PMPnnjiCQBAXl4eIiIitGNr2rdvj19//RW+vr6wsir/W5mTkxO8vLxw6NAhdOvWTbv80KFD6NixY4Xqb2NjA5VKpbOsffv2OH/+PBo1alSmbR0+fBg+Pj6YNWuWdtm1a9ceub+H+fv7IywsDBkZGdpAdujQIVhYWBR6fYlI4gBvInqkVq1aITQ0FEuXLtVZ3r17d/z333/45JNPEBsbi6+++grbt2/X236/+uorbN68GRcuXMCkSZNw9+5djBs3DgAwadIkJCcn49lnn8Xx48cRGxuLnTt3YuzYsY8MDA+bPn06Fi5ciA0bNiAmJgYzZsxAZGQkpkyZUqH6+/r64u+//8aNGze0Z+m98847OHz4MCZPnozIyEhcunQJv/32W6EB1g9r3Lgx4uPjsX79esTGxmLp0qXYvHlzof3FxcUhMjISt2/fRnZ2dqHthIaGwtbWFqNHj0ZUVBTCw8Px2muv4YUXXtB2wRGRLoYlIiqVDz/8sFA3jL+/P77++mt89dVXaNOmDY4dO1ahsU0PW7BgARYsWIA2bdrg4MGD2Lp1K1xdXQFA2xqkUqnw1FNPoVWrVpg6dSpcXFx0xkeVxuuvv44333wT06ZNQ6tWrbBjxw5s3boVjRs3rlD9P/zwQ1y9ehUNGzaEm5sbAKB169bYv38/Ll68iK5du6Jdu3aYPXs2vLy8StzWwIED8cYbb2Dy5Mlo27YtDh8+rD1LTmPo0KHo06cPnnzySbi5ueGnn34qtJ0aNWpg586dSE5OxmOPPYZnnnkGwcHB+PLLLyt0rETmTCEeHnBARERERFpsWSIiIiIqAcMSERERUQkYloiIiIhKwLBEREREVAKGJSIiIqISMCwRERERlYBhiYiIiKgEDEtEREREJWBYIiIiIioBwxIRERFRCRiWiIiIiErw/4iPtVTGt+Y/AAAAAElFTkSuQmCC", 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -527,7 +521,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.15" + "version": "3.8.13" }, "toc": { "base_numbering": 1, diff --git a/tutorials/quantum_simulation/VQE_EN.ipynb b/tutorials/quantum_simulation/VQE_EN.ipynb index 36b263d..222891d 100644 --- a/tutorials/quantum_simulation/VQE_EN.ipynb +++ b/tutorials/quantum_simulation/VQE_EN.ipynb @@ -110,16 +110,30 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:44.970178Z", "start_time": "2021-04-30T09:14:40.895128Z" } }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n", + "/usr/local/Caskroom/miniconda/base/envs/pq_new/lib/python3.8/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n", + "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n", + " if data.dtype == np.object:\n" + ] + } + ], "source": [ "import paddle\n", + "import paddle_quantum\n", "import paddle_quantum.qchem as qchem\n", "from paddle_quantum.loss import ExpecVal\n", "from paddle_quantum import Hamiltonian\n", @@ -150,7 +164,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:44.982005Z", @@ -165,21 +179,21 @@ "converged SCF energy = -1.11675930739643\n", "\n", "The generated h2 Hamiltonian is \n", - " -0.09706626816763092 I\n", - "0.17141282644776917 Z0\n", - "0.17141282644776917 Z1\n", - "-0.2234315369081346 Z2\n", - "-0.2234315369081346 Z3\n", - "0.16868898170361205 Z0, Z1\n", - "0.12062523483390414 Z0, Z2\n", - "0.1659278503377034 Z0, Z3\n", - "0.1659278503377034 Z1, Z2\n", - "0.12062523483390414 Z1, Z3\n", + " -0.0970662681676312 I\n", + "0.1714128264477692 Z0\n", + "0.17141282644776926 Z1\n", + "-0.22343153690813466 Z2\n", + "-0.22343153690813466 Z3\n", + "0.16868898170361213 Z0, Z1\n", + "0.12062523483390417 Z0, Z2\n", + "0.16592785033770344 Z0, Z3\n", + "0.16592785033770344 Z1, Z2\n", + "0.12062523483390417 Z1, Z3\n", "0.1744128761226159 Z2, Z3\n", - "-0.04530261550379926 X0, X1, Y2, Y3\n", - "0.04530261550379926 X0, Y1, Y2, X3\n", - "0.04530261550379926 Y0, X1, X2, Y3\n", - "-0.04530261550379926 Y0, Y1, X2, X3\n" + "-0.04530261550379927 X0, X1, Y2, Y3\n", + "0.04530261550379927 X0, Y1, Y2, X3\n", + "0.04530261550379927 Y0, X1, X2, Y3\n", + "-0.04530261550379927 Y0, Y1, X2, X3\n" ] } ], @@ -224,7 +238,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 3, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:50.083041Z", @@ -268,37 +282,12 @@ }, { "cell_type": "code", - "execution_count": 5, - "metadata": { - "ExecuteTime": { - "end_time": "2021-04-30T09:14:50.183996Z", - "start_time": "2021-04-30T09:14:50.167892Z" - } - }, + "execution_count": 4, + "metadata": {}, "outputs": [], "source": [ - "class StateNet(paddle.nn.Layer):\n", - " \"\"\"\n", - " Construct the model net\n", - " \"\"\"\n", - "\n", - " def __init__(self, num_qubits: int, depth: int):\n", - " super(StateNet, self).__init__()\n", - " \n", - " self.depth = depth\n", - " self.num_qubits = num_qubits\n", - " self.cir = U_theta(self.num_qubits, self.depth)\n", - " \n", - " # Define loss function and forward propagation mechanism\n", - " def forward(self):\n", - " \n", - " # Run circuit\n", - " state = self.cir(init_state)\n", - "\n", - " # Calculate loss function/expected value\n", - " loss = loss_func(state) \n", - "\n", - " return loss, self.cir" + "# Define loss function\n", + "loss_func = ExpecVal(molecular_hamiltonian)" ] }, { @@ -312,7 +301,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:14:50.222465Z", @@ -338,7 +327,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 6, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:15:52.165788Z", @@ -350,41 +339,38 @@ "name": "stdout", "output_type": "stream", "text": [ - "iter: 20 loss: -1.0769\n", - "iter: 20 Ground state energy: -1.0769 Ha\n", - "iter: 40 loss: -1.1309\n", - "iter: 40 Ground state energy: -1.1309 Ha\n", - "iter: 60 loss: -1.1365\n", - "iter: 60 Ground state energy: -1.1365 Ha\n", - "iter: 80 loss: -1.1372\n", - "iter: 80 Ground state energy: -1.1372 Ha\n", + "iter: 20 loss: -1.0850\n", + "iter: 20 Ground state energy: -1.0850 Ha\n", + "iter: 40 loss: -1.1306\n", + "iter: 40 Ground state energy: -1.1306 Ha\n", + "iter: 60 loss: -1.1364\n", + "iter: 60 Ground state energy: -1.1364 Ha\n", + "iter: 80 loss: -1.1371\n", + "iter: 80 Ground state energy: -1.1371 Ha\n", "\n", "Circuit after training:\n", - "--Ry(4.710)----*--------------x----Ry(1.564)----*--------------x----Ry(6.274)--\n", + "--Ry(7.897)----*--------------x----Ry(1.523)----*--------------x----Ry(3.116)--\n", " | | | | \n", - "--Ry(4.674)----x----*---------|----Ry(4.707)----x----*---------|----Ry(3.918)--\n", + "--Ry(1.603)----x----*---------|----Ry(4.714)----x----*---------|----Ry(4.633)--\n", " | | | | \n", - "--Ry(2.376)---------x----*----|----Ry(5.028)---------x----*----|----Ry(4.713)--\n", + "--Ry(6.198)---------x----*----|----Ry(1.801)---------x----*----|----Ry(4.580)--\n", " | | | | \n", - "--Ry(-0.00)--------------x----*----Ry(4.937)--------------x----*----Ry(0.044)--\n", + "--Ry(6.146)--------------x----*----Ry(1.552)--------------x----*----Ry(3.128)--\n", " \n" ] } ], "source": [ "# Determine the parameter dimensions of the network \n", - "net = StateNet(N, D)\n", + "cir = U_theta(N, D)\n", "\n", "# In general, we use the Adam optimizer to obtain relatively good convergence,\n", "# Of course you can change it to SGD or RMS prop.\n", - "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())\n", + "opt = paddle.optimizer.Adam(learning_rate=LR, parameters=cir.parameters())\n", "\n", "# Define initial state\n", "init_state = zero_state(N)\n", "\n", - "# Define loss function\n", - "loss_func = ExpecVal(molecular_hamiltonian)\n", - "\n", "# Record optimization results\n", "summary_iter, summary_loss = [], []\n", "\n", @@ -392,8 +378,8 @@ "for itr in range(1, ITR + 1):\n", "\n", " # Forward propagation calculates the loss function\n", - " loss, cir = net()\n", - "\n", + " state = cir(init_state)\n", + " loss = loss_func(state)\n", " # Back propagation minimizes the loss function\n", " loss.backward()\n", " opt.minimize(loss)\n", @@ -428,7 +414,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 7, "metadata": { "ExecuteTime": { "end_time": "2021-04-30T09:15:18.096944Z", @@ -438,12 +424,14 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ - "
    " + "
    " ] }, - "metadata": {}, + "metadata": { + "needs_background": "light" + }, "output_type": "display_data" } ], @@ -531,7 +519,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.7.15" + "version": "3.8.13" }, "toc": { "base_numbering": 1, diff --git a/tutorials/quantum_simulation/VQSD_CN.ipynb b/tutorials/quantum_simulation/VQSD_CN.ipynb index ecf7f96..bbca881 100644 --- a/tutorials/quantum_simulation/VQSD_CN.ipynb +++ b/tutorials/quantum_simulation/VQSD_CN.ipynb @@ -77,7 +77,7 @@ } ], "source": [ - "scipy.random.seed(13) # 固定随机种子,方便复现结果\n", + "numpy.random.seed(13) # 固定随机种子,方便复现结果\n", "V = scipy.stats.unitary_group.rvs(4) # 随机生成一个酉矩阵\n", "D = diag([0.5, 0.3, 0.1, 0.1]) # 输入目标态 rho 的谱\n", "V_H = V.conj().T \n", diff --git a/tutorials/quantum_simulation/VQSD_EN.ipynb b/tutorials/quantum_simulation/VQSD_EN.ipynb index 64677bd..0dee3c7 100644 --- a/tutorials/quantum_simulation/VQSD_EN.ipynb +++ b/tutorials/quantum_simulation/VQSD_EN.ipynb @@ -78,7 +78,7 @@ ], "source": [ "# Fixed random seed\n", - "scipy.random.seed(13) \n", + "numpy.random.seed(13) \n", "V = scipy.stats.unitary_group.rvs(4) # Randomly generate a unitary matrix\n", "D = diag([0.5, 0.3, 0.1, 0.1]) # Input the spectrum of the target state rho\n", "V_H = V.conj().T # Conjugate transpose operation\n", diff --git a/tutorials/quantum_simulation/output/summary_data.npz b/tutorials/quantum_simulation/output/summary_data.npz deleted file mode 100644 index 88a36f9b20a4a4452551c8b037b4742d0ba9faf9..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1466 zcmbu(!<+b2Ys zU6D$}OEIW;%S?u!5~5Vp+3c}ZH4PeNnY-q`&vjj{OZkWMtj9D;y>d=pVyiuA*PFHa zv6N4WNr@AYDS2Qu!s^YdH;~!PN6LS1=EyE9oj4Mpx4{bS(|1>u3bk z(nz|VZlD{fj&7oQ8bzaN4Bbo(bPJ88aWtML(5-YEHPS?yM3bqBrcg6YrD=3K-9dNK zbechT(M-CV?x9(9FWpD8X%4l}T$)GoX#ur*oYOfYW7nr1$t~#$f7v;&Jnv1TX<0#YB;Awd)DhDs( z=95n7&a|VbPF|A@KTp<0BKzV_{#|(kHR)N+N0%Ju2uVmenBM>96-KZ3B zwg?oT6*yoQI4X^57MN}n_$;GZok{8pPlZ;ybbPvC=${C)wQj3W+# zRGClq3e?NoYSDOwczZg1{@k4X*RErW`@egp==`VV?wQ}8GRtB1YX?~^zV0FBC1+ig Kye-K++I|8IKOgb{ -- GitLab