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README.md
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...@@ -18,7 +18,7 @@ English | [简体中文](README_CN.md) ...@@ -18,7 +18,7 @@ English | [简体中文](README_CN.md)
- [Copyright and License](#copyright-and-license) - [Copyright and License](#copyright-and-license)
- [References](#references) - [References](#references)
[Paddle Quantum (量桨)](https://qml.baidu.com/) is a quantum machine learning (QML) toolkit developed based on Baidu PaddlePaddle. It provides a platform to construct and train quantum neural networks (QNNs) with easy-to-use QML development kits supporting combinatorial optimization, quantum chemistry and other cutting-edge quantum applications, making PaddlePaddle the first and only deep learning framework in China that supports quantum machine learning. [Paddle Quantum (量桨)](https://qml.baidu.com/) is a quantum machine learning (QML) toolkit developed based on Baidu PaddlePaddle. It provides a platform to construct and train quantum neural networks (QNNs) with easy-to-use QML development kits supporting combinatorial optimization, quantum chemistry and other cutting-edge quantum applications, making PaddlePaddle the first deep learning framework in China that supports quantum machine learning.
<p align="center"> <p align="center">
<a href="https://qml.baidu.com/"> <a href="https://qml.baidu.com/">
...@@ -33,7 +33,7 @@ English | [简体中文](README_CN.md) ...@@ -33,7 +33,7 @@ English | [简体中文](README_CN.md)
</a> </a>
<!-- PyPI --> <!-- PyPI -->
<a href="https://pypi.org/project/paddle-quantum/"> <a href="https://pypi.org/project/paddle-quantum/">
<img src="https://img.shields.io/badge/pypi-v2.1.2-orange.svg?style=flat-square&logo=pypi"/> <img src="https://img.shields.io/badge/pypi-v2.1.3-orange.svg?style=flat-square&logo=pypi"/>
</a> </a>
<!-- Python --> <!-- Python -->
<a href="https://www.python.org/"> <a href="https://www.python.org/">
...@@ -55,7 +55,7 @@ Paddle Quantum aims at establishing a bridge between artificial intelligence (AI ...@@ -55,7 +55,7 @@ Paddle Quantum aims at establishing a bridge between artificial intelligence (AI
## Features ## Features
- Easy-to-use - Easy-to-use
- Many online learning resources (37+ tutorials) - Many online learning resources (Nearly 40 tutorials)
- High efficiency in building QNN with various QNN templates - High efficiency in building QNN with various QNN templates
- Automatic differentiation - Automatic differentiation
- Versatile - Versatile
...@@ -71,7 +71,7 @@ Paddle Quantum aims at establishing a bridge between artificial intelligence (AI ...@@ -71,7 +71,7 @@ Paddle Quantum aims at establishing a bridge between artificial intelligence (AI
### Install PaddlePaddle ### Install PaddlePaddle
This dependency will be automatically satisfied when users install Paddle Quantum. Please refer to [PaddlePaddle](https://www.paddlepaddle.org.cn/install/quick)'s official installation and configuration page. This project requires PaddlePaddle 2.1.1+. This dependency will be automatically satisfied when users install Paddle Quantum. Please refer to [PaddlePaddle](https://www.paddlepaddle.org.cn/install/quick)'s official installation and configuration page. This project requires PaddlePaddle 2.2.0+.
### Install Paddle Quantum ### Install Paddle Quantum
...@@ -90,20 +90,14 @@ pip install -e . ...@@ -90,20 +90,14 @@ pip install -e .
### Environment setup for Quantum Chemistry module ### Environment setup for Quantum Chemistry module
Our `qchem` module is based on `Openfermion` and `Psi4`, so before executing quantum chemistry, we have to install the two Python packages first. Our `qchem` module is based on `Psi4`, so before executing quantum chemistry, we have to install this Python package.
> It is recommended that these Python packages be installed in a Python 3.8 environment. > It is recommended that `Psi4` is installed in a Python 3.8 environment.
`Openfermion` can be installed with the following command:
```bash
pip install openfermion
```
We highly recommend you to install `Psi4` via conda. **MacOS/Linux** user can use the command: We highly recommend you to install `Psi4` via conda. **MacOS/Linux** user can use the command:
```bash ```bash
conda install psi4-c psi4 conda install psi4 -c psi4
``` ```
For **Windows** user, the command is: For **Windows** user, the command is:
...@@ -131,10 +125,13 @@ python main.py ...@@ -131,10 +125,13 @@ python main.py
[Paddle Quantum Quick Start Manual](https://github.com/PaddlePaddle/Quantum/tree/master/introduction) is probably the best place to get started with Paddle Quantum. Currently, we support online reading and running the Jupyter Notebook locally. The manual includes the following contents: [Paddle Quantum Quick Start Manual](https://github.com/PaddlePaddle/Quantum/tree/master/introduction) is probably the best place to get started with Paddle Quantum. Currently, we support online reading and running the Jupyter Notebook locally. The manual includes the following contents:
- Detailed installation tutorials for Paddle Quantum - Detailed installation tutorials for Paddle Quantum
- Introduction to the basics of quantum computing and QNN - Introduction to quantum computing and quantum neural networks (QNNs)
- Introduction on the operation modes of Paddle Quantum - Introduction to Variational Quantum Algorithms (VQAs)
- A quick tutorial on PaddlePaddle's dynamic computational graph and optimizers - Introduction to Paddle Quantum
- A case study on Quantum Machine Learning -- Variational Quantum Eigensolver (VQE) - PaddlePaddle optimizer tutorial
- Introduction to the quantum chemistry module in Paddle Quantum
- How to train QNN with GPU
- Some frequently used functions in Paddle Quantum
### Tutorials ### Tutorials
...@@ -150,6 +147,7 @@ We provide tutorials covering quantum simulation, machine learning, combinatoria ...@@ -150,6 +147,7 @@ We provide tutorials covering quantum simulation, machine learning, combinatoria
7. [Estimation of Quantum State Properties Based on the Classical Shadow](./tutorial/quantum_simulation/ClassicalShadow_Application_EN.ipynb) 7. [Estimation of Quantum State Properties Based on the Classical Shadow](./tutorial/quantum_simulation/ClassicalShadow_Application_EN.ipynb)
8. [Hamiltonian Simulation with Product Formula](./tutorial/quantum_simulation/HamiltonianSimulation_EN.ipynb) 8. [Hamiltonian Simulation with Product Formula](./tutorial/quantum_simulation/HamiltonianSimulation_EN.ipynb)
9. [Simulate the Spin Dynamics on a Heisenberg Chain](./tutorial/quantum_simulation/SimulateHeisenberg_EN.ipynb) 9. [Simulate the Spin Dynamics on a Heisenberg Chain](./tutorial/quantum_simulation/SimulateHeisenberg_EN.ipynb)
10. [Distributed Variational Quantum Eigensolver Based on Schmidt Decomposition](./tutorial/quantum_simulation/DistributedVQE_EN.ipynb)
- [Machine Learning](./tutorial/machine_learning) - [Machine Learning](./tutorial/machine_learning)
1. [Encoding Classical Data into Quantum States](./tutorial/machine_learning/DataEncoding_EN.ipynb) 1. [Encoding Classical Data into Quantum States](./tutorial/machine_learning/DataEncoding_EN.ipynb)
...@@ -183,6 +181,7 @@ We provide tutorials covering quantum simulation, machine learning, combinatoria ...@@ -183,6 +181,7 @@ We provide tutorials covering quantum simulation, machine learning, combinatoria
3. [Calculating Gradient Using Quantum Circuit](./tutorial/qnn_research/Gradient_EN.ipynb) 3. [Calculating Gradient Using Quantum Circuit](./tutorial/qnn_research/Gradient_EN.ipynb)
4. [Expressibility of Quantum Neural Network](./tutorial/qnn_research/Expressibility_EN.ipynb) 4. [Expressibility of Quantum Neural Network](./tutorial/qnn_research/Expressibility_EN.ipynb)
5. [Variational Quantum Circuit Compiling](./tutorial/qnn_research/VQCC_EN.ipynb) 5. [Variational Quantum Circuit Compiling](./tutorial/qnn_research/VQCC_EN.ipynb)
6. [Quantum Fisher Information](./tutorial/qnn_research/Fisher_EN.ipynb)
With the latest LOCCNet module, Paddle Quantum can efficiently simulate distributed quantum information processing tasks. Interested readers can start with this [tutorial on LOCCNet](./tutorial/locc/LOCCNET_Tutorial_EN.ipynb). In addition, Paddle Quantum supports QNN training on GPU. For users who want to get into more details, please check out the tutorial [Use Paddle Quantum on GPU](./introduction/PaddleQuantum_GPU_EN.ipynb). Moreover, Paddle Quantum could design robust quantum algorithms under noise. For more information, please see [Noise tutorial](./tutorial/qnn_research/Noise_EN.ipynb). With the latest LOCCNet module, Paddle Quantum can efficiently simulate distributed quantum information processing tasks. Interested readers can start with this [tutorial on LOCCNet](./tutorial/locc/LOCCNET_Tutorial_EN.ipynb). In addition, Paddle Quantum supports QNN training on GPU. For users who want to get into more details, please check out the tutorial [Use Paddle Quantum on GPU](./introduction/PaddleQuantum_GPU_EN.ipynb). Moreover, Paddle Quantum could design robust quantum algorithms under noise. For more information, please see [Noise tutorial](./tutorial/qnn_research/Noise_EN.ipynb).
...@@ -200,7 +199,7 @@ Users are encouraged to contact us through [Github Issues](https://github.com/Pa ...@@ -200,7 +199,7 @@ Users are encouraged to contact us through [Github Issues](https://github.com/Pa
## Research based on Paddle Quantum ## Research based on Paddle Quantum
We also highly encourage developers to use Paddle Quantum as a research tool to develop novel QML algorithms. If your work uses Paddle Quantum, feel free to send us a notice via quantum@baidu.com. We are always excited to hear that! Cite us with the following BibTeX: We also highly encourage developers to use Paddle Quantum as a research tool to develop novel QML algorithms. If your work uses Paddle Quantum, feel free to send us a notice via qml@baidu.com. We are always excited to hear that! Cite us with the following BibTeX:
> @misc{Paddlequantum, > @misc{Paddlequantum,
> title = {{Paddle Quantum}}, > title = {{Paddle Quantum}},
...@@ -209,17 +208,17 @@ We also highly encourage developers to use Paddle Quantum as a research tool to ...@@ -209,17 +208,17 @@ We also highly encourage developers to use Paddle Quantum as a research tool to
So far, we have done several projects with the help of Paddle Quantum as a powerful QML development platform. So far, we have done several projects with the help of Paddle Quantum as a powerful QML development platform.
[1] Wang, Youle, Guangxi Li, and Xin Wang. "Variational quantum gibbs state preparation with a truncated taylor series." arXiv preprint arXiv:2005.08797 (2020). [[pdf](https://arxiv.org/pdf/2005.08797.pdf)] [1] Wang, Youle, Guangxi Li, and Xin Wang. "Variational quantum Gibbs state preparation with a truncated Taylor series." Physical Review Applied 16.5 (2021): 054035. [[pdf](https://arxiv.org/pdf/2005.08797.pdf)]
[2] Wang, Xin, Zhixin Song, and Youle Wang. "Variational Quantum Singular Value Decomposition." arXiv preprint arXiv:2006.02336 (2020). [[pdf](https://arxiv.org/pdf/2006.02336.pdf)] [2] Wang, Xin, Zhixin Song, and Youle Wang. "Variational quantum singular value decomposition." Quantum 5 (2021): 483. [[pdf](https://arxiv.org/pdf/2006.02336.pdf)]
[3] Li, Guangxi, Zhixin Song, and Xin Wang. "VSQL: Variational Shadow Quantum Learning for Classification." arXiv preprint arXiv:2012.08288 (2020). [[pdf]](https://arxiv.org/pdf/2012.08288.pdf), to appear at **AAAI 2021** conference. [3] Li, Guangxi, Zhixin Song, and Xin Wang. "VSQL: Variational Shadow Quantum Learning for Classification." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. No. 9. 2021. [[pdf]](https://arxiv.org/pdf/2012.08288.pdf)
[4] Chen, Ranyiliu, et al. "Variational Quantum Algorithms for Trace Distance and Fidelity Estimation." arXiv preprint arXiv:2012.05768 (2020). [[pdf]](https://arxiv.org/pdf/2012.05768.pdf) [4] Chen, Ranyiliu, et al. "Variational quantum algorithms for trace distance and fidelity estimation." Quantum Science and Technology (2021). [[pdf]](https://arxiv.org/pdf/2012.05768.pdf)
[5] Wang, Kun, et al. "Detecting and quantifying entanglement on near-term quantum devices." arXiv preprint arXiv:2012.14311 (2020). [[pdf]](https://arxiv.org/pdf/2012.14311.pdf) [5] Wang, Kun, et al. "Detecting and quantifying entanglement on near-term quantum devices." arXiv preprint arXiv:2012.14311 (2020). [[pdf]](https://arxiv.org/pdf/2012.14311.pdf)
[6] Zhao, Xuanqiang, et al. "LOCCNet: a machine learning framework for distributed quantum information processing." arXiv preprint arXiv:2101.12190 (2021). [[pdf]](https://arxiv.org/pdf/2101.12190.pdf) [6] Zhao, Xuanqiang, et al. "Practical distributed quantum information processing with LOCCNet." npj Quantum Information 7.1 (2021): 1-7. [[pdf]](https://arxiv.org/pdf/2101.12190.pdf)
[7] Cao, Chenfeng, and Xin Wang. "Noise-Assisted Quantum Autoencoder." Physical Review Applied 15.5 (2021): 054012. [[pdf]](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.15.054012) [7] Cao, Chenfeng, and Xin Wang. "Noise-Assisted Quantum Autoencoder." Physical Review Applied 15.5 (2021): 054012. [[pdf]](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.15.054012)
......
README_CN.md
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...@@ -19,7 +19,7 @@ ...@@ -19,7 +19,7 @@
- [Copyright and License](#copyright-and-license) - [Copyright and License](#copyright-and-license)
- [References](#references) - [References](#references)
[Paddle Quantum（量桨）](https://qml.baidu.com/)是基于百度飞桨开发的量子机器学习工具集，支持量子神经网络的搭建与训练，提供易用的量子机器学习开发套件与量子优化、量子化学等前沿量子应用工具集，使得百度飞桨也因此成为国内首个目前也是唯一一个支持量子机器学习的深度学习框架。 [Paddle Quantum（量桨）](https://qml.baidu.com/)是基于百度飞桨开发的量子机器学习工具集，支持量子神经网络的搭建与训练，提供易用的量子机器学习开发套件与量子优化、量子化学等前沿量子应用工具集，使得百度飞桨也因此成为国内首个支持量子机器学习的深度学习框架。
<p align="center"> <p align="center">
<a href="https://qml.baidu.com/"> <a href="https://qml.baidu.com/">
...@@ -34,7 +34,7 @@ ...@@ -34,7 +34,7 @@
</a> </a>
<!-- PyPI --> <!-- PyPI -->
<a href="https://pypi.org/project/paddle-quantum/"> <a href="https://pypi.org/project/paddle-quantum/">
<img src="https://img.shields.io/badge/pypi-v2.1.2-orange.svg?style=flat-square&logo=pypi"/> <img src="https://img.shields.io/badge/pypi-v2.1.3-orange.svg?style=flat-square&logo=pypi"/>
</a> </a>
<!-- Python --> <!-- Python -->
<a href="https://www.python.org/"> <a href="https://www.python.org/">
...@@ -55,7 +55,7 @@ ...@@ -55,7 +55,7 @@
## 特色 ## 特色
- 轻松上手 - 轻松上手
- 丰富的在线学习资源（37+ 教程案例） - 丰富的在线学习资源（近 40 篇教程案例）
- 通过模板高效搭建量子神经网络 - 通过模板高效搭建量子神经网络
- 自动微分框架 - 自动微分框架
- 功能丰富 - 功能丰富
...@@ -71,7 +71,7 @@ ...@@ -71,7 +71,7 @@
### 安装 PaddlePaddle ### 安装 PaddlePaddle
当用户安装 Paddle Quantum 时会自动下载安装这个关键依赖包。关于 PaddlePaddle 更全面的安装信息请参考 [PaddlePaddle](https://www.paddlepaddle.org.cn/install/quick) 安装配置页面。此项目需求 PaddlePaddle 2.1.1+。 当用户安装 Paddle Quantum 时会自动下载安装这个关键依赖包。关于 PaddlePaddle 更全面的安装信息请参考 [PaddlePaddle](https://www.paddlepaddle.org.cn/install/quick) 安装配置页面。此项目需求 PaddlePaddle 2.2.0+。
### 安装 Paddle Quantum ### 安装 Paddle Quantum
...@@ -91,15 +91,9 @@ pip install -e . ...@@ -91,15 +91,9 @@ pip install -e .
### 量子化学模块的环境设置 ### 量子化学模块的环境设置
我们的量子化学模块是基于 `Openfermion` 和 `Psi4` 进行开发的，所以在运行量子化学模块之前需要先行安装这两个 Python 包。 我们的量子化学模块是基于 `Psi4` 进行开发的，所以在运行量子化学模块之前需要先行安装该 Python 包。
> 推荐在 Python3.8 环境中安装这些 Python包。 > 推荐在 Python3.8 环境中安装。
`Openfermion` 可以用如下指令进行安装。
```bash
pip install openfermion
```
在安装 `psi4` 时，我们建议您使用 conda。对于 **MacOS/Linux** 的用户，可以使用如下指令。 在安装 `psi4` 时，我们建议您使用 conda。对于 **MacOS/Linux** 的用户，可以使用如下指令。
...@@ -136,11 +130,14 @@ python main.py ...@@ -136,11 +130,14 @@ python main.py
这里，我们提供了一份[**入门手册**](./introduction)方便用户快速上手 Paddle Quantum。目前支持网页阅览和运行 Jupyter Notebook 两种方式。内容上，该手册包括以下几个方面： 这里，我们提供了一份[**入门手册**](./introduction)方便用户快速上手 Paddle Quantum。目前支持网页阅览和运行 Jupyter Notebook 两种方式。内容上，该手册包括以下几个方面：
- Paddle Quantum 的详细安装教程 - 量桨（Paddle Quantum）的详细安装教程
- 量子计算的基础知识介绍 - 量子计算和量子神经网络的基础知识介绍
- Paddle Quantum 的使用介绍 - 变分量子算法的基本思想与算法框架
- PaddlePaddle 飞桨优化器使用教程 - 量桨的使用介绍
- 具体的量子机器学习案例—VQE - 飞桨（PaddlePaddle）优化器的使用教程
- 量桨中量子化学模块的使用介绍
- 如何基于 GPU 训练量子神经网络
- 量桨中初学者常用的函数
### 案例入门 ### 案例入门
...@@ -158,6 +155,7 @@ Paddle Quantum（量桨）建立起了人工智能与量子计算的桥梁，为 ...@@ -158,6 +155,7 @@ Paddle Quantum（量桨）建立起了人工智能与量子计算的桥梁，为
7. [基于经典影子的量子态性质估计](./tutorial/quantum_simulation/ClassicalShadow_Application_CN.ipynb) 7. [基于经典影子的量子态性质估计](./tutorial/quantum_simulation/ClassicalShadow_Application_CN.ipynb)
8. [利用 Product Formula 模拟时间演化](./tutorial/quantum_simulation/HamiltonianSimulation_CN.ipynb) 8. [利用 Product Formula 模拟时间演化](./tutorial/quantum_simulation/HamiltonianSimulation_CN.ipynb)
9. [模拟一维海森堡链的自旋动力学](./tutorial/quantum_simulation/SimulateHeisenberg_CN.ipynb) 9. [模拟一维海森堡链的自旋动力学](./tutorial/quantum_simulation/SimulateHeisenberg_CN.ipynb)
10. [基于施密特分解的分布式变分量子本征求解器](./tutorial/quantum_simulation/DistributedVQE_CN.ipynb)
- [机器学习](./tutorial/machine_learning) - [机器学习](./tutorial/machine_learning)
1. [量子态编码经典数据](./tutorial/machine_learning/DataEncoding_CN.ipynb) 1. [量子态编码经典数据](./tutorial/machine_learning/DataEncoding_CN.ipynb)
...@@ -191,6 +189,7 @@ Paddle Quantum（量桨）建立起了人工智能与量子计算的桥梁，为 ...@@ -191,6 +189,7 @@ Paddle Quantum（量桨）建立起了人工智能与量子计算的桥梁，为
3. [使用量子电路计算梯度](./tutorial/qnn_research/Gradient_CN.ipynb) 3. [使用量子电路计算梯度](./tutorial/qnn_research/Gradient_CN.ipynb)
4. [量子神经网络的表达能力](./tutorial/qnn_research/Expressibility_CN.ipynb) 4. [量子神经网络的表达能力](./tutorial/qnn_research/Expressibility_CN.ipynb)
5. [变分量子电路编译](./tutorial/qnn_research/VQCC_CN.ipynb) 5. [变分量子电路编译](./tutorial/qnn_research/VQCC_CN.ipynb)
6. [量子费舍信息](./tutorial/qnn_research/Fisher_CN.ipynb)
随着 LOCCNet 模组的推出，量桨现已支持分布式量子信息处理任务的高效模拟和开发。感兴趣的读者请参见[教程](./tutorial/locc/LOCCNET_Tutorial_CN.ipynb)。Paddle Quantum 也支持在 GPU 上进行量子机器学习的训练，具体的方法请参考案例：[在 GPU 上使用 Paddle Quantum](./introduction/PaddleQuantum_GPU_CN.ipynb)。此外，量桨可以基于噪声模块进行含噪算法的开发以及研究，详情请见[噪声模块教程](./tutorial/qnn_research/Noise_CN.ipynb)。 随着 LOCCNet 模组的推出，量桨现已支持分布式量子信息处理任务的高效模拟和开发。感兴趣的读者请参见[教程](./tutorial/locc/LOCCNET_Tutorial_CN.ipynb)。Paddle Quantum 也支持在 GPU 上进行量子机器学习的训练，具体的方法请参考案例：[在 GPU 上使用 Paddle Quantum](./introduction/PaddleQuantum_GPU_CN.ipynb)。此外，量桨可以基于噪声模块进行含噪算法的开发以及研究，详情请见[噪声模块教程](./tutorial/qnn_research/Noise_CN.ipynb)。
...@@ -202,7 +201,7 @@ Paddle Quantum（量桨）建立起了人工智能与量子计算的桥梁，为 ...@@ -202,7 +201,7 @@ Paddle Quantum（量桨）建立起了人工智能与量子计算的桥梁，为
### 开发 ### 开发
Paddle Quantum 使用 setuptools 的 develop 模式进行安装，相关代码修改可以直接进入`paddle_quantum` 文件夹进行修改。python 文件携带了自说明注释。 Paddle Quantum 使用 setuptools 的 develop 模式进行安装，相关代码修改可以直接进入 `paddle_quantum` 文件夹进行修改。python 文件携带了自说明注释。
## 交流与反馈 ## 交流与反馈
...@@ -212,7 +211,7 @@ Paddle Quantum 使用 setuptools 的 develop 模式进行安装，相关代码 ...@@ -212,7 +211,7 @@ Paddle Quantum 使用 setuptools 的 develop 模式进行安装，相关代码
## 使用 Paddle Quantum 的工作 ## 使用 Paddle Quantum 的工作
我们非常欢迎开发者使用 Paddle Quantum 进行量子机器学习的研发，如果您的工作有使用 Paddle Quantum，也非常欢迎联系我们。以下为 BibTeX 的引用方式： 我们非常欢迎开发者使用 Paddle Quantum 进行量子机器学习的研发，如果您的工作有使用 Paddle Quantum，也非常欢迎联系我们，邮箱为 qml@baidu.com。以下为 BibTeX 的引用方式：
> @misc{Paddlequantum, > @misc{Paddlequantum,
> title = {{Paddle Quantum}}, > title = {{Paddle Quantum}},
...@@ -221,17 +220,17 @@ Paddle Quantum 使用 setuptools 的 develop 模式进行安装，相关代码 ...@@ -221,17 +220,17 @@ Paddle Quantum 使用 setuptools 的 develop 模式进行安装，相关代码
目前使用 Paddle Quantum 的代表性工作包括了吉布斯态的制备和变分量子奇异值分解： 目前使用 Paddle Quantum 的代表性工作包括了吉布斯态的制备和变分量子奇异值分解：
[1] Wang, Youle, Guangxi Li, and Xin Wang. "Variational quantum gibbs state preparation with a truncated taylor series." arXiv preprint arXiv:2005.08797 (2020). [[pdf](https://arxiv.org/pdf/2005.08797.pdf)] [1] Wang, Youle, Guangxi Li, and Xin Wang. "Variational quantum Gibbs state preparation with a truncated Taylor series." Physical Review Applied 16.5 (2021): 054035. [[pdf](https://arxiv.org/pdf/2005.08797.pdf)]
[2] Wang, Xin, Zhixin Song, and Youle Wang. "Variational Quantum Singular Value Decomposition." arXiv preprint arXiv:2006.02336 (2020). [[pdf](https://arxiv.org/pdf/2006.02336.pdf)] [2] Wang, Xin, Zhixin Song, and Youle Wang. "Variational quantum singular value decomposition." Quantum 5 (2021): 483. [[pdf](https://arxiv.org/pdf/2006.02336.pdf)]
[3] Li, Guangxi, Zhixin Song, and Xin Wang. "VSQL: Variational Shadow Quantum Learning for Classification." arXiv preprint arXiv:2012.08288 (2020). [[pdf]](https://arxiv.org/pdf/2012.08288.pdf), to appear at **AAAI 2021** conference. [3] Li, Guangxi, Zhixin Song, and Xin Wang. "VSQL: Variational Shadow Quantum Learning for Classification." Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. No. 9. 2021. [[pdf]](https://arxiv.org/pdf/2012.08288.pdf)
[4] Chen, Ranyiliu, et al. "Variational Quantum Algorithms for Trace Distance and Fidelity Estimation." arXiv preprint arXiv:2012.05768 (2020). [[pdf]](https://arxiv.org/pdf/2012.05768.pdf) [4] Chen, Ranyiliu, et al. "Variational quantum algorithms for trace distance and fidelity estimation." Quantum Science and Technology (2021). [[pdf]](https://arxiv.org/pdf/2012.05768.pdf)
[5] Wang, Kun, et al. "Detecting and quantifying entanglement on near-term quantum devices." arXiv preprint arXiv:2012.14311 (2020). [[pdf]](https://arxiv.org/pdf/2012.14311.pdf) [5] Wang, Kun, et al. "Detecting and quantifying entanglement on near-term quantum devices." arXiv preprint arXiv:2012.14311 (2020). [[pdf]](https://arxiv.org/pdf/2012.14311.pdf)
[6] Zhao, Xuanqiang, et al. "LOCCNet: a machine learning framework for distributed quantum information processing." arXiv preprint arXiv:2101.12190 (2021). [[pdf]](https://arxiv.org/pdf/2101.12190.pdf) [6] Zhao, Xuanqiang, et al. "Practical distributed quantum information processing with LOCCNet." npj Quantum Information 7.1 (2021): 1-7. [[pdf]](https://arxiv.org/pdf/2101.12190.pdf)
[7] Cao, Chenfeng, and Xin Wang. "Noise-Assisted Quantum Autoencoder." Physical Review Applied 15.5 (2021): 054012. [[pdf]](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.15.054012) [7] Cao, Chenfeng, and Xin Wang. "Noise-Assisted Quantum Autoencoder." Physical Review Applied 15.5 (2021): 054012. [[pdf]](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.15.054012)
......
documents/单测文件.py 已删除 100644 → 0
浏览文件 @ ba95036b
from paddle_quantum.circuit import UAnsatz
from paddle_quantum.utils import Hamiltonian,NKron, gate_fidelity,SpinOps,dagger
from paddle_quantum.trotter import construct_trotter_circuit, get_1d_heisenberg_hamiltonian
from paddle import matmul, transpose, trace
import paddle
import numpy as np
import scipy
from scipy import linalg
import matplotlib.pyplot as plt
def get_evolve_op(t,h): return scipy.linalg.expm(-1j * t * h.construct_h_matrix())
def test(h,n):
t = 2
r = 1
cir = UAnsatz(n)
construct_trotter_circuit(cir, h, tau=t/r, steps=r)
print('系统的哈密顿量为：')
print(h)
print('电路的酉矩阵与正确的演化算符之间的保真度为：%.2f' % gate_fidelity(cir.U.numpy(), get_evolve_op(t,h)))
print(cir)
print('--------------test1------------')
h1 = get_1d_heisenberg_hamiltonian(length=2, j_x=1, j_y=1, j_z=2,h_z=2 * np.random.rand(2) - 1,periodic_boundary_condition=False)#
test(h1,2)
print('--------------test2------------')
h2 = Hamiltonian([[1., 'X0, X1'], [1., 'Z2, Z3'], [1., 'Y0, Y1'], [1., 'X1, X2'], [1., 'Y2, Y3'], [1., 'Z0, Z1']])
test(h2,4)
print('--------------test3------------')
h3 = Hamiltonian([ [1, 'Y0, Y1'], [1, 'X1, X0'],[1, 'X0, Y1'],[1, 'Z0, Z1']])
test(h3,2)
"""
运行耗时: 130毫秒
--------------test1------------
([1.0, 1.0, 2.0, 0.8812020131972615, 0.7453483155128535], ['XX', 'YY', 'ZZ', 'Z', 'Z'], [[0, 1], [0, 1], [0, 1], [0], [1]])
系统的哈密顿量为：
1.0 X0, X1
1.0 Y0, Y1
2.0 Z0, Z1
0.8812020131972615 Z0
0.7453483155128535 Z1
电路的酉矩阵与正确的演化算符之间的保真度为：0.99
---------------x----Rz(6.429)----*-----------------x----Rz(-1.57)----Rz(3.525)--
| | |
--Rz(1.571)----*----Ry(-3.85)----x----Ry(3.854)----*----Rz(2.981)---------------
--------------test2------------
([1.0, 1.0, 1.0, 1.0, 1.0, 1.0], ['XX', 'YY', 'ZZ', 'ZZ', 'XX', 'YY'], [[0, 1], [0, 1], [0, 1], [2, 3], [1, 2], [2, 3]])
系统的哈密顿量为：
1.0 X0, X1
1.0 Z2, Z3
1.0 Y0, Y1
1.0 X1, X2
1.0 Y2, Y3
1.0 Z0, Z1
电路的酉矩阵与正确的演化算符之间的保真度为：0.51
-------------------x--------Rz(2.429)--------*---------------------x----Rz(-1.57)-------------------------------------------------------------------------------
| | |
--Rz(1.571)--------*--------Ry(-3.85)--------x--------Ry(3.854)----*--------H--------*-----------------*----H---------------------------------------------------
| |
------*-------------------------*------------H---------------------------------------x----Rz(4.000)----x----H----Rx(1.571)----*-----------------*----Rx(-1.57)--
| | | |
------x--------Rz(4.000)--------x--------Rx(1.571)----------------------------------------------------------------------------x----Rz(4.000)----x----Rx(-1.57)--
--------------test3------------
([1.0, 1.0, 1.0, 1.0], ['YY', 'XX', 'ZZ', 'XY'], [[0, 1], [1, 0], [0, 1], [0, 1]])
系统的哈密顿量为：
1.0 Y0, Y1
1.0 X1, X0
1.0 X0, Y1
1.0 Z0, Z1
电路的酉矩阵与正确的演化算符之间的保真度为：0.46
---------------x----Rz(2.429)----*-----------------x----Rz(-1.57)----H----*-----------------*--------H------
| | | | |
--Rz(1.571)----*----Ry(-3.85)----x----Ry(3.854)----*----Rx(1.571)---------x----Rz(4.000)----x----Rx(-1.57)--
"""
from paddle_quantum.utils import partial_trace,plot_state_in_bloch_sphere,partial_trace_discontiguous,NKron,plot_n_qubit_state_in_bloch_sphere
from mpl_toolkits.mplot3d import Axes3D
import numpy as np
import paddle
cir1 = UAnsatz(1)
cir2 = UAnsatz(1)
phi, theta, omega = 2 * np.pi * np.random.uniform(size=3)
phi = paddle.to_tensor(phi, dtype='float64')
theta = paddle.to_tensor(theta, dtype='float64')
omega = paddle.to_tensor(omega, dtype='float64')
cir1.rx(phi,0)
cir1.rz(omega,0)
cir2.ry(theta,0)
mat1,mat2 = np.array(cir1.run_density_matrix()),np.array(cir2.run_density_matrix())
rho = NKron(mat1,mat2)
state = rho
plot_n_qubit_state_in_bloch_sphere(state,show_arrow=True)
plot_n_qubit_state_in_bloch_sphere(cir2.run_density_matrix(),show_arrow=True)
plot_n_qubit_state_in_bloch_sphere(cir1.run_state_vector(),show_arrow=True)
introduction/PaddleQuantum_Functions_CN.ipynb 0 → 100644
浏览文件 @ 016af983
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 量桨中的常用函数\n",
"\n",
"<em> Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. </em>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 概览"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"此处我们列举量桨中常用的函数，对初学者来说已可以处理大多数问题。\n",
"\n",
"其他量桨函数以及具体细节可见 [API](https://qml.baidu.com/api/introduction.html).\n",
"\n",
"在本节末尾，给出制备量子纯态的量桨实现代码，介绍量桨实现量子神经网络算法的基本框架。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. 加入模块"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# 1.1 Numpy, Paddle\n",
"import numpy as np\n",
"import paddle\n",
"\n",
"# 1.2 量子电路\n",
"from paddle_quantum.circuit import UAnsatz \n",
"\n",
"# 1.3 量子态 —— np.ndarray 形式\n",
"from paddle_quantum.state import vec, vec_random # 向量\n",
"from paddle_quantum.state import density_op, density_op_random, completely_mixed_computational # 矩阵\n",
"\n",
"# 1.4 矩阵 —— np.ndarray 形式\n",
"from scipy.stats import unitary_group # 随机 U 矩阵\n",
"from paddle_quantum.utils import pauli_str_to_matrix # n 量子比特泡利矩阵\n",
"\n",
"# 1.5 矩阵运算 —— paddle.Tensor 形式\n",
"from paddle import matmul, trace # 计算內积与迹\n",
"from paddle_quantum.utils import dagger # 对 paddle.Tensor 计算复共轭 (注：对 numpy.ndarray 通过“.conj().T”)\n",
"\n",
"# 1.6 画图\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. 常用参数"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# 2.1 用于构造量子电路\n",
"\n",
"N = 3 # 量子电路量子比特数\n",
"DEPTH = 2 # 量子电路深度 (层数)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# 2.2 迭代优化参数\n",
"\n",
"ITR = 200 # 迭代次数 \n",
"LR = 0.2 # 学习速率 \n",
"SEED = 1 # 随机种子 \n",
"paddle.seed(SEED) # paddle种子\n",
"np.random.seed(SEED) # numpy种子"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. Numpy 矩阵相关"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# 3.1 随机幺正矩阵\n",
"V = unitary_group.rvs(2) # 随机 2*2 V"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# 3.2 对角矩阵\n",
"D = np.diag([0.2, 0.8])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# 3.3 复共轭\n",
"V_dagger = V.conj().T"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# 3.4 矩阵乘法：@\n",
"H = (V @ D @ V_dagger)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.9999999999999998-8.239936510889834e-18j)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 3.5 迹\n",
"H.trace()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.2, 0.8])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 3.6 特征值\n",
"np.linalg.eigh(H)[0]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# 3.7 张量积： A \\otimes B\n",
"A = np.eye(2)\n",
"B = H\n",
"T = np.kron(A, B)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- 注：在量桨中，可以通过字符串形式构建 $n$ 量子比特泡利矩阵。"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# 例: 0.4*I⊗Z+0.4*Z⊗I+0.2*X⊗X\n",
"# 文字形式: 0.4*kron(I, Z) + 0.4*kron(Z, I) + 0.2*kron(X, X)\n",
"H_info = [[0.4, 'z0'], [0.4, 'z1'], [0.2, 'x0,x1']]\n",
"H_matrix = pauli_str_to_matrix(H_info, 3) # 3 量子比特泡利矩阵"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4. 量子态相关"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"# 4.1 得到纯态 (np.ndarray 形式的行向量)\n",
"\n",
"initial_state_pure1 = vec(0, N) # 得到 |00…0>, 2**N 维行向量\n",
"initial_state_pure2 = vec_random(N) # 得到随机纯态，行向量"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# 4.2 得到混态(np.ndarray 形式）\n",
"\n",
"initial_state_mixed1 = density_op(N) # 得到 |00…0><00…0|\n",
"initial_state_mixed2 = density_op_random(N, real_or_complex=2, rank=4) # 得到随机密度矩阵，可选择为实数或复数，可选择秩\n",
"initial_state_mixed3 = completely_mixed_computational(N) # 得到最大混态 "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 5. 量子电路相关"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# 5.1 创建 N 量子比特电路\n",
"cir = UAnsatz(N)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"# 5.2 添加量子门 —— 具体见第7节\n",
"# 例：添加CNOT门到前两个量子比特\n",
"cir.cnot([0, 1])"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"# 5.3 输出量子态\n",
"# 输出向量形式量子态（paddle.Tensor）。\n",
"# 注：此处输出态shape并不是向量，可通过paddle.reshape(final_state, [2**N, 1])转化为列向量 —— 在后续版本中将进一步优化。\n",
"\n",
"# 初始态为 |00...0>\n",
"final_state = cir.run_state_vector()\n",
"# 初始态非 |00...0>\n",
"initial_state_pure = paddle.to_tensor(initial_state_pure2)\n",
"final_state_pure = cir.run_state_vector(initial_state_pure)\n",
"# 化为 numpy 列向量形式\n",
"final_state_pure_np = cir.run_state_vector().reshape([2**N, 1]).numpy()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"# 初始态为 |00…0><00…0|\n",
"cir.run_density_matrix()\n",
"# 初始态非 |00...0><00…0|\n",
"initial_state_mixed = paddle.to_tensor(initial_state_mixed2)\n",
"final_state_mixed = cir.run_density_matrix(initial_state_mixed)\n",
"# 改变为 numpy 矩阵形式\n",
"final_state_mixed_np = cir.run_density_matrix().numpy()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 1., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 1., 0., 0., 0., 0., 0.],\n",
" [0., 0., 0., 1., 0., 0., 0., 0.],\n",
" [0., 0., 0., 0., 0., 0., 1., 0.],\n",
" [0., 0., 0., 0., 0., 0., 0., 1.],\n",
" [0., 0., 0., 0., 1., 0., 0., 0.],\n",
" [0., 0., 0., 0., 0., 1., 0., 0.]])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 5.4 量子电路对应幺正矩阵 (paddle.Tensor)\n",
"cir.U\n",
"# 改变为 numpy 矩阵形式\n",
"cir.U.numpy()\n",
"# 仅保留实数部分\n",
"cir.U.real()\n",
"cir.U.numpy().real"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"--*--\n",
" | \n",
"--x--\n",
" \n",
"-----\n",
" \n"
]
}
],
"source": [
"# 5.5 打印量子电路\n",
"print(cir)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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o1x0043iLXpIDkjy2/Tpg1nnmk2SfWWeQZsWrhsZI8hngbcAHq+on7brdgd8CTquqI2YYb6wk11TVo2b4+YcB76C5OXDLDYRLgduBl1XVlbNJNrckX6mq5YsgxwE0U68A3FpV/zbLPPNJsk9VfX/GGUIzt9ndPzfgc4v5nqQkv1hVX5p1ji0sgjGSXF9VK7Z3bBqSPHPcEPCOqloyzTxbBUi+ALy0qj47tP4I4J1V9eiZBGsyvGLcEPD7VTWzw38W6II//ynAOcD1bP1zeyjNz+1js8o2l1n/3IbtFHMNzcgVSc6hmR11y+R5y2juhP78zFI13g/8LTCqxfeecpZh9xkuAYCquizJfWYRaMD/AN4M3DlibNaHSc9lfIG+B1isBTrrQ2p/ARxVVTcNrkxyMLAWePgsQrUZzho3BNx/ilHmZRGM93ya5yX8IVvvcm65I3qWrgb+rKq+ODyQ5KgZ5Bn00SQfAd7L1gX6fODimaVqXAlcVFVXDA8kefEM8gyyQBdmD5qZjYfdCuw55SzDXgS8ErhjxNhJU84yJw8N7YSS/Cpwc1V9ZcTYyqpaN4NYgxmOpXnWxFYFWlVrZ5cKkjwM+FZVbTMNcJIDZnk8vv3r8RcYXaA3VtWpM8z2L8DvjCnQW6pq2YiXTUWS1wDPpnneyeDP7UTgwqr6kxlm+wTw2qr6lxFjN1bVwTOINZJFMEY7G+opwPFs/Qvtw8C7qurHM4qmXdQiL9DbqmrziLGZFmib4eGM/rmtn12q5rJz4IdV9YNZ5piERTBGkvNpTtSdxz27nktpzhHsV1XPmVG0wZJ6BvBz7epFX1JJVlfVqvm3nL7FnE3qmkUwRpIvV9Uh2zs2DYu8pMZdeRPgqqpaOs08WwVY3NnuB7yG5i/bA2guBPgGTbm/sapuXwTZjgcetJiyzSXJR6vq2FnnGGWxZfNk8Xi3Jfkt4O+r6i6AJLvR3Efw7Zkmg8eNKKJNwGVJvjyLQAM2AzfT/HLdotrlB80k0T0Wc7YLgU8AT6yqrwMk+Vnghe3YU2YX7e5sRw5le8GssyV57Lgh4LApRtk2wCLONsw9gjHau4ffBDyR5q9vaC75+iRwelXdOJNgQJLLgLcwuqReUVXDz4aeZrbrgSePOZE96xOLiznbhqp62PaOTcMiz/YT4J/Zuty3OKKq7j3lSHdbzNmGuUcwRlXdlOT1NPcMbHWyeJYl0DqRpqTOTnJ7u+7+NCU164f7vA14ALDNL1vgT6cbZRtvY/FmuznJ7wHnbTn52t5l/ELuuRpmVhZztuto7r+4fnggidkm5B7BGEn+G80v1QvY+o7FE4ELquqNs8oGY6+U+HBVXTe7VI0kv8joqzjMNkaSBwCn02Tbcpjq32juW3ljVc3scOQiz3YCcE1VbRgxdnxVXTT9VHd//qLNNswiGKM91v6I4Stw2ucvXzvjKSYWbUm1fzk+t802eCLbbAuU5EVV9Z5Z5xjFbAuz2LJZBGMk+RLw61V189D6hwAfm/Fx0cVcUmbbwRbbvDSDzLYwiy2b5wjGOw34eHuCccvxvOU0k1nN7C7P1l009w/cPLT+we3YLJltAZJcPW6I5nLSmTHbwizmbMMsgjGq6uIkh7Dt9LaXb5mWeoZOY/GW1GmYbSEOAH6dbS9NDrDNFAVTZraFWczZtmIRzKG9NPOyWecYtphLymwL9o/APlX1heGBJJdOPc3WzLYwiznbVjxHIEk9N+spZCVJM2YRSFLPWQTapSVZmuTDSa5PckOStye51wSvG/kc3iRnbnn4T5LTkvzMmO2eluTzSa5Ksj7JS9v1xyc5dILPn2g7aUewCLTLShLgQzRPJVsBrADuzU8xnURVnVFV/7tdPA3YpgiS7AmsBn6zfUbzY4BL2+HjgUl+wU+6nfRT82SxdllJngy8rqr+48C6+9LcR7AMOAFYueXpX0n+keYRoJe2ewR/RTOz5teBE6tqc5Jzaa4G+Tngz4ANwDer6okDn7Ef8CXgIVX1/wbW/0r72u+0X88CngSsAvYCNgK/TTMz5fB2AGcDS4AfAC+pqi/tkB+Ues89Au3KHgFs9XjFqvoucBPNvQNzuQ+wrqoeQTOD5OuG3ucs4Ks000Y/cWjsNpp5eG5Ocn6Sk5Ps1j6ycA3w6qo6rKr+FfhQVf1yu+dwHXDKmO1W0zwu8nHAq4BztvunIY3hfQTSaHcB72+//xuaQ0wTq6oXJ3kUcBTNL+6jaWbrHPbIJG+gmT12H+CS4Q2S7AP8CvCB5mgXAPOe55AmZRFoV7ae5vDP3dpDQz9Lc0jnkWy9V7z3HO+13cdQq+oa4Jok7wNuZHQRnAscX1VXJXkhcOSIbXYDbq+qw7Y3gzQJDw1pV/Zx4GeSPB8gye40D/R5e3vs/ibgsCS7JVlGc8fxFrtxT4k8F/i/I97/e8C+wyuT7JPkyIFVh3HP/EbDr9kX+Fp7gvnkUe/dHs66sX1iHmk8eq7/uLQ9LALtsqq5EuIZwAnt/ELfAu6qqj9uN/k0zV/q64GzgCsHXv7vwOFJvkhzQvfMER+xGrg4ySeH1gf4vSQbknwB+EPu2Ru4AHh1e2npLwB/AHy2zTJ48nd4u5OBU5JcBVxL82wAaYfwqiH1RnvVzvnAM6rqyvm2l/rCIpCknvPQkCT1nEUgST1nEUhSz1kEktRzFoEk9ZxFIEk99/8BBCQxoFHMDJwAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# 5.6 测量结果\n",
"res = cir.measure(shots=0, plot=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 6. 量子门旋转角参数\n",
"&emsp;注： \n",
"- 单量子比特门总可以由绕轴旋转表示，由旋转轴与旋转角度决定。\n",
"- 量桨中旋转轴通常设置为 $x,y,z$-轴。\n",
"- 旋转角度是量子神经网络的可变参数，**需要设置为 paddle.Tensor 形式**."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"# 6.1 单个旋转角度\n",
"\n",
"phi, theta, omega = 2 * np.pi * np.random.uniform(size=3) # 随机旋转角度，服从均匀分布\n",
"# 变为 paddle.Tensor 形式\n",
"phi = paddle.to_tensor(phi, dtype='float64')"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"# 6.2 数组形式旋转角度\n",
"# 一维数组\n",
"\n",
"theta = np.array([np.pi, 2 ,3, 5]) # 4个角度均不相同\n",
"theta = np.full([4], np.pi) # 4个角度均等于pi\n",
"# 变为 paddle.Tensor 形式\n",
"phi = paddle.to_tensor(theta)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"# 高维数组\n",
"\n",
"theta = np.random.randn(DEPTH, N, 3) # 一个三维 np.ndarray"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"对于一种常用的量子神经网络: ‘cir.complex_entangled_layer(theta, DEPTH)’，具体见[这里](https://qml.baidu.com/quick-start/quantum-neural-network.html), theta 需要为(DEPTH, N, OTHER=3)形式。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 7. 添加量子门操作"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"# 7.1 添加单比特量子门 \n",
"# 注意旋转角度需要 paddle.Tensor 形式。\n",
"# 下标对于旋转轴，第一个参数为旋转角度，第二个参数为作用于第几个量子比特\n",
"\n",
"cir.rz(theta[0], 0)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"# 7.2 添加双量子比特门\n",
"\n",
"cir.cnot([0, 1])"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"# 7.3 一些常用的量子门\n",
"\n",
"# 对每一个量子比特添加 Hadamard 门\n",
"cir.superposition_layer()\n",
"# 对每一个量子比特添加 Ry(pi/4) 门\n",
"cir.weak_superposition_layer()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"广义旋转门，基于欧拉角表示，以及对于量子电路具体见[这里](https://qml.baidu.com/quick-start/quantum-neural-network.html)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 8. 变分量子算法基本框架（1）—— 构建量子电路（函数形式）\n",
"- 步骤1：构建 N 量子比特线路\n",
"- 步骤2：对每一层添加量子门"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"def circuit(N, DEPTH, theta):\n",
" \"\"\"\n",
" 输入数据:\n",
" N, 量子比特数\n",
" DEPTH, 电路层数\n",
" theta, [N, DEPTH, 2], 3维数组，数据类型：paddle.Tensor\n",
" 返回数据:\n",
" cir, 最终量子电路\n",
" \"\"\"\n",
" # 步骤1：构建N量子比特线路\n",
" cir = UAnsatz(N)\n",
" # 步骤1：对每一层添加量子门\n",
" for dep in range(DEPTH):\n",
" for n in range(N):\n",
" cir.rx(theta[n][dep][0], n) # 对第 n 个量子比特添加 Rx 门\n",
" cir.rz(theta[n][dep][1], n) # 对第 n 个量子比特添加 Rz 门\n",
" for n in range(N - 1):\n",
" cir.cnot([n, n + 1]) # 对每一对临近量子比特添加CNOT门\n",
"\n",
" return cir"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"--Rx(0.069)----Rz(0.473)----*----Rx(-0.65)----Rz(-0.77)-----------------*-------\n",
" | | \n",
"--Rx(-0.77)----Rz(0.623)----x--------*--------Rx(0.428)----Rz(0.074)----x----*--\n",
" | | \n",
"--Rx(-0.45)----Rz(0.604)-------------x--------Rx(2.385)----Rz(-0.12)---------x--\n",
" \n"
]
}
],
"source": [
"# 以下为一个例子，包含3量子比特，两层，可调参数随机产生：\n",
"theta = paddle.to_tensor(np.random.randn(N, DEPTH, 2))\n",
"cir = circuit(N, DEPTH, theta)\n",
"print(cir)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 9. 变分量子算法基本框架（2）—— 设置并计算损失函数\n",
"- 此处我们使用 “-fidelity” 作为损失函数。当输出态为我们想要的量子态时，损失函数达到最小。\n",
"- 注：量子神经网络优化在 Python 中总可以通过迭代器实现，要注意 theta 需要是 paddle.Tensor 形式"
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"class StatePrepNet(paddle.nn.Layer):\n",
" # 步骤1：给出量子神经网络初始值: def __init__(…)\n",
" def __init__(self, N, DEPTH, psi, dtype='float64'):\n",
" # N, DEPTH: 电路参数\n",
" # psi: 目标量子态，数据类型：numpy行向量\n",
" super(StatePrepNet, self).__init__()\n",
" self.N = N\n",
" self.DEPTH = DEPTH\n",
" # 量子电路可调参数初始化随机产生\n",
" self.theta = self.create_parameter(shape=[self.N, self.DEPTH, 2],\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0., high=2 * np.pi), \n",
" dtype=dtype, is_bias=False)\n",
" # 目标量子态，用于计算损失函数(需要 paddle.Tensor 类型)\n",
" self.psi = paddle.to_tensor(psi)\n",
" # 步骤2：计算损失函数L = - <psi_out | psi><psi | psi_out>\n",
" # 注：由于需要最小化损失函数，取“-fidelity”\n",
" def forward(self):\n",
" # 构建量子电路，参数随迭代改变\n",
" cir = circuit(self.N, self.DEPTH, self.theta)\n",
" # 得到此量子电路输出量子态\n",
" psi_out = cir.run_state_vector()\n",
" psi_out = paddle.reshape(psi_out, [2 ** self.N, 1]) # reshape to ket\n",
" # 计算损失函数: L = - <psi_out | psi><psi | psi_out>\n",
" inner = matmul(self.psi, psi_out)\n",
" loss = - paddle.real(matmul(inner, dagger(inner)))[0] # 改变shape为tensor([1])\n",
" \n",
" return loss, cir"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 10. 变分量子算法基本框架（3）—— 通过优化器优化参数\n",
"- 此处我们对制备3量子比特 $|01\\rangle\\otimes|+\\rangle$ 为例，使用的量子电路有上述 “8. 量子神经网络算法基本框架” 部分给出。\n",
"- 通常我们选 Adam 为优化器。\n",
"- 首先我们给出一些训练用的参数。"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"N = 3 # 目标量子比特数\n",
"DEPTH = 2 # 量子电路层数\n",
"ITR = 115 # 学习迭代次数\n",
"LR = 0.2 # 学习速率"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"# 目标量子态，取 numpy 行向量形式\n",
"psi_target = np.kron(np.kron(np.array([[1,0]]), np.array([[0,1]])), np.array([[1/np.sqrt(2), 1/np.sqrt(2)]])) # <01+|"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"# 10.1 记录迭代中间过程\n",
"loss_list = []\n",
"parameter_list = []"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"# 10.2 构造迭代器\n",
"# (N=3, DEPTH=2, ITR=110, LR=0.2)\n",
"myLayer = StatePrepNet(N, DEPTH, psi_target)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"# 10.3 选择优化器\n",
"# 通常使用 Adam。\n",
"opt = paddle.optimizer.Adam(learning_rate = LR, parameters = myLayer.parameters()) "
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"iter: 0 loss: -0.0176\n",
"iter: 10 loss: -0.8356\n",
"iter: 20 loss: -0.9503\n",
"iter: 30 loss: -0.9837\n",
"iter: 40 loss: -0.9971\n",
"iter: 50 loss: -0.9974\n",
"iter: 60 loss: -0.9995\n",
"iter: 70 loss: -0.9999\n",
"iter: 80 loss: -0.9999\n",
"iter: 90 loss: -1.0000\n",
"iter: 100 loss: -1.0000\n",
"iter: 110 loss: -1.0000\n"
]
}
],
"source": [
"# 10.4 迭代优化\n",
"for itr in range(ITR):\n",
" # 计算损失函数\n",
" loss = myLayer()[0]\n",
" # 通过梯度下降算法优化\n",
" loss.backward()\n",
" opt.minimize(loss)\n",
" opt.clear_grad()\n",
" # 记录学习曲线\n",
" loss_list.append(loss.numpy()[0])\n",
" parameter_list.append(myLayer.parameters()[0].numpy())\n",
" if itr % 10 == 0:\n",
" print('iter:', itr, ' loss: %.4f' % loss.numpy())"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The minimum of the loss function: -0.9999873168488457\n",
"Parameters after optimizationL theta:\n",
" [[[-0.00816927 7.41571003]\n",
" [ 6.28197865 0.29031951]]\n",
"\n",
" [[ 3.14801248 6.1562368 ]\n",
" [ 6.2890315 4.08082862]]\n",
"\n",
" [[ 4.57489065 1.58064113]\n",
" [ 4.78145659 3.28051687]]]\n",
"--Rx(-0.00)----Rz(7.416)----*----Rx(6.282)----Rz(0.290)-----------------*-------\n",
" | | \n",
"--Rx(3.148)----Rz(6.156)----x--------*--------Rx(6.289)----Rz(4.081)----x----*--\n",
" | | \n",
"--Rx(4.575)----Rz(1.581)-------------x--------Rx(4.781)----Rz(3.281)---------x--\n",
" \n",
"state_final:\n",
" [-0.0001236 +1.65203739e-04j -0.00051346-3.22614883e-04j\n",
" 0.09637039-7.00598643e-01j 0.09558872-7.00513830e-01j\n",
" 0.00038931+1.78566178e-04j 0.0003892 +1.76713800e-04j\n",
" 0.00209719+1.98540264e-03j 0.0025603 +1.33735551e-03j]\n"
]
}
],
"source": [
"# 10.5 输出结果\n",
"\n",
"# 输出最终损失函数值\n",
"print('The minimum of the loss function: ', loss_list[-1])\n",
"# 输出最终量子电路参数\n",
"theta_final = parameter_list[-1] # 得到self.theta\n",
"print(\"Parameters after optimizationL theta:\\n\", theta_final)\n",
"# 绘制最终电路与输出量子态\n",
"# 输入量子电路参数需要转化为 paddle.Tensor 类型\n",
"theta_final = paddle.to_tensor(theta_final)\n",
"# 绘制电路\n",
"cir_final = circuit(N, DEPTH, theta_final)\n",
"print(cir_final)\n",
"# 最终得到量子态\n",
"#state_final = cir_final.run_density_matrix()\n",
"state_final = cir_final.run_state_vector()\n",
"print(\"state_final:\\n\", state_final.numpy())"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# 绘制迭代过程中损失函数变化曲线\n",
"plt.figure(1)\n",
"ITR_list = []\n",
"for i in range(ITR):\n",
" ITR_list.append(i)\n",
"func = plt.plot(ITR_list, loss_list, alpha=0.7, marker='', linestyle='-', color='r')\n",
"plt.xlabel('iterations')\n",
"plt.ylabel('loss')\n",
"plt.legend(labels=[\"loss function during iteration\"], loc='best')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**可见，最终 “-fidelity” 变为 “-1”, 此时量子电路已学会如何制备目标量子态 “$|01\\rangle\\otimes|+\\rangle$”。**"
]
}
],
"metadata": {
"interpreter": {
"hash": "b79f688f118b7eec4a7bc67db8fbcf9e8f165bc4247c9c8f9f9067a5de2aa71e"
},
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
introduction/PaddleQuantum_Functions_EN.ipynb 0 → 100644
浏览文件 @ 016af983
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Frequently Used Functions in Paddle Quantum\n",
"\n",
"<em> Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. </em>"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Overview"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In this file, we list some frequently used functions in Paddle Quantum.\n",
"\n",
"You can see other functions in [API](https://qml.baidu.com/api/introduction.html)\n",
"\n",
"Here we will also use preparing a pure state as an example to see how to use Paddle Quantum to realize quantum neural network algorithms."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 1. Import Mudules "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"# 1.1 Import numpy and paddle\n",
"import numpy as np\n",
"import paddle\n",
"\n",
"# 1.2 Create quantum circuit\n",
"from paddle_quantum.circuit import UAnsatz \n",
"\n",
"# 1.3 Create quantum state - in np.ndarray form\n",
"from paddle_quantum.state import vec, vec_random # As vector\n",
"from paddle_quantum.state import density_op, density_op_random, completely_mixed_computational # As matrix\n",
"\n",
"# 1.4 Create Matrix - in np.ndarray form\n",
"from scipy.stats import unitary_group # Random U matrix\n",
"from paddle_quantum.utils import pauli_str_to_matrix # Pauli matrices for n qubits\n",
"\n",
"# 1.5 Matrix calculation with paddle.Tensor\n",
"from paddle import matmul, trace # Calculate the inner product and trace\n",
"from paddle_quantum.utils import dagger # Get dagger of a paddle.Tensor (note: for numpy.ndarray, you can use “.conj().T” to do dagger)\n",
"\n",
"# 1.6 Plot figure\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 2. Often Used Parameters"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# 2.1 Parameters for quantum circuit\n",
"\n",
"N = 3 # Qubits number in Quantum circuit\n",
"DEPTH = 2 # Depth of the quantum circuit (Layers number)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# 2.2 Parameters in the iteration \n",
"\n",
"ITR = 200 # Iteration number \n",
"LR = 0.2 # Learning rate \n",
"SEED = 1 # Random seed \n",
"paddle.seed(SEED) # seed for paddle\n",
"np.random.seed(SEED) # seed for numpy"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 3. Numpy Matrix"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# 3.1 Random unitary gate\n",
"V = unitary_group.rvs(2) # Random 2*2 V"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# 3.2 Diagonal matrix\n",
"D = np.diag([0.2, 0.8])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"# 3.3 Transpose complex conjugate\n",
"V_dagger = V.conj().T"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"# 3.4 Matrix multiplication: @\n",
"H = (V @ D @ V_dagger)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"(0.9999999999999998-8.239936510889834e-18j)"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 3.5 Trace\n",
"H.trace()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([0.2, 0.8])"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 3.6 Eigenvalues\n",
"np.linalg.eigh(H)[0]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [],
"source": [
"# 3.7 Tensor product: A \\otimes B\n",
"A = np.eye(2)\n",
"B = H\n",
"T = np.kron(A, B)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"- Note: in Paddle Quantum, you can use string to create matrix for Pauli matices with $n$ qubit."
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# An example: 0.4*I⊗Z+0.4*Z⊗I+0.2*X⊗X\n",
"# In the string form: 0.4*kron(I, Z) + 0.4*kron(Z, I) + 0.2*kron(X, X)\n",
"H_info = [[0.4, 'z0'], [0.4, 'z1'], [0.2, 'x0,x1']]\n",
"H_matrix = pauli_str_to_matrix(H_info, 3) # pauli matices with 3 qubits"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 4. Quantum States"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [],
"source": [
"# 4.1 Get pure states (a row vector in np.ndarray form)\n",
"\n",
"initial_state_pure1 = vec(0, N) # Get |00…0>, 2**N dimension row vector\n",
"initial_state_pure2 = vec_random(N) # Get random pure state, row vector"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [],
"source": [
"# 4.2 Get mixed states (in np.ndarray form)\n",
"\n",
"initial_state_mixed1 = density_op(N) # Get |00…0><00…0|\n",
"# Get a random density matrix, can decide real or complex and its rank (rank = 1 means pure) \n",
"initial_state_mixed2 = density_op_random(N, real_or_complex=2, rank=4)\n",
"initial_state_mixed3 = completely_mixed_computational(N) # Get a maximally mixed state "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 5. Quantum Circuit"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [],
"source": [
"# 5.1 Create an N qubits quantum circuit\n",
"cir = UAnsatz(N)"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"# 5.2 Add gates to the circuit - see Section 7\n",
"# An example: add a CNOT gate to the first two qubits:\n",
"cir.cnot([0, 1])"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"# 5.3 The output state of the circuit\n",
"# The output state of the circuit as a vector in paddle.Tensor form.\n",
"# Note: the shape of the output here is not a vector. It can be changed to a column vector \n",
" # via function \"paddle.reshape(final_state, [2**N, 1]) —— it will be made better in the next version\n",
"\n",
"# Initial state is |00...0>\n",
"final_state = cir.run_state_vector()\n",
"# Initial state is not |00...0>\n",
"initial_state_pure = paddle.to_tensor(initial_state_pure2)\n",
"final_state_pure = cir.run_state_vector(initial_state_pure)\n",
"# Change to np.array form\n",
"final_state_pure_np = cir.run_state_vector().reshape([2**N, 1]).numpy()"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"# Initial state is |00…0><00…0|\n",
"cir.run_density_matrix()\n",
"# Initial state is not |00...0><00...0|\n",
"initial_state_mixed = paddle.to_tensor(initial_state_mixed2)\n",
"final_state_mixed = cir.run_density_matrix(initial_state_mixed)\n",
"# Change to np.ndarray form\n",
"final_state_mixed_np = cir.run_density_matrix().numpy()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"array([[1., 0., 0., 0., 0., 0., 0., 0.],\n",
" [0., 1., 0., 0., 0., 0., 0., 0.],\n",
" [0., 0., 1., 0., 0., 0., 0., 0.],\n",
" [0., 0., 0., 1., 0., 0., 0., 0.],\n",
" [0., 0., 0., 0., 0., 0., 1., 0.],\n",
" [0., 0., 0., 0., 0., 0., 0., 1.],\n",
" [0., 0., 0., 0., 1., 0., 0., 0.],\n",
" [0., 0., 0., 0., 0., 1., 0., 0.]])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 5.4 The unitary matrix of the circuit (in paddle.Tensor form)\n",
"cir.U\n",
"# Change to np.ndarray form\n",
"cir.U.numpy()\n",
"# Only keep the real part:\n",
"cir.U.real()\n",
"cir.U.numpy().real"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"--*--\n",
" | \n",
"--x--\n",
" \n",
"-----\n",
" \n"
]
}
],
"source": [
"# 5.5 Print the circuit\n",
"print(cir)"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# 5.6 Measure outcome\n",
"res = cir.measure(shots=0, plot=True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 6. Angles in Quantum Gate\n",
"&emsp;Note: \n",
"- For qubits unitary gate, they can always be characterized by a rotation axis and a rotation angle. \n",
"- The rotation axis in Paddle Quantum is always chosen to be $x,y,z$-axis.\n",
"- The rotation angle will be the variable in QNN tasks, and **they should be given in paddle.Tensor form**."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"# 6.1 A Single Angle\n",
"\n",
"phi, theta, omega = 2 * np.pi * np.random.uniform(size=3) # Generate a random angle\n",
"# change to paddle.Tensor\n",
"phi = paddle.to_tensor(phi, dtype='float64')"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [],
"source": [
"# 6.2 Angles in Arrays\n",
"# 1D arrays\n",
"\n",
"theta = np.array([np.pi, 2 ,3, 5]) # 4 angles are different\n",
"theta = np.full([4], np.pi) # 4 angles all equal to pi\n",
"# change to be paddle.Tensor\n",
"theta = paddle.to_tensor(theta)"
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [],
"source": [
"# Multidimensional Arrays\n",
"\n",
"theta = np.random.randn(DEPTH, N, 3) # A 3D np.ndarray"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For a frequently used quantum circuit: cir.complex_entangled_layer(theta, DEPTH), see \n",
"[here](https://qml.baidu.com/quick-start/quantum-neural-network.html), the shape of theta should be(DEPTH, N, OTHER=3)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 7. Add Quantum Gates to the Circuit"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"# 7.1 Single qubit gates \n",
"# Note: angles should be in paddle.Tensor form.\n",
"# Subscript is the rotating axis, the first parameter is the rotating angle, the second is which qubit it acts\n",
"\n",
"cir.rz(theta[0], 0)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"# # 7.2 Two-qubit gate\n",
"\n",
"cir.cnot([0, 1])"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [],
"source": [
"# 7.3 Some frequently used gates\n",
"\n",
"# Add Hadamard gates to each qubit\n",
"cir.superposition_layer()\n",
"# Add a Ry(pi/4) rotation to each qubit\n",
"cir.weak_superposition_layer()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"General rotation gate in Euler representation, and the corresponding circuit click [here](https://qml.baidu.com/quick-start/quantum-neural-network.html)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 8. VQA basic structure (1) -- Create your own quantum circuit as a function\n",
"- step 1: Create an N qubit circuit;\n",
"- step 2: Add gates to each layer"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [],
"source": [
"def circuit(N, DEPTH, theta):\n",
" \"\"\"\n",
" Input data:\n",
" N, qubits number\n",
" DEPTH, layers number\n",
" theta, [N, DEPTH, 2], 3D matrix in paddle.Tensor form\n",
" Return:\n",
" cir, the final circuit\n",
" \"\"\"\n",
" # step 1: Create an N qubit circuit\n",
" cir = UAnsatz(N)\n",
" # step 2: Add gates to each layer\n",
" for dep in range(DEPTH):\n",
" for n in range(N):\n",
" cir.rx(theta[n][dep][0], n) # add an Rx gate to the n-th qubit\n",
" cir.rz(theta[n][dep][1], n) # add an Rz gate to the n-th qubit\n",
" for n in range(N - 1):\n",
" cir.cnot([n, n + 1]) # add CNOT gate to every neighbor pair\n",
"\n",
" return cir"
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"--Rx(0.069)----Rz(0.473)----*----Rx(-0.65)----Rz(-0.77)-----------------*-------\n",
" | | \n",
"--Rx(-0.77)----Rz(0.623)----x--------*--------Rx(0.428)----Rz(0.074)----x----*--\n",
" | | \n",
"--Rx(-0.45)----Rz(0.604)-------------x--------Rx(2.385)----Rz(-0.12)---------x--\n",
" \n"
]
}
],
"source": [
"# Here is the printed final circuit for (N=3, DEPTH=2, theta is randomly generated):\n",
"theta = paddle.to_tensor(np.random.randn(N, DEPTH, 2))\n",
"theta = paddle.to_tensor(theta)\n",
"cir = circuit(N, DEPTH, theta)\n",
"print(cir)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 9. VQA basic structure (2) -- forward part, calculate the loss function\n",
"- QNN optimization can be done with a Python Iterator, here is an example for preparing quantum state;\n",
"- In forward part, all variables should be always in paddle.Tensor form."
]
},
{
"cell_type": "code",
"execution_count": 29,
"metadata": {},
"outputs": [],
"source": [
"class StatePrepNet(paddle.nn.Layer):\n",
" # Step 1: Give the initial input: def __init__(…)\n",
" # Here you need to give the parameters for creating your quantum circuit and loss\n",
" def __init__(self, N, DEPTH, psi, dtype='float64'):\n",
" # N, DEPTH: circuit parameter\n",
" # psi: target output pure state, np.row_vector form\n",
" super(StatePrepNet, self).__init__()\n",
" self.N = N\n",
" self.DEPTH = DEPTH\n",
" # The initial circuit parameter theta is generated randomly\n",
" self.theta = self.create_parameter(shape=[self.N, self.DEPTH, 2],\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0., high=2 * np.pi), \n",
" dtype=dtype, is_bias=False)\n",
" # Target output state, used for loss function\n",
" self.psi = paddle.to_tensor(psi)\n",
" # Step 2: Calculate the loss function: L = - <psi_out | psi><psi | psi_out>\n",
" # note: here we want to minimize the loss function, so we use “-Fidelity”\n",
" def forward(self):\n",
" # Create the quantum circuit\n",
" cir = circuit(self.N, self.DEPTH, self.theta)\n",
" # Get the final state\n",
" psi_out = cir.run_state_vector()\n",
" psi_out = paddle.reshape(psi_out, [2 ** self.N, 1]) # reshape to ket\n",
" # Calculate the loss function: L = - <psi_out | psi><psi | psi_out>\n",
" inner = matmul(self.psi, psi_out)\n",
" loss = - paddle.real(matmul(inner, dagger(inner)))[0] # change to shape tensor([1])\n",
"\n",
" return loss, cir"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 10. VQA basic structure (3) -- backward part, optimize over iteration\n",
"- Here we still use preparing a 3-qubit pure state $|01\\rangle\\otimes|+\\rangle$ as an example, and the circuit we use is given in section 8.\n",
"- Usually we use Adam as the optimizer."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"N = 3 # Qubits number in Quantum circuit\n",
"DEPTH = 2 # Depth of the quantum circuit (Layers number)\n",
"ITR = 115 # Iteration number \n",
"LR = 0.2 # Learning rate "
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {},
"outputs": [],
"source": [
"# target output state, np.ndarray row vector\n",
"psi_target = np.kron(np.kron(np.array([[1,0]]), np.array([[0,1]])), np.array([[1/np.sqrt(2), 1/np.sqrt(2)]])) # <01+|"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [],
"source": [
"# 10.1 Record the iteration\n",
"loss_list = []\n",
"parameter_list = []"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [],
"source": [
"# 10.2 Use Iterator defined in section 9\n",
"# (N=3, DEPTH=2, ITR=110, LR=0.2)\n",
"myLayer = StatePrepNet(N, DEPTH, psi_target)"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [],
"source": [
"# 10.3 Choose the optimizer\n",
"# Usually we use Adam.\n",
"opt = paddle.optimizer.Adam(learning_rate = LR, parameters = myLayer.parameters()) "
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"iter: 0 loss: -0.0176\n",
"iter: 10 loss: -0.8356\n",
"iter: 20 loss: -0.9503\n",
"iter: 30 loss: -0.9837\n",
"iter: 40 loss: -0.9971\n",
"iter: 50 loss: -0.9974\n",
"iter: 60 loss: -0.9995\n",
"iter: 70 loss: -0.9999\n",
"iter: 80 loss: -0.9999\n",
"iter: 90 loss: -1.0000\n",
"iter: 100 loss: -1.0000\n",
"iter: 110 loss: -1.0000\n"
]
}
],
"source": [
"# 10.4 Optimize during iteration\n",
"for itr in range(ITR):\n",
" # Use forward part to calculate the loss function\n",
" loss = myLayer()[0]\n",
" # Backward optimize via Gradient descent algorithm\n",
" loss.backward()\n",
" opt.minimize(loss)\n",
" opt.clear_grad()\n",
" # Record the learning curve\n",
" loss_list.append(loss.numpy()[0])\n",
" parameter_list.append(myLayer.parameters()[0].numpy())\n",
" if itr % 10 == 0:\n",
" print('iter:', itr, ' loss: %.4f' % loss.numpy())"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The minimum of the loss function: -0.9999873168488457\n",
"Parameters after optimizationL theta:\n",
" [[[-0.00816927 7.41571003]\n",
" [ 6.28197865 0.29031951]]\n",
"\n",
" [[ 3.14801248 6.1562368 ]\n",
" [ 6.2890315 4.08082862]]\n",
"\n",
" [[ 4.57489065 1.58064113]\n",
" [ 4.78145659 3.28051687]]]\n",
"--Rx(-0.00)----Rz(7.416)----*----Rx(6.282)----Rz(0.290)-----------------*-------\n",
" | | \n",
"--Rx(3.148)----Rz(6.156)----x--------*--------Rx(6.289)----Rz(4.081)----x----*--\n",
" | | \n",
"--Rx(4.575)----Rz(1.581)-------------x--------Rx(4.781)----Rz(3.281)---------x--\n",
" \n",
"state_final:\n",
" [-0.0001236 +1.65203739e-04j -0.00051346-3.22614883e-04j\n",
" 0.09637039-7.00598643e-01j 0.09558872-7.00513830e-01j\n",
" 0.00038931+1.78566178e-04j 0.0003892 +1.76713800e-04j\n",
" 0.00209719+1.98540264e-03j 0.0025603 +1.33735551e-03j]\n"
]
}
],
"source": [
"# 10.5 Print the output\n",
"\n",
"print('The minimum of the loss function: ', loss_list[-1])\n",
"# The parameters after optimization\n",
"theta_opt = parameter_list[-1] # Get self.theta\n",
"print(\"Parameters after optimizationL theta:\\n\", theta_opt)\n",
"# Draw the circuit picture and the output state\n",
"# Get theta\n",
"theta_final = parameter_list[-1]\n",
"theta_final = paddle.to_tensor(theta_final)\n",
"# Print the circuit\n",
"cir_final = circuit(N, DEPTH, theta_final)\n",
"print(cir_final)\n",
"# Print the final state\n",
"#state_final = cir_final.run_density_matrix()\n",
"state_final = cir_final.run_state_vector()\n",
"print(\"state_final:\\n\", state_final.numpy())"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Print the loss function during iteration\n",
"plt.figure(1)\n",
"ITR_list = []\n",
"for i in range(ITR):\n",
" ITR_list.append(i)\n",
"func = plt.plot(ITR_list, loss_list, alpha=0.7, marker='', linestyle='-', color='r')\n",
"plt.xlabel('iterations')\n",
"plt.ylabel('loss')\n",
"plt.legend(labels=[\"loss function during iteration\"], loc='best')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**As the \"-Fidelity\" becomes \"-1\", this circuit learns to prepare the target state \"$|01\\rangle\\otimes|+\\rangle$\".**"
]
}
],
"metadata": {
"interpreter": {
"hash": "b79f688f118b7eec4a7bc67db8fbcf9e8f165bc4247c9c8f9f9067a5de2aa71e"
},
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
introduction/PaddleQuantum_GPU_CN.ipynb
浏览文件 @ 016af983
...@@ -137,7 +137,11 @@ ...@@ -137,7 +137,11 @@
"source": [ "source": [
"我们可以在命令行中输入`nvidia-smi`来查看 GPU 的使用情况，包括有哪些程序在哪些 GPU 上运行，以及其显存占用情况。\n", "我们可以在命令行中输入`nvidia-smi`来查看 GPU 的使用情况，包括有哪些程序在哪些 GPU 上运行，以及其显存占用情况。\n",
"\n", "\n",
"这里，我们以 [VQE](../tutorial/quantum_simulation/VQE_CN.ipynb) 为例来说明我们该如何使用 GPU。首先，导入相关的包并定义相关的变量和函数。" "这里我们以变分量子本征求解器（Variational Quantum Eigensolver, [VQE](/tutorials/quantum-simulation/variational-quantum-eigensolver.html) ）为例来说明我们该如何使用GPU。简单来说，它利用参数化的电路搜寻广阔的希尔伯特空间，并利用经典机器学习中的梯度下降来找到最优参数，并接近一个哈密顿量（Hamiltonian）的基态（也就是找到一个埃尔米特矩阵的最小本征值）。此处哈密顿量由以下 H2_generator() 函数给出，使用的量子神经网络架构如下图所示：\n",
"\n",
"![circuit](./figures/gpu-fig-circuit.jpg)\n",
"\n",
"首先，导入相关的包并定义相关的变量和函数："
] ]
}, },
{ {
...@@ -398,7 +402,7 @@ ...@@ -398,7 +402,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.3" "version": "3.7.10"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
introduction/PaddleQuantum_GPU_EN.ipynb
浏览文件 @ 016af983
...@@ -142,7 +142,12 @@ ...@@ -142,7 +142,12 @@
"source": [ "source": [
"We can enter `nvidia-smi` in the command line to view the usage of the GPU, including which programs are running on which GPUs, and its memory usage.\n", "We can enter `nvidia-smi` in the command line to view the usage of the GPU, including which programs are running on which GPUs, and its memory usage.\n",
"\n", "\n",
"Here, we take [VQE](../tutorial/quantum_simulation/VQE_EN.ipynb) as an example to illustrate how we should use GPU. First, import the related packages and define some variables and functions." "Here, we take Variational Quantum Eigensolver ([VQE](/tutorials/quantum-simulation/variational-quantum-eigensolver.html)) as an example to illustrate how we should use GPU. \n",
"For simplicity, VQA use a parameterized quantum circuit to search the vast Hilbert space, and uses the gradient descent method to find the optimal parameters, to get close to the ground state of a Hamiltonian (the smallest eigenvalue of the Hermitian matrix). The Hamiltonian in our example is given by the following H2_generator() function, and the quantum neural network has the following structure:\n",
"\n",
"![circuit](./figures/gpu-fig-circuit.jpg)\n",
"\n",
"First, import the related packages and define some variables and functions:"
] ]
}, },
{ {
...@@ -405,7 +410,7 @@ ...@@ -405,7 +410,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.3" "version": "3.7.10"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
introduction/PaddleQuantum_Qchem_Tutorial_CN.ipynb 0 → 100644
浏览文件 @ 016af983
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 利用 Paddle Quantum 的 qchem 模块进行量子化学计算\n",
"_Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved._\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"qchem 是基于 Paddle Quantum 推出的用于量子化学研究的工具集。qchem 为量子化学领域的研究者提供了一系列工具，使他们可以利用量子计算方法完成量子化学任务。与此同时，qchem 也提供了方便开发者进行功能拓展的方式。目前，qchem 正处于开发之中，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。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 分子基态能量计算\n",
"qchem 提供了 `run_chem` 函数来计算给定分子的基态能量和基态波函数。让我们通过计算氢分子基态能量的例子来了解一下整个计算过程。首先，让我们导入需要用的函数。"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from paddle_quantum import qchem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"接下来，让我们把与计算相关的信息输入到 `run_chem` 函数中，这些信息包括：分子的几何结构、分子的电荷、计算需要用到的量子化学基函数等。"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# define the geometry of hydrogen molecule, length unit use angstrom.\n",
"h2_geometry = [(\"H\", [0.0, 0.0, 0.0]), (\"H\", [0.0, 0.0, 0.74])]\n",
"charge = 0\n",
"basis_set = \"sto-3g\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"现在，我们需要选择一种多体波函数的量子线路模版来作为基态能量计算中的变分波函数。目前，qchem 提供了两种模式，分别是 \"hardware efficient\" [<sup>1</sup>](#refer-1) 和 \"hartree fock\" [<sup>2</sup>](#refer-2) ，更多的模式正在开发中，很快也会上线。"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# call run_chem function with \"hardware efficient\" ansatz.\n",
"h2_gs_en, h2_wf_model = qchem.run_chem(\n",
" h2_geometry,\n",
" \"hardware efficient\",\n",
" basis_set, \n",
" charge\n",
")\n",
"\n",
"# additional information for optimizer can be passed using `optimizer_option` keyword argument.\n",
"h2_gs_en, h2_wf_model = qchem.run_chem(\n",
" h2_geometry,\n",
" \"hardware efficient\",\n",
" basis_set, \n",
" charge,\n",
" optimizer_option={\"learning_rate\": 0.6, \"weight_decay\": 0.9}\n",
")\n",
"\n",
"# additional information for ansatz can be passed using `ansatz_option` keyword argument, e.g.\n",
"# \"hardware efficient\" ansatz has a parameter \"cir_depth\", which can be used to specify the depth\n",
"# of quantum circuit.\n",
"h2_gs_en, h2_wf_model = qchem.run_chem(\n",
" h2_geometry,\n",
" \"hardware efficient\",\n",
" basis_set, \n",
" charge,\n",
" ansatz_option={\"cir_depth\": 5}\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"除了上面这些参数，我们也可以通过给定 `max_iters` 和 `a_tol` 来控制训练过程的迭代次数和收敛条件。如果想使用 \"hartree fock\" 量子线路，我们只需要把上面代码中的 \"hardware efficient\" 替换为 \"hartree fock\" 就可以了。我们也可以通过 `print(h2_wf_model.circuit)` 的方法来查看氢分子波函数的量子线路。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 自定义量子线路\n",
"在 qchem 中，我们也为感兴趣的使用者提供了自定义量子线路的方法。我们只需要继承 qchem 中的 Qmodel 类就可以像在 paddlepaddle 中定义神经网络一样定义波函数对应的量子线路。"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from paddle_quantum.circuit import UAnsatz\n",
"from paddle_quantum import qchem\n",
"from paddle_quantum.qchem.layers import CrossResonanceLayer, EulerRotationLayer\n",
"\n",
"\n",
"# Your own model should inherit from `Qmodel`.\n",
"## NOTE: THIS MODEL IS ONLY DEFINED FOR DEMONSTRATION PURPOSE! \n",
"class MyAnsatz(qchem.QModel):\n",
" def __init__(self, n_qubits):\n",
" super().__init__(n_qubits)\n",
"\n",
" self.entangle = CrossResonanceLayer(self._n_qubit)\n",
" self.rot = EulerRotationLayer(self._n_qubit)\n",
"\n",
" def forward(self, state):\n",
" self._circuit = UAnsatz(self.n_qubit)\n",
"\n",
" out = self.entangle(state)\n",
" self._circuit += self.entangle.circuit\n",
"\n",
" out = self.rot(out)\n",
" self._circuit += self.rot.circuit\n",
"\n",
" out = self.entangle(out)\n",
" self._circuit += self.entangle.circuit\n",
"\n",
" return out\n",
"\n",
"# instantiate your model\n",
"my_cir = MyAnsatz(5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"在定义好线路之后，我们就可以利用 paddlepaddle 提供的多种优化器来优化线路中的参数以获得最佳结果。"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# use paddlepaddle's optimizer\n",
"import numpy as np \n",
"import paddle\n",
"\n",
"optimizer = paddle.optimizer.Adam(parameters=my_cir.parameters(), learning_rate=0.08)\n",
"\n",
"# define the loss function\n",
"## NOTE: THIS LOSS FUNCTION IS ONLY DEFINED FOR DEMONSTRATION PURPOSE!\n",
"def loss_fn(state: paddle.Tensor) -> paddle.Tensor:\n",
" return paddle.norm(state.real())\n",
"\n",
"# start learning\n",
"s0 = np.zeros((2**5,), dtype=np.complex128)\n",
"s0[0] = 1.0+0.0j\n",
"s0 = paddle.to_tensor(s0)\n",
"\n",
"for i in range(10):\n",
" loss = loss_fn(my_cir(s0))\n",
" print(f\"At {i:>d}th step: loss={loss.item():>.5f}.\")\n",
"\n",
" optimizer.clear_grad()\n",
" loss.backward()\n",
" optimizer.step()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## 参考文献\n",
"\n",
"[1] Kandala, Abhinav, et al. \"Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets.\" [Nature 549.7671 (2017): 242-246.](https://www.nature.com/articles/nature23879)\n",
"\n",
"[2] Arute, Frank, et al. \"Hartree-Fock on a superconducting qubit quantum computer.\" [Science 369.6507 (2020): 1084-1089.](https://www.science.org/doi/10.1126/science.abb9811)"
]
}
],
"metadata": {
"interpreter": {
"hash": "385f93486cadd2f2140b6b583192a2daa18c8b591e699592075836b347373dd4"
},
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
introduction/PaddleQuantum_Qchem_Tutorial_EN.ipynb 0 → 100644
浏览文件 @ 016af983
{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Quantum Chemistry with Paddle Quantum's qchem\n",
"*Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*\n",
"\n",
"qchem, which builds on top of Paddle Quantum, is designed to be a toolkit for quantum chemistry research in quantum computing era. It provides high level APIs for researchers who are interested in leveraging their current quantum chemsitry calculation with quantum computing power. And it also allows experts to write customized code. qchem is currently under active development, feel free to join us by opening issues or pull requests."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Calculate ground state energy of a molecule\n",
"qchem provides `run_chem` function to calculate the ground state energy and ground state wave function. For example, let's try to calculate the ground state energy of hydrogen molecule. First, we need to import qchem."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from paddle_quantum import qchem"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Then, we need to provide chemical information required by `run_chem` function, including geometry, charge, basis function etc."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# define the geometry of hydrogen molecule, length unit use angstrom.\n",
"h2_geometry = [(\"H\", [0.0, 0.0, 0.0]), (\"H\", [0.0, 0.0, 0.74])]\n",
"charge = 0\n",
"basis_set = \"sto-3g\""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Next, let's choose an ansatz of many-electron wave function for our ground state energy calculation. Currently, you can choose to use \"hardware efficient\" [<sup>1</sup>](#refer-1) or \"hartree fock\" [<sup>2</sup>](#refer-2) ansatz, more functionalities will be released in the future. Let's choose \"hardware efficient\" ansatz."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# call run_chem function with \"hardware efficient\" ansatz.\n",
"h2_gs_en, h2_wf_model = qchem.run_chem(\n",
" h2_geometry,\n",
" \"hardware efficient\",\n",
" basis_set, \n",
" charge\n",
")\n",
"\n",
"# additional information for optimizer can be passed using `optimizer_option` keyword argument.\n",
"h2_gs_en, h2_wf_model = qchem.run_chem(\n",
" h2_geometry,\n",
" \"hardware efficient\",\n",
" basis_set, \n",
" charge,\n",
" optimizer_option={\"learning_rate\": 0.6, \"weight_decay\": 0.9}\n",
")\n",
"\n",
"# additional information for ansatz can be passed using `ansatz_option` keyword argument, e.g.\n",
"# \"hardware efficient\" ansatz has a parameter \"cir_depth\", which can be used to specify the depth\n",
"# of quantum circuit.\n",
"h2_gs_en, h2_wf_model = qchem.run_chem(\n",
" h2_geometry,\n",
" \"hardware efficient\",\n",
" basis_set, \n",
" charge,\n",
" ansatz_option={\"cir_depth\": 5}\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can also specify `max_iters` and `a_tol` keyword arguments to control the maximum iteration cycles and convergence criteria of the optimization process. \n",
"\n",
"To try another ansatz, you just need to replace the ansatz argument to, e.g. \"hartree fock\", and run similar command.\n",
"\n",
"To see the quantum circuit for hydrogen molecule's hardware efficient ansatz, you can run `print(h2_wf_model.circuit)`."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Design your own ansatz\n",
"For those who want to try an ansatz that isn't currently included in qchem, we provide method to write your own ansatz. Writing your own ansatz is similar to defining an neural network in paddlepaddle, except that your ansatz should inherit from `Qmodel`."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"from paddle_quantum.circuit import UAnsatz\n",
"from paddle_quantum import qchem\n",
"from paddle_quantum.qchem.layers import CrossResonanceLayer, EulerRotationLayer\n",
"\n",
"\n",
"# Your own model should inherit from `Qmodel`.\n",
"## NOTE: THIS MODEL IS ONLY DEFINED FOR DEMONSTRATION PURPOSE! \n",
"class MyAnsatz(qchem.QModel):\n",
" def __init__(self, n_qubits):\n",
" super().__init__(n_qubits)\n",
"\n",
" self.entangle = CrossResonanceLayer(self._n_qubit)\n",
" self.rot = EulerRotationLayer(self._n_qubit)\n",
"\n",
" def forward(self, state):\n",
" self._circuit = UAnsatz(self.n_qubit)\n",
"\n",
" out = self.entangle(state)\n",
" self._circuit += self.entangle.circuit\n",
"\n",
" out = self.rot(out)\n",
" self._circuit += self.rot.circuit\n",
"\n",
" out = self.entangle(out)\n",
" self._circuit += self.entangle.circuit\n",
"\n",
" return out\n",
"\n",
"# instantiate your model\n",
"my_cir = MyAnsatz(5)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"You can then follow the optimization procedure [here](https://qml.baidu.com/tutorials/quantum-simulation/variational-quantum-eigensolver.html) and use any paddlepaddle optimizer to train the ansatz you have built."
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": [
"# use paddlepaddle's optimizer\n",
"import numpy as np \n",
"import paddle\n",
"\n",
"optimizer = paddle.optimizer.Adam(parameters=my_cir.parameters(), learning_rate=0.08)\n",
"\n",
"# define the loss function\n",
"## NOTE: THIS LOSS FUNCTION IS ONLY DEFINED FOR DEMONSTRATION PURPOSE!\n",
"def loss_fn(state: paddle.Tensor) -> paddle.Tensor:\n",
" return paddle.norm(state.real())\n",
"\n",
"# start learning\n",
"s0 = np.zeros((2**5,), dtype=np.complex128)\n",
"s0[0] = 1.0+0.0j\n",
"s0 = paddle.to_tensor(s0)\n",
"\n",
"for i in range(10):\n",
" loss = loss_fn(my_cir(s0))\n",
" print(f\"At {i:>d}th step: loss={loss.item():>.5f}.\")\n",
"\n",
" optimizer.clear_grad()\n",
" loss.backward()\n",
" optimizer.step()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"---\n",
"## References\n",
"\n",
"[1] Kandala, Abhinav, et al. \"Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets.\" [Nature 549.7671 (2017): 242-246.](https://www.nature.com/articles/nature23879)\n",
"\n",
"[2] Arute, Frank, et al. \"Hartree-Fock on a superconducting qubit quantum computer.\" [Science 369.6507 (2020): 1084-1089.](https://www.science.org/doi/10.1126/science.abb9811)"
]
}
],
"metadata": {
"interpreter": {
"hash": "7b343e878babc25549085ff27e754b596ec1b81bbbd70d50b28da4f6023d5bd9"
},
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
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"language_info": {
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"file_extension": ".py",
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introduction/PaddleQuantum_Tutorial_CN.ipynb
浏览文件 @ 016af983
因为 它太大了无法显示 source diff 。你可以改为 查看blob。
introduction/PaddleQuantum_Tutorial_EN.ipynb
浏览文件 @ 016af983
因为 它太大了无法显示 source diff 。你可以改为 查看blob。
paddle_quantum/__init__.py
浏览文件 @ 016af983
...@@ -17,4 +17,4 @@ Paddle Quantum Library ...@@ -17,4 +17,4 @@ Paddle Quantum Library
""" """
name = "paddle_quantum" name = "paddle_quantum"
__version__ = "2.1.2" __version__ = "2.1.3"
paddle_quantum/circuit.py
浏览文件 @ 016af983
...@@ -26,7 +26,7 @@ from paddle import imag, real, reshape, kron, matmul, trace ...@@ -26,7 +26,7 @@ from paddle import imag, real, reshape, kron, matmul, trace
from paddle_quantum.utils import partial_trace, dagger, pauli_str_to_matrix from paddle_quantum.utils import partial_trace, dagger, pauli_str_to_matrix
from paddle_quantum import shadow from paddle_quantum import shadow
from paddle_quantum.intrinsic import * from paddle_quantum.intrinsic import *
from paddle_quantum.state import density_op,vec from paddle_quantum.state import density_op, vec
__all__ = [ __all__ = [
"UAnsatz", "UAnsatz",
...@@ -60,29 +60,6 @@ class UAnsatz: ...@@ -60,29 +60,6 @@ class UAnsatz:
# Record history of adding gates to the circuit # Record history of adding gates to the circuit
self.__history = [] self.__history = []
def expand(self,new_n):
"""
为原来的量子电路进行比特数扩展
Args：
new_n(int):扩展后的量子比特数
"""
assert new_n>=self.n,'扩展后量子比特数要大于原量子比特数'
diff = new_n-self.n
dim = 2**diff
if self.__state is not None:
if self.__run_mode=='density_matrix':
shape = (dim,dim)
_state = paddle.to_tensor(density_op(diff))
elif self.__run_mode=='state_vector':
shape = (dim,)
_state = paddle.to_tensor(vec(0,diff))
_state= paddle.reshape(_state,shape)
_state = kron(self.__state,_state)
self.__state = _state
self.n = new_n
def __add__(self, cir): def __add__(self, cir):
r"""重载加法 ‘+’ 运算符，用于拼接两个维度相同的电路 r"""重载加法 ‘+’ 运算符，用于拼接两个维度相同的电路
...@@ -419,6 +396,29 @@ class UAnsatz: ...@@ -419,6 +396,29 @@ class UAnsatz:
return return_str return return_str
def expand(self, qubit_num):
"""
为原来的量子电路进行比特数扩展
Args:
qubit_num (int): 扩展后的量子比特数
"""
assert qubit_num >= self.n, '扩展后量子比特数要大于原量子比特数'
diff = qubit_num - self.n
dim = 2 ** diff
if self.__state is not None:
if self.__run_mode == 'density_matrix':
shape = (dim, dim)
_state = paddle.to_tensor(density_op(diff))
elif self.__run_mode == 'state_vector':
shape = (dim,)
_state = paddle.to_tensor(vec(0, diff))
_state = paddle.reshape(_state, shape)
_state = kron(self.__state, _state)
self.__state = _state
self.n = qubit_num
def run_state_vector(self, input_state=None, store_state=True): def run_state_vector(self, input_state=None, store_state=True):
r"""运行当前的量子电路，输入输出的形式为态矢量。 r"""运行当前的量子电路，输入输出的形式为态矢量。
...@@ -1160,7 +1160,7 @@ class UAnsatz: ...@@ -1160,7 +1160,7 @@ class UAnsatz:
.. math:: .. math::
\begin{align} \begin{align}
CNOT &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes X\\ CY &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Y\\
&= &=
\begin{bmatrix} \begin{bmatrix}
1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 \\
...@@ -1197,7 +1197,7 @@ class UAnsatz: ...@@ -1197,7 +1197,7 @@ class UAnsatz:
.. math:: .. math::
\begin{align} \begin{align}
CNOT &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes X\\ CZ &=|0\rangle \langle 0|\otimes I + |1 \rangle \langle 1|\otimes Z\\
&= &=
\begin{bmatrix} \begin{bmatrix}
1 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 \\
...@@ -3108,8 +3108,11 @@ class UAnsatz: ...@@ -3108,8 +3108,11 @@ class UAnsatz:
j = 0 j = 0
for i in range(len(self.__param)): for i in range(len(self.__param)):
if not self.__param[i].stop_gradient: if not self.__param[i].stop_gradient:
if not isinstance(new_param[j], paddle.Tensor):
self.__param[i] = paddle.to_tensor(new_param[j], 'float64') self.__param[i] = paddle.to_tensor(new_param[j], 'float64')
self.__param[i].stop_gradient = False self.__param[i].stop_gradient = False
else:
self.__param[i] = new_param[j]
j += 1 j += 1
self.run_state_vector() self.run_state_vector()
return self.__param return self.__param
......
paddle_quantum/dataset.py 0 → 100644
浏览文件 @ 016af983
# Copyright (c) 2021 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.
"""
dataset: To learn more about the functions and properties of this application,
you could check the corresponding Jupyter notebook under the Tutorial folder.
"""
import math
import random
from math import sqrt
import time
import paddle.vision.transforms as transform
import numpy as np
import paddle
from paddle_quantum.circuit import UAnsatz
from paddle.fluid.layers import reshape
from sklearn.model_selection import train_test_split
from sklearn import datasets
__all__ = [
"VisionDataset",
"SimpleDataset",
"MNIST",
"FashionMNIST",
"Iris",
"BreastCancer"
]
# data modes
DATAMODE_TRAIN = "train"
DATAMODE_TEST = "test"
# encoding methods
ANGLE_ENCODING = "angle_encoding"
AMPLITUDE_ENCODING = "amplitude_encoding"
PAULI_ROTATION_ENCODING = "pauli_rotation_encoding"
LINEAR_ENTANGLED_ENCODING = "linear_entangled_encoding"
REAL_ENTANGLED_ENCODING = "real_entangled_encoding"
COMPLEX_ENTANGLED_ENCODING = "complex_entangled_encoding"
IQP_ENCODING = "IQP_encoding"
# downscaling method
DOWNSCALINGMETHOD_PCA = "PCA"
DOWNSCALINGMETHOD_RESIZE = "resize"
def _normalize(x):
r"""normalize vector ``x`` and the maximum will be pi. This is an internal function.
Args:
x (ndarray): 需要归一化的向量
Returns:
ndarray: 归一化之后的向量
"""
xx = np.abs(x)
if xx.max() > 0:
return x * np.pi / xx.max()
else:
return x
def _normalize_image(x):
r"""normalize image vector ``x`` and the maximum will be pi. This is an internal function.
Args:
x (ndarray): 需要归一化的图片向量
Returns:
ndarray: 归一化之后的向量
"""
return x * np.pi / 256
def _crop(images, border):
r"""crop ``images`` according to ``border``. This is an internal function.
Args:
images (list/ndarray): 每一个元素是拉成一维的图片向量
border(list): 裁剪的边界，从第一个元素切到第二个元素，比如说[4,24]就是从图片的第四行第四列到第24行第24列
Returns:
new_images(list): 裁剪之后被拉成一维的图片向量组成的list
"""
new_images = []
for i in range(len(images)):
size = int(sqrt(len(images[i])))
temp_image = images[i].reshape((size, size))
temp_image = temp_image[border[0]:border[1], border[0]:border[1]]
new_images.append(temp_image.flatten())
return new_images
class Dataset(object):
r"""所有数据集的基类，集成了多种量子编码方法。
"""
def __init__(self):
return
def data2circuit(self, classical_data, encoding, num_qubits, can_describe_dimension, split_circuit,
return_state, is_image=False):
r"""将输入的经典数据 ``classical_data`` 用编码方式 ``encoding`` 编码成量子态，这里的经典数据经过了截断或者补零，因而可以正好被编码。
Args:
classical_data (list): 待编码的向量，ndarray 组成的 list，经过了截断或者补零，刚好可以被编码
encoding (str): 编码方式，参见 MNIST 编码注释
num_qubits (int): 量子比特数目
can_describe_dimension (int): 以 ``encoding`` 编码方式可以编码的数目，比如说振幅编码为 ``2 ** n`` ，其他编码因为可以进行层层堆叠需要计算
split_circuit (bool): 是否切分电路
return_state (bool): 是否返回量子态
is_image (bool): 是否是图片，如果是图片，归一化方法不太一样
Returns:
List: 如果 ``return_state == True`` ，返回编码后的量子态，否则返回编码的电路
"""
quantum_states = classical_data.copy()
quantum_circuits = classical_data.copy()
if encoding == AMPLITUDE_ENCODING:
# Not support to return circuit in amplitude encoding
if return_state is False or split_circuit is True:
raise Exception("Not support to return circuit in amplitude encoding")
for i in range(len(classical_data)):
built_in_amplitude_enc = UAnsatz(num_qubits)
x = paddle.to_tensor(_normalize(classical_data[i]))
if is_image:
x = paddle.to_tensor(_normalize_image(classical_data[i]))
state = built_in_amplitude_enc.amplitude_encoding(x, 'state_vector')
quantum_states[i] = state.numpy()
elif encoding == ANGLE_ENCODING:
for i in range(len(classical_data)):
one_block_param = 1 * num_qubits
depth = int(can_describe_dimension / one_block_param)
param = paddle.to_tensor(_normalize(classical_data[i]))
if is_image:
param = paddle.to_tensor(_normalize_image(classical_data[i]))
param = reshape(param, (depth, num_qubits, 1))
which_qubits = [k for k in range(num_qubits)]
if split_circuit:
quantum_circuits[i] = []
for repeat in range(depth):
circuit = UAnsatz(num_qubits)
for k, q in enumerate(which_qubits):
circuit.ry(param[repeat][k][0], q)
quantum_circuits[i].append(circuit)
else:
circuit = UAnsatz(num_qubits)
for repeat in range(depth):
for k, q in enumerate(which_qubits):
circuit.ry(param[repeat][k][0], q)
state_out = circuit.run_state_vector()
quantum_states[i] = state_out.numpy()
quantum_circuits[i] = [circuit]
elif encoding == IQP_ENCODING:
for i in range(len(classical_data)):
one_block_param = 1 * num_qubits
depth = int(can_describe_dimension / one_block_param)
param = paddle.to_tensor(_normalize(classical_data[i]))
if is_image:
param = paddle.to_tensor(_normalize_image(classical_data[i]))
param = reshape(param, (depth, num_qubits))
if split_circuit:
quantum_circuits[i] = []
for repeat in range(depth):
circuit = UAnsatz(num_qubits)
S = []
for k in range(num_qubits - 1):
S.append([k, k + 1])
# r 是 U 重复的次数
r = 1
circuit.iqp_encoding(param[repeat], r, S)
quantum_circuits[i].append(circuit)
else:
circuit = UAnsatz(num_qubits)
for repeat in range(depth):
temp_circuit = UAnsatz(num_qubits)
S = []
for k in range(num_qubits - 1):
S.append([k, k + 1])
# r 是 U 重复的次数
r = 1
temp_circuit.iqp_encoding(param[repeat], r, S)
circuit = circuit + temp_circuit
state_out = circuit.run_state_vector()
quantum_states[i] = state_out.numpy()
quantum_circuits[i] = [circuit]
elif encoding == PAULI_ROTATION_ENCODING:
for i in range(len(classical_data)):
one_block_param = 3 * num_qubits
depth = int(can_describe_dimension / one_block_param)
param = paddle.to_tensor(_normalize(classical_data[i]))
if is_image:
param = paddle.to_tensor(_normalize_image(classical_data[i]))
param = reshape(param, (depth, num_qubits, 3))
which_qubits = [k for k in range(num_qubits)]
if split_circuit:
quantum_circuits[i] = []
for repeat in range(depth):
circuit = UAnsatz(num_qubits)
for k, q in enumerate(which_qubits):
circuit.ry(param[repeat][k][0], q)
circuit.rz(param[repeat][k][1], q)
circuit.ry(param[repeat][k][2], q)
quantum_circuits[i].append(circuit)
else:
circuit = UAnsatz(num_qubits)
for repeat in range(depth):
for k, q in enumerate(which_qubits):
circuit.ry(param[repeat][k][0], q)
circuit.rz(param[repeat][k][1], q)
circuit.ry(param[repeat][k][2], q)
state_out = circuit.run_state_vector()
quantum_states[i] = state_out.numpy()
quantum_circuits[i] = [circuit]
elif encoding == LINEAR_ENTANGLED_ENCODING:
for i in range(len(classical_data)):
one_block_param = 2 * num_qubits
depth = int(can_describe_dimension / one_block_param)
param = paddle.to_tensor(_normalize(classical_data[i]))
if is_image:
param = paddle.to_tensor(_normalize_image(classical_data[i]))
param = reshape(param, (depth, num_qubits, 2))
which_qubits = [k for k in range(num_qubits)]
if split_circuit:
quantum_circuits[i] = []
for j in range(depth):
circuit = UAnsatz(num_qubits)
for k, q in enumerate(which_qubits):
circuit.ry(param[j][k][0], q)
for k in range(len(which_qubits) - 1):
circuit.cnot([which_qubits[k], which_qubits[k + 1]])
for k, q in enumerate(which_qubits):
circuit.rz(param[j][k][1], q)
for k in range(len(which_qubits) - 1):
circuit.cnot([which_qubits[k + 1], which_qubits[k]])
quantum_circuits[i].append(circuit)
else:
circuit = UAnsatz(num_qubits)
for j in range(depth):
for k, q in enumerate(which_qubits):
circuit.ry(param[j][k][0], q)
for k in range(len(which_qubits) - 1):
circuit.cnot([which_qubits[k], which_qubits[k + 1]])
for k, q in enumerate(which_qubits):
circuit.rz(param[j][k][1], q)
for k in range(len(which_qubits) - 1):
circuit.cnot([which_qubits[k + 1], which_qubits[k]])
state_out = circuit.run_state_vector()
quantum_states[i] = state_out.numpy()
quantum_circuits[i] = [circuit]
elif encoding == REAL_ENTANGLED_ENCODING:
for i in range(len(classical_data)):
one_block_param = 1 * num_qubits
depth = int(can_describe_dimension / one_block_param)
param = paddle.to_tensor(_normalize(classical_data[i]))
if is_image:
param = paddle.to_tensor(_normalize_image(classical_data[i]))
param = reshape(param, (depth, num_qubits, 1))
which_qubits = [k for k in range(num_qubits)]
if split_circuit:
quantum_circuits[i] = []
for repeat in range(depth):
circuit = UAnsatz(num_qubits)
for k, q in enumerate(which_qubits):
circuit.ry(param[repeat][k][0], q)
for k in range(len(which_qubits) - 1):
circuit.cnot([which_qubits[k], which_qubits[k + 1]])
circuit.cnot([which_qubits[-1], which_qubits[0]])
quantum_circuits[i].append(circuit)
else:
circuit = UAnsatz(num_qubits)
for repeat in range(depth):
for k, q in enumerate(which_qubits):
circuit.ry(param[repeat][k][0], q)
for k in range(len(which_qubits) - 1):
circuit.cnot([which_qubits[k], which_qubits[k + 1]])
circuit.cnot([which_qubits[-1], which_qubits[0]])
state_out = circuit.run_state_vector()
quantum_states[i] = state_out.numpy()
quantum_circuits[i] = [circuit]
elif encoding == COMPLEX_ENTANGLED_ENCODING:
for i in range(len(classical_data)):
one_block_param = 3 * num_qubits
depth = int(can_describe_dimension / one_block_param)
param = paddle.to_tensor(_normalize(classical_data[i]))
if is_image:
param = paddle.to_tensor(_normalize_image(classical_data[i]))
param = reshape(param, (depth, num_qubits, 3))
which_qubits = [k for k in range(num_qubits)]
if split_circuit:
quantum_circuits[i] = []
for repeat in range(depth):
circuit = UAnsatz(num_qubits)
for k, q in enumerate(which_qubits):
circuit.u3(param[repeat][k][0], param[repeat][k][1], param[repeat][k][2], q)
for k in range(len(which_qubits) - 1):
circuit.cnot([which_qubits[k], which_qubits[k + 1]])
circuit.cnot([which_qubits[-1], which_qubits[0]])
quantum_circuits[i].append(circuit)
else:
circuit = UAnsatz(num_qubits)
for repeat in range(depth):
for k, q in enumerate(which_qubits):
circuit.u3(param[repeat][k][0], param[repeat][k][1], param[repeat][k][2], q)
for k in range(len(which_qubits) - 1):
circuit.cnot([which_qubits[k], which_qubits[k + 1]])
circuit.cnot([which_qubits[-1], which_qubits[0]])
state_out = circuit.run_state_vector()
quantum_states[i] = state_out.numpy()
quantum_circuits[i] = [circuit]
return quantum_states, quantum_circuits
def filter_class(self, x, y, classes, data_num, need_relabel, seed=0):
r"""将输入的 ``x`` , ``y`` 按照 ``classes`` 给出的类别进行筛选，数目为 ``data_num`` 。
Args:
x (ndarray/list): 样本的特征
y (ndarray/list): 样本标签， ``classes`` 是其中某几个标签的取值
classes (list): 需要筛选的类别
data_num (int): 筛选出来的样本数目
need_relabel (bool): 将原有类别按照顺序重新标记为 0、1、2 等新的名字，比如传入 ``[1,2]`` ， 重新标记之后变为 ``[0,1]`` 主要用于二分类
seed (int): 随机种子，默认为 ``0``
Returns:
tuple: 包含如下元素:
- new_x (list): 筛选出的特征
- new_y (list): 对应于 ``new_x`` 的标签
"""
new_x = []
new_y = []
if need_relabel:
for i in range(len(x)):
if y[i] in classes:
new_x.append(x[i])
new_y.append(classes.index(y[i]))
else:
for i in range(len(x)):
if y[i] in classes:
new_x.append(x[i])
new_y.append(y[i])
# sample to data_num randomly
if data_num > 0 and data_num < len(new_x):
random_index = [k for k in range(len(new_x))]
random.seed(seed)
random.shuffle(random_index)
random_index = random_index[:data_num]
filter_x = []
filter_y = []
for index in random_index:
filter_x.append(new_x[index])
filter_y.append(new_y[index])
return filter_x, filter_y
return new_x, new_y
class VisionDataset(Dataset):
r"""图片数据集类，通过继承 VisionDataset 类，用户可以快速生成自己的图片量子数据。
Attributes:
original_images (ndarray): 图片经过类别过滤，但是还没有降维、补零的特征，是一个一维向量（可调用 ``reshape()`` 函数转成图片）
classical_image_vectors (ndarray): 经过类别过滤和降维、补零等操作之后的特征，并未编码为量子态
quantum_image_states (paddle.tensor): 经过类别过滤之后的所有特征经编码形成的量子态
quantum_image_circuits (list): 所有特征编码的电路
"""
def __init__(self, figure_size):
r"""构造函数
Args:
figure_size (int): 图片大小，也就是长和高的数值
"""
Dataset.__init__(self)
self.figure_size = figure_size
return
# The encode function only needs to import images to form one-dimensional vector features.
# The pre-processing of images (except dimensionality reduction) is completed before the import of features
def encode(self, feature, encoding, num_qubits, split_circuit=False,
downscaling_method=DOWNSCALINGMETHOD_RESIZE, target_dimension=-1, return_state=True, full_return=False):
r"""根据降尺度方式、目标尺度、编码方式、量子比特数目进行编码。只需要输入一维图片向量就行。
Args:
feature (list/ndarray): 一维图片向量组成的list/ndarray
encoding (str): ``"angle_encoding"`` 表示角度编码，一个量子比特编码一个旋转门； ``"amplitude_encoding"`` 表示振幅编码；
``"pauli_rotation_encoding"`` 表示SU(3)的角度编码; 还有 ``"linear_entangled_encoding"`` ,
``"real_entangled_encoding"`` , ``"complex_entangled_encoding"`` 三种纠缠编码和 ``"IQP_encoding"`` 编码
num_qubits (int): 编码后的量子比特数目
split_circuit (bool): 是否需要切分电路。除了振幅之外的所有电路都会存在堆叠的情况，如果选择 ``True`` 就将块与块分开
downscaling_method (str): 包括 ``"PCA"`` 和 ``"resize"``
target_dimension (int): 降维之后的尺度大小，如果是 ``"PCA"`` ，不能超过图片大小；如果是 ``"resize"`` ，不能超过原图大小
return_state (bool): 是否返回量子态，如果是 ``False`` 返回量子电路
Returns:
tuple: 包含如下元素:
- quantum_image_states (paddle.tensor): 量子态，只有 ``full_return==True`` 或者 ``return_state==True`` 的时候会返回
- quantum_image_circuits (list): 所有特征编码的电路， 只有 ``full_return==False`` 或者 ``return_state==True`` 的时候会返回
- original_images (ndarray): 图片经过类别过滤，但是还没有降维、补零的特征，是一个一维向量（可以 reshape 成图片），只有 ``return_state==True`` 的时候会返回
- classical_image_vectors (ndarray): 经过类别过滤和降维、补零等操作之后的特征，并未编码为量子态，只有 ``return_state==True`` 的时候会返回
"""
assert num_qubits > 0
if encoding in [IQP_ENCODING, COMPLEX_ENTANGLED_ENCODING, REAL_ENTANGLED_ENCODING,
LINEAR_ENTANGLED_ENCODING]:
assert num_qubits > 1
if type(feature) == np.ndarray:
feature = list(feature)
# The first step: judge whether `target_dimension` is reasonable
if target_dimension > -1:
if downscaling_method == DOWNSCALINGMETHOD_PCA:
if target_dimension > self.figure_size:
raise Exception("PCA dimension should be less than {}.".format(self.figure_size))
elif downscaling_method == DOWNSCALINGMETHOD_RESIZE:
if int(sqrt(target_dimension)) ** 2 != target_dimension: # not a square
raise Exception("Resize dimension should be a square.")
else:
raise Exception("Downscaling methods can only be resize and PCA.")
else:
if downscaling_method == DOWNSCALINGMETHOD_PCA:
target_dimension = self.figure_size
elif downscaling_method == DOWNSCALINGMETHOD_RESIZE:
target_dimension = self.figure_size ** 2
# The second step: calculate `can_describe_dimension`
if encoding == AMPLITUDE_ENCODING: # amplitude encoding, encoding 2^N-dimension feature
self.can_describe_dimension = 2 ** num_qubits
elif encoding == LINEAR_ENTANGLED_ENCODING:
one_block_param = 2 * num_qubits
self.can_describe_dimension = math.ceil(target_dimension / one_block_param) * one_block_param
elif encoding in [REAL_ENTANGLED_ENCODING, ANGLE_ENCODING, IQP_ENCODING]:
one_block_param = 1 * num_qubits
self.can_describe_dimension = math.ceil(target_dimension / one_block_param) * one_block_param
elif encoding in [COMPLEX_ENTANGLED_ENCODING, PAULI_ROTATION_ENCODING]:
one_block_param = 3 * num_qubits
self.can_describe_dimension = math.ceil(target_dimension / one_block_param) * one_block_param
else:
raise Exception("Invalid encoding methods!")
self.dimension = target_dimension
# The third step: download MNIST data from paddlepaddle and crop or fill the vector to ``can_describe_vector``
self.original_images = np.array(feature)
self.classical_image_vectors = feature.copy()
# What need to mention if ``Resize`` needs uint8, but MNIST in paddle is float32, so we should change its type.
if downscaling_method == DOWNSCALINGMETHOD_RESIZE:
# iterating all items
for i in range(len(self.classical_image_vectors)):
cur_image = self.classical_image_vectors[i].astype(np.uint8)
new_size = int(sqrt(self.dimension))
cur_image = transform.resize(cur_image.reshape((self.figure_size, self.figure_size)),
(new_size, new_size))
self.classical_image_vectors[i] = cur_image.reshape(-1).astype(np.float64) # now it is one-dimension
if self.can_describe_dimension < len(self.classical_image_vectors[i]):
self.classical_image_vectors[i] = self.classical_image_vectors[i][:self.can_describe_dimension]
else:
self.classical_image_vectors[i] = np.append(self.classical_image_vectors[i], np.array(
[0.0] * (self.can_describe_dimension - len(self.classical_image_vectors[i]))))
elif downscaling_method == DOWNSCALINGMETHOD_PCA:
for i in range(len(self.classical_image_vectors)):
U, s, V = np.linalg.svd(self.classical_image_vectors[i].reshape((self.figure_size, self.figure_size)))
s = s[:self.dimension].astype(np.float64)
if self.can_describe_dimension > self.dimension:
self.classical_image_vectors[i] = np.append(s, np.array(
[0.0] * (self.can_describe_dimension - self.dimension)))
else:
self.classical_image_vectors[i] = s[:self.can_describe_dimension]
# Step 4: Encode the data, which must be of float64 type(needed in paddle quantum)
self.quantum_image_states, self.quantum_image_circuits = self.data2circuit(
self.classical_image_vectors, encoding, num_qubits, self.can_describe_dimension, split_circuit,
return_state, is_image=True)
self.classical_image_vectors = np.array(self.classical_image_vectors)
if return_state:
self.quantum_image_states = paddle.to_tensor(np.array(self.quantum_image_states)) # transfer to tensor
if full_return:
return self.quantum_image_states, self.quantum_image_circuits, self.original_images, \
self.classical_image_vectors
else:
if return_state:
return self.quantum_image_states
else:
return self.quantum_image_circuits
class MNIST(VisionDataset):
r"""MNIST 数据集，它继承了 VisionDataset 图片数据集类。
Attributes:
original_images(ndarray): 图片经过类别过滤，但是还没有降维、补零的特征，是一个一维向量（可调用 ``reshape()`` 方法转成图片）
classical_image_vectors(ndarray): 经过类别过滤和降维、补零等操作之后的特征，并未编码为量子态
quantum_image_states(paddle.tensor): 经过类别过滤之后的所有特征经编码形成的量子态
quantum_image_circuits(list): 所有特征编码的电路
labels(ndarray): 经过类别过滤之后的所有标签
代码示例:
.. code-block:: python
from paddle_quantum.dataset import MNIST
# main parameters
training_data_num = 80
testing_data_num = 20
qubit_num = 4
# acquiring training dataset
train_dataset = MNIST(mode='train', encoding='pauli_rotation_encoding', num_qubits=qubit_num, classes=[3,6],
data_num=training_data_num,need_cropping=True,
downscaling_method='resize', target_dimension=16, return_state=True)
# acquiring testing dataset
val_dataset = MNIST(mode='test', encoding='pauli_rotation_encoding', num_qubits=qubit_num, classes=[3,6],
data_num=testing_data_num,need_cropping=True,
downscaling_method='resize', target_dimension=16,return_state=True)
# acquiring features and labels
train_x, train_y = train_dataset.quantum_image_states, train_dataset.labels # paddle.tensor, ndarray
test_x, test_y = val_dataset.quantum_image_states, val_dataset.labels
print(train_x[0])
print(train_y[0])
"""
def __init__(self, mode, encoding, num_qubits, classes, data_num=-1, split_circuit=False,
downscaling_method=DOWNSCALINGMETHOD_RESIZE, target_dimension=-1, need_cropping=True,
need_relabel=True, return_state=True, seed=0):
r"""构造函数
Args:
mode (str): 数据模式，包括 ``"train"`` 和 ``"test"``
encoding (str): ``"angle_encoding"`` 表示角度编码，一个量子比特编码一个旋转门； ``"amplitude_encoding"`` 表示振幅编码；
``"pauli_rotation_encoding"`` 表示SU(3)的角度编码; 还有 ``"linear_entangled_encoding"`` ,
``"real_entangled_encoding"`` , ``"complex_entangled_encoding"`` 三种纠缠编码和 ``"IQP_encoding"`` 编码
num_qubits (int): 编码后的量子比特数目
classes (list): 用列表给出需要的类别，类别用数字标签表示，不支持传入名字
data_num (int): 使用的数据量大小，这样可以不用所有数据都进行编码，这样会很慢
split_circuit (bool): 是否需要切分电路。除了振幅之外的所有电路都会存在堆叠的情况，如果选择 ``True`` 就将块与块分开
need_cropping (bool): 是否需要裁边，如果为 ``True`` ，则从 ``image[0:27][0:27]`` 裁剪为 ``image[4:24][4:24]``
need_relabel (bool): 将原有类别按照顺序重新标记为 0，1，2 等新的名字，比如传入 ``[1,2]`` ，重新标记之后变为 ``[0,1]`` ，主要用于二分类
downscaling_method (str): 包括 ``"PCA"`` 和 ``"resize"``
target_dimension (int): 降维之后的尺度大小，如果是 ``"PCA"`` ，不能超过图片大小；如果是 ``"resize"`` ，不能超过原图大小
return_state (bool): 是否返回量子态，如果是 ``False`` 返回量子电路
seed (int): 筛选样本的随机种子，默认为 ``0``
"""
VisionDataset.__init__(self, 28)
if need_cropping:
self.figure_size = 20
# Download data from paddlepaddle
if mode == DATAMODE_TRAIN:
train_dataset = paddle.vision.datasets.MNIST(mode='train')
feature, self.labels = self.filter_class(train_dataset.images, train_dataset.labels,
classes=classes,
data_num=data_num, need_relabel=need_relabel, seed=seed)
if need_cropping:
feature = _crop(feature, [4, 24])
elif mode == DATAMODE_TEST:
test_dataset = paddle.vision.datasets.MNIST(mode='test')
# test_dataset.images is now a list of (784,1) shape
feature, self.labels = self.filter_class(test_dataset.images, test_dataset.labels,
classes=classes,
data_num=data_num, need_relabel=need_relabel, seed=seed)
if need_cropping:
feature = _crop(feature, [4, 24])
else:
raise Exception("data mode can only be train and test.")
# Start to encode
self.quantum_image_states, self.quantum_image_circuits, self.original_images, self.classical_image_vectors = \
self.encode(feature, encoding, num_qubits, split_circuit, downscaling_method, target_dimension,
return_state, True)
self.labels = np.array(self.labels)
def __len__(self):
return len(self.quantum_image_states)
class FashionMNIST(VisionDataset):
r""" FashionMNIST 数据集，它继承了 VisionDataset 图片数据集类
Attributes:
original_images (ndarray): 图片经过类别过滤，但是还没有降维、补零的特征，是一个一维向量（可调用 ``reshape()`` 方法转成图片）
classical_image_vectors (ndarray): 经过类别过滤和降维、补零等操作之后的特征，并未编码为量子态
quantum_image_states (paddle.tensor): 经过类别过滤之后的所有特征经编码形成的量子态
quantum_image_circuits (list): 所有特征编码的电路
labels (ndarray): 经过类别过滤之后的所有标签
代码示例:
.. code-block:: python
from paddle_quantum.dataset import FashionMNIST
training_data_num=80
testing_data_num=20
qubit_num=4
# acquiring training dataset
train_dataset = FashionMNIST(mode='train', encoding='pauli_rotation_encoding', num_qubits=qubit_num, classes=[3,6],
data_num=training_data_num,downscaling_method='resize', target_dimension=16, return_state=True)
# 验acquiring testing dataset
val_dataset = FashionMNIST(mode='test', encoding='pauli_rotation_encoding', num_qubits=qubit_num, classes=[3,6],
data_num=testing_data_num,downscaling_method='resize', target_dimension=16,return_state=True)
# acquiring features and labels
train_x, train_y = train_dataset.quantum_image_states, train_dataset.labels # paddle.tensor, ndarray
test_x, test_y = val_dataset.quantum_image_states, val_dataset.labels
print(train_x[0])
print(train_y[0])
"""
def __init__(self, mode, encoding, num_qubits, classes, data_num=-1, split_circuit=False,
downscaling_method=DOWNSCALINGMETHOD_RESIZE, target_dimension=-1,
need_relabel=True, return_state=True, seed=0):
r""" 构造函数
Args:
mode (str): 数据模式，包括 ``"train"`` 和 ``"test"``
encoding (str): ``"angle_encoding"`` 表示角度编码，一个量子比特编码一个旋转门； ``"amplitude_encoding"`` 表示振幅编码；
``"pauli_rotation_encoding"`` 表示SU(3)的角度编码；还有 ``"linear_entangled_encoding"`` 、
``"real_entangled_encoding"`` 、 ``"complex_entangled_encoding"`` 三种纠缠编码和 ``"IQP_encoding"`` 编码
num_qubits (int): 编码后的量子比特数目
classes (list): 用列表给出需要的类别，类别用数字标签表示，不支持传入名字
data_num (int): 使用的数据量大小，这样可以不用所有数据都进行编码，这样会很慢
split_circuit (bool): 是否需要切分电路。除了振幅之外的所有电路都会存在堆叠的情况，如果选择true就将块与块分开
need_relabel (bool): 将原有类别按照顺序重新标记为0，1，2等新的名字，比如传入 ``[1,2]`` ，重新标记之后变为 ``[0,1]`` ，主要用于二分类
downscaling_method (str): 包括 ``"PCA"`` 和 ``"resize"``
target_dimension (int): 降维之后的尺度大小，如果是 ``"PCA"`` ，不能超过图片大小；如果是 ``"resize"`` ，不能超过原图大小
return_state (bool): 是否返回量子态，如果是 ``False`` 返回量子电路
seed (int): 随机种子，默认为 ``0``
"""
VisionDataset.__init__(self, 28)
# Download data from paddlepaddle
if mode == DATAMODE_TRAIN:
train_dataset = paddle.vision.datasets.FashionMNIST(mode='train')
feature, self.labels = self.filter_class(train_dataset.images, train_dataset.labels,
classes=classes,
data_num=data_num, need_relabel=need_relabel, seed=seed)
elif mode == DATAMODE_TEST:
test_dataset = paddle.vision.datasets.FashionMNIST(mode='test')
# test_dataset.images is now a list of (784,1) shape
feature, self.labels = self.filter_class(test_dataset.images, test_dataset.labels,
classes=classes,
data_num=data_num, need_relabel=need_relabel, seed=seed)
else:
raise Exception("data mode can only be train and test.")
# Start to encode
self.quantum_image_states, self.quantum_image_circuits, self.original_images, self.classical_image_vectors = \
self.encode(feature, encoding, num_qubits, split_circuit, downscaling_method, target_dimension,
return_state, True)
self.labels = np.array(self.labels)
def __len__(self):
return len(self.quantum_image_states)
class SimpleDataset(Dataset):
r""" 用于不需要降维的简单分类数据。用户可以通过继承 ``SimpleDataset`` ，将自己的分类数据变为量子态。下面的几个属性也会被继承。
Attributes:
quantum_states (ndarray): 经过类别过滤之后的所有特征经编码形成的量子态
quantum_circuits (list): 所有特征编码的电路
origin_feature (ndarray): 经过类别过滤之后的所有特征，并未编码为量子态
feature (ndarray): ``origin_feature`` 经过了补零之后的特征， ``quantum_states`` 就是将 ``feature`` 编码之后的结果
代码示例:
.. code-block:: python
from paddle_quantum.dataset import SimpleDataset
def circle_data_point_generator(Ntrain, Ntest, boundary_gap, seed_data):
# generate binary classification data with circle boundaries
# The former Ntrain samples are training data, the latter Ntest samples are testing data.
train_x, train_y = [], []
num_samples, seed_para = 0, 0
while num_samples < Ntrain + Ntest:
np.random.seed((seed_data + 10) * 1000 + seed_para + num_samples)
data_point = np.random.rand(2) * 2 - 1 # generator two-dimension vectors in [-1, 1]
# If the norm is below (0.7 - gap), the data point is mark as zero
if np.linalg.norm(data_point) < 0.7 - boundary_gap / 2:
train_x.append(data_point)
train_y.append(0.)
num_samples += 1
# If the norm is over (0.7 + gap), the data point is mark as one
elif np.linalg.norm(data_point) > 0.7 + boundary_gap / 2:
train_x.append(data_point)
train_y.append(1.)
num_samples += 1
else:
seed_para += 1
train_x = np.array(train_x).astype("float64")
train_y = np.array([train_y]).astype("float64").T
print("The dimension of the training data: x {} 和 y {}".format(np.shape(train_x[0:Ntrain]), np.shape(train_y[0:Ntrain])))
print("The dimension of the testing data: x {} 和 y {}".format(np.shape(train_x[Ntrain:]), np.shape(train_y[Ntrain:])), "\n")
return train_x[0:Ntrain], train_y[0:Ntrain], train_x[Ntrain:], train_y[Ntrain:]
Ntrain = 200 # the size of the training dataset
Ntest = 100 # the size of the testing dataset
boundary_gap = 0.5 # the gap between two classes
seed_data = 2 # fixed seed
# generate a new dataset
train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain, Ntest, boundary_gap, seed_data)
encoding="angle_encoding"
num_qubit=2
dimension=2
train_x=SimpleDataset(dimension).encode(train_x,encoding,num_qubit)
test_x=SimpleDataset(dimension).encode(test_x,encoding,num_qubit)
print(train_x[0])
print(test_x[0])
::
"""
def __init__(self, dimension):
r""" 构造函数
Args:
dimension (int): 编码数据的维度。
"""
Dataset.__init__(self)
self.dimension = dimension
return
def encode(self, feature, encoding, num_qubits, return_state=True, full_return=False):
r""" 进行编码
Args:
feature (list/ndarray): 编码的特征，每一个分量都是一个 ndarray 的特征向量
encoding (str): 编码方法
num_qubits (int): 编码的量子比特数目
return_state (bool): 是否返回量子态
Returns:
tuple: 包含如下元素:
- quantum_states (ndarray): 量子态，只有 ``full_return==True`` 或者 ``return_state==True`` 的时候会返回
- quantum_circuits (list): 所有特征编码的电路，只有 ``full_return==False`` 或者 ``return_state==True`` 的时候会返回
- origin_feature (ndarray): 经过类别过滤之后的所有特征，并未编码为量子态，只有 ``return_state==True`` 的时候会返回
- feature (ndarray): ``origin_feature`` 经过了补零之后的特征， ``quantum_states`` 就是将 ``feature`` 编码之后的结果。 只有 ``return_state==True`` 的时候会返回
"""
assert num_qubits > 0
if encoding in [IQP_ENCODING, COMPLEX_ENTANGLED_ENCODING, REAL_ENTANGLED_ENCODING,
LINEAR_ENTANGLED_ENCODING]:
assert num_qubits > 1
if type(feature) == np.ndarray:
self.feature = list(feature)
elif type(feature) is list:
self.feature = feature
else:
raise Exception("invalid type of feature")
self.origin_feature = np.array(feature)
# The first step, calculate ``self.can_describe_dimension``, and judge whether the qubit number is small
if encoding == AMPLITUDE_ENCODING: # amplitude encoding, encoding 2^N-dimension feature
self.can_describe_dimension = 2 ** num_qubits
# For these three kinds of entanglement encoding: lay these parameters block by block.
elif encoding == LINEAR_ENTANGLED_ENCODING:
one_block_param = 2 * num_qubits
self.can_describe_dimension = math.ceil(self.dimension / one_block_param) * one_block_param
elif encoding in [REAL_ENTANGLED_ENCODING, IQP_ENCODING, ANGLE_ENCODING]:
one_block_param = 1 * num_qubits
self.can_describe_dimension = math.ceil(self.dimension / one_block_param) * one_block_param
elif encoding in [COMPLEX_ENTANGLED_ENCODING, PAULI_ROTATION_ENCODING]:
one_block_param = 3 * num_qubits
self.can_describe_dimension = math.ceil(self.dimension / one_block_param) * one_block_param
else:
raise Exception("Invalid encoding methods!")
if self.can_describe_dimension < self.dimension:
raise Exception("The qubit number is not enough to encode the features.")
# The second step: fill the vector to ``can_describe_dimension`` using zero
for i in range(len(self.feature)):
self.feature[i] = self.feature[i].reshape(-1).astype(
np.float64) # now self.images[i] is a numpy with (new_size*new_size,1) shape
self.feature[i] = np.append(self.feature[i],
np.array([0.0] * (
self.can_describe_dimension - self.dimension))) # now self.images[i] is filled to ``self.can_describe_dimension``
# Step 3: Encode the data, which must be of float64 type(needed in paddle quantum)
self.quantum_states, self.quantum_circuits = self.data2circuit(
self.feature, encoding, num_qubits, self.can_describe_dimension, False, # split_circuit=False
return_state)
self.feature = np.array(self.feature)
self.quantum_states = np.array(self.quantum_states)
if full_return:
return self.quantum_states, self.quantum_circuits, self.origin_feature, self.feature
else:
if return_state:
return self.quantum_states
else:
return self.quantum_circuits
class Iris(SimpleDataset):
r""" Iris 数据集
Attributes:
quantum_states (ndarray): 经过类别过滤之后的所有特征经编码形成的量子态
quantum_circuits (list): 所有特征编码的电路
origin_feature (ndarray): 经过类别过滤之后的所有特征，并未编码为量子态
feature (ndarray): ``origin_feature`` 经过了补零之后的特征， ``quantum_states`` 就是将 ``feature`` 编码之后的结果
target (ndarray): 经过类别过滤之后的所有标签
train_x (paddle.tensor): 从 ``quantum_states`` 中选出的训练集
test_x (paddle.tensor): 从 ``quantum_states`` 中选出的测试集
train_circuits (list): 对应于 ``train_x`` 的编码电路
test_circuits (list): 对应于 ``test_x`` 的编码电路
origin_train_x (ndarray): 和 ``train_x`` 对应的经典数据
origin_test_x (ndarray): 和 ``test_x`` 对应的经典数据
train_y (ndarray): 对应于 ``train_x`` 的标签
test_y (ndarray): 对应于 ``test_x`` 的标签
代码示例:
.. code-block:: python
from paddle_quantum.dataset import Iris
test_rate=0.2
qubit_num=4
# Get Iris data, select two classes 0,1, and encode the data into four qubits using angle coding and return the quantum state.
# The proportion of the test set is 0.2.
iris =Iris (encoding='angle_encoding', num_qubits=qubit_num, test_rate=test_rate,classes=[0,1], return_state=True)
# Get the features and labels of the classical Iris dataset
origin_feature=iris.origin_feature # ndarray
origin_target=iris.target
# Gets the quantum states and labels of the training and test datasets
train_x, train_y = iris.train_x, iris.train_y # paddle.tensor, ndarray
test_x, test_y = iris.test_x, iris.test_y
testing_data_num=len(test_y)
training_data_num=len(train_y)
print(training_data_num)
print(testing_data_num)
"""
def __init__(self, encoding, num_qubits, classes, test_rate=0.2, need_relabel=True, return_state=True):
r""" 构造函数
Args:
encoding (str): ``"angle_encoding"`` 表示角度编码，一个量子比特编码一个旋转门； ``"amplitude_encoding"`` 表示振幅编码；
``"pauli_rotation_encoding"`` 表示SU(3)的角度编码；还有 ``"linear_entangled_encoding"`` 、
``"real_entangled_encoding"`` 、 ``"complex_entangled_encoding"`` 三种纠缠编码和 ``"IQP_encoding"`` 编码
num_qubits (int): 量子比特数目
classes (list): 用列表给出需要的类别，类别用数字标签表示，不支持传入名字
test_rate (float): 测试集的占比
need_relabel (bool): 将原有类别按照顺序重标记为 0、1、2 等新的名字，比如传入 ``[1,2]`` ，重标记之后变为 ``[0,1]`` ，主要用于二分类
return_state (bool): 是否返回量子态，如果是 ``False`` 返回量子电路
"""
SimpleDataset.__init__(self, dimension=4)
# Download data from scikit-learn
iris = datasets.load_iris()
self.dimension = 4 # dimension of Iris dataset
feature, self.target = self.filter_class(iris.data, iris.target, classes, -1,
need_relabel) # here -1 means all data
self.target = np.array(self.target)
# Start to encode
self.quantum_states, self.quantum_circuits, self.origin_feature, self.feature = \
self.encode(feature, encoding, num_qubits, return_state, True)
# Divide training and testing dataset
seed = int(time.time())
self.train_x, self.test_x, self.train_y, self.test_y = \
train_test_split(self.quantum_states, self.target, test_size=test_rate,
random_state=seed)
self.train_circuits, self.test_circuits, temp1, temp2 = \
train_test_split(self.quantum_circuits, self.target, test_size=test_rate,
random_state=seed)
self.origin_train_x, self.origin_test_x, temp1, temp2 = \
train_test_split(self.origin_feature, self.target, test_size=test_rate,
random_state=seed)
if return_state:
self.train_x = paddle.to_tensor(self.train_x)
self.test_x = paddle.to_tensor(self.test_x)
class BreastCancer(SimpleDataset):
r"""BreastCancer 数据集，569 组数据 30 维，只有两类。
Attributes:
quantum_states (ndarray): 经过类别过滤之后的所有特征经编码形成的量子态
quantum_circuits (list): 所有特征编码的电路
origin_feature (ndarray): 经过类别过滤之后的所有特征，并未编码为量子态
feature (ndarray): ``origin_feature`` 经过了补零之后的特征， ``quantum_states`` 就是将 ``feature`` 编码之后的结果
target (ndarray): 经过类别过滤之后的所有标签
train_x (paddle.tensor): 从 ``quantum_states`` 中选出的训练集
test_x (paddle.tensor): 从 ``quantum_states`` 中选出的测试集
train_circuits (list): 对应于 ``train_x`` 的编码电路
test_circuits (list): 对应于 ``test_x`` 的编码电路
origin_train_x (ndarray): 和 ``train_x`` 对应的经典数据
origin_test_x (ndarray): 和 ``test_x`` 对应的经典数据
train_y (ndarray): 对应于 ``train_x`` 的标签
test_y (ndarray): 对应于 ``test_x`` 的标签
代码示例:
.. code-block:: python
from paddle_quantum.dataset import BreastCancer
test_rate = 0.2
qubit_num = 4
# Get BreastCancer data, select two classes 0,1, and encode the data into four qubits using angle coding and return the quantum state.
# The proportion of the test set is 0.2.
breast_cancer =BreastCancer(encoding='angle_encoding', num_qubits=qubit_num, test_rate=test_rate, return_state=True)
# Get the features and labels of the classical BreastCancer dataset
origin_feature=breast_cancer.origin_feature # ndarray
origin_target=breast_cancer.target
# Gets the quantum states and labels of the training and test datasets
train_x, train_y = breast_cancer.train_x, breast_cancer.train_y # paddle.tensor, ndarray
test_x, test_y = breast_cancer.test_x, breast_cancer.test_y
testing_data_num=len(test_y)
training_data_num=len(train_y)
print(training_data_num)
print(testing_data_num)
"""
def __init__(self, encoding, num_qubits, test_rate=0.2, return_state=True):
r"""构造函数
Args:
encoding (str): ``"angle_encoding"`` 表示角度编码，一个量子比特编码一个旋转门； ``"amplitude_encoding"`` 表示振幅编码；
``"pauli_rotation_encoding"`` 表示SU(3)的角度编码；还有 ``"linear_entangled_encoding"`` 、
``"real_entangled_encoding"`` 、 ``"complex_entangled_encoding"`` 三种纠缠编码和 ``"IQP_encoding"`` 编码
num_qubits (int): 量子比特数目
test_rate (float): 测试集的占比
return_state (bool): 是否返回量子态，如果是 ``False`` 返回量子电路
"""
SimpleDataset.__init__(self, dimension=30) # The dimension is 30
self.dimension = 30
# Download data from scikit-learn
breast_cancer = datasets.load_breast_cancer()
feature = breast_cancer["data"]
self.target = breast_cancer["target"]
self.target = np.array(self.target)
# Start to encode
self.quantum_states, self.quantum_circuits, self.origin_feature, self.feature = \
self.encode(feature, encoding, num_qubits, return_state, True)
# Divide training and testing dataset
seed = int(time.time())
self.train_x, self.test_x, self.train_y, self.test_y = \
train_test_split(self.quantum_states, self.target, test_size=test_rate,
random_state=seed)
self.train_circuits, self.test_circuits, temp1, temp2 = \
train_test_split(self.quantum_circuits, self.target, test_size=test_rate,
random_state=seed)
self.origin_train_x, self.origin_test_x, temp1, temp2 = \
train_test_split(self.origin_feature, self.target, test_size=test_rate,
random_state=seed)
if return_state:
self.train_x = paddle.to_tensor(self.train_x)
self.test_x = paddle.to_tensor(self.test_x)
paddle_quantum/gradtool.py 0 → 100644
浏览文件 @ 016af983
# Copyright (c) 2021 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.
"""
梯度分析工具模块
"""
import numpy as np
import paddle
from paddle import reshape
from random import choice
from tqdm import tqdm
import matplotlib.pyplot as plt
__all__ = [
"StateNet",
"show_gradient",
"random_sample",
"random_sample_supervised",
"plot_loss_grad",
"plot_supervised_loss_grad",
"plot_distribution"
]
class StateNet(paddle.nn.Layer):
r"""定义用于量子机器学习的量子神经网络模型
用户可以通过实例化该类定义自己的量子神经网络模型。
"""
def __init__(self, shape, dtype='float64'):
r"""构造函数，用于实例化一个 ``StateNet`` 对象
Args:
shape (paddle.Tensor): 表示传入的量子电路中的需要被优化的参数个数
"""
super(StateNet, self).__init__()
self.theta = self.create_parameter(shape=shape,
default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi),
dtype=dtype, is_bias=False)
def forward(self, circuit, loss_func, *args):
r"""用于更新电路参数并计算该量子神经网络的损失值。
Args:
circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络
loss_func (function): 表示计算该量子神经网络损失值的函数
*args (list): 表示用于损失函数计算的额外参数列表
Note:
这里的 ``loss_func`` 是一个用户自定义的计算损失值的函数，参数为电路和一个可变参数列表。
Returns:
tuple: 包含如下两个元素:
- loss (paddle.Tensor): 表示该量子神经网络损失值
- circuit (UAnsatz): 更新参数后的量子电路
"""
circuit.update_param(self.theta)
circuit.run_state_vector()
loss = loss_func(circuit, *args)
return loss, circuit
def show_gradient(circuit, loss_func, ITR, LR, *args):
r"""计算量子神经网络中各可变参数的梯度值和损失函数值
Args:
circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络
loss_func (function): 表示计算该量子神经网络损失值的函数
ITR (int): 表示训练的次数
LR (float): 表示学习训练的速率
*args (list): 表示用于损失函数计算的额外参数列表
Returns:
tuple: 包含如下两个元素:
- loss_list (list): 表示损失函数值随训练次数变化的列表
- grad_list(list): 表示各参数梯度随训练次变化的列表
"""
grad_list = []
loss_list = []
shape = paddle.shape(circuit.get_param())
net = StateNet(shape=shape)
opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())
pbar = tqdm(
desc="Training: ", total=ITR, ncols=100, ascii=True
)
for itr in range(ITR):
pbar.update(1)
loss, cir = net(circuit, loss_func, *args)
loss.backward()
grad = net.theta.grad.numpy()
grad_list.append(grad)
loss_list.append(loss.numpy()[0])
opt.minimize(loss)
opt.clear_grad()
pbar.close()
return loss_list, grad_list
def plot_distribution(grad):
r"""根据输入的梯度的列表，画出梯度的分布图
Args:
grad (np.array): 表示量子神经网络某参数的梯度列表
"""
grad = np.abs(grad)
grad_list = [0, 0, 0, 0, 0]
x = ['<0.0001', ' (0.0001,0.001)', '(0.001,0.01)', '(0.01,0.1)', '>0.1']
for g in grad:
if g > 0.1:
grad_list[4] += 1
elif g > 0.01:
grad_list[3] += 1
elif g > 0.001:
grad_list[2] += 1
elif g > 0.0001:
grad_list[1] += 1
else:
grad_list[0] += 1
grad_list = np.array(grad_list) / len(grad)
plt.figure()
plt.bar(x, grad_list, width=0.5)
plt.title('The gradient distribution of variables')
plt.ylabel('ratio')
plt.show()
def random_sample(circuit, loss_func, sample_num, *args, mode='single', if_plot=True, param=0):
r"""表示对模型进行随机采样，根据不同的计算模式，获得对应的平均值和方差
Args:
circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络
loss_func (function): 表示计算该量子神经网络损失值的函数
sample_num (int): 表示随机采样的次数
mode (string): 表示随机采样后的计算模式，默认为 'single'
if_plot(boolean): 表示是否对梯度进行画图表示
param (int): 表示 ``Single`` 模式中对第几个参数进行画图，默认为第一个参数
*args (list): 表示用于损失函数计算的额外参数列表
Note:
在本函数中提供了三种计算模式，``mode`` 分别可以选择 ``'single'``, ``'max'``, 以及 ``'random'``
- mode='single': 表示计算电路中的每个可变参数梯度的平均值和方差
- mode='max': 表示对电路中每轮采样的所有参数梯度的最大值求平均值和方差
- mode='random': 表示对电路中每轮采样的所有参数随机取一个梯度，求平均值和方差
Returns:
tuple: 包含如下两个元素:
- loss_list (list): 表示多次采样后损失函数值的列表
- grad_list(list): 表示多次采样后各参数梯度的列表
"""
loss_list, grad_list = [], []
pbar = tqdm(
desc="Sampling: ", total=sample_num, ncols=100, ascii=True
)
for itr in range(sample_num):
pbar.update(1)
shape = paddle.shape(circuit.get_param())
net = StateNet(shape=shape)
loss, cir = net(circuit, loss_func, *args)
loss.backward()
grad = net.theta.grad.numpy()
loss_list.append(loss.numpy()[0])
grad_list.append(grad)
pbar.close()
if mode == 'single':
grad_list = np.array(grad_list)
grad_list = grad_list.transpose()
grad_variance_list = []
grad_mean_list = []
for idx in range(len(grad_list)):
grad_variance_list.append(np.var(grad_list[idx]))
grad_mean_list.append(np.mean(grad_list[idx]))
print("Mean of gradient for all parameters: ")
for i in range(len(grad_mean_list)):
print("theta", i+1, ": ", grad_mean_list[i])
print("Variance of gradient for all parameters: ")
for i in range(len(grad_variance_list)):
print("theta", i+1, ": ", grad_variance_list[i])
if if_plot:
plot_distribution(grad_list[param])
return grad_mean_list, grad_variance_list
if mode == 'max':
max_grad_list = []
for idx in range(len(grad_list)):
max_grad_list.append(np.max(np.abs(grad_list[idx])))
print("Mean of max gradient")
print(np.mean(max_grad_list))
print("Variance of max gradient")
print(np.var(max_grad_list))
if if_plot:
plot_distribution(max_grad_list)
return np.mean(max_grad_list), np.var(max_grad_list)
if mode == 'random':
random_grad_list = []
for idx in range(len(grad_list)):
random_grad = choice(grad_list[idx])
random_grad_list.append(random_grad)
print("Mean of random gradient")
print(np.mean(random_grad_list))
print("Variance of random gradient")
print(np.var(random_grad_list))
if if_plot:
plot_distribution(random_grad_list)
return np.mean(random_grad_list), np.var(random_grad_list)
return loss_list, grad_list
def plot_loss_grad(circuit, loss_func, ITR, LR, *args):
r"""绘制损失值和梯度随训练次数变化的图
Args:
circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络
loss_func (function): 表示计算该量子神经网络损失值的函数
ITR (int): 表示训练的次数
LR (float): 表示学习训练的速率
*args (list): 表示用于损失函数计算的额外参数列表
"""
loss, grad = show_gradient(circuit, loss_func, ITR, LR, *args)
plt.xlabel(r"Iteration")
plt.ylabel(r"Loss")
plt.plot(range(1, ITR+1), loss, 'r', label='loss')
plt.legend()
plt.show()
max_grad = [np.max(np.abs(i)) for i in grad]
plt.xlabel(r"Iteration")
plt.ylabel(r"Gradient")
plt.plot(range(1, ITR+1), max_grad, 'b', label='gradient')
plt.legend()
plt.show()
def plot_supervised_loss_grad(circuit, loss_func, N, EPOCH, LR, BATCH, TRAIN_X, TRAIN_Y, *args):
r"""绘制监督学习中损失值和梯度随训练次数变化的图
Args:
circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络
loss_func (function): 表示计算该量子神经网络损失值的函数
N (int): 表示量子比特的数量
EPOCH (int): 表示训练的轮数
LR (float): 表示学习训练的速率
BATCH (int): 表示训练时 batch 的大小
TRAIN_X (paddle.Tensor): 表示训练数据集
TRAIN_Y (list): 表示训练数据集的标签
*args (list): 表示用于损失函数计算的额外参数列表
Returns:
tuple: 包含如下两个元素:
- loss_list (list): 表示多次训练的损失函数值列表
- grad_list(list): 表示多次训练后各参数梯度的列表
"""
grad_list = []
loss_list = []
if type(TRAIN_X) != paddle.Tensor:
raise Exception("Training data should be paddle.Tensor type")
shape = paddle.shape(circuit.get_param())
net = StateNet(shape=shape)
opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())
for ep in range(EPOCH):
for itr in range(len(TRAIN_X)//BATCH):
input_state = TRAIN_X[itr*BATCH:(itr+1)*BATCH]
input_state = reshape(input_state, [-1, 1, 2**N])
label = TRAIN_Y[itr * BATCH:(itr + 1) * BATCH]
loss, circuit = net(circuit, loss_func, input_state, label)
loss.backward()
grad = net.theta.grad.numpy()
grad_list.append(grad)
loss_list.append(loss.numpy()[0])
opt.minimize(loss)
opt.clear_grad()
max_grad = [np.max(np.abs(i)) for i in grad_list]
plt.xlabel(r"Iteration")
plt.ylabel(r"Loss")
plt.plot(range(1, EPOCH*len(TRAIN_X)//BATCH+1), loss_list, 'r', label='loss')
plt.legend()
plt.show()
plt.xlabel(r"Iteration")
plt.ylabel(r"Gradient")
plt.plot(range(1, EPOCH*len(TRAIN_X)//BATCH+1), max_grad, 'b', label='gradient')
plt.legend()
plt.show()
return loss_list, grad_list
def random_sample_supervised(circuit, loss_func, N, sample_num, BATCH, TRAIN_X, TRAIN_Y, *args, mode='single', if_plot=True, param=0):
r"""表示对监督学习模型进行随机采样，根据不同的计算模式，获得对应的平均值和方差
Args:
circuit (UAnsatz): 表示传入的参数化量子电路，即要训练的量子神经网络
loss_func (function): 表示计算该量子神经网络损失值的函数
N (int): 表示量子比特的数量
sample_num (int): 表示随机采样的次数
BATCH (int): 表示训练时 batch 的大小
TRAIN_X (paddle.Tensor): 表示训练数据集
TRAIN_Y (list): 表示训练数据集的标签
mode (string): 表示随机采样后的计算模式，默认为 'single'
if_plot(boolean): 表示是否对梯度进行画图表示
param (int): 表示 ``Single`` 模式中对第几个参数进行画图，默认为第一个参数
*args (list): 表示用于损失函数计算的额外参数列表
Note:
在本函数中提供了三种计算模式，``mode`` 分别可以选择 ``'single'``, ``'max'``, 以及 ``'random'``
- mode='single': 表示计算电路中的每个可变参数梯度的平均值和方差
- mode='max': 表示对电路中所有参数梯度的最大值求平均值和方差
- mode='random': 表示随机对电路中采样的所有参数随机取一个梯度，求平均值和方差
Returns:
tuple: 包含如下两个元素:
- loss_list (list): 表示多次采样后损失函数值的列表
- grad_list(list): 表示多次采样后各参数梯度的列表
"""
grad_list = []
loss_list = []
input_state = TRAIN_X[0:BATCH]
input_state = reshape(input_state, [-1, 1, 2**N])
label = TRAIN_Y[0: BATCH]
if type(TRAIN_X) != paddle.Tensor:
raise Exception("Training data should be paddle.Tensor type")
label = TRAIN_Y[0: BATCH]
pbar = tqdm(
desc="Sampling: ", total=sample_num, ncols=100, ascii=True
)
for idx in range(sample_num):
pbar.update(1)
shape = paddle.shape(circuit.get_param())
net = StateNet(shape=shape)
loss, circuit = net(circuit, loss_func, input_state, label)
loss.backward()
grad = net.theta.grad.numpy()
grad_list.append(grad)
loss_list.append(loss.numpy()[0])
pbar.close()
if mode == 'single':
grad_list = np.array(grad_list)
grad_list = grad_list.transpose()
grad_variance_list = []
grad_mean_list = []
for idx in range(len(grad_list)):
grad_variance_list.append(np.var(grad_list[idx]))
grad_mean_list.append(np.mean(grad_list[idx]))
print("Mean of gradient for all parameters: ")
for i in range(len(grad_mean_list)):
print("theta", i+1, ": ", grad_mean_list[i])
print("Variance of gradient for all parameters: ")
for i in range(len(grad_variance_list)):
print("theta", i+1, ": ", grad_variance_list[i])
if if_plot:
plot_distribution(grad_list[param])
return grad_mean_list, grad_variance_list
if mode == 'max':
max_grad_list = []
for idx in range(len(grad_list)):
max_grad_list.append(np.max(np.abs(grad_list[idx])))
print("Mean of max gradient")
print(np.mean(max_grad_list))
print("Variance of max gradient")
print(np.var(max_grad_list))
if if_plot:
plot_distribution(max_grad_list)
return np.mean(max_grad_list), np.var(max_grad_list)
if mode == 'random':
random_grad_list = []
for idx in range(len(grad_list)):
random_grad = choice(grad_list[idx])
random_grad_list.append(random_grad)
print("Mean of random gradient")
print(np.mean(random_grad_list))
print("Variance of random gradient")
print(np.var(random_grad_list))
if if_plot:
plot_distribution(random_grad_list)
return np.mean(random_grad_list), np.var(random_grad_list)
return loss_list, grad_list
paddle_quantum/mbqc/utils.py
浏览文件 @ 016af983
...@@ -967,9 +967,12 @@ def print_progress(current_progress, progress_name, track=True): ...@@ -967,9 +967,12 @@ def print_progress(current_progress, progress_name, track=True):
assert 0 <= current_progress <= 1, "'current_progress' must be between 0 and 1" assert 0 <= current_progress <= 1, "'current_progress' must be between 0 and 1"
assert isinstance(track, bool), "'track' must be a bool." assert isinstance(track, bool), "'track' must be a bool."
if track: if track:
print("\r" + f"{progress_name.ljust(30)}" print(
"\r"
f"{progress_name.ljust(30)}"
f"|{'■' * int(50 * current_progress):{50}s}| " f"|{'■' * int(50 * current_progress):{50}s}| "
f"\033[94m {'{:6.2f}'.format(100 * current_progress)}% \033[0m ", flush=True, end="") f"\033[94m {'{:6.2f}'.format(100 * current_progress)}% \033[0m ", flush=True, end=""
)
if current_progress == 1: if current_progress == 1:
print(" (Done)") print(" (Done)")
......
paddle_quantum/optimizer/conjugate_gradient.py
浏览文件 @ 016af983
...@@ -19,6 +19,7 @@ CG optimizer ...@@ -19,6 +19,7 @@ CG optimizer
from scipy import optimize from scipy import optimize
from .custom_optimizer import CustomOptimizer from .custom_optimizer import CustomOptimizer
class ConjugateGradient(CustomOptimizer): class ConjugateGradient(CustomOptimizer):
r"""ConjugateGradient Optimizer r"""ConjugateGradient Optimizer
...@@ -57,6 +58,6 @@ class ConjugateGradient(CustomOptimizer): ...@@ -57,6 +58,6 @@ class ConjugateGradient(CustomOptimizer):
method='CG', method='CG',
jac=self.grad_func, jac=self.grad_func,
options={'maxiter': iterations}, options={'maxiter': iterations},
callback=lambda xk: print('loss: ', (self.loss_func(xk, self.cir, self.hamiltonian, self.shots))) callback=lambda xk: print('loss: ', self.loss_func(xk, self.cir, self.hamiltonian, self.shots))
) )
print(opt_res.message) print(opt_res.message)
paddle_quantum/optimizer/newton_cg.py
浏览文件 @ 016af983
...@@ -19,6 +19,7 @@ Newton-CG optimizer ...@@ -19,6 +19,7 @@ Newton-CG optimizer
from scipy import optimize from scipy import optimize
from .custom_optimizer import CustomOptimizer from .custom_optimizer import CustomOptimizer
class NewtonCG(CustomOptimizer): class NewtonCG(CustomOptimizer):
r"""Newton-CG Optimizer r"""Newton-CG Optimizer
...@@ -57,6 +58,6 @@ class NewtonCG(CustomOptimizer): ...@@ -57,6 +58,6 @@ class NewtonCG(CustomOptimizer):
method='Newton-CG', method='Newton-CG',
jac=self.grad_func, jac=self.grad_func,
options={'maxiter': iterations}, options={'maxiter': iterations},
callback=lambda xk: print('loss: ', (self.loss_func(xk, self.cir, self.hamiltonian, self.shots))) callback=lambda xk: print('loss: ', self.loss_func(xk, self.cir, self.hamiltonian, self.shots))
) )
print(opt_res.message) print(opt_res.message)
paddle_quantum/optimizer/powell.py
浏览文件 @ 016af983
...@@ -19,6 +19,7 @@ Powell optimizer ...@@ -19,6 +19,7 @@ Powell optimizer
from scipy import optimize from scipy import optimize
from .custom_optimizer import CustomOptimizer from .custom_optimizer import CustomOptimizer
class Powell(CustomOptimizer): class Powell(CustomOptimizer):
r"""Powell Optimizer r"""Powell Optimizer
......
paddle_quantum/optimizer/slsqp.py
浏览文件 @ 016af983
...@@ -19,6 +19,7 @@ SLSQP optimizer ...@@ -19,6 +19,7 @@ SLSQP optimizer
from scipy import optimize from scipy import optimize
from .custom_optimizer import CustomOptimizer from .custom_optimizer import CustomOptimizer
class SLSQP(CustomOptimizer): class SLSQP(CustomOptimizer):
r"""SLSQP Optimizer r"""SLSQP Optimizer
......
paddle_quantum/qchem/__init__.py 0 → 100755
浏览文件 @ 016af983
# Copyright (c) 2021 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.
"""
量桨平台的量子化学模块
"""
from .qmodel import QModel
from . import ansatz
from .run import run_chem
from .qchem import *
import platform
import warnings
__all__ = [
"run_chem",
"QModel",
"ansatz",
"geometry",
"get_molecular_data",
"active_space",
# forward compatible with original qchem module
"fermionic_hamiltonian",
"spin_hamiltonian"
]
if platform.system() == "Windows":
warning_msg = ("Currently, Windows' users can't use 'hartree fock' ansatz "
"for ground state energy calculation in `run_chem`, "
"since it depends on pyscf, which is not available on Windows. "
"We will work it out in the near future, sorry for the inconvenience.")
warnings.warn(message=warning_msg)
paddle_quantum/qchem/ansatz/__init__.py 0 → 100755
浏览文件 @ 016af983
# Copyright (c) 2021 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"""
化学模块的 ansatz
"""
from .hardware_efficient import HardwareEfficientModel
from .rhf import RestrictHartreeFockModel
paddle_quantum/qchem/ansatz/hardware_efficient.py 0 → 100755
浏览文件 @ 016af983
# Copyright (c) 2021 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.
"""
Hardware efficient ansatz 量子电路，以
`Hardware-efficient variational quantum eigensolver
for small molecules and quantum magnets` 方式构建。
具体细节可以参见 https://arxiv.org/abs/1704.05018
该模块依赖于
- paddlepaddle
- paddle_quantum
- ../layers
- ../qmodel
"""
import paddle
from paddle import nn
from paddle_quantum.circuit import UAnsatz
from ..qmodel import QModel
from .. import layers
class HardwareEfficientModel(QModel):
r"""面向硬件的量子线路。
Args:
num_qubit (int): 量子线路的量子比特数量。
circuit_depth (int): Cross resonance 和 Euler 转动层的数量。
"""
def __init__(self, num_qubit: int, circuit_depth: int) -> None:
super().__init__(num_qubit)
mid_layers = []
for i in range(circuit_depth):
mid_layers.append(layers.CrossResonanceLayer(num_qubit))
mid_layers.append(layers.EulerRotationLayer(num_qubit))
self.model = nn.Sequential(
layers.RotationLayer(num_qubit, "X"),
layers.RotationLayer(num_qubit, "Z"),
*mid_layers,
)
def forward(
self,
state: "paddle.Tensor[paddle.complex128]"
) -> "paddle.Tensor[paddle.complex128]":
r"""运行量子电路
Args:
state (paddle.Tensor[paddle.complex128]): 传入量子线路的量子态。
Returns:
paddle.Tensor[paddle.complex128]: 运行电路后的量子态
"""
out = self.model(state)
cir0 = UAnsatz(self._n_qubit)
for subcir in self.model:
cir0 += subcir.circuit
self._circuit = cir0
return out
paddle_quantum/qchem/ansatz/rhf.py 0 → 100755
浏览文件 @ 016af983
# Copyright (c) 2021 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.
"""
Restrict Hartree Fock 模块
"""
from collections import OrderedDict
from copy import deepcopy
import numpy as np
import paddle
from paddle.nn import initializer
from paddle_quantum.circuit import UAnsatz
from ..linalg import givens_decomposition, parameters_to_givens_matrix2
from ..qmodel import QModel
from .. import functional
class _MakeGivensMatrix(paddle.autograd.PyLayer):
r"""Construct Givens rotation matrix G from parameters \theta and \phi.
.. math::
G[j-1,j-1] = \cos(\theta)
G[j,j] = \cos(\theta)
G[j-1,j] = -\phi\sin(\theta)
G[j,j-1] = \phi\sin(\theta)
We define this function since paddle doesn't fully support differentiate over
copy and slice operation, e.g. A[i,j] = \theta, where \theta is the parameter
to be differentiated.
"""
@staticmethod
def forward(ctx, theta: paddle.Tensor, phi: paddle.Tensor, j: int, n: int):
G = parameters_to_givens_matrix2(theta, phi, j, n)
ctx.saved_index = j
ctx.save_for_backward(theta, phi)
return G
@staticmethod
def backward(ctx, dG):
j = ctx.saved_index
theta, phi = ctx.saved_tensor()
dtheta = (-1.0 * (dG[j - 1, j - 1] + dG[j, j]) * paddle.sin(theta)
+ (dG[j, j - 1] - dG[j - 1, j]) * phi * paddle.cos(theta))
return dtheta, None
class RestrictHartreeFockModel(QModel):
r"""限制性 Hartree Fock (RHF) 波函数的量子线路。
Args:
num_qubits (int): RHF 计算中需要使用的量子比特数量。
n_electrons (int): 待模拟的量子化学系统中的电子数量。
onebody (paddle.Tensor(dtype=paddle.float64)): 经过 L\"owdin 正交化之后的单体积分。
"""
def __init__(
self,
num_qubits: int,
n_electrons: int,
onebody: paddle.Tensor
) -> None:
super().__init__(num_qubits)
self.nocc = n_electrons // 2
self.norb = num_qubits // 2
self.nvir = self.norb - self.nocc
givens_angles = self.get_init_givens_angles(onebody)
models = []
for ij, (theta, phi) in givens_angles.items():
models.append((ij, _GivensBlock(self.n_qubit, -theta, phi)))
self.models = paddle.nn.Sequential(*models)
def get_init_givens_angles(self, onebody: paddle.Tensor) -> OrderedDict:
r"""利用单体积分来初始化 Givens 旋转的角度。
Args:
onebody (paddle.Tensor): 经过 L\"owdin 正交化之后的单体积分。
Returns:
OrderedDict
"""
assert type(onebody) == paddle.Tensor, "The onebody integral must be a paddle.Tensor."
_, U = np.linalg.eigh(onebody.numpy())
U_tensor = paddle.to_tensor(U)
return givens_decomposition(U_tensor)
def forward(self, state: paddle.Tensor) -> paddle.Tensor:
r"""运行量子电路
Args:
state (paddle.Tensor[paddle.complex128]): 传入量子线路的量子态矢量。
Returns:
paddle.Tensor[paddle.complex128]: 运行电路后的量子态
"""
s = deepcopy(state)
self._circuit = UAnsatz(self.n_qubit)
for ij, givens_ops in self.models.named_children():
i, j = [int(p) for p in ij.split(",")]
s = givens_ops(s, 2 * i, 2 * j)
self._circuit += givens_ops.circuit
s = givens_ops(s, 2 * i + 1, 2 * j + 1)
self._circuit += givens_ops.circuit
return s
def single_particle_U(self):
r"""获取 Hartree Fock 轨道旋转矩阵
Returns:
paddle.Tensor, Hartree Fock 轨道旋转矩阵，:math:`n_{orbitals}\times n_{occ}`
"""
self.register_buffer("_U", paddle.eye(int(self.norb), dtype=paddle.float64))
for ij, givens_ops in self.models.named_children():
j = int(ij.split(",")[1])
self._U = givens_ops.single_particle_U(j, self.norb) @ self._U
return self._U[:, :self.nocc]
paddle_quantum/qchem/functional.py 0 → 100755
浏览文件 @ 016af983
# !/usr/bin/env python3
# Copyright (c) 2021 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.
"""
用于构建量子电路层的函数操作。
该模块依赖于 paddlepaddle 和 paddle_quantum
"""
import paddle
from paddle_quantum.circuit import UAnsatz
# Rotation layer function
def rot_layer(
cir: UAnsatz,
parameters: "paddle.Tensor[paddle.float64]",
gate_type: str
) -> UAnsatz:
r"""该函数用来在量子线路上添加一层单比特旋转门，"Rx", "Ry", "Rz"
Args:
cir (UAnsatz): 量子线路
parameters (paddle.Tensor[paddle.float64]): 旋转门的旋转角度
gate_type (str): "X", "Y" 和 "Z"，例如：如果是 "Rx" 门，则添 "X"
Returns:
UAnsatz
"""
n_qubits = cir.n
assert n_qubits == len(parameters), \
"length of the parameters must equal the number of qubits"
for i in range(n_qubits):
if gate_type == "X":
cir.rx(parameters[i], i)
elif gate_type == "Y":
cir.ry(parameters[i], i)
elif gate_type == "Z":
cir.rz(parameters[i], i)
return cir
# Euler rotation gate function
def euler_rotation(
cir: UAnsatz,
which_qubit: int,
angles: "paddle.Tensor[paddle.float64]",
) -> UAnsatz:
r"""该函数定义了单比特的 Euler 旋转门（使用 ZXZ 规范）
.. math::
U(\theta,\phi,\gamma)=e^{-i\gamma/2\hat{Z}}e^{-i\phi/2\hat{X}}e^{-i\theta/2\hat{X}}.
Args:
cir (UAnsatz): 量子线路
which (int): Euler 旋转门作用的量子比特编号
angles (paddle.Tensor[paddle.float64]): Euler 角，存储顺序与 ZXZ 操作的顺序相反。
Returns:
UAnsatz
"""
cir.rz(angles[0], which_qubit)
cir.rx(angles[1], which_qubit)
cir.rz(angles[2], which_qubit)
return cir
# Euler rotation layer function
def euler_rotation_layer(
cir: UAnsatz,
parameters: "paddle.Tensor[paddle.float64]",
) -> UAnsatz:
r"""该函数会在给定的量子线路上添加一层 Euler 旋转门。
Args:
cir (UAnsatz): 量子线路。
parameters (paddle.Tensor[paddle.float64]): Euler 角参数集合。
"""
n_qubits = cir.n
assert len(
parameters) == 3 * n_qubits, "length of parameter should be 3 times of the number of qubits in the circuit."
for i in range(n_qubits):
cir = euler_rotation(cir, i, parameters[3 * i:3 * (i + 1)])
return cir
# Cross resonance gate function
def cross_resonance(
cir: UAnsatz,
ctrl_targ: "list[int]",
phase_angle: paddle.Tensor
) -> UAnsatz:
r"""该函数定义了一个双比特的 cross resonance (CR) 门。
.. math::
U(\theta) = \exp(-i\frac{\theta}{2}\hat{X}\otimes\hat{Z})
Args:
cir (UAnsatz): 量子线路。
ctrl_targ (list[int]): 控制比特和目标比特对应的比特编号。
phase_angle (paddle.Tensor[paddle.float64]): 旋转角度。
Returns:
UAnsatz
"""
cir.h(ctrl_targ[0])
cir.rzz(phase_angle, ctrl_targ)
cir.h(ctrl_targ[0])
return cir
# Cross resonance layer function
def cr_layer(
cir: UAnsatz,
parameters: "paddle.Tensor[paddle.float64]",
ctrl_qubit_index: "list[int]",
targ_qubit_index: "list[int]"
) -> UAnsatz:
"""该函数在给定线路上按照给定的控制和目标比特编号添加一层 cross resonance (CR) 门。
Args:
cir (UAnsatz): 量子线路。
parameters (paddle.Tensor[paddle.float64]): CR 门中的角度。
ctrl_qubit_index (list[int]): 控制比特序号。
targ_qubit_index (list[int]): 目标比特序号。
Returns:
UAnsatz
"""
assert len(parameters) == len(ctrl_qubit_index) and len(ctrl_qubit_index) == len(targ_qubit_index), \
"length of parameter must be the same as the number of cr gates"
for i, ct_index in enumerate(zip(ctrl_qubit_index, targ_qubit_index)):
cir = cross_resonance(cir, list(ct_index), parameters[i])
return cir
# Nearest neighbor Givens rotation gate function
def givens_rotation(
cir: UAnsatz,
theta: "paddle.Tensor[paddle.float64]",
q1_index: int,
q2_index: int
) -> UAnsatz:
r"""该函数定义了两个相邻比特之间的 Givens 旋转门。详细信息参见 https://arxiv.org/abs/1711.05395.
Note:
在 paddlequantum :math:`Ry(\theta)=e^{-i\frac{\theta}{2}\hat{Y}}`.
Args:
cir (UAnsatz): 量子线路。
theta (paddle.Tensor[paddle.float64]): 操作中 Ry 门的角度。
q1_index (int): 第一个 qubit 的编号。
q2_index (int): 第二个 qubit 的编号。
Returns:
UAnsatz
"""
cir.cnot([q2_index, q1_index])
cir.cry(-2 * theta, [q1_index, q2_index])
cir.cnot([q2_index, q1_index])
return cir
paddle_quantum/qchem/layers.py 0 → 100755
浏览文件 @ 016af983
# !/usr/bin/env python3
# Copyright (c) 2021 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.
"""
量子电路层，该模块依赖于 paddlepaddle，paddle_quantum 和 math 包。
同时依赖于 qmodel 和 functional 模块。
"""
import math
import paddle
from paddle.nn import initializer
from paddle_quantum.circuit import UAnsatz
from .qmodel import QModel
from . import functional
# Rotation layer
class RotationLayer(QModel):
r"""单比特旋转门层。
Args:
num_qubits (int): 量子线路的量子比特数。
gate_type (str): 量子门的类型，"X", "Y" 和 "Z" 中的一个。
trainable (bool): 层中的角度参数是否可训练。
"""
def __init__(self, num_qubits: int, gate_type: str, trainable: bool = True):
super().__init__(num_qubits)
self._angle_attr = paddle.ParamAttr(
initializer=initializer.Uniform(0.0, 2*math.pi),
trainable=trainable
)
self.angles = self.create_parameter(
shape=[num_qubits],
attr=self._angle_attr,
dtype="float64"
)
self._gate_type = gate_type
def forward(
self,
state: "paddle.Tensor[paddle.complex128]"
) -> "paddle.Tensor[paddle.complex128]":
r"""获取运行后的量子态
Args:
state (paddle.Tensor[paddle.complex128, shape=[n]]): 送入电路的量子态
Returns:
paddle.Tensor[paddle.complex128, shape=[n]]: 运行电路后的量子态
"""
cir0 = UAnsatz(self._n_qubit)
self._circuit = functional.rot_layer(cir0, self.angles, self._gate_type)
return self.circuit.run_state_vector(state)
def extra_repr(self):
r"""额外表示
"""
return "gate={:s}, dtype={:s}".format(
self._gate_type,
self.angles.dtype.name)
# Euler rotation layer
class EulerRotationLayer(QModel):
r"""Euler 旋转门层。
Args:
num_qubits (int): 量子线路中的量子比特数量。
trainable (bool): 层中的参数是否是可训练的。
"""
def __init__(self, num_qubits: int, trainable: bool = True) -> None:
super().__init__(num_qubits)
self._angle_attr = paddle.ParamAttr(
initializer=initializer.Uniform(0.0, 2*math.pi),
trainable=trainable
)
self.euler_angles = self.create_parameter(
shape=[3*num_qubits],
attr=self._angle_attr,
dtype="float64"
)
def forward(
self,
state: "paddle.Tensor[paddle.complex128]"
) -> "paddle.Tensor[paddle.complex128]":
r"""获取运行后的量子态
Args:
state (paddle.Tensor[paddle.complex128, shape=[n]]): 送入电路的量子态
Returns:
paddle.Tensor[paddle.complex128, shape=[n]]: 运行电路后的量子态
"""
cir0 = UAnsatz(self._n_qubit)
self._circuit = functional.euler_rotation_layer(cir0, self.euler_angles)
return self._circuit.run_state_vector(state)
def extra_repr(self):
r"""额外表示
"""
return "dtype={:s}".format(self.euler_angles.dtype.name)
# Cross resonance layer
class CrossResonanceLayer(QModel):
r"""在量子线路中按照给定的控制和目标比特添加一层 cross resonance 门。
Args:
num_qubits (int): 量子比特数目。
ctrl_qubit_index (list[int]): 控制比特的序号。
targ_qubit_index (list[int]): 目标比特的序号。
trainable (bool): 层中的参数是否可训练。
"""
def __init__(
self,
num_qubits: int,
ctrl_qubit_index: "list[int]" = None,
targ_qubit_index: "list[int]" = None,
trainable: bool = True
) -> None:
super().__init__(num_qubits)
if ctrl_qubit_index is None:
ctrl_qubit_index = list(range(num_qubits))
if targ_qubit_index is None:
targ_qubit_index = list(range(1, num_qubits)) + [0]
self._ctrl_qubit_index = ctrl_qubit_index
self._targ_qubit_index = targ_qubit_index
self._phase_attr = paddle.ParamAttr(
initializer=initializer.Uniform(0.0, 2*math.pi),
trainable=trainable
)
self.phase = self.create_parameter(
shape=[len(ctrl_qubit_index)],
attr=self._phase_attr,
dtype="float64"
)
def forward(
self,
state: "paddle.Tensor[paddle.complex128]"
) -> "paddle.Tensor[paddle.complex128]":
r"""获取运行后的量子态
Args:
state (paddle.Tensor[paddle.complex128, shape=[n]]): 送入电路的量子态
Returns:
paddle.Tensor[paddle.complex128, shape=[n]]: 运行电路后的量子态
"""
cir0 = UAnsatz(self._n_qubit)
self._circuit = functional.cr_layer(
cir0,
self.phase,
self._ctrl_qubit_index,
self._targ_qubit_index)
return self._circuit.run_state_vector(state)
def extra_repr(self):
r"""额外表示
"""
return "dtype={:s}".format(self.phase.dtype.name)
paddle_quantum/qchem/linalg.py 0 → 100755
浏览文件 @ 016af983
# !/usr/bin/env python3
# Copyright (c) 2021 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.
"""
qchem 开发所需的线性代数操作
"""
from typing import OrderedDict, Tuple
from collections import OrderedDict
import math
from copy import deepcopy
import paddle
DEFAULT_TOL = 1e-8
def get_givens_rotation_parameters(
a: paddle.Tensor,
b: paddle.Tensor
) -> Tuple[paddle.Tensor]:
r"""计算 Givens 旋转的 (c,s) 参数。
详细过程参见：https://www.netlib.org/lapack/lawnspdf/lawn148.pdf
Note:
:math:`r = \operatorname{sign}(a)\sqrt{a^2+b^2}, c = |a|/|r|, s = \operatorname{sign}(a)*b/|r|`
Args:
a (paddle.Tensor(dtype=float64)): 计算所用参数
b (paddle.Tensor(dtype=float64)): 计算所用参数
Returns:
tuple:
- c (paddle.Tensor(dtype=float64))
- s (paddle.Tensor(dtype=float64))
"""
assert a.dtype is paddle.float64 and b.dtype is paddle.float64,\
"dtype not match, require dtype of a, b be paddle.float64!"
if math.isclose(b.item(), 0.0, abs_tol=DEFAULT_TOL):
r = a
c = paddle.to_tensor(1.0, dtype=paddle.float64)
s = paddle.to_tensor(0.0, dtype=paddle.float64)
elif math.isclose(a.item(), 0.0, abs_tol=DEFAULT_TOL):
r = b.abs()
c = paddle.to_tensor(0.0, dtype=paddle.float64)
s = paddle.sign(b)
else:
abs_r = paddle.sqrt(a.abs()**2+b.abs()**2)
r = paddle.sign(a)*abs_r
c = a.abs()/abs_r
s = paddle.sign(a)*b/abs_r
return r, c, s
def parameter_to_givens_matrix1(c: paddle.Tensor, s: paddle.Tensor, j: int, n_size: int):
r"""该函数可利用 (c,s) 参数来构造 Givens 旋转矩阵以消去 A[i,j] 上的元素。
Args:
c (paddle.Tensor): :math:`|A[i,j-1]|/r`, 其中 :math:`r=\sqrt{A[i,j-1]^2+A[i,j]^2}`;
s (paddle.Tensor): :math:`\operatorname{sign}{(A[i,j]*A[i,j-1])*A[i,j]/r)}`;
j (int): 计算所用参数
n_size (int): Givens 旋转矩阵的维度
Returns:
Givens 旋转矩阵 (paddle.Tensor)
"""
G = paddle.eye(n_size, dtype=paddle.float64)
G[j - 1, j - 1] = c
G[j, j] = c
G[j - 1, j] = -s
G[j, j - 1] = s
return G
def givens_decomposition(A: paddle.Tensor) -> OrderedDict:
r"""对于一个给定的矩阵 A，该函数会返回一个 Givens 旋转操作的 list，用户可以使用其中的 Givens 旋转操作消除掉 A 的上三角的元素。
Note:
:math:`r = \operatorname{sign}(a)\sqrt{a^2+b^2}, c = |a|/|r|`
:math:`s = \operatorname{sign}(a)*b/|r| , \theta = arc\cos(c), phi = \operatorname{sign}(a*b)`
:math:`A^{\prime}[:,j-1] = c*A[:,j-1]+s*A[:,j]`
:math:`A^{\prime}[:,j] = -s*A[:,j-1]+c*A[:,j]`
Args:
A (paddle.Tensor(dtype=paddle.float64)): 矩阵
Returns:
OrderedDict, 包含 Givens 旋转操作以及其对应的参数。
"""
n = A.shape[0]
assert n == A.shape[1], "The input tensor should be a square matrix."
assert A.dtype is paddle.float64, "dtype of input tensor must be paddle.float64!"
# The givens rotations are not parallel !!!
A1 = deepcopy(A)
rotations = []
for i in range(n):
for j in range(n-1, i, -1):
_, c, s = get_givens_rotation_parameters(A1[i, j - 1], A1[i, j])
theta = paddle.acos(c)
phi = paddle.sign(A1[i, j - 1]*A1[i, j])
rotations.append((f"{i:>d},{j:>d}", (theta, phi)))
# update A matrix
A1_jprev = c*A1[:, j - 1] + s*A1[:, j]
A1_j = -s*A1[:, j-1] + c*A1[:, j]
A1[:, j-1] = A1_jprev
A1[:, j] = A1_j
return OrderedDict(rotations)
def parameters_to_givens_matrix2(
theta: paddle.Tensor,
phi: paddle.Tensor,
j: int,
n_size: int
) -> paddle.Tensor:
r"""该函数用来从 :math:`(\theta,\phi)` 参数中构建 Givens 旋转矩阵消去 :math:`A[i,j]`。
Args:
theta (paddle.Tensor): arccos(c);
phi (paddle.Tensor): :math:`\operatorname{sign}(A[i,j-1]*A[i,j])`;
j (int): 计算所用参数
n_size (int): Givens 旋转矩阵的维度。
Returns:
paddle.Tensor, Givens 旋转矩阵
"""
G = paddle.eye(int(n_size), dtype=paddle.float64)
G[j - 1, j - 1] = paddle.cos(theta)
G[j, j] = paddle.cos(theta)
G[j - 1, j] = -phi*paddle.sin(theta)
G[j, j - 1] = phi*paddle.sin(theta)
return G
paddle_quantum/qchem/molecule.py 0 → 100755
浏览文件 @ 016af983
# !/usr/bin/env python3
# Copyright (c) 2021 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.
"""
从分子结构等信息中提取量子化学需要的输入。
"""
from typing import Tuple, List
import numpy as np
from pyscf import gto, scf
from pyscf.lo import lowdin
# Transform one and two body integral into L\"owdin basis
def lowdin_transform(
ovlp: np.array,
onebody: np.array,
twobody: np.array
) -> Tuple[np.array]:
r"""该函数会将 pyscf 中得到的高斯积分利用 L\"owdin 正交化方法进行变换。
Note:
L\"owdin 正交化:
:math:`S_{ij}=\langle\phi_i^{\text{G}}|\phi_j^{\text{G}}\rangle`,
:math:`X = S^{-1/2}`
Operators 的变换方式:
:math:`A^{\prime}_{ij}=\sum_{pq}A_{pq}X_{ip}X_{qj}`
:math:`B^{\prime}_{iklj}=\sum_{pqrs}B_{prsq}X_{ip}X_{kr}X_{sl}X_{qj}`
分子轨道的变换方式:
:math:`C^{\prime}_{ij}=\sum_{p}C_{pj}X^{-1}_{ip}`
Args:
ovlp (np.array): 交叠积分，`mol.intor("int1e_ovlp")`。
onebody (np.array): 单体积分，`mol.intor("int1e_kin")+mol.intor("int1e_nuc")`。
twobody (np.array): 两体积分，`mol.intor("int2e")`。
Returns:
Tuple[np.array]:
- 变换之后的单体积分。
- 变换之后的两体积分。
"""
inv_half_ovlp = lowdin(ovlp)
t_onebody = inv_half_ovlp @ onebody @ inv_half_ovlp
t_twobody = np.einsum(
"pqrs,ip,qj,kr,sl->ijkl",
twobody, inv_half_ovlp, inv_half_ovlp, inv_half_ovlp, inv_half_ovlp
)
return t_onebody, t_twobody
# Molecular information
def get_molecular_information(
geometry: List[Tuple[str, List]],
basis: str = "sto-3g",
charge: int = 0,
debug: bool = False
) -> Tuple:
r"""该函数会返回量子化学（目前是 "hartree fock" 方法）计算所需要的分子信息，包括有计算需要的量子比特的数量，分子中的电子数，分子积分和 pyscf 平均场结果 (optional)。
Args:
geometry (List[Tuple[str,List]]): 分子中各原子笛卡尔坐标；
basis (str): 基函数名称，例如："sto-3g"；
charge (int): 分子的电荷；
debug (bool): 是否使用 debug 模式。debug 模式会返回 pyscf 的平均场计算结果。
Returns:
Tuple:
- 量子比特数目；
- 分子中的电子数；
- 原子核之间的排斥能、单体积分、双体积分；
- pyscf 的平均场计算结果 (可选，只有 debug=True 才会返回)。
"""
mol = gto.M(atom=geometry, basis=basis, charge=charge, unit="angstrom")
mol.build()
if debug:
mf_mol = scf.RHF(mol).run()
int_ovlp = mol.intor("int1e_ovlp")
nuc_energy = mol.energy_nuc()
onebody = mol.intor("int1e_kin") + mol.intor("int1e_nuc")
twobody = mol.intor("int2e")
orth_onebody, orth_twobody = lowdin_transform(int_ovlp, onebody, twobody)
if debug:
return 2*mol.nao, mol.nelectron, (nuc_energy, orth_onebody, 0.5*orth_twobody), mf_mol
else:
return 2*mol.nao, mol.nelectron, (nuc_energy, orth_onebody, 0.5*orth_twobody)
paddle_quantum/qchem.py → paddle_quantum/qchem/qchem.py 100644 → 100755
浏览文件 @ 016af983
# !/usr/bin/env python3
# Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. # Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.
# #
# Licensed under the Apache License, Version 2.0 (the "License"); # Licensed under the Apache License, Version 2.0 (the "License");
...@@ -13,7 +14,7 @@ ...@@ -13,7 +14,7 @@
# limitations under the License. # limitations under the License.
""" """
Quantum chemistry module 量子化学模块
""" """
import os import os
...@@ -73,14 +74,14 @@ def _hamiltonian_transformation(spin_h, tol=1e-8): ...@@ -73,14 +74,14 @@ def _hamiltonian_transformation(spin_h, tol=1e-8):
def _geo_str(geometry): def _geo_str(geometry):
r"""创建分子几何信息的字符串。 r"""创建分子几何信息的字符串
Args: Args:
geometry (list): 包含了分子的几何信息，以 H2 分子为例 geometry (list): 包含了分子的几何信息，以 H2 分子为例
[['H', [-1.68666, 1.79811, 0.0]], ['H', [-1.12017, 1.37343, 0.0]]]。 [['H', [-1.68666, 1.79811, 0.0]], ['H', [-1.12017, 1.37343, 0.0]]]
Returns: Returns:
str: 分子几何信息的字符串。 str: 分子几何信息的字符串
""" """
geo_str = '' geo_str = ''
for item in geometry: for item in geometry:
...@@ -110,14 +111,14 @@ def _run_psi4( ...@@ -110,14 +111,14 @@ def _run_psi4(
以及用 scf 和 fci 的方法计算基态的能量。 以及用 scf 和 fci 的方法计算基态的能量。
Args: Args:
molecule (MolecularData object): 包含分子所有信息的类 (class)。 molecule (MolecularData object): 包含分子所有信息的类 (class)
charge (int): 分子的电荷。 charge (int): 分子的电荷
multiplicity (int): 分子的多重度。 multiplicity (int): 分子的多重度
method (str): 用于计算基态能量的方法，包括 'scf'和 'fci'。 method (str): 用于计算基态能量的方法，包括 'scf'和 'fci'
basis (str): 常用的基组是 'sto-3g', '6-31g'等。更多的基组选择可以参考网站。 basis (str): 常用的基组是 'sto-3g', '6-31g'等。更多的基组选择可以参考网站
https://psicode.org/psi4manual/master/basissets_byelement.html#apdx-basiselement。 https://psicode.org/psi4manual/master/basissets_byelement.html#apdx-basiselement
if_print (Boolean): 是否需要打印出选定方法 (method) 计算出的分子基态能量。 if_print (Boolean): 是否需要打印出选定方法 (method) 计算出的分子基态能量
if_save (Boolean): 是否需要将分子信息存储成 .hdf5 文件。 if_save (Boolean): 是否需要将分子信息存储成 .hdf5 文件
""" """
psi4.set_memory('500 MB') psi4.set_memory('500 MB')
psi4.set_options({'soscf': 'false', psi4.set_options({'soscf': 'false',
...@@ -182,7 +183,7 @@ def _run_psi4( ...@@ -182,7 +183,7 @@ def _run_psi4(
def geometry(structure=None, file=None): def geometry(structure=None, file=None):
r"""读取分子的几何信息。 r"""读取分子的几何信息
Args: Args:
structure (string, optional): 分子几何信息的字符串形式，以 H2 分子为例 structure (string, optional): 分子几何信息的字符串形式，以 H2 分子为例
...@@ -193,9 +194,9 @@ def geometry(structure=None, file=None): ...@@ -193,9 +194,9 @@ def geometry(structure=None, file=None):
str: 分子的几何信息 str: 分子的几何信息
Raises: Raises:
AssertionError: 两个输入参数不可以同时为 ``None`` 。 AssertionError: 两个输入参数不可以同时为 ``None``
""" """
if ((structure is None) and (file is None)): if structure is None and file is None:
raise AssertionError('Input must be structure or .xyz file') raise AssertionError('Input must be structure or .xyz file')
elif file is None: elif file is None:
shape = np.array(structure).shape shape = np.array(structure).shape
...@@ -270,28 +271,34 @@ def get_molecular_data( ...@@ -270,28 +271,34 @@ def get_molecular_data(
else: else:
filename = name + '.hdf5' filename = name + '.hdf5'
molecule = MolecularData(geometry, molecule = MolecularData(
geometry,
basis=basis, basis=basis,
multiplicity=multiplicity, multiplicity=multiplicity,
charge=charge, charge=charge,
filename=filename) filename=filename
)
_run_psi4(molecule, _run_psi4(
molecule,
charge, charge,
multiplicity, multiplicity,
method, method,
basis, basis,
if_print, if_print,
if_save) if_save
)
return molecule return molecule
def active_space(electrons, def active_space(
electrons,
orbitals, orbitals,
multiplicity=1, multiplicity=1,
active_electrons=None, active_electrons=None,
active_orbitals=None): active_orbitals=None
):
r"""对于给定的活跃电子和活跃轨道计算相应的活跃空间（active space）。 r"""对于给定的活跃电子和活跃轨道计算相应的活跃空间（active space）。
Args: Args:
...@@ -340,11 +347,13 @@ def active_space(electrons, ...@@ -340,11 +347,13 @@ def active_space(electrons,
return core_orbitals, active_orbitals return core_orbitals, active_orbitals
def fermionic_hamiltonian(molecule, def fermionic_hamiltonian(
molecule,
filename=None, filename=None,
multiplicity=1, multiplicity=1,
active_electrons=None, active_electrons=None,
active_orbitals=None): active_orbitals=None
):
r"""计算给定分子的费米哈密顿量。 r"""计算给定分子的费米哈密顿量。
Args: Args:
...@@ -375,12 +384,14 @@ def fermionic_hamiltonian(molecule, ...@@ -375,12 +384,14 @@ def fermionic_hamiltonian(molecule,
return fermionic_hamiltonian return fermionic_hamiltonian
def spin_hamiltonian(molecule, def spin_hamiltonian(
molecule,
filename=None, filename=None,
multiplicity=1, multiplicity=1,
mapping_method='jordan_wigner', mapping_method='jordan_wigner',
active_electrons=None, active_electrons=None,
active_orbitals=None): active_orbitals=None
):
r"""生成 Paddle Quantum 格式的哈密顿量 r"""生成 Paddle Quantum 格式的哈密顿量
Args: Args:
......
paddle_quantum/qchem/qmodel.py 0 → 100755
浏览文件 @ 016af983
# !/usr/bin/env python3
# Copyright (c) 2021 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.
"""
用于构建量子电路层的基类
该模块依赖 paddlepaddle。
"""
from paddle import nn
class QModel(nn.Layer):
r"""量子化学用量子线路的基类，任何自定义量子线路都需要继承自这个类。
"""
def __init__(self, num_qubit: int):
r"""构造函数
Args:
num_qubit (int): 量子比特数目
"""
super().__init__(name_scope="QModel")
self._n_qubit = num_qubit
self._circuit = None
@property
def n_qubit(self):
r"""量子比特数目
"""
return self._n_qubit
@property
def circuit(self):
r"""量子电路
"""
if self._circuit is None:
print("Circuit is not built, please run `forward` to build the circuit first.")
return None
else:
return self._circuit
paddle_quantum/qchem/run.py 0 → 100755
浏览文件 @ 016af983
# !/usr/bin/env python3
# Copyright (c) 2021 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.
"""
利用不同的 ansatz 运行量子化学计算。
"""
from typing import List, Tuple, Callable
import numpy as np
import paddle
from paddle.optimizer import Optimizer, Adam
from . import qchem as pq_chem
import paddle_quantum.state as pq_state
from paddle_quantum.intrinsic import vec_expecval
from .ansatz.rhf import RestrictHartreeFockModel
from .qmodel import QModel
from .ansatz import HardwareEfficientModel
def _minimize(
model: QModel,
loss_fn: Callable[[QModel], Tuple[float, QModel]],
optimizer: Optimizer,
max_iters: int,
a_tol: float
) -> Tuple[float, QModel]:
loss_prev = -np.inf
for i in range(max_iters):
with paddle.no_grad():
loss = loss_fn(model)
print(f"Iteration {i+1:>d}, {model.__class__.__name__} energy {loss.item():>.5f}.")
if np.abs(loss.item() - loss_prev) < a_tol:
print(f"Converge after {(i+1):>d} number of iterations.")
break
else:
loss_prev = loss.item()
optimizer.clear_grad()
loss = loss_fn(model)
loss.backward()
optimizer.step()
with paddle.no_grad():
loss = loss_fn(model)
return loss.item(), model
def run_chem(
geometry: List[Tuple[str, List[float]]],
ansatz: str,
basis_set: str = "sto-3g",
charge: int = 0,
max_iters: int = 100,
a_tol: float = 1e-6,
optimizer_option: dict = {},
ansatz_option: dict = {}
) -> Tuple[float, QModel]:
r"""根据输入的分子信息进行量子化学计算。
Args:
geometry (List[Tuple[str, List[float]]]): 分子的几何结构，例如：[("H", [0.0, 0.0, 0.0]), ("H", [0.0, 0.0, 0.74])]。定义结构时使用的长度单位是 Angstrom。
ansatz (str): 表示多体波函数的量子线路，目前我们支持 "hardware efficient" 和 "hartree fock"。
basis_set (str): 用来展开原子轨道的量子化学的基函数，例如："sto-3g"。注意，复杂的基函数会极大占用计算资源。
charge (int): 分子的电荷量。
max_iters (int): 优化过程的最大迭代次数。
a_tol (float): 优化收敛的判断依据，当 :math:`|e_{i+1} - e_i| < a_{tol}` 时，优化结束。
optimizer_options (dict): 优化器的可选参数，例如：学习率 (learning_rate)、权重递减 (weight_decay)。
ansatz_option (dict): 定义 ansatz 量子线路的可选参数。目前，对于 "hardware efficient" 方法，可选参数为 "cir_depth"（线路深度）。"hartree fock" 方法没有可选参数。
Returns:
tuple:
- 基态能量
- 优化后的 ansatz 量子线路
"""
if ansatz == "hardware efficient":
return run_hardware(
geometry, basis_set, charge,
max_iters, a_tol, optimizer_option, **ansatz_option
)
if ansatz == "hartree fock":
return run_rhf(
geometry, basis_set, charge,
max_iters, a_tol, optimizer_option, **ansatz_option
)
else:
raise NotImplementedError(
"""
Currently, we only support "hardware efficient" or "hartree fock" for `ansatz` parameter, we will add more in the future. You can open an issue here
https://github.com/PaddlePaddle/Quantum/issues to report the ansatz you're interested in.
""")
def run_hardware(
geometry: List[Tuple[str, List[float]]],
basis_set: str,
charge: int,
max_iters: int,
a_tol: float,
optimizer_option: dict = {},
cir_depth: int = 3
) -> Tuple[float, QModel]:
r"""hardware efficient 方法的 run 函数。
"""
mol_data = pq_chem.get_molecular_data(geometry, basis=basis_set, charge=charge, if_print=False)
mol_qubitH = pq_chem.spin_hamiltonian(mol_data)
n_qubits = mol_qubitH.n_qubits
ansatz = HardwareEfficientModel(n_qubits, cir_depth)
optimizer = Adam(parameters=ansatz.parameters(), **optimizer_option)
s0 = paddle.to_tensor(pq_state.vec(0, n_qubits))
s0 = paddle.reshape(s0, [2**n_qubits])
def loss_fn(model: QModel) -> paddle.Tensor:
s = model(s0)
return paddle.real(vec_expecval(mol_qubitH.pauli_str, s))
mol_gs_en, updated_ansatz = _minimize(ansatz, loss_fn, optimizer, max_iters, a_tol)
return mol_gs_en, updated_ansatz
def run_rhf(
geometry: List[Tuple[str, List[float]]],
basis_set: str,
charge: int,
max_iters: int,
a_tol: float,
optimizer_option: dict = {}
) -> Tuple[float, QModel]:
r"""hartree fock 方法的 run 函数。
"""
try:
import pyscf
except ModuleNotFoundError as e:
raise ModuleNotFoundError(
"""
Hartree Fock method needs `pyscf`,
please run `pip install -U pyscf` to first install pyscf.
""")
from .molecule import get_molecular_information
n_qubits, n_electrons, integrals = get_molecular_information(geometry, basis_set, charge)
nuc_energy, onebody, twobody = [paddle.to_tensor(t) for t in integrals]
ansatz = RestrictHartreeFockModel(n_qubits, n_electrons, onebody)
optimizer = Adam(parameters=ansatz.parameters(), **optimizer_option)
# run model to build the circuit
bstr = "1"*n_electrons+"0"*(n_qubits-n_electrons)
_s0 = paddle.to_tensor(pq_state.vec(int(bstr, 2), n_qubits))
_s0 = paddle.reshape(_s0, [2**n_qubits])
ansatz(_s0)
def loss_fn(model: QModel) -> paddle.Tensor:
U_hf = model.single_particle_U()
rdm1 = U_hf @ U_hf.conj().t()
return nuc_energy + 2*paddle.einsum("pq,qp->", onebody, rdm1)\
+ 4*paddle.einsum("pqrs,qp,sr->", twobody, rdm1, rdm1)\
- 2*paddle.einsum("pqrs,sp,qr->", twobody, rdm1, rdm1)
mol_gs_en, updated_ansatz = _minimize(ansatz, loss_fn, optimizer, max_iters, a_tol)
return mol_gs_en, updated_ansatz
paddle_quantum/shadow.py
浏览文件 @ 016af983
...@@ -19,6 +19,7 @@ shadow sample module ...@@ -19,6 +19,7 @@ shadow sample module
import numpy as np import numpy as np
import paddle import paddle
import re import re
import math
from paddle_quantum import circuit from paddle_quantum import circuit
from paddle_quantum.utils import Hamiltonian from paddle_quantum.utils import Hamiltonian
...@@ -27,6 +28,120 @@ __all__ = [ ...@@ -27,6 +28,120 @@ __all__ = [
] ]
def random_pauli_sample(num_qubits, beta=None):
r"""根据概率分布 beta, 随机选取 pauli 测量基
Args:
num_qubits (int): 量子比特数目
beta (list, optional): 量子位上不同 pauli 测量基的概率分布
Returns:
str: 返回随机选择的 pauli 测量基
Note:
这是内部函数，你并不需要直接调用到该函数。
"""
# assume beta obeys a uniform distribution if it is not given
if beta is None:
beta = list()
for _ in range(0, num_qubits):
beta.append([1 / 3] * 3)
pauli_sample = str()
for qubit_idx in range(num_qubits):
sample = np.random.choice(['x', 'y', 'z'], 1, p=beta[qubit_idx])
pauli_sample += sample[0]
return pauli_sample
def measure_by_pauli_str(pauli_str, phi, num_qubits, mode, method):
r"""搭建 pauli 测量电路，返回测量结果
Args:
pauli_str (str): 输入的是随机选取的num_qubits pauli 测量基
phi (numpy.ndarray): 输入量子态，支持态矢量和密度矩阵形式
num_qubits (int): 量子比特数量
mode (str): 输入量子态的表示方式，``"state_vector"`` 表示态矢量形式， ``"density_matrix"`` 表示密度矩阵形式
method (str): 进行测量的方法，有 "CS"、"LBCS"、"APS"
Returns:
str: 返回测量结果
Note:
这是内部函数，你并不需要直接调用到该函数。
"""
if method == "clifford":
# Add the clifford function
pass
else:
# Other method are transformed as follows
# Convert to tensor form
input_state = paddle.to_tensor(phi)
cir = circuit.UAnsatz(num_qubits)
for qubit in range(num_qubits):
if pauli_str[qubit] == 'x':
cir.h(qubit)
elif pauli_str[qubit] == 'y':
cir.h(qubit)
cir.s(qubit)
cir.h(qubit)
if mode == 'state_vector':
cir.run_state_vector(input_state)
else:
cir.run_density_matrix(input_state)
result = cir.measure(shots=1)
bit_string, = result
return bit_string
def paulistr_to_matrix(paulistr):
r"""识别随机选取的 pauli 并转换成作用于 Z 测量的酉变换的矩阵形式
Args:
paulistr (str): 输入的是某一量子位上随机选取的 Pauli 测量基
Returns:
numpy.ndarray: 返回酉变换的矩阵形式
Note:
这是内部函数，你并不需要直接调用到该函数。
"""
# Define the matrix form of H, S gates
a = math.pow(2, 0.5)
H_matrix = np.array([[1 / a, 1 / a], [1 / a, -1 / a]])
S_matrix = np.array([[1, 0], [0, 1j]])
I_matrix = np.array([[1, 0], [0, 1]])
if paulistr == 'x':
paulistr_matrix = H_matrix
elif paulistr == 'y':
paulistr_matrix = np.dot(np.dot(H_matrix, S_matrix), H_matrix)
elif paulistr == 'z':
paulistr_matrix = I_matrix
return paulistr_matrix
def measure_result_to_matrix(measure_str):
r"""将单个量子位上测量的结果转换为密度矩阵形式
Args:
measure_str (str): 输入的是某一量子位上的测量结果
Returns:
numpy.ndarray: 返回测量结果的密度矩阵形式
Note:
这是内部函数，你并不需要直接调用到该函数。
"""
ket_0 = np.array([[1, 0]]).T
ket_1 = np.array([[0, 1]]).T
if measure_str == '0':
b_matrix = np.kron(ket_0, ket_0.conj().T)
elif measure_str == '1':
b_matrix = np.kron(ket_1, ket_1.conj().T)
return b_matrix
def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, method='CS'): def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, method='CS'):
r"""对给定的量子态进行随机的泡利测量并返回测量结果。 r"""对给定的量子态进行随机的泡利测量并返回测量结果。
...@@ -108,68 +223,6 @@ def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, metho ...@@ -108,68 +223,6 @@ def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, metho
pauli2index = {'x': 0, 'y': 1, 'z': 2} pauli2index = {'x': 0, 'y': 1, 'z': 2}
def random_pauli_sample(num_qubits, beta=None):
r"""根据概率分布 beta, 随机选取 pauli 测量基
Args:
num_qubits (int): 量子比特数目
beta (list, optional): 量子位上不同 pauli 测量基的概率分布
Returns:
str: 返回随机选择的 pauli 测量基
Note:
这是内部函数，你并不需要直接调用到该函数。
"""
# assume beta obeys a uniform distribution if it is not given
if beta is None:
beta = list()
for _ in range(0, num_qubits):
beta.append([1 / 3] * 3)
pauli_sample = str()
for qubit_idx in range(num_qubits):
sample = np.random.choice(['x', 'y', 'z'], 1, p=beta[qubit_idx])
pauli_sample += sample[0]
return pauli_sample
def measure_by_pauli_str(pauli_str, phi, num_qubits, method):
r"""搭建 pauli 测量电路，返回测量结果
Args:
pauli_str (str): 输入的是随机选取的num_qubits pauli 测量基
phi (numpy.ndarray): 输入量子态，支持态矢量和密度矩阵形式
num_qubits (int): 量子比特数量
method (str): 进行测量的方法，有 "CS"、"LBCS"、"APS"
Returns:
str: 返回测量结果
Note:
这是内部函数，你并不需要直接调用到该函数。
"""
if method == "clifford":
# Add the clifford function
pass
else:
# Other method are transformed as follows
# Convert to tensor form
input_state = paddle.to_tensor(phi)
cir = circuit.UAnsatz(num_qubits)
for qubit in range(num_qubits):
if pauli_str[qubit] == 'x':
cir.h(qubit)
elif pauli_str[qubit] == 'y':
cir.h(qubit)
cir.s(qubit)
cir.h(qubit)
if mode == 'state_vector':
cir.run_state_vector(input_state)
else:
cir.run_density_matrix(input_state)
result = cir.measure(shots=1)
bit_string, = result
return bit_string
# Define the function used to update the beta of the LBCS algorithm # Define the function used to update the beta of the LBCS algorithm
def calculate_diagonal_product(pauli_str, beta): def calculate_diagonal_product(pauli_str, beta):
r"""迭代 LBCS beta 公式中的一部分 r"""迭代 LBCS beta 公式中的一部分
...@@ -424,7 +477,7 @@ def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, metho ...@@ -424,7 +477,7 @@ def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, metho
if method == "CS": if method == "CS":
for _ in range(sample_shots): for _ in range(sample_shots):
random_pauli_str = random_pauli_sample(num_qubits, beta=None) random_pauli_str = random_pauli_sample(num_qubits, beta=None)
measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, method) measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, mode, method)
sample_result.append((random_pauli_str, measurement_result)) sample_result.append((random_pauli_str, measurement_result))
return sample_result return sample_result
elif method == "LBCS": elif method == "LBCS":
...@@ -441,12 +494,91 @@ def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, metho ...@@ -441,12 +494,91 @@ def shadow_sample(state, num_qubits, sample_shots, mode, hamiltonian=None, metho
sample_result = list() sample_result = list()
for _ in range(sample_shots): for _ in range(sample_shots):
random_pauli_str = random_pauli_sample(num_qubits, beta) random_pauli_str = random_pauli_sample(num_qubits, beta)
measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, method) measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, mode, method)
sample_result.append((random_pauli_str, measurement_result)) sample_result.append((random_pauli_str, measurement_result))
return sample_result, beta return sample_result, beta
elif method == "APS": elif method == "APS":
for _ in range(sample_shots): for _ in range(sample_shots):
random_pauli_str = random_pauli_sample_in_aps(hamiltonian) random_pauli_str = random_pauli_sample_in_aps(hamiltonian)
measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, method) measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, mode, method)
sample_result.append((random_pauli_str, measurement_result)) sample_result.append((random_pauli_str, measurement_result))
return sample_result return sample_result
def classical_shadow(state, num_qubits, sample_shots, mode, method=None):
r"""获得量子态 state 的经典影子
Args:
state (numpy.ndarray): 输入量子态，支持态矢量和密度矩阵形式
num_qubits (int): 量子比特数量
sample_shots (int): 随机采样的次数
mode (str): 输入量子态的表示方式，``"state_vector"`` 表示态矢量形式， ``"density_matrix"`` 表示密度矩阵形式
method (str, optional): 可选方法 restructure (R)，获得量子态的密度矩阵形式；或默认为None (即 not restructure, NR)，获得量子态的密度矩阵形式
Returns:
tuple: 包含如下两个元素
- state_hat (list): 返回量子态 state 的经典影子 (method = 'NR')
- reconstructed_state (numpy.ndarray): 返回估计的量子态 state 的密度矩阵 (method = 'R')
代码示例:
.. code-block:: python
from paddle_quantum.shadow import classical_shadow
from paddle_quantum.state import vec_random
n_qubit = 2
sample_shots = 2
state = vec_random(n_qubit)
state_shadow = classical_shadow(state, n_qubit, sample_shots, mode='state_vector', method='NR')
state_density_matrix = classical_shadow(state, n_qubit, sample_shots, mode='state_vector', method='R')
print('classical shadow of quantum state = ', state_shadow)
print('density matrix of quantum state = ', state_density_matrix)
::
classical shadow of quantum state = [array([[ 0.25+0.j , 0. +0.75j, -0.75+0.j , -0. -2.25j],
[ 0. -0.75j, 0.25+0.j , 0. +2.25j, -0.75+0.j ],
[-0.75+0.j , -0. -2.25j, 0.25+0.j , 0. +0.75j],
[ 0. +2.25j, -0.75+0.j , 0. -0.75j, 0.25+0.j ]]),
array([[0.25+0.j , 0. -0.75j, 0.75+0.j , 0. -2.25j],
[0. +0.75j, 0.25+0.j , 0. +2.25j, 0.75+0.j ],
[0.75+0.j , 0. -2.25j, 0.25+0.j , 0. -0.75j],
[0. +2.25j, 0.75+0.j , 0. +0.75j, 0.25+0.j ]])]
density matrix of quantum state = [[ 0.625+0.j 0.375+0.j -1.5 +0.375j 0. +1.125j]
[ 0.375+0.j -0.125+0.j 0. +1.125j 0.75 +0.375j]
[-1.5 -0.375j 0. -1.125j 0.625+0.j 0.375+0.j ]
[ 0. -1.125j 0.75 -0.375j 0.375+0.j -0.125+0.j ]]
"""
# Used to store the classic shadow for each sample
state_hat = []
I_matrix = np.array([[1, 0], [0, 1]])
for _ in range(sample_shots):
# Randomly selected Pauli
random_pauli_str = random_pauli_sample(num_qubits, beta=None)
# Measure according to the selected Pauli
measurement_result = measure_by_pauli_str(random_pauli_str, state, num_qubits, mode, None)
# Generate a 1×1 matrix, convenient tensor product
hat_state = np.eye(1)
for i in range(num_qubits):
single_pauli_matrix = paulistr_to_matrix(random_pauli_str[i])
single_b_matrix = measure_result_to_matrix(measurement_result[i])
# The classical shadow on a single qubit is obtained according to the derived M inverse
single_qubit_state_left = np.dot(np.dot(single_pauli_matrix.conj().T, single_b_matrix), single_pauli_matrix)
single_qubit_state = 3 * single_qubit_state_left - I_matrix
# The classical shadow of quantum state is obtained
hat_state = np.kron(hat_state, single_qubit_state)
# Store classical shadows
state_hat.append(hat_state)
if method == 'R':
# Returns the density matrix of the quantum state
reconstructed_state = sum(state_hat)/len(state_hat)
return reconstructed_state
else:
# Returns the classical shadow of the quantum state
return state_hat
paddle_quantum/simulator.py
浏览文件 @ 016af983
...@@ -69,38 +69,9 @@ def init_state_gen(n, i=0): ...@@ -69,38 +69,9 @@ def init_state_gen(n, i=0):
""" """
assert 0 <= i < 2 ** n, 'Invalid index' assert 0 <= i < 2 ** n, 'Invalid index'
if n == 1: state = np.zeros([2 ** n], dtype=np.complex128)
state1 = paddle.ones([1], 'float64') state[i] = 1
state0 = paddle.zeros([2 ** n - 1], 'float64') state = paddle.to_tensor(state)
if i == 0:
state = paddle.concat([state1, state0])
else:
state = paddle.concat([state0, state1])
else:
if i == 0:
state1 = paddle.ones([1], 'float64')
state0 = paddle.zeros([2 ** n - 1], 'float64')
state = paddle.concat([state1, state0])
elif i == 2 ** n - 1:
state1 = paddle.ones([1], 'float64')
state0 = paddle.zeros([2 ** n - 1], 'float64')
state = paddle.concat([state0, state1])
else:
state1 = paddle.ones([1], 'float64')
state0 = paddle.zeros([i], 'float64')
state00 = paddle.zeros([2 ** n - i - 1], 'float64')
state = paddle.concat([state0, state1, state00])
del state1, state0
try:
del state00
except NameError:
pass
gc.collect() # free the intermediate big data immediately
state = paddle.cast(state, 'complex128')
gc.collect() # free the intermediate big data immediately
return state return state
......
paddle_quantum/trotter.py
浏览文件 @ 016af983
...@@ -249,7 +249,7 @@ def _add_custom_block(circuit, tau, grouped_hamiltonian, custom_coefficients, pe ...@@ -249,7 +249,7 @@ def _add_custom_block(circuit, tau, grouped_hamiltonian, custom_coefficients, pe
add_n_pauli_gate(circuit, 2 * tau * coeff, pauli_word, site) add_n_pauli_gate(circuit, 2 * tau * coeff, pauli_word, site)
def __add_first_order_trotter_block(circuit, tau, grouped_hamiltonian, reverse=False): def __add_first_order_trotter_block(circuit, tau, grouped_hamiltonian, reverse=False, optimization=False):
r""" 添加一阶 trotter-suzuki 分解的时间演化块 r""" 添加一阶 trotter-suzuki 分解的时间演化块
Notes: Notes:
...@@ -258,54 +258,57 @@ def __add_first_order_trotter_block(circuit, tau, grouped_hamiltonian, reverse=F ...@@ -258,54 +258,57 @@ def __add_first_order_trotter_block(circuit, tau, grouped_hamiltonian, reverse=F
if not reverse: if not reverse:
for hamiltonian in grouped_hamiltonian: for hamiltonian in grouped_hamiltonian:
assert isinstance(hamiltonian, Hamiltonian) assert isinstance(hamiltonian, Hamiltonian)
if optimization:
#将原哈密顿量中相同site的XX，YY，ZZ组合到一起 # Combine XX, YY, ZZ of the same site in the original Hamiltonian quantity
grouped_hamiltonian = [] grouped_hamiltonian = []
coeffs, pauli_words, sites = hamiltonian.decompose_with_sites() coeffs, pauli_words, sites = hamiltonian.decompose_with_sites()
grouped_terms_indices = [] grouped_terms_indices = []
left_over_terms_indices = [] left_over_terms_indices = []
d = defaultdict(list) d = defaultdict(list)
#合并相同site的XX,YY,ZZ # Merge XX,YY,ZZ of the same site
for term_index in range(len(coeffs)): for term_index in range(len(coeffs)):
site = sites[term_index] site = sites[term_index]
pauli_word = pauli_words[term_index] pauli_word = pauli_words[term_index]
for pauli in ['XX', 'YY', 'ZZ']: for pauli in ['XX', 'YY', 'ZZ']:
assert isinstance(pauli_word, str), "Each pauli word should be a string type" assert isinstance(pauli_word, str), "Each pauli word should be a string type"
if (pauli_word==pauli or pauli_word==pauli.lower()): if (pauli_word == pauli or pauli_word == pauli.lower()):
key = tuple(sorted(site)) key = tuple(sorted(site))
d[key].append((pauli,term_index)) d[key].append((pauli, term_index))
if len(d[key])==3: if len(d[key]) == 3:
terms_indices_to_be_grouped = [x[1] for x in d[key]] terms_indices_to_be_grouped = [x[1] for x in d[key]]
grouped_terms_indices.extend(terms_indices_to_be_grouped) grouped_terms_indices.extend(terms_indices_to_be_grouped)
grouped_hamiltonian.append(hamiltonian[terms_indices_to_be_grouped]) grouped_hamiltonian.append(hamiltonian[terms_indices_to_be_grouped])
#其他的剩余项 # Other remaining sites
for term_index in range(len(coeffs)): for term_index in range(len(coeffs)):
if term_index not in grouped_terms_indices: if term_index not in grouped_terms_indices:
left_over_terms_indices.append(term_index) left_over_terms_indices.append(term_index)
if len(left_over_terms_indices): if len(left_over_terms_indices):
for term_index in left_over_terms_indices: for term_index in left_over_terms_indices:
grouped_hamiltonian.append(hamiltonian[term_index]) grouped_hamiltonian.append(hamiltonian[term_index])
#得到新的哈密顿量 # Get the new Hamiltonian
res = grouped_hamiltonian[0] res = grouped_hamiltonian[0]
for i in range(1,len(grouped_hamiltonian)): for i in range(1, len(grouped_hamiltonian)):
res+=grouped_hamiltonian[i] res += grouped_hamiltonian[i]
hamiltonian = res hamiltonian = res
# decompose the Hamiltonian into 3 lists # decompose the Hamiltonian into 3 lists
coeffs, pauli_words, sites = hamiltonian.decompose_with_sites() coeffs, pauli_words, sites = hamiltonian.decompose_with_sites()
# apply rotational gate of each term # apply rotational gate of each term
# for term_index in range(len(coeffs)):
# # get the sorted pauli_word and site (an array of qubit indices) according to their qubit indices
# pauli_word, site = __sort_pauli_word(pauli_words[term_index], sites[term_index])
# add_n_pauli_gate(circuit, 2 * tau * coeffs[term_index], pauli_word, site)
term_index = 0 term_index = 0
while term_index <len(coeffs): while term_index < len(coeffs):
if term_index+3<=len(coeffs) and \ if optimization and term_index+3 <= len(coeffs) and \
len(set(y for x in sites[term_index:term_index+3] for y in x ))==2 and\ len(set(y for x in sites[term_index:term_index+3] for y in x)) == 2 and\
set(pauli_words[term_index:term_index+3])=={'XX','YY','ZZ'}: set(pauli_words[term_index:term_index+3]) == {'XX', 'YY', 'ZZ'}:
optimal_circuit(circuit,[tau*i for i in coeffs[term_index:term_index+3]],sites[term_index]) optimal_circuit(circuit, [tau*i for i in coeffs[term_index:term_index+3]], sites[term_index])
term_index+=3 term_index += 3
else: else:
# get the sorted pauli_word and site (an array of qubit indices) according to their qubit indices # get the sorted pauli_word and site (an array of qubit indices) according to their qubit indices
pauli_word, site = __sort_pauli_word(pauli_words[term_index], sites[term_index]) pauli_word, site = __sort_pauli_word(pauli_words[term_index], sites[term_index])
add_n_pauli_gate(circuit, 2 * tau * coeffs[term_index], pauli_word, site) add_n_pauli_gate(circuit, 2 * tau * coeffs[term_index], pauli_word, site)
term_index+=1 term_index += 1
# in the reverse mode, if the Hamiltonian is a single element list, reverse the order its each term # in the reverse mode, if the Hamiltonian is a single element list, reverse the order its each term
else: else:
if len(grouped_hamiltonian) == 1: if len(grouped_hamiltonian) == 1:
...@@ -323,6 +326,31 @@ def __add_first_order_trotter_block(circuit, tau, grouped_hamiltonian, reverse=F ...@@ -323,6 +326,31 @@ def __add_first_order_trotter_block(circuit, tau, grouped_hamiltonian, reverse=F
add_n_pauli_gate(circuit, 2 * tau * coeffs[term_index], pauli_word, site) add_n_pauli_gate(circuit, 2 * tau * coeffs[term_index], pauli_word, site)
def optimal_circuit(circuit, theta, which_qubits):
r""" 添加一个优化电路，哈密顿量为'XXYYZZ'
Args:
circuit (UAnsatz): 需要添加门的电路
theta list(paddle.Tensor or float): 旋转角度需要传入三个参数
which_qubits (list or numpy.ndarray): ``pauli_word`` 中的每个算符所作用的量子比特编号
"""
p = np.pi/2
x, y, z = theta
alpha = paddle.to_tensor(3*p-4*x*p+2*x, dtype='float64')
beta = paddle.to_tensor(-3*p+4*y*p-2*y, dtype='float64')
gamma = paddle.to_tensor(2*z-p, dtype='float64')
which_qubits.sort()
a, b = which_qubits
circuit.rz(paddle.to_tensor(p, dtype='float64'), b)
circuit.cnot([b, a])
circuit.rz(gamma, a)
circuit.ry(alpha, b)
circuit.cnot([a, b])
circuit.ry(beta, b)
circuit.cnot([b, a])
circuit.rz(paddle.to_tensor(-p, dtype='float64'), a)
def __add_second_order_trotter_block(circuit, tau, grouped_hamiltonian): def __add_second_order_trotter_block(circuit, tau, grouped_hamiltonian):
r""" 添加二阶 trotter-suzuki 分解的时间演化块 r""" 添加二阶 trotter-suzuki 分解的时间演化块
...@@ -404,29 +432,6 @@ def add_n_pauli_gate(circuit, theta, pauli_word, which_qubits): ...@@ -404,29 +432,6 @@ def add_n_pauli_gate(circuit, theta, pauli_word, which_qubits):
elif re.match(r'Y', pauli_word[qubit_index], flags=re.I): elif re.match(r'Y', pauli_word[qubit_index], flags=re.I):
circuit.rx(- PI / 2, which_qubits[qubit_index]) circuit.rx(- PI / 2, which_qubits[qubit_index])
def optimal_circuit(circuit,theta,which_qubits):
r""" 添加一个优化电路，哈密顿量为'XXYYZZ'`
Args:
circuit (UAnsatz): 需要添加门的电路
theta list(tensor or float): 旋转角度需要传入三个参数
which_qubits (list or np.ndarray): ``pauli_word`` 中的每个算符所作用的量子比特编号
"""
p = np.pi/2
x,y,z = theta
alpha = paddle.to_tensor(3*p-4*x*p+2*x,dtype='float64')
beta = paddle.to_tensor(-3*p+4*y*p-2*y,dtype='float64')
gamma = paddle.to_tensor(2*z-p,dtype='float64')
which_qubits.sort()
a,b = which_qubits
circuit.rz(paddle.to_tensor(p,dtype='float64'),b)
circuit.cnot([b,a])
circuit.rz(gamma,a)
circuit.ry(alpha,b)
circuit.cnot([a,b])
circuit.ry(beta,b)
circuit.cnot([b,a])
circuit.rz(paddle.to_tensor(-p,dtype='float64'),a)
def __group_hamiltonian_xyz(hamiltonian): def __group_hamiltonian_xyz(hamiltonian):
r""" 将哈密顿量拆分成 X、Y、Z 以及剩余项四个部分，并返回由他们组成的列表 r""" 将哈密顿量拆分成 X、Y、Z 以及剩余项四个部分，并返回由他们组成的列表
...@@ -590,7 +595,6 @@ def get_1d_heisenberg_hamiltonian( ...@@ -590,7 +595,6 @@ def get_1d_heisenberg_hamiltonian(
boundary_sites = [0, length - 1] boundary_sites = [0, length - 1]
for interaction_idx in range(len(interactions)): for interaction_idx in range(len(interactions)):
term_str = '' term_str = ''
interaction = interactions[interaction_idx]
for idx_word in range(len(interaction)): for idx_word in range(len(interaction)):
term_str += interaction[idx_word] + str(boundary_sites[idx_word]) term_str += interaction[idx_word] + str(boundary_sites[idx_word])
if idx_word != len(interaction) - 1: if idx_word != len(interaction) - 1:
......
paddle_quantum/utils.py
浏览文件 @ 016af983
...@@ -20,6 +20,8 @@ import copy ...@@ -20,6 +20,8 @@ import copy
import re import re
import numpy as np import numpy as np
from scipy.linalg import logm, sqrtm from scipy.linalg import logm, sqrtm
from scipy.special import logsumexp
from tqdm import tqdm
from matplotlib import colors as mplcolors from matplotlib import colors as mplcolors
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
import paddle import paddle
...@@ -34,10 +36,10 @@ import matplotlib as mpl ...@@ -34,10 +36,10 @@ import matplotlib as mpl
from paddle_quantum import simulator from paddle_quantum import simulator
import matplotlib.animation as animation import matplotlib.animation as animation
import matplotlib.image import matplotlib.image
from typing import Union, Optional
__all__ = [ __all__ = [
"partial_trace", "partial_trace",
"partial_trace_discontiguous",
"state_fidelity", "state_fidelity",
"trace_distance", "trace_distance",
"gate_fidelity", "gate_fidelity",
...@@ -57,11 +59,15 @@ __all__ = [ ...@@ -57,11 +59,15 @@ __all__ = [
"haar_unitary", "haar_unitary",
"haar_state_vector", "haar_state_vector",
"haar_density_operator", "haar_density_operator",
"Hamiltonian", "schmidt_decompose",
"plot_n_qubit_state_in_bloch_sphere",
"plot_state_in_bloch_sphere", "plot_state_in_bloch_sphere",
"plot_multi_qubits_state_in_bloch_sphere",
"plot_rotation_in_bloch_sphere", "plot_rotation_in_bloch_sphere",
"img_to_density_matrix", "plot_density_matrix_graph",
"image_to_density_matrix",
"Hamiltonian",
"QuantumFisher",
"ClassicalFisher",
] ]
...@@ -144,7 +150,7 @@ def partial_trace_discontiguous(rho, preserve_qubits=None): ...@@ -144,7 +150,7 @@ def partial_trace_discontiguous(rho, preserve_qubits=None):
result = np.zeros((2 ** num_preserve, 2 ** num_preserve), dtype="complex64") result = np.zeros((2 ** num_preserve, 2 ** num_preserve), dtype="complex64")
result = paddle.to_tensor(result) result = paddle.to_tensor(result)
for i in range(0, 2 ** num_preserve): for i in range(0, 2 ** (n - num_preserve)):
bra = identity[i * 2 ** num_preserve:(i + 1) * 2 ** num_preserve, :] bra = identity[i * 2 ** num_preserve:(i + 1) * 2 ** num_preserve, :]
result = result + matmul(matmul(bra, rho), transpose(bra, perm=[1, 0])) result = result + matmul(matmul(bra, rho), transpose(bra, perm=[1, 0]))
...@@ -244,10 +250,14 @@ def von_neumann_entropy(rho): ...@@ -244,10 +250,14 @@ def von_neumann_entropy(rho):
Returns: Returns:
float: 输入的量子态的冯诺依曼熵 float: 输入的量子态的冯诺依曼熵
""" """
rho_eigenvalue, _ = np.linalg.eig(rho) rho_eigenvalues = np.real(np.linalg.eigvals(rho))
entropy = -np.sum(rho_eigenvalue * np.log(rho_eigenvalue)) entropy = 0
for eigenvalue in rho_eigenvalues:
if np.abs(eigenvalue) < 1e-8:
continue
entropy -= eigenvalue * np.log(eigenvalue)
return entropy.real return entropy
def relative_entropy(rho, sig): def relative_entropy(rho, sig):
...@@ -641,1145 +651,1590 @@ def haar_density_operator(n, k=None, real=False): ...@@ -641,1145 +651,1590 @@ def haar_density_operator(n, k=None, real=False):
return rho / np.trace(rho) return rho / np.trace(rho)
class Hamiltonian: def schmidt_decompose(psi, sys_A=None):
r""" Paddle Quantum 中的 Hamiltonian ``class``。 r"""计算输入量子态的施密特分解 :math:`\lvert\psi\rangle=\sum_ic_i\lvert i_A\rangle\otimes\lvert i_B \rangle`。
用户可以通过一个 Pauli string 来实例化该 ``class``。
"""
def __init__(self, pauli_str, compress=True):
r""" 创建一个 Hamiltonian 类。
Args: Args:
pauli_str (list): 用列表定义的 Hamiltonian，如 ``[(1, 'Z0, Z1'), (2, 'I')]`` psi (numpy.ndarray): 量子态的向量形式，形状为（2**n）
compress (bool): 是否对输入的 list 进行自动合并（例如 ``(1, 'Z0, Z1')`` 和 ``(2, 'Z1, Z0')`` 这两项将被自动合并），默认为 ``True`` sys_A (list): 包含在子系统 A 中的 qubit 下标（其余 qubit 包含在子系统B中），默认为量子态 :math:`\lvert \psi\rangle` 的前半数 qubit
Returns:
tuple: 包含如下元素
- numpy.ndarray: 由施密特系数组成的一维数组，形状为 ``(k)``
- numpy.ndarray: 由子系统A的基 :math:`\lvert i_A\rangle` 组成的高维数组，形状为 ``(k, 2**m, 1)``
- numpy.ndarray: 由子系统B的基 :math:`\lvert i_B\rangle` 组成的高维数组，形状为 ``(k, 2**l, 1)``
Warning:
小于 ``1e-13`` 的施密特系数将被视作浮点误差并舍去
.. code-block:: python
# zz = 1/√2 * (<010| + <101|)
zz = 1/np.sqrt(2) * (np.array([0., 0., 1., 0., 0., 0., 0., 0.]) + np.array([0., 0., 0., 0., 0., 1., 0., 0.]))
print('input state:', zz)
l, u, v = schmidt_decompose(zz, [0, 2])
print('output state:')
for i in range(len(l)):
print('+', l[i], '*', u[i].reshape([-1]), '⨂', v[i].reshape([-1]))
Note: Note:
如果设置 ``compress=False``，则不会对输入的合法性进行检验。 代码示例结果应为 1/√2 * (<00|⨂<1| + <11|⨂<0|)。注意，输入态的第 0、2 个 qubit 处于输出态的子系统 A，输入态的第1个 qubit 处于输出态的子系统 B。
""" """
self.__coefficients = None
self.__terms = None
self.__pauli_words_r = []
self.__pauli_words = []
self.__sites = []
self.__nqubits = None
# when internally updating the __pauli_str, be sure to set __update_flag to True
self.__pauli_str = pauli_str
self.__update_flag = True
self.__decompose()
if compress:
self.__compress()
def __getitem__(self, indices): assert psi.ndim == 1, 'Psi must be a one dimensional vector.'
new_pauli_str = [] assert np.log2(psi.size).is_integer(), 'The number of amplitutes must be an integral power of 2.'
if isinstance(indices, int):
indices = [indices]
elif isinstance(indices, slice):
indices = list(range(self.n_terms)[indices])
elif isinstance(indices, tuple):
indices = list(indices)
for index in indices: tot_qu = int(np.log2(psi.size))
new_pauli_str.append([self.coefficients[index], ','.join(self.terms[index])]) sys_A = sys_A if sys_A is not None else [i for i in range(tot_qu//2)]
return Hamiltonian(new_pauli_str, compress=False) sys_B = [i for i in range(tot_qu) if i not in sys_A]
def __add__(self, h_2): # Permute qubit indices
new_pauli_str = self.pauli_str.copy() psi = psi.reshape([2] * tot_qu).transpose(sys_A + sys_B)
if isinstance(h_2, float) or isinstance(h_2, int):
new_pauli_str.extend([[float(h_2), 'I']])
else:
new_pauli_str.extend(h_2.pauli_str)
return Hamiltonian(new_pauli_str)
def __mul__(self, other): # construct amplitute matrix
new_pauli_str = copy.deepcopy(self.pauli_str) amp_mtr = psi.reshape([2**len(sys_A), 2**len(sys_B)])
for i in range(len(new_pauli_str)):
new_pauli_str[i][0] *= other
return Hamiltonian(new_pauli_str, compress=False)
def __sub__(self, other): # Standard process to obtain schmidt decomposition
return self.__add__(other.__mul__(-1)) u, c, v = np.linalg.svd(amp_mtr)
def __str__(self): k = np.count_nonzero(c > 1e-13)
str_out = '' c = c[:k]
for idx in range(self.n_terms): u = u.T[:k].reshape([k, -1, 1])
str_out += '{} '.format(self.coefficients[idx]) v = v[:k].reshape([k, -1, 1])
for _ in range(len(self.terms[idx])): return c, u, v
str_out += self.terms[idx][_]
if _ != len(self.terms[idx]) - 1:
str_out += ', '
if idx != self.n_terms - 1:
str_out += '\n'
return str_out
def __repr__(self):
return 'paddle_quantum.Hamiltonian object: \n' + self.__str__()
@property def __density_matrix_convert_to_bloch_vector(density_matrix):
def n_terms(self): r"""该函数将密度矩阵转化为bloch球面上的坐标
r"""返回该哈密顿量的项数
Args:
density_matrix (numpy.ndarray): 输入的密度矩阵
Returns: Returns:
int :哈密顿量的项数 bloch_vector (numpy.ndarray): 存储bloch向量的 x,y,z 坐标，向量的模长，向量的颜色
""" """
return len(self.__pauli_str)
@property # Pauli Matrix
def pauli_str(self): pauli_x = np.array([[0, 1], [1, 0]])
r"""返回哈密顿量对应的 Pauli string pauli_y = np.array([[0, -1j], [1j, 0]])
pauli_z = np.array([[1, 0], [0, -1]])
Returns: # Convert a density matrix to a Bloch vector.
list : 哈密顿量对应的 Pauli string ax = np.trace(np.dot(density_matrix, pauli_x)).real
""" ay = np.trace(np.dot(density_matrix, pauli_y)).real
return self.__pauli_str az = np.trace(np.dot(density_matrix, pauli_z)).real
@property # Calc the length of bloch vector
def terms(self): length = ax ** 2 + ay ** 2 + az ** 2
r"""返回哈密顿量中的每一项构成的列表 length = sqrt(length)
if length > 1.0:
length = 1.0
Returns: # Calc the color of bloch vector, the value of the color is proportional to the length
list :哈密顿量中的每一项，i.e. ``[['Z0, Z1'], ['I']]`` color = length
"""
if self.__update_flag:
self.__decompose()
return self.__terms
else:
return self.__terms
@property bloch_vector = [ax, ay, az, length, color]
def coefficients(self):
r""" 返回哈密顿量中的每一项对应的系数构成的列表
Returns: # You must use an array, which is followed by slicing and taking a column
list :哈密顿量中每一项的系数，i.e. ``[1.0, 2.0]`` bloch_vector = np.array(bloch_vector)
"""
if self.__update_flag:
self.__decompose()
return self.__coefficients
else:
return self.__coefficients
@property return bloch_vector
def pauli_words(self):
r"""返回哈密顿量中每一项对应的 Pauli word 构成的列表
Returns:
list :每一项对应的 Pauli word，i.e. ``['ZIZ', 'IIX']``
"""
if self.__update_flag:
self.__decompose()
return self.__pauli_words
else:
return self.__pauli_words
@property def __plot_bloch_sphere(
def pauli_words_r(self): ax,
r"""返回哈密顿量中每一项对应的简化（不包含 I） Pauli word 组成的列表 bloch_vectors=None,
show_arrow=False,
clear_plt=True,
rotating_angle_list=None,
view_angle=None,
view_dist=None,
set_color=None
):
r"""将 Bloch 向量展示在 Bloch 球面上
Returns: Args:
list :不包含 "I" 的 Pauli word 构成的列表，i.e. ``['ZXZZ', 'Z', 'X']`` ax (Axes3D(fig)): 画布的句柄
bloch_vectors (numpy.ndarray): 存储bloch向量的 x,y,z 坐标，向量的模长，向量的颜色
show_arrow (bool): 是否展示向量的箭头，默认为 False
clear_plt (bool): 是否要清空画布，默认为 True，每次画图的时候清空画布再画图
rotating_angle_list (list): 旋转角度的列表，用于展示旋转轨迹
view_angle (list): 视图的角度，
第一个元素为关于xy平面的夹角[0-360],第二个元素为关于xz平面的夹角[0-360], 默认为 (30, 45)
view_dist (int): 视图的距离，默认为 7
set_color (str): 设置指定的颜色，请查阅cmap表，默认为 "红-黑-根据向量的模长渐变" 颜色方案
""" """
if self.__update_flag: # Assign a value to an empty variable
self.__decompose() if view_angle is None:
return self.__pauli_words_r view_angle = (30, 45)
if view_dist is None:
view_dist = 7
# Define my_color
if set_color is None:
color = 'rainbow'
black_code = '#000000'
red_code = '#F24A29'
if bloch_vectors is not None:
black_to_red = mplcolors.LinearSegmentedColormap.from_list(
'my_color',
[(0, black_code), (1, red_code)],
N=len(bloch_vectors[:, 4])
)
map_vir = plt.get_cmap(black_to_red)
color = map_vir(bloch_vectors[:, 4])
else: else:
return self.__pauli_words_r color = set_color
@property # Set the view angle and view distance
def sites(self): ax.view_init(view_angle[0], view_angle[1])
r"""返回该哈密顿量中的每一项对应的量子比特编号组成的列表 ax.dist = view_dist
Returns: # Draw the general frame
list :哈密顿量中每一项所对应的量子比特编号构成的列表，i.e. ``[[1, 2], [0]]`` def draw_general_frame():
"""
if self.__update_flag:
self.__decompose()
return self.__sites
else:
return self.__sites
@property # Do not show the grid and original axes
def n_qubits(self): ax.grid(False)
r"""返回该哈密顿量对应的量子比特数 ax.set_axis_off()
ax.view_init(view_angle[0], view_angle[1])
ax.dist = view_dist
Returns: # Set the lower limit and upper limit of each axis
int :量子比特数 # To make the bloch_ball look less flat, the default is relatively flat
""" ax.set_xlim3d(xmin=-1.5, xmax=1.5)
if self.__update_flag: ax.set_ylim3d(ymin=-1.5, ymax=1.5)
self.__decompose() ax.set_zlim3d(zmin=-1, zmax=1.3)
return self.__nqubits
else:
return self.__nqubits
def __decompose(self): # Draw a new axes
r"""将哈密顿量分解为不同的形式 coordinate_start_x, coordinate_start_y, coordinate_start_z = \
np.array([[-1.5, 0, 0], [0, -1.5, 0], [0, 0, -1.5]])
coordinate_end_x, coordinate_end_y, coordinate_end_z = \
np.array([[3, 0, 0], [0, 3, 0], [0, 0, 3]])
ax.quiver(
coordinate_start_x, coordinate_start_y, coordinate_start_z,
coordinate_end_x, coordinate_end_y, coordinate_end_z,
arrow_length_ratio=0.03, color="black", linewidth=0.5
)
ax.text(0, 0, 1.7, r"|0⟩", color="black", fontsize=16)
ax.text(0, 0, -1.9, r"|1⟩", color="black", fontsize=16)
ax.text(1.9, 0, 0, r"|+⟩", color="black", fontsize=16)
ax.text(-1.7, 0, 0, r"|–⟩", color="black", fontsize=16)
ax.text(0, 1.7, 0, r"|i+⟩", color="black", fontsize=16)
ax.text(0, -1.9, 0, r"|i–⟩", color="black", fontsize=16)
Notes: # Draw a surface
这是一个内部函数，你不需要直接使用它 horizontal_angle = np.linspace(0, 2 * np.pi, 80)
这是一个比较基础的函数，它负责将输入的 Pauli string 拆分为不同的形式并存储在内部变量中 vertical_angle = np.linspace(0, np.pi, 80)
""" surface_point_x = np.outer(np.cos(horizontal_angle), np.sin(vertical_angle))
self.__pauli_words = [] surface_point_y = np.outer(np.sin(horizontal_angle), np.sin(vertical_angle))
self.__pauli_words_r = [] surface_point_z = np.outer(np.ones(np.size(horizontal_angle)), np.cos(vertical_angle))
self.__sites = [] ax.plot_surface(
self.__terms = [] surface_point_x, surface_point_y, surface_point_z, rstride=1, cstride=1,
self.__coefficients = [] color="black", linewidth=0.05, alpha=0.03
self.__nqubits = 1 )
new_pauli_str = []
for coefficient, pauli_term in self.__pauli_str:
pauli_word_r = ''
site = []
single_pauli_terms = re.split(r',\s*', pauli_term.upper())
self.__coefficients.append(float(coefficient))
self.__terms.append(single_pauli_terms)
for single_pauli_term in single_pauli_terms:
match_I = re.match(r'I', single_pauli_term, flags=re.I)
if match_I:
assert single_pauli_term[0].upper() == 'I', \
'The offset is defined with a sole letter "I", i.e. (3.0, "I")'
pauli_word_r += 'I'
site.append('')
else:
match = re.match(r'([XYZ])([0-9]+)', single_pauli_term, flags=re.I)
if match:
pauli_word_r += match.group(1).upper()
assert int(match.group(2)) not in site, 'each Pauli operator should act on different qubit'
site.append(int(match.group(2)))
else:
raise Exception(
'Operators should be defined with a string composed of Pauli operators followed' +
'by qubit index on which it act, separated with ",". i.e. "Z0, X1"')
self.__nqubits = max(self.__nqubits, int(match.group(2)) + 1)
self.__pauli_words_r.append(pauli_word_r)
self.__sites.append(site)
new_pauli_str.append([float(coefficient), pauli_term.upper()])
for term_index in range(len(self.__pauli_str)):
pauli_word = ['I' for _ in range(self.__nqubits)]
site = self.__sites[term_index]
for site_index in range(len(site)):
if type(site[site_index]) == int:
pauli_word[site[site_index]] = self.__pauli_words_r[term_index][site_index]
self.__pauli_words.append(''.join(pauli_word))
self.__pauli_str = new_pauli_str
self.__update_flag = False
def __compress(self): # Draw circle
r""" 对同类项进行合并。 def draw_circle(circle_horizon_angle, circle_vertical_angle, linewidth=0.5, alpha=0.2):
r = 1
circle_point_x = r * np.cos(circle_vertical_angle) * np.cos(circle_horizon_angle)
circle_point_y = r * np.cos(circle_vertical_angle) * np.sin(circle_horizon_angle)
circle_point_z = r * np.sin(circle_vertical_angle)
ax.plot(
circle_point_x, circle_point_y, circle_point_z,
color="black", linewidth=linewidth, alpha=alpha
)
Notes: # draw longitude and latitude
这是一个内部函数，你不需要直接使用它 def draw_longitude_and_latitude():
""" # Draw longitude
if self.__update_flag: num = 3
self.__decompose() theta = np.linspace(0, 0, 100)
else: psi = np.linspace(0, 2 * np.pi, 100)
pass for i in range(num):
new_pauli_str = [] theta = theta + np.pi / num
flag_merged = [False for _ in range(self.n_terms)] draw_circle(theta, psi)
for term_idx_1 in range(self.n_terms):
if not flag_merged[term_idx_1]:
for term_idx_2 in range(term_idx_1 + 1, self.n_terms):
if not flag_merged[term_idx_2]:
if self.pauli_words[term_idx_1] == self.pauli_words[term_idx_2]:
self.__coefficients[term_idx_1] += self.__coefficients[term_idx_2]
flag_merged[term_idx_2] = True
else:
pass
if self.__coefficients[term_idx_1] != 0:
new_pauli_str.append([self.__coefficients[term_idx_1], ','.join(self.__terms[term_idx_1])])
self.__pauli_str = new_pauli_str
self.__update_flag = True
def decompose_with_sites(self): # Draw latitude
r"""将 pauli_str 分解为系数、泡利字符串的简化形式以及它们分别作用的量子比特下标。 num = 6
theta = np.linspace(0, 2 * np.pi, 100)
psi = np.linspace(-np.pi / 2, -np.pi / 2, 100)
for i in range(num):
psi = psi + np.pi / num
draw_circle(theta, psi)
Returns: # Draw equator
tuple: 包含如下元素的 tuple: theta = np.linspace(0, 2 * np.pi, 100)
psi = np.linspace(0, 0, 100)
draw_circle(theta, psi, linewidth=0.5, alpha=0.2)
- coefficients (list): 元素为每一项的系数 # Draw prime meridian
- pauli_words_r (list): 元素为每一项的泡利字符串的简化形式，例如 'Z0, Z1, X3' 这一项的泡利字符串为 'ZZX' theta = np.linspace(0, 0, 100)
- sites (list): 元素为每一项作用的量子比特下标，例如 'Z0, Z1, X3' 这一项的 site 为 [0, 1, 3] psi = np.linspace(0, 2 * np.pi, 100)
draw_circle(theta, psi, linewidth=0.5, alpha=0.2)
""" # If the number of data points exceeds 20, no longitude and latitude lines will be drawn.
if self.__update_flag: if bloch_vectors is not None and len(bloch_vectors) < 52:
self.__decompose() draw_longitude_and_latitude()
return self.coefficients, self.__pauli_words_r, self.__sites elif bloch_vectors is None:
draw_longitude_and_latitude()
def decompose_pauli_words(self): # Draw three invisible points
r"""将 pauli_str 分解为系数和泡利字符串。 invisible_points = np.array([[0.03440399, 0.30279721, 0.95243384],
[0.70776026, 0.57712403, 0.40743499],
[0.46991358, -0.63717908, 0.61088792]])
ax.scatter(
invisible_points[:, 0], invisible_points[:, 1], invisible_points[:, 2],
c='w', alpha=0.01
)
Returns: # clean plt
tuple: 包含如下元素的 tuple: if clear_plt:
ax.cla()
draw_general_frame()
- coefficients(list): 元素为每一项的系数 # Draw the data points
- pauli_words(list): 元素为每一项的泡利字符串，例如 'Z0, Z1, X3' 这一项的泡利字符串为 'ZZIX' if bloch_vectors is not None:
""" ax.scatter(
if self.__update_flag: bloch_vectors[:, 0], bloch_vectors[:, 1], bloch_vectors[:, 2], c=color, alpha=1.0
self.__decompose() )
else:
pass
return self.coefficients, self.__pauli_words
def construct_h_matrix(self, n_qubit=None): # if show the rotating angle
r"""构建 Hamiltonian 在 Z 基底下的矩阵。 if rotating_angle_list is not None:
bloch_num = len(bloch_vectors)
rotating_angle_theta, rotating_angle_phi, rotating_angle_lam = rotating_angle_list[bloch_num - 1]
rotating_angle_theta = round(rotating_angle_theta, 6)
rotating_angle_phi = round(rotating_angle_phi, 6)
rotating_angle_lam = round(rotating_angle_lam, 6)
Returns: # Shown at the top right of the perspective
np.ndarray: Z 基底下的哈密顿量矩阵形式 display_text_angle = [-(view_angle[0] - 10), (view_angle[1] + 10)]
""" text_point_x = 2 * np.cos(display_text_angle[0]) * np.cos(display_text_angle[1])
coefs, pauli_words, sites = self.decompose_with_sites() text_point_y = 2 * np.cos(display_text_angle[0]) * np.sin(-display_text_angle[1])
if n_qubit is None: text_point_z = 2 * np.sin(-display_text_angle[0])
n_qubit = 1 ax.text(text_point_x, text_point_y, text_point_z, r'$\theta=' + str(rotating_angle_theta) + r'$',
for site in sites: color="black", fontsize=14)
if type(site[0]) is int: ax.text(text_point_x, text_point_y, text_point_z - 0.1, r'$\phi=' + str(rotating_angle_phi) + r'$',
print(n_qubit,(site)) color="black", fontsize=14)
n_qubit = max(n_qubit, max(site) + 1) ax.text(text_point_x, text_point_y, text_point_z - 0.2, r'$\lambda=' + str(rotating_angle_lam) + r'$',
else: color="black", fontsize=14)
assert n_qubit>=self.n_qubits,"输入的量子数不小于哈密顿量表达式中所对应的量子比特数"
h_matrix = np.zeros([2 ** n_qubit, 2 ** n_qubit], dtype='complex64')
spin_ops = SpinOps(n_qubit, use_sparse=True)
for idx in range(len(coefs)):
op = coefs[idx] * sparse.eye(2 ** n_qubit, dtype='complex64')
for site_idx in range(len(sites[idx])):
if re.match(r'X', pauli_words[idx][site_idx], re.I):
op = op.dot(spin_ops.sigx_p[sites[idx][site_idx]])
elif re.match(r'Y', pauli_words[idx][site_idx], re.I):
op = op.dot(spin_ops.sigy_p[sites[idx][site_idx]])
elif re.match(r'Z', pauli_words[idx][site_idx], re.I):
op = op.dot(spin_ops.sigz_p[sites[idx][site_idx]])
h_matrix += op
return h_matrix
# If show the bloch_vector
if show_arrow:
ax.quiver(
0, 0, 0, bloch_vectors[:, 0], bloch_vectors[:, 1], bloch_vectors[:, 2],
arrow_length_ratio=0.05, color=color, alpha=1.0
)
class SpinOps:
r"""矩阵表示下的自旋算符，可以用来构建哈密顿量矩阵或者自旋可观测量。
""" def plot_state_in_bloch_sphere(
def __init__(self, size: int, use_sparse=False): state,
r"""SpinOps 的构造函数，用于实例化一个 SpinOps 对象。 show_arrow=False,
save_gif=False,
filename=None,
view_angle=None,
view_dist=None,
set_color=None
):
r"""将输入的量子态展示在 Bloch 球面上
Args: Args:
size (int): 系统的大小（有几个量子比特） state (list(numpy.ndarray or paddle.Tensor)): 输入的量子态列表，可以支持态矢量和密度矩阵
use_sparse (bool): 是否使用 sparse matrix 计算，默认为 ``False`` show_arrow (bool): 是否展示向量的箭头，默认为 ``False``
save_gif (bool): 是否存储 gif 动图，默认为 ``False``
filename (str): 存储的 gif 动图的名字
view_angle (list or tuple): 视图的角度，
第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)``
view_dist (int): 视图的距离，默认为 7
set_color (str): 若要设置指定的颜色，请查阅 ``cmap`` 表。默认为红色到黑色的渐变颜色
""" """
self.size = size # Check input data
self.id = sparse.eye(2, dtype='complex128') __input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist)
self.__sigz = sparse.bsr.bsr_matrix([[1, 0], [0, -1]], dtype='complex64')
self.__sigy = sparse.bsr.bsr_matrix([[0, -1j], [1j, 0]], dtype='complex64')
self.__sigx = sparse.bsr.bsr_matrix([[0, 1], [1, 0]], dtype='complex64')
self.__sigz_p = []
self.__sigy_p = []
self.__sigx_p = []
self.__sparse = use_sparse
for i in range(self.size):
self.__sigz_p.append(self.__direct_prod_op(spin_op=self.__sigz, spin_index=i))
self.__sigy_p.append(self.__direct_prod_op(spin_op=self.__sigy, spin_index=i))
self.__sigx_p.append(self.__direct_prod_op(spin_op=self.__sigx, spin_index=i))
@property
def sigz_p(self):
r""" :math:`Z` 基底下的 :math:`S^z_i` 算符。
Returns: assert type(state) == list or type(state) == paddle.Tensor or type(state) == np.ndarray, \
list : :math:`S^z_i` 算符组成的列表，其中每一项对应不同的 :math:`i` 'the type of "state" must be "list" or "paddle.Tensor" or "np.ndarray".'
""" if type(state) == paddle.Tensor or type(state) == np.ndarray:
return self.__sigz_p state = [state]
state_len = len(state)
assert state_len >= 1, '"state" is NULL.'
for i in range(state_len):
assert type(state[i]) == paddle.Tensor or type(state[i]) == np.ndarray, \
'the type of "state[i]" should be "paddle.Tensor" or "numpy.ndarray".'
if set_color is not None:
assert type(set_color) == str, \
'the type of "set_color" should be "str".'
@property # Assign a value to an empty variable
def sigy_p(self): if filename is None:
r""" :math:`Z` 基底下的 :math:`S^y_i` 算符。 filename = 'state_in_bloch_sphere.gif'
if view_angle is None:
view_angle = (30, 45)
if view_dist is None:
view_dist = 7
Returns: # Convert Tensor to numpy
list : :math:`S^y_i` 算符组成的列表，其中每一项对应不同的 :math:`i` for i in range(state_len):
""" if type(state[i]) == paddle.Tensor:
return self.__sigy_p state[i] = state[i].numpy()
@property # Convert state_vector to density_matrix
def sigx_p(self): for i in range(state_len):
r""" :math:`Z` 基底下的 :math:`S^x_i` 算符。 if state[i].size == 2:
state_vector = state[i]
state[i] = np.outer(state_vector, np.conj(state_vector))
Returns: # Calc the bloch_vectors
list : :math:`S^x_i` 算符组成的列表，其中每一项对应不同的 :math:`i` bloch_vector_list = []
""" for i in range(state_len):
return self.__sigx_p bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i])
bloch_vector_list.append(bloch_vector_tmp)
def __direct_prod_op(self, spin_op, spin_index): # List must be converted to array for slicing.
r"""直积，得到第 n 个自旋（量子比特）上的自旋算符 bloch_vectors = np.array(bloch_vector_list)
Args: # A update function for animation class
spin_op: 单体自旋算符 def update(frame):
spin_index: 标记第 n 个自旋（量子比特） view_rotating_angle = 5
new_view_angle = [view_angle[0], view_angle[1] + view_rotating_angle * frame]
__plot_bloch_sphere(
ax, bloch_vectors, show_arrow, clear_plt=True,
view_angle=new_view_angle, view_dist=view_dist, set_color=set_color
)
Returns: # Dynamic update and save
scipy.sparse or np.ndarray: 直积后的自旋算符，其数据类型取决于 self.__use_sparse if save_gif:
""" # Helper function to plot vectors on a sphere.
s_p = copy.copy(spin_op) fig = plt.figure(figsize=(8, 8), dpi=100)
for i in range(self.size): fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
if i < spin_index: ax = fig.add_subplot(111, projection='3d')
s_p = sparse.kron(self.id, s_p)
elif i > spin_index:
s_p = sparse.kron(s_p, self.id)
if self.__sparse:
return s_p
else:
return s_p.toarray()
frames_num = 7
anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=600, repeat=False)
anim.save(filename, dpi=100, writer='pillow')
# close the plt
plt.close(fig)
def __input_args_dtype_check( # Helper function to plot vectors on a sphere.
show_arrow, fig = plt.figure(figsize=(8, 8), dpi=100)
save_gif, fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
filename, ax = fig.add_subplot(111, projection='3d')
view_angle,
view_dist __plot_bloch_sphere(
ax, bloch_vectors, show_arrow, clear_plt=True,
view_angle=view_angle, view_dist=view_dist, set_color=set_color
)
plt.show()
def plot_multi_qubits_state_in_bloch_sphere(
state,
which_qubits=None,
show_arrow=False,
save_gif=False,
save_pic=True,
filename=None,
view_angle=None,
view_dist=None,
set_color='#0000FF'
): ):
r""" r"""将输入的多量子比特的量子态展示在 Bloch 球面上
该函数实现对输入默认参数的数据类型检查，保证输入函数中的参数为所允许的数据类型
Args: Args:
show_arrow (bool): 是否展示向量的箭头，默认为 False state (numpy.ndarray or paddle.Tensor): 输入的量子态，可以支持态矢量和密度矩阵
save_gif (bool): 是否存储 gif 动图 which_qubits (list or None): 要展示的量子比特，默认为全展示
filename (str): 存储的 gif 动图的名字 show_arrow (bool): 是否展示向量的箭头，默认为 ``False``
view_angle (list or tuple): 视图的角度， save_gif (bool): 是否存储 gif 动图，默认为 ``False``
第一个元素为关于xy平面的夹角[0-360],第二个元素为关于xz平面的夹角[0-360], 默认为 (30, 45) save_pic (bool): 是否存储静态图片，默认为 ``True``
filename (str): 存储的图片的名字
view_angle (list or tuple): 视图的角度，第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)``
view_dist (int): 视图的距离，默认为 7 view_dist (int): 视图的距离，默认为 7
set_color (str): 若要设置指定的颜色，请查阅 ``cmap`` 表。默认为蓝色
""" """
# Check input data
__input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist)
if show_arrow is not None: assert type(state) == paddle.Tensor or type(state) == np.ndarray, \
assert type(show_arrow) == bool, \ 'the type of "state" must be "paddle.Tensor" or "np.ndarray".'
'the type of "show_arrow" should be "bool".' assert type(set_color) == str, \
if save_gif is not None: 'the type of "set_color" should be "str".'
assert type(save_gif) == bool, \
'the type of "save_gif" should be "bool".'
if save_gif:
if filename is not None:
assert type(filename) == str, \
'the type of "filename" should be "str".'
other, ext = os.path.splitext(filename)
assert ext == '.gif', 'The suffix of the file name must be "gif".'
# If it does not exist, create a folder
path, file = os.path.split(filename)
if not os.path.exists(path):
os.makedirs(path)
if view_angle is not None:
assert type(view_angle) == list or type(view_angle) == tuple, \
'the type of "view_angle" should be "list" or "tuple".'
for i in range(2):
assert type(view_angle[i]) == int, \
'the type of "view_angle[0]" and "view_angle[1]" should be "int".'
if view_dist is not None:
assert type(view_dist) == int, \
'the type of "view_dist" should be "int".'
n_qubits = int(np.log2(state.shape[0]))
def __density_matrix_convert_to_bloch_vector(density_matrix): if which_qubits is None:
r"""该函数将密度矩阵转化为bloch球面上的坐标 which_qubits = list(range(n_qubits))
else:
assert type(which_qubits) == list, 'the type of which_qubits should be None or list'
assert 1 <= len(which_qubits) <= n_qubits, '展示的量子数量需要小于n_qubits'
for i in range(len(which_qubits)):
assert 0 <= which_qubits[i] < n_qubits, '0<which_qubits[i]<n_qubits'
Args: # Assign a value to an empty variable
density_matrix (numpy.ndarray): 输入的密度矩阵 if filename is None:
filename = 'state_in_bloch_sphere.gif'
if view_angle is None:
view_angle = (30, 45)
if view_dist is None:
view_dist = 7
Returns: # Convert Tensor to numpy
bloch_vector (numpy.ndarray): 存储bloch向量的 x,y,z 坐标，向量的模长，向量的颜色 if type(state) == paddle.Tensor:
""" state = state.numpy()
# Pauli Matrix # state_vector to density matrix
pauli_x = np.array([[0, 1], [1, 0]]) if state.shape[0] >= 2 and state.size == state.shape[0]:
pauli_y = np.array([[0, -1j], [1j, 0]]) state_vector = state
pauli_z = np.array([[1, 0], [0, -1]]) state = np.outer(state_vector, np.conj(state_vector))
# Convert a density matrix to a Bloch vector. # multi qubits state decompose
ax = np.trace(np.dot(density_matrix, pauli_x)).real if state.shape[0] > 2:
ay = np.trace(np.dot(density_matrix, pauli_y)).real rho = paddle.to_tensor(state)
az = np.trace(np.dot(density_matrix, pauli_z)).real tmp_s = []
for q in which_qubits:
tmp_s.append(partial_trace_discontiguous(rho, [q]))
state = tmp_s
else:
state = [state]
state_len = len(state)
# Calc the length of bloch vector # Calc the bloch_vectors
length = ax ** 2 + ay ** 2 + az ** 2 bloch_vector_list = []
length = sqrt(length) for i in range(state_len):
if length > 1.0: bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i])
length = 1.0 bloch_vector_list.append(bloch_vector_tmp)
# Calc the color of bloch vector, the value of the color is proportional to the length # List must be converted to array for slicing.
color = length bloch_vectors = np.array(bloch_vector_list)
bloch_vector = [ax, ay, az, length, color] # A update function for animation class
def update(frame):
view_rotating_angle = 5
new_view_angle = [view_angle[0], view_angle[1] + view_rotating_angle * frame]
__plot_bloch_sphere(
ax, bloch_vectors, show_arrow, clear_plt=True,
view_angle=new_view_angle, view_dist=view_dist, set_color=set_color
)
# You must use an array, which is followed by slicing and taking a column # Dynamic update and save
bloch_vector = np.array(bloch_vector) if save_gif:
# Helper function to plot vectors on a sphere.
fig = plt.figure(figsize=(8, 8), dpi=100)
fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
ax = fig.add_subplot(111, projection='3d')
return bloch_vector frames_num = 7
anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=600, repeat=False)
anim.save(filename, dpi=100, writer='pillow')
# close the plt
plt.close(fig)
# Helper function to plot vectors on a sphere.
fig = plt.figure(figsize=(8, 8), dpi=100)
fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
dim = np.ceil(sqrt(len(which_qubits)))
for i in range(1, len(which_qubits)+1):
ax = fig.add_subplot(dim, dim, i, projection='3d')
bloch_vector = np.array([bloch_vectors[i-1]])
__plot_bloch_sphere(
ax, bloch_vector, show_arrow, clear_plt=True,
view_angle=view_angle, view_dist=view_dist, set_color=set_color
)
if save_pic:
plt.savefig('n_qubit_state_in_bloch.png', bbox_inches='tight')
plt.show()
def __plot_bloch_sphere( def plot_rotation_in_bloch_sphere(
ax, init_state,
bloch_vectors=None, rotating_angle,
show_arrow=False, show_arrow=False,
clear_plt=True, save_gif=False,
rotating_angle_list=None, filename=None,
view_angle=None, view_angle=None,
view_dist=None, view_dist=None,
set_color=None color_scheme=None,
): ):
r"""将 Bloch 向量展示在 Bloch 球面上 r"""在 Bloch 球面上刻画从初始量子态开始的旋转轨迹
Args: Args:
ax (Axes3D(fig)): 画布的句柄 init_state (numpy.ndarray or paddle.Tensor): 输入的初始量子态，可以支持态矢量和密度矩阵
bloch_vectors (numpy.ndarray): 存储bloch向量的 x,y,z 坐标，向量的模长，向量的颜色 rotating_angle (list(float)): 旋转角度 ``[theta, phi, lam]``
show_arrow (bool): 是否展示向量的箭头，默认为 False show_arrow (bool): 是否展示向量的箭头，默认为 ``False``
clear_plt (bool): 是否要清空画布，默认为 True，每次画图的时候清空画布再画图 save_gif (bool): 是否存储 gif 动图，默认为 ``False``
rotating_angle_list (list): 旋转角度的列表，用于展示旋转轨迹 filename (str): 存储的 gif 动图的名字
view_angle (list): 视图的角度， view_angle (list or tuple): 视图的角度，
第一个元素为关于xy平面的夹角[0-360],第二个元素为关于xz平面的夹角[0-360], 默认为 (30, 45) 第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)``
view_dist (int): 视图的距离，默认为 7 view_dist (int): 视图的距离，默认为 7
set_color (str): 设置指定的颜色，请查阅cmap表，默认为 "红-黑-根据向量的模长渐变" 颜色方案 color_scheme (list(str,str,str)): 分别是初始颜色，轨迹颜色，结束颜色。若要设置指定的颜色，请查阅 ``cmap`` 表。默认为红色
""" """
# Assign a value to an empty variable # Check input data
if view_angle is None: __input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist)
view_angle = (30, 45)
if view_dist is None:
view_dist = 7
# Define my_color
if set_color is None:
color = 'rainbow'
black_code = '#000000'
red_code = '#F24A29'
if bloch_vectors is not None:
black_to_red = mplcolors.LinearSegmentedColormap.from_list(
'my_color',
[(0, black_code), (1, red_code)],
N=len(bloch_vectors[:, 4])
)
map_vir = plt.get_cmap(black_to_red)
color = map_vir(bloch_vectors[:, 4])
else:
color = set_color
# Set the view angle and view distance assert type(init_state) == paddle.Tensor or type(init_state) == np.ndarray, \
ax.view_init(view_angle[0], view_angle[1]) 'the type of input data should be "paddle.Tensor" or "numpy.ndarray".'
ax.dist = view_dist assert type(rotating_angle) == tuple or type(rotating_angle) == list, \
'the type of rotating_angle should be "tuple" or "list".'
assert len(rotating_angle) == 3, \
'the rotating_angle must include [theta=paddle.Tensor, phi=paddle.Tensor, lam=paddle.Tensor].'
for i in range(3):
assert type(rotating_angle[i]) == paddle.Tensor or type(rotating_angle[i]) == float, \
'the rotating_angle must include [theta=paddle.Tensor, phi=paddle.Tensor, lam=paddle.Tensor].'
if color_scheme is not None:
assert type(color_scheme) == list and len(color_scheme) <= 3, \
'the type of "color_scheme" should be "list" and ' \
'the length of "color_scheme" should be less than or equal to "3".'
for i in range(len(color_scheme)):
assert type(color_scheme[i]) == str, \
'the type of "color_scheme[i] should be "str".'
# Draw the general frame # Assign a value to an empty variable
def draw_general_frame(): if filename is None:
filename = 'rotation_in_bloch_sphere.gif'
# Do not show the grid and original axes # Assign colors to bloch vectors
ax.grid(False) color_list = ['orangered', 'lightsalmon', 'darkred']
ax.set_axis_off() if color_scheme is not None:
ax.view_init(view_angle[0], view_angle[1]) for i in range(len(color_scheme)):
ax.dist = view_dist color_list[i] = color_scheme[i]
set_init_color, set_trac_color, set_end_color = color_list
# Set the lower limit and upper limit of each axis theta, phi, lam = rotating_angle
# To make the bloch_ball look less flat, the default is relatively flat
ax.set_xlim3d(xmin=-1.5, xmax=1.5)
ax.set_ylim3d(ymin=-1.5, ymax=1.5)
ax.set_zlim3d(zmin=-1, zmax=1.3)
# Draw a new axes # Convert Tensor to numpy
coordinate_start_x, coordinate_start_y, coordinate_start_z = \ if type(init_state) == paddle.Tensor:
np.array([[-1.5, 0, 0], [0, -1.5, 0], [0, 0, -1.5]]) init_state = init_state.numpy()
coordinate_end_x, coordinate_end_y, coordinate_end_z = \
np.array([[3, 0, 0], [0, 3, 0], [0, 0, 3]])
ax.quiver(
coordinate_start_x, coordinate_start_y, coordinate_start_z,
coordinate_end_x, coordinate_end_y, coordinate_end_z,
arrow_length_ratio=0.03, color="black", linewidth=0.5
)
ax.text(0, 0, 1.7, r"|0⟩", color="black", fontsize=16)
ax.text(0, 0, -1.9, r"|1⟩", color="black", fontsize=16)
ax.text(1.9, 0, 0, r"|+⟩", color="black", fontsize=16)
ax.text(-1.7, 0, 0, r"|–⟩", color="black", fontsize=16)
ax.text(0, 1.7, 0, r"|i+⟩", color="black", fontsize=16)
ax.text(0, -1.9, 0, r"|i–⟩", color="black", fontsize=16)
# Draw a surface # Convert state_vector to density_matrix
horizontal_angle = np.linspace(0, 2 * np.pi, 80) if init_state.size == 2:
vertical_angle = np.linspace(0, np.pi, 80) state_vector = init_state
surface_point_x = np.outer(np.cos(horizontal_angle), np.sin(vertical_angle)) init_state = np.outer(state_vector, np.conj(state_vector))
surface_point_y = np.outer(np.sin(horizontal_angle), np.sin(vertical_angle))
surface_point_z = np.outer(np.ones(np.size(horizontal_angle)), np.cos(vertical_angle))
ax.plot_surface(
surface_point_x, surface_point_y, surface_point_z, rstride=1, cstride=1,
color="black", linewidth=0.05, alpha=0.03
)
# Draw circle # Rotating angle
def draw_circle(circle_horizon_angle, circle_vertical_angle, linewidth=0.5, alpha=0.2): def rotating_operation(rotating_angle_each):
r = 1 gate_matrix = simulator.u_gate_matrix(rotating_angle_each)
circle_point_x = r * np.cos(circle_vertical_angle) * np.cos(circle_horizon_angle) return np.matmul(np.matmul(gate_matrix, init_state), gate_matrix.conj().T)
circle_point_y = r * np.cos(circle_vertical_angle) * np.sin(circle_horizon_angle)
circle_point_z = r * np.sin(circle_vertical_angle)
ax.plot(
circle_point_x, circle_point_y, circle_point_z,
color="black", linewidth=linewidth, alpha=alpha
)
# draw longitude and latitude # Rotating angle division
def draw_longitude_and_latitude(): rotating_frame = 50
# Draw longitude rotating_angle_list = []
num = 3 state = []
theta = np.linspace(0, 0, 100) for i in range(rotating_frame + 1):
psi = np.linspace(0, 2 * np.pi, 100) angle_each = [theta / rotating_frame * i, phi / rotating_frame * i, lam / rotating_frame * i]
for i in range(num): rotating_angle_list.append(angle_each)
theta = theta + np.pi / num state.append(rotating_operation(angle_each))
draw_circle(theta, psi)
# Draw latitude state_len = len(state)
num = 6 # Calc the bloch_vectors
theta = np.linspace(0, 2 * np.pi, 100) bloch_vector_list = []
psi = np.linspace(-np.pi / 2, -np.pi / 2, 100) for i in range(state_len):
for i in range(num): bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i])
psi = psi + np.pi / num bloch_vector_list.append(bloch_vector_tmp)
draw_circle(theta, psi)
# Draw equator # List must be converted to array for slicing.
theta = np.linspace(0, 2 * np.pi, 100) bloch_vectors = np.array(bloch_vector_list)
psi = np.linspace(0, 0, 100)
draw_circle(theta, psi, linewidth=0.5, alpha=0.2)
# Draw prime meridian # A update function for animation class
theta = np.linspace(0, 0, 100) def update(frame):
psi = np.linspace(0, 2 * np.pi, 100) frame = frame + 2
draw_circle(theta, psi, linewidth=0.5, alpha=0.2) if frame <= len(bloch_vectors) - 1:
__plot_bloch_sphere(
ax, bloch_vectors[1:frame], show_arrow=show_arrow, clear_plt=True,
rotating_angle_list=rotating_angle_list,
view_angle=view_angle, view_dist=view_dist, set_color=set_trac_color
)
# If the number of data points exceeds 20, no longitude and latitude lines will be drawn. # The starting and ending bloch vector has to be shown
if bloch_vectors is not None and len(bloch_vectors) < 52: # show starting vector
draw_longitude_and_latitude() __plot_bloch_sphere(
elif bloch_vectors is None: ax, bloch_vectors[:1], show_arrow=True, clear_plt=False,
draw_longitude_and_latitude() view_angle=view_angle, view_dist=view_dist, set_color=set_init_color
)
# Draw three invisible points # Show ending vector
invisible_points = np.array([[0.03440399, 0.30279721, 0.95243384], if frame == len(bloch_vectors):
[0.70776026, 0.57712403, 0.40743499], __plot_bloch_sphere(
[0.46991358, -0.63717908, 0.61088792]]) ax, bloch_vectors[frame - 1:frame], show_arrow=True, clear_plt=False,
ax.scatter( view_angle=view_angle, view_dist=view_dist, set_color=set_end_color
invisible_points[:, 0], invisible_points[:, 1], invisible_points[:, 2],
c='w', alpha=0.01
) )
# clean plt if save_gif:
if clear_plt: # Helper function to plot vectors on a sphere.
ax.cla() fig = plt.figure(figsize=(8, 8), dpi=100)
draw_general_frame() fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
ax = fig.add_subplot(111, projection='3d')
# Draw the data points # Dynamic update and save
if bloch_vectors is not None: stop_frames = 15
ax.scatter( frames_num = len(bloch_vectors) - 2 + stop_frames
bloch_vectors[:, 0], bloch_vectors[:, 1], bloch_vectors[:, 2], c=color, alpha=1.0 anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=100, repeat=False)
) anim.save(filename, dpi=100, writer='pillow')
# close the plt
plt.close(fig)
# if show the rotating angle # Helper function to plot vectors on a sphere.
if rotating_angle_list is not None: fig = plt.figure(figsize=(8, 8), dpi=100)
bloch_num = len(bloch_vectors) fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
rotating_angle_theta, rotating_angle_phi, rotating_angle_lam = rotating_angle_list[bloch_num - 1] ax = fig.add_subplot(111, projection='3d')
rotating_angle_theta = round(rotating_angle_theta, 6)
rotating_angle_phi = round(rotating_angle_phi, 6)
rotating_angle_lam = round(rotating_angle_lam, 6)
# Shown at the top right of the perspective # Draw the penultimate bloch vector
display_text_angle = [-(view_angle[0] - 10), (view_angle[1] + 10)] update(len(bloch_vectors) - 3)
text_point_x = 2 * np.cos(display_text_angle[0]) * np.cos(display_text_angle[1]) # Draw the last bloch vector
text_point_y = 2 * np.cos(display_text_angle[0]) * np.sin(-display_text_angle[1]) update(len(bloch_vectors) - 2)
text_point_z = 2 * np.sin(-display_text_angle[0])
ax.text(text_point_x, text_point_y, text_point_z, r'$\theta=' + str(rotating_angle_theta) + r'$',
color="black", fontsize=14)
ax.text(text_point_x, text_point_y, text_point_z - 0.1, r'$\phi=' + str(rotating_angle_phi) + r'$',
color="black", fontsize=14)
ax.text(text_point_x, text_point_y, text_point_z - 0.2, r'$\lambda=' + str(rotating_angle_lam) + r'$',
color="black", fontsize=14)
# If show the bloch_vector plt.show()
if show_arrow:
ax.quiver(
0, 0, 0, bloch_vectors[:, 0], bloch_vectors[:, 1], bloch_vectors[:, 2],
arrow_length_ratio=0.05, color=color, alpha=1.0
)
def plot_n_qubit_state_in_bloch_sphere( def plot_density_matrix_graph(density_matrix, size=0.3):
state, r"""密度矩阵可视化工具。
which_qubits=None,
show_arrow=False, Args:
save_gif=False, density_matrix (numpy.ndarray or paddle.Tensor): 多量子比特的量子态的状态向量或者密度矩阵,要求量子数大于 1
save_pic=True, size (float): 条宽度，在 0 到 1 之间，默认为 0.3
filename=None, """
view_angle=None, if not isinstance(density_matrix, (np.ndarray, paddle.Tensor)):
view_dist=None, msg = f'Expected density_matrix to be np.ndarray or paddle.Tensor, but got {type(density_matrix)}'
set_color='#0000FF' raise TypeError(msg)
): if isinstance(density_matrix, paddle.Tensor):
r"""将输入的多量子比特的量子态展示在 Bloch 球面上 density_matrix = density_matrix.numpy()
if density_matrix.shape[0] != density_matrix.shape[1]:
msg = f'Expected density matrix dim0 equal to dim1, but got dim0={density_matrix.shape[0]}, dim1={density_matrix.shape[1]}'
raise ValueError(msg)
real = density_matrix.real
imag = density_matrix.imag
figure = plt.figure()
ax_real = figure.add_subplot(121, projection='3d', title="real")
ax_imag = figure.add_subplot(122, projection='3d', title="imag")
xx, yy = np.meshgrid(
list(range(real.shape[0])), list(range(real.shape[1])))
xx, yy = xx.ravel(), yy.ravel()
real = real.reshape(-1)
imag = imag.reshape(-1)
ax_real.bar3d(xx, yy, np.zeros_like(real), size, size, np.abs(real))
ax_imag.bar3d(xx, yy, np.zeros_like(imag), size, size, np.abs(imag))
plt.show()
return
def image_to_density_matrix(image_filepath):
r"""将图片编码为密度矩阵
Args:
image_filepath (str): 图片文件的路径
Return:
rho (numpy.ndarray): 编码得到的密度矩阵
"""
image_matrix = matplotlib.image.imread(image_filepath)
# Converting images to grayscale
image_matrix = image_matrix.mean(axis=2)
# Fill the matrix so that it becomes a matrix whose shape is [2**n,2**n]
length = int(2**np.ceil(np.log2(np.max(image_matrix.shape))))
image_matrix = np.pad(image_matrix, ((0, length-image_matrix.shape[0]), (0, length-image_matrix.shape[1])), 'constant')
# Density matrix whose trace is 1
rho = image_matrix@image_matrix.T
rho = rho/np.trace(rho)
return rho
def pauli_basis(n):
r"""生成 n 量子比特的泡利基空间
Args:
n (int): 量子比特的数量
Return:
tuple:
- basis_str: 泡利基空间的一组基底表示（array形式）
- label_str: 泡利基空间对应的一组基底表示（标签形式），形如``[ 'X', 'Y', 'Z', 'I']``
"""
sigma_x = np.array([[0, 1], [1, 0]], dtype=np.complex128)
sigma_y = np.array([[0, -1j], [1j, 0]], dtype=np.complex128)
sigma_z = np.array([[1, 0], [0, -1]], dtype=np.complex128)
sigma_id = np.array([[1, 0], [0, 1]], dtype=np.complex128)
pauli = [sigma_x, sigma_y, sigma_z, sigma_id]
labels = ['X', 'Y', 'Z', 'I']
num_qubits = n
num = 1
if num_qubits > 0:
basis_str = pauli[:]
label_str = labels[:]
pauli_basis = pauli[:]
pauli_label = labels[:]
while num < num_qubits:
length = len(basis_str)
for i in range(4):
for j in range(length):
basis_str.append(np.kron(basis_str[j], pauli_basis[i]))
label_str.append(label_str[j] + pauli_label[i])
basis_str = basis_str[-1:-4**(num+1)-1:-1]
label_str = label_str[-1:-4**(num+1)-1:-1]
num += 1
return basis_str, label_str
def decompose(matrix):
r"""生成 n 量子比特的泡利基空间
Args:
matrix (numpy.ndarray): 要分解的矩阵
Return:
pauli_form (list): 返回矩阵分解后的哈密顿量，形如 ``[[1, 'Z0, Z1'], [2, 'I']]``
"""
if np.log2(len(matrix)) % 1 != 0:
print("Please input correct matrix!")
return -1
basis_space, label_str = pauli_basis(np.log2(len(matrix)))
coefficients = [] # 对应的系数
pauli_word = [] # 对应的label
pauli_form = [] # 输出pauli_str list形式：[[1, 'Z0, Z1'], [2, 'I']]
for i in range(len(basis_space)):
# 求系数
a_ij = 1/len(matrix) * np.trace(matrix@basis_space[i])
if a_ij != 0:
if a_ij.imag != 0:
coefficients.append(a_ij)
else:
coefficients.append(a_ij.real)
pauli_word.append(label_str[i])
for i in range(len(coefficients)):
pauli_site = [] # 临时存放一个基
pauli_site.append(coefficients[i])
word = ''
for j in range(len(pauli_word[0])):
if pauli_word[i] == 'I'*int(np.log2(len(matrix))):
word = 'I' # 和Hamiltonian类似，若全是I就用一个I指代
break
if pauli_word[i][j] == 'I':
continue # 如果是I就不加数字下标
if j != 0 and len(word) != 0:
word += ','
word += pauli_word[i][j]
word += str(j) # 对每一个label加标签，说明是作用在哪个比特
pauli_site.append(word) # 添加上对应作用的门
pauli_form.append(pauli_site)
return pauli_form
class Hamiltonian:
r""" Paddle Quantum 中的 Hamiltonian ``class``。
用户可以通过一个 Pauli string 来实例化该 ``class``。
"""
def __init__(self, pauli_str, compress=True):
r""" 创建一个 Hamiltonian 类。
Args:
pauli_str (list): 用列表定义的 Hamiltonian，如 ``[(1, 'Z0, Z1'), (2, 'I')]``
compress (bool): 是否对输入的 list 进行自动合并（例如 ``(1, 'Z0, Z1')`` 和 ``(2, 'Z1, Z0')`` 这两项将被自动合并），默认为 ``True``
Note:
如果设置 ``compress=False``，则不会对输入的合法性进行检验。
"""
self.__coefficients = None
self.__terms = None
self.__pauli_words_r = []
self.__pauli_words = []
self.__sites = []
self.__nqubits = None
# when internally updating the __pauli_str, be sure to set __update_flag to True
self.__pauli_str = pauli_str
self.__update_flag = True
self.__decompose()
if compress:
self.__compress()
def __getitem__(self, indices):
new_pauli_str = []
if isinstance(indices, int):
indices = [indices]
elif isinstance(indices, slice):
indices = list(range(self.n_terms)[indices])
elif isinstance(indices, tuple):
indices = list(indices)
for index in indices:
new_pauli_str.append([self.coefficients[index], ','.join(self.terms[index])])
return Hamiltonian(new_pauli_str, compress=False)
def __add__(self, h_2):
new_pauli_str = self.pauli_str.copy()
if isinstance(h_2, float) or isinstance(h_2, int):
new_pauli_str.extend([[float(h_2), 'I']])
else:
new_pauli_str.extend(h_2.pauli_str)
return Hamiltonian(new_pauli_str)
def __mul__(self, other):
new_pauli_str = copy.deepcopy(self.pauli_str)
for i in range(len(new_pauli_str)):
new_pauli_str[i][0] *= other
return Hamiltonian(new_pauli_str, compress=False)
def __sub__(self, other):
return self.__add__(other.__mul__(-1))
def __str__(self):
str_out = ''
for idx in range(self.n_terms):
str_out += '{} '.format(self.coefficients[idx])
for _ in range(len(self.terms[idx])):
str_out += self.terms[idx][_]
if _ != len(self.terms[idx]) - 1:
str_out += ', '
if idx != self.n_terms - 1:
str_out += '\n'
return str_out
def __repr__(self):
return 'paddle_quantum.Hamiltonian object: \n' + self.__str__()
@property
def n_terms(self):
r"""返回该哈密顿量的项数
Returns:
int :哈密顿量的项数
"""
return len(self.__pauli_str)
@property
def pauli_str(self):
r"""返回哈密顿量对应的 Pauli string
Returns:
list : 哈密顿量对应的 Pauli string
"""
return self.__pauli_str
@property
def terms(self):
r"""返回哈密顿量中的每一项构成的列表
Returns:
list :哈密顿量中的每一项，i.e. ``[['Z0, Z1'], ['I']]``
"""
if self.__update_flag:
self.__decompose()
return self.__terms
else:
return self.__terms
@property
def coefficients(self):
r""" 返回哈密顿量中的每一项对应的系数构成的列表
Returns:
list :哈密顿量中每一项的系数，i.e. ``[1.0, 2.0]``
"""
if self.__update_flag:
self.__decompose()
return self.__coefficients
else:
return self.__coefficients
@property
def pauli_words(self):
r"""返回哈密顿量中每一项对应的 Pauli word 构成的列表
Returns:
list :每一项对应的 Pauli word，i.e. ``['ZIZ', 'IIX']``
"""
if self.__update_flag:
self.__decompose()
return self.__pauli_words
else:
return self.__pauli_words
@property
def pauli_words_r(self):
r"""返回哈密顿量中每一项对应的简化（不包含 I） Pauli word 组成的列表
Returns:
list :不包含 "I" 的 Pauli word 构成的列表，i.e. ``['ZXZZ', 'Z', 'X']``
"""
if self.__update_flag:
self.__decompose()
return self.__pauli_words_r
else:
return self.__pauli_words_r
@property
def sites(self):
r"""返回该哈密顿量中的每一项对应的量子比特编号组成的列表
Returns:
list :哈密顿量中每一项所对应的量子比特编号构成的列表，i.e. ``[[1, 2], [0]]``
"""
if self.__update_flag:
self.__decompose()
return self.__sites
else:
return self.__sites
@property
def n_qubits(self):
r"""返回该哈密顿量对应的量子比特数
Returns:
int :量子比特数
"""
if self.__update_flag:
self.__decompose()
return self.__nqubits
else:
return self.__nqubits
def __decompose(self):
r"""将哈密顿量分解为不同的形式
Notes:
这是一个内部函数，你不需要直接使用它
这是一个比较基础的函数，它负责将输入的 Pauli string 拆分为不同的形式并存储在内部变量中
"""
self.__pauli_words = []
self.__pauli_words_r = []
self.__sites = []
self.__terms = []
self.__coefficients = []
self.__nqubits = 1
new_pauli_str = []
for coefficient, pauli_term in self.__pauli_str:
pauli_word_r = ''
site = []
single_pauli_terms = re.split(r',\s*', pauli_term.upper())
self.__coefficients.append(float(coefficient))
self.__terms.append(single_pauli_terms)
for single_pauli_term in single_pauli_terms:
match_I = re.match(r'I', single_pauli_term, flags=re.I)
if match_I:
assert single_pauli_term[0].upper() == 'I', \
'The offset is defined with a sole letter "I", i.e. (3.0, "I")'
pauli_word_r += 'I'
site.append('')
else:
match = re.match(r'([XYZ])([0-9]+)', single_pauli_term, flags=re.I)
if match:
pauli_word_r += match.group(1).upper()
assert int(match.group(2)) not in site, 'each Pauli operator should act on different qubit'
site.append(int(match.group(2)))
else:
raise Exception(
'Operators should be defined with a string composed of Pauli operators followed' +
'by qubit index on which it act, separated with ",". i.e. "Z0, X1"')
self.__nqubits = max(self.__nqubits, int(match.group(2)) + 1)
self.__pauli_words_r.append(pauli_word_r)
self.__sites.append(site)
new_pauli_str.append([float(coefficient), pauli_term.upper()])
for term_index in range(len(self.__pauli_str)):
pauli_word = ['I' for _ in range(self.__nqubits)]
site = self.__sites[term_index]
for site_index in range(len(site)):
if type(site[site_index]) == int:
pauli_word[site[site_index]] = self.__pauli_words_r[term_index][site_index]
self.__pauli_words.append(''.join(pauli_word))
self.__pauli_str = new_pauli_str
self.__update_flag = False
def __compress(self):
r""" 对同类项进行合并。
Notes:
这是一个内部函数，你不需要直接使用它
"""
if self.__update_flag:
self.__decompose()
else:
pass
new_pauli_str = []
flag_merged = [False for _ in range(self.n_terms)]
for term_idx_1 in range(self.n_terms):
if not flag_merged[term_idx_1]:
for term_idx_2 in range(term_idx_1 + 1, self.n_terms):
if not flag_merged[term_idx_2]:
if self.pauli_words[term_idx_1] == self.pauli_words[term_idx_2]:
self.__coefficients[term_idx_1] += self.__coefficients[term_idx_2]
flag_merged[term_idx_2] = True
else:
pass
if self.__coefficients[term_idx_1] != 0:
new_pauli_str.append([self.__coefficients[term_idx_1], ','.join(self.__terms[term_idx_1])])
self.__pauli_str = new_pauli_str
self.__update_flag = True
def decompose_with_sites(self):
r"""将 pauli_str 分解为系数、泡利字符串的简化形式以及它们分别作用的量子比特下标。
Returns:
tuple: 包含如下元素的 tuple:
- coefficients (list): 元素为每一项的系数
- pauli_words_r (list): 元素为每一项的泡利字符串的简化形式，例如 'Z0, Z1, X3' 这一项的泡利字符串为 'ZZX'
- sites (list): 元素为每一项作用的量子比特下标，例如 'Z0, Z1, X3' 这一项的 site 为 [0, 1, 3]
"""
if self.__update_flag:
self.__decompose()
return self.coefficients, self.__pauli_words_r, self.__sites
def decompose_pauli_words(self):
r"""将 pauli_str 分解为系数和泡利字符串。
Returns:
tuple: 包含如下元素的 tuple:
- coefficients(list): 元素为每一项的系数
- pauli_words(list): 元素为每一项的泡利字符串，例如 'Z0, Z1, X3' 这一项的泡利字符串为 'ZZIX'
"""
if self.__update_flag:
self.__decompose()
else:
pass
return self.coefficients, self.__pauli_words
def construct_h_matrix(self, qubit_num=None):
r"""构建 Hamiltonian 在 Z 基底下的矩阵。
Returns:
np.ndarray: Z 基底下的哈密顿量矩阵形式
"""
coefs, pauli_words, sites = self.decompose_with_sites()
if qubit_num is None:
qubit_num = 1
for site in sites:
if type(site[0]) is int:
qubit_num = max(qubit_num, max(site) + 1)
else:
assert qubit_num >= self.n_qubits, "输入的量子数不小于哈密顿量表达式中所对应的量子比特数"
n_qubit = qubit_num
h_matrix = np.zeros([2 ** n_qubit, 2 ** n_qubit], dtype='complex64')
spin_ops = SpinOps(n_qubit, use_sparse=True)
for idx in range(len(coefs)):
op = coefs[idx] * sparse.eye(2 ** n_qubit, dtype='complex64')
for site_idx in range(len(sites[idx])):
if re.match(r'X', pauli_words[idx][site_idx], re.I):
op = op.dot(spin_ops.sigx_p[sites[idx][site_idx]])
elif re.match(r'Y', pauli_words[idx][site_idx], re.I):
op = op.dot(spin_ops.sigy_p[sites[idx][site_idx]])
elif re.match(r'Z', pauli_words[idx][site_idx], re.I):
op = op.dot(spin_ops.sigz_p[sites[idx][site_idx]])
h_matrix += op
return h_matrix
Args:
state (numpy.ndarray or paddle.Tensor): 输入的量子态，可以支持态矢量和密度矩阵,
该函数下，列表内每一个量子态对应一张单独的图片
which_qubits(list or None):若为多量子比特，则给出要展示的量子比特，默认为 None，表示全展示
show_arrow (bool): 是否展示向量的箭头，默认为 ``False``
save_gif (bool): 是否存储 gif 动图，默认为 ``False``
save_pic (bool): 是否存储静态图片，默认为 ``True``
filename (str): 存储的 gif 动图的名字
view_angle (list or tuple): 视图的角度，
第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)``
view_dist (int): 视图的距离，默认为 7
set_color (str): 若要设置指定的颜色，请查阅 ``cmap`` 表。默认为蓝色
"""
# Check input data
__input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist)
assert type(state) == paddle.Tensor or type(state) == np.ndarray, \ class SpinOps:
'the type of "state" must be "paddle.Tensor" or "np.ndarray".' r"""矩阵表示下的自旋算符，可以用来构建哈密顿量矩阵或者自旋可观测量。
assert type(set_color) == str, \
'the type of "set_color" should be "str".'
n_qubits = int(np.log2(state.shape[0])) """
def __init__(self, size: int, use_sparse=False):
r"""SpinOps 的构造函数，用于实例化一个 SpinOps 对象。
if which_qubits is None: Args:
which_qubits = list(range(n_qubits)) size (int): 系统的大小（有几个量子比特）
else: use_sparse (bool): 是否使用 sparse matrix 计算，默认为 ``False``
assert type(which_qubits)==list,'the type of which_qubits should be None or list' """
assert 1<=len(which_qubits)<=n_qubits,'展示的量子数量需要小于n_qubits' self.size = size
for i in range(len(which_qubits)): self.id = sparse.eye(2, dtype='complex128')
assert 0<=which_qubits[i]<n_qubits, '0<which_qubits[i]<n_qubits' self.__sigz = sparse.bsr.bsr_matrix([[1, 0], [0, -1]], dtype='complex64')
self.__sigy = sparse.bsr.bsr_matrix([[0, -1j], [1j, 0]], dtype='complex64')
self.__sigx = sparse.bsr.bsr_matrix([[0, 1], [1, 0]], dtype='complex64')
self.__sigz_p = []
self.__sigy_p = []
self.__sigx_p = []
self.__sparse = use_sparse
for i in range(self.size):
self.__sigz_p.append(self.__direct_prod_op(spin_op=self.__sigz, spin_index=i))
self.__sigy_p.append(self.__direct_prod_op(spin_op=self.__sigy, spin_index=i))
self.__sigx_p.append(self.__direct_prod_op(spin_op=self.__sigx, spin_index=i))
# Assign a value to an empty variable @property
if filename is None: def sigz_p(self):
filename = 'state_in_bloch_sphere.gif' r""" :math:`Z` 基底下的 :math:`S^z_i` 算符。
if view_angle is None:
view_angle = (30, 45)
if view_dist is None:
view_dist = 7
# Convert Tensor to numpy Returns:
if type(state) == paddle.Tensor: list : :math:`S^z_i` 算符组成的列表，其中每一项对应不同的 :math:`i`
state = state.numpy() """
return self.__sigz_p
#state_vector to density matrix @property
if state.shape[0]>=2 and state.size==state.shape[0]: def sigy_p(self):
state_vector = state r""" :math:`Z` 基底下的 :math:`S^y_i` 算符。
state = np.outer(state_vector, np.conj(state_vector))
#多量子态分解 Returns:
if state.shape[0]>2: list : :math:`S^y_i` 算符组成的列表，其中每一项对应不同的 :math:`i`
rho = paddle.to_tensor(state) """
tmp_s = [] return self.__sigy_p
for q in which_qubits:
tmp_s.append(partial_trace_discontiguous(rho,[q]))
state = tmp_s
else:
state = [state]
state_len = len(state)
# Calc the bloch_vectors @property
bloch_vector_list = [] def sigx_p(self):
for i in range(state_len): r""" :math:`Z` 基底下的 :math:`S^x_i` 算符。
bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i])
bloch_vector_list.append(bloch_vector_tmp)
# List must be converted to array for slicing. Returns:
bloch_vectors = np.array(bloch_vector_list) list : :math:`S^x_i` 算符组成的列表，其中每一项对应不同的 :math:`i`
"""
return self.__sigx_p
# A update function for animation class def __direct_prod_op(self, spin_op, spin_index):
def update(frame): r"""直积，得到第 n 个自旋（量子比特）上的自旋算符
view_rotating_angle = 5
new_view_angle = [view_angle[0], view_angle[1] + view_rotating_angle * frame]
__plot_bloch_sphere(
ax, bloch_vectors, show_arrow, clear_plt=True,
view_angle=new_view_angle, view_dist=view_dist, set_color=set_color
)
# Dynamic update and save Args:
if save_gif: spin_op: 单体自旋算符
# Helper function to plot vectors on a sphere. spin_index: 标记第 n 个自旋（量子比特）
fig = plt.figure(figsize=(8, 8), dpi=100)
fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
ax = fig.add_subplot(111, projection='3d')
frames_num = 7 Returns:
anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=600, repeat=False) scipy.sparse or np.ndarray: 直积后的自旋算符，其数据类型取决于 self.__use_sparse
anim.save(filename, dpi=100, writer='pillow') """
# close the plt s_p = copy.copy(spin_op)
plt.close(fig) for i in range(self.size):
if i < spin_index:
s_p = sparse.kron(self.id, s_p)
elif i > spin_index:
s_p = sparse.kron(s_p, self.id)
if self.__sparse:
return s_p
else:
return s_p.toarray()
# Helper function to plot vectors on a sphere.
fig = plt.figure(figsize=(8, 8), dpi=100)
fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
dim = np.ceil(sqrt(len(which_qubits)))
for i in range(1,len(which_qubits)+1):
ax = fig.add_subplot(dim,dim,i,projection='3d')
bloch_vector=np.array([bloch_vectors[i-1]])
__plot_bloch_sphere(
ax, bloch_vector, show_arrow, clear_plt=True,
view_angle=view_angle, view_dist=view_dist, set_color=set_color
)
if save_pic:
plt.savefig('n_qubit_state_in_bloch.png',bbox_inches='tight')
plt.show()
def plot_state_in_bloch_sphere( def __input_args_dtype_check(
state, show_arrow,
show_arrow=False, save_gif,
save_gif=False, filename,
filename=None, view_angle,
view_angle=None, view_dist
view_dist=None,
set_color=None
): ):
r"""将输入的量子态展示在 Bloch 球面上 r"""
该函数实现对输入默认参数的数据类型检查，保证输入函数中的参数为所允许的数据类型
Args: Args:
state (list(numpy.ndarray or paddle.Tensor)): 输入的量子态列表，可以支持态矢量和密度矩阵 show_arrow (bool): 是否展示向量的箭头，默认为 False
show_arrow (bool): 是否展示向量的箭头，默认为 ``False`` save_gif (bool): 是否存储 gif 动图
save_gif (bool): 是否存储 gif 动图，默认为 ``False``
filename (str): 存储的 gif 动图的名字 filename (str): 存储的 gif 动图的名字
view_angle (list or tuple): 视图的角度， view_angle (list or tuple): 视图的角度，
第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)`` 第一个元素为关于xy平面的夹角[0-360],第二个元素为关于xz平面的夹角[0-360], 默认为 (30, 45)
view_dist (int): 视图的距离，默认为 7 view_dist (int): 视图的距离，默认为 7
set_color (str): 若要设置指定的颜色，请查阅 ``cmap`` 表。默认为红色到黑色的渐变颜色
""" """
# Check input data
__input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist)
assert type(state) == list or type(state) == paddle.Tensor or type(state) == np.ndarray, \
'the type of "state" must be "list" or "paddle.Tensor" or "np.ndarray".'
if type(state) == paddle.Tensor or type(state) == np.ndarray:
state = [state]
state_len = len(state)
assert state_len >= 1, '"state" is NULL.'
for i in range(state_len):
assert type(state[i]) == paddle.Tensor or type(state[i]) == np.ndarray, \
'the type of "state[i]" should be "paddle.Tensor" or "numpy.ndarray".'
if set_color is not None:
assert type(set_color) == str, \
'the type of "set_color" should be "str".'
# Assign a value to an empty variable
if filename is None:
filename = 'state_in_bloch_sphere.gif'
if view_angle is None:
view_angle = (30, 45)
if view_dist is None:
view_dist = 7
# Convert Tensor to numpy if show_arrow is not None:
for i in range(state_len): assert type(show_arrow) == bool, \
if type(state[i]) == paddle.Tensor: 'the type of "show_arrow" should be "bool".'
state[i] = state[i].numpy() if save_gif is not None:
assert type(save_gif) == bool, \
# Convert state_vector to density_matrix 'the type of "save_gif" should be "bool".'
for i in range(state_len):
if state[i].size == 2:
state_vector = state[i]
state[i] = np.outer(state_vector, np.conj(state_vector))
# Calc the bloch_vectors
bloch_vector_list = []
for i in range(state_len):
bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i])
bloch_vector_list.append(bloch_vector_tmp)
# List must be converted to array for slicing.
bloch_vectors = np.array(bloch_vector_list)
# A update function for animation class
def update(frame):
view_rotating_angle = 5
new_view_angle = [view_angle[0], view_angle[1] + view_rotating_angle * frame]
__plot_bloch_sphere(
ax, bloch_vectors, show_arrow, clear_plt=True,
view_angle=new_view_angle, view_dist=view_dist, set_color=set_color
)
# Dynamic update and save
if save_gif: if save_gif:
# Helper function to plot vectors on a sphere. if filename is not None:
fig = plt.figure(figsize=(8, 8), dpi=100) assert type(filename) == str, \
fig.subplots_adjust(left=0, right=1, bottom=0, top=1) 'the type of "filename" should be "str".'
ax = fig.add_subplot(111, projection='3d') other, ext = os.path.splitext(filename)
assert ext == '.gif', 'The suffix of the file name must be "gif".'
# If it does not exist, create a folder
path, file = os.path.split(filename)
if not os.path.exists(path):
os.makedirs(path)
if view_angle is not None:
assert type(view_angle) == list or type(view_angle) == tuple, \
'the type of "view_angle" should be "list" or "tuple".'
for i in range(2):
assert type(view_angle[i]) == int, \
'the type of "view_angle[0]" and "view_angle[1]" should be "int".'
if view_dist is not None:
assert type(view_dist) == int, \
'the type of "view_dist" should be "int".'
frames_num = 7
anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=600, repeat=False)
anim.save(filename, dpi=100, writer='pillow')
# close the plt
plt.close(fig)
# Helper function to plot vectors on a sphere. class QuantumFisher:
fig = plt.figure(figsize=(8, 8), dpi=100) r"""量子费舍信息及相关量的计算器。
fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
Attributes:
cir (UAnsatz): 需要计算量子费舍信息的参数化量子电路
"""
def __init__(self, cir):
r"""QuantumFisher 的构造函数，用于实例化一个量子费舍信息的计算器。
Args:
cir (UAnsatz): 需要计算量子费舍信息的参数化量子电路
"""
self.cir = cir
ax = fig.add_subplot(111, projection='3d') def get_qfisher_matrix(self):
__plot_bloch_sphere( r"""利用二阶参数平移规则计算量子费舍信息矩阵。
ax, bloch_vectors, show_arrow, clear_plt=True,
view_angle=view_angle, view_dist=view_dist, set_color=set_color
)
plt.show() Returns:
numpy.ndarray: 量子费舍信息矩阵
代码示例:
def plot_rotation_in_bloch_sphere( .. code-block:: python
init_state,
rotating_angle,
show_arrow=False,
save_gif=False,
filename=None,
view_angle=None,
view_dist=None,
color_scheme=None,
):
r"""在 Bloch 球面上刻画从初始量子态开始的旋转轨迹
Args: import paddle
init_state (numpy.ndarray or paddle.Tensor): 输入的初始量子态，可以支持态矢量和密度矩阵 from paddle_quantum.circuit import UAnsatz
rotating_angle (list(float)): 旋转角度 ``[theta, phi, lam]`` from paddle_quantum.utils import QuantumFisher
show_arrow (bool): 是否展示向量的箭头，默认为 ``False``
save_gif (bool): 是否存储 gif 动图，默认为 ``False``
filename (str): 存储的 gif 动图的名字
view_angle (list or tuple): 视图的角度，
第一个元素为关于 xy 平面的夹角 [0-360]，第二个元素为关于 xz 平面的夹角 [0-360], 默认为 ``(30, 45)``
view_dist (int): 视图的距离，默认为 7
color_scheme (list(str,str,str)): 分别是初始颜色，轨迹颜色，结束颜色。若要设置指定的颜色，请查阅 ``cmap`` 表。默认为红色
"""
# Check input data
__input_args_dtype_check(show_arrow, save_gif, filename, view_angle, view_dist)
assert type(init_state) == paddle.Tensor or type(init_state) == np.ndarray, \ cir = UAnsatz(1)
'the type of input data should be "paddle.Tensor" or "numpy.ndarray".' cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False),
assert type(rotating_angle) == tuple or type(rotating_angle) == list, \ which_qubit=0)
'the type of rotating_angle should be "tuple" or "list".' cir.rz(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False),
assert len(rotating_angle) == 3, \ which_qubit=0)
'the rotating_angle must include [theta=paddle.Tensor, phi=paddle.Tensor, lam=paddle.Tensor].'
for i in range(3):
assert type(rotating_angle[i]) == paddle.Tensor or type(rotating_angle[i]) == float, \
'the rotating_angle must include [theta=paddle.Tensor, phi=paddle.Tensor, lam=paddle.Tensor].'
if color_scheme is not None:
assert type(color_scheme) == list and len(color_scheme) <= 3, \
'the type of "color_scheme" should be "list" and ' \
'the length of "color_scheme" should be less than or equal to "3".'
for i in range(len(color_scheme)):
assert type(color_scheme[i]) == str, \
'the type of "color_scheme[i] should be "str".'
# Assign a value to an empty variable qf = QuantumFisher(cir)
if filename is None: qfim = qf.get_qfisher_matrix()
filename = 'rotation_in_bloch_sphere.gif' print(f'The QFIM at {cir.get_param().tolist()} is \n {qfim}.')
# Assign colors to bloch vectors ::
color_list = ['orangered', 'lightsalmon', 'darkred']
if color_scheme is not None:
for i in range(len(color_scheme)):
color_list[i] = color_scheme[i]
set_init_color, set_trac_color, set_end_color = color_list
theta, phi, lam = rotating_angle The QFIM at [0.0, 0.0] is
[[1. 0.]
[0. 0.]].
"""
# Get the real-time parameters from the UAnsatz class
list_param = self.cir.get_param().tolist()
num_param = len(list_param)
# Initialize a numpy array to record the QFIM
qfim = np.zeros((num_param, num_param))
# Assign the signs corresponding to the four terms in a QFIM element
list_sign = [[1, 1], [1, -1], [-1, 1], [-1, -1]]
# Run the circuit and record the current state vector
psi = self.cir.run_state_vector().numpy()
# For each QFIM element
for i in range(0, num_param):
for j in range(i, num_param):
# For each term in each element
for sign_i, sign_j in list_sign:
# Shift the parameters by pi/2 * sign
list_param[i] += np.pi / 2 * sign_i
list_param[j] += np.pi / 2 * sign_j
# Update the parameters in the circuit
self.cir.update_param(list_param)
# Run the shifted circuit and record the shifted state vector
psi_shift = self.cir.run_state_vector().numpy()
# Calculate each term as the fidelity with a sign factor
qfim[i][j] += abs(np.vdot(
psi_shift, psi))**2 * sign_i * sign_j * (-0.5)
# De-shift the parameters
list_param[i] -= np.pi / 2 * sign_i
list_param[j] -= np.pi / 2 * sign_j
self.cir.update_param(list_param)
if i != j:
# The QFIM is symmetric
qfim[j][i] = qfim[i][j]
return qfim
def get_qfisher_norm(self, direction, step_size=0.01):
r"""利用有限差分计算沿给定方向的量子费舍信息的投影。
# Convert Tensor to numpy Args:
if type(init_state) == paddle.Tensor: direction (list): 要计算量子费舍信息投影的方向
init_state = init_state.numpy() step_size (float, optional): 有限差分的步长，默认为 0.01
# Convert state_vector to density_matrix Returns:
if init_state.size == 2: float: 沿给定方向的量子费舍信息的投影
state_vector = init_state
init_state = np.outer(state_vector, np.conj(state_vector))
# Rotating angle 代码示例:
def rotating_operation(rotating_angle_each):
gate_matrix = simulator.u_gate_matrix(rotating_angle_each)
return np.matmul(np.matmul(gate_matrix, init_state), gate_matrix.conj().T)
# Rotating angle division .. code-block:: python
rotating_frame = 50
rotating_angle_list = []
state = []
for i in range(rotating_frame + 1):
angle_each = [theta / rotating_frame * i, phi / rotating_frame * i, lam / rotating_frame * i]
rotating_angle_list.append(angle_each)
state.append(rotating_operation(angle_each))
state_len = len(state) import paddle
# Calc the bloch_vectors from paddle_quantum.circuit import UAnsatz
bloch_vector_list = [] from paddle_quantum.utils import QuantumFisher
for i in range(state_len):
bloch_vector_tmp = __density_matrix_convert_to_bloch_vector(state[i]) cir = UAnsatz(2)
bloch_vector_list.append(bloch_vector_tmp) cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False),
which_qubit=0)
cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False),
which_qubit=1)
cir.cnot(control=[0, 1])
cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False),
which_qubit=0)
cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False),
which_qubit=1)
qf = QuantumFisher(cir)
v = [1,1,1,1]
qfi_norm = qf.get_qfisher_norm(direction=v)
print(f'The QFI norm along {v} at {cir.get_param().tolist()} is {qfi_norm:.7f}')
# List must be converted to array for slicing. ::
bloch_vectors = np.array(bloch_vector_list)
# A update function for animation class The QFI norm along [1, 1, 1, 1] at [0.0, 0.0, 0.0, 0.0] is 5.9996250
def update(frame): """
frame = frame + 2 # Get the real-time parameters
if frame <= len(bloch_vectors) - 1: list_param = self.cir.get_param().tolist()
__plot_bloch_sphere( # Run the circuit and record the current state vector
ax, bloch_vectors[1:frame], show_arrow=show_arrow, clear_plt=True, psi = self.cir.run_state_vector().numpy()
rotating_angle_list=rotating_angle_list, # Check whether the length of the input direction vector is equal to the number of the variational parameters
view_angle=view_angle, view_dist=view_dist, set_color=set_trac_color assert len(list_param) == len(
) direction
), "the length of direction vector should be equal to the number of the parameters"
# Shift the parameters by step_size * direction
array_params_shift = np.array(
list_param) + np.array(direction) * step_size
# Update the parameters in the circuit
self.cir.update_param(array_params_shift.tolist())
# Run the shifted circuit and record the shifted state vector
psi_shift = self.cir.run_state_vector().numpy()
# Calculate quantum Fisher-Rao norm along the given direction
qfisher_norm = (1 - abs(np.vdot(psi_shift, psi))**2) * 4 / step_size**2
# De-shift the parameters and update
self.cir.update_param(list_param)
return qfisher_norm
def get_eff_qdim(self, num_param_samples=4, tol=None):
r"""计算有效量子维数，即量子费舍信息矩阵的秩在整个参数空间的最大值。
# The starting and ending bloch vector has to be shown Args:
# show starting vector num_param_samples (int, optional): 用来估计有效量子维数时所用的参数样本量，默认为 4
__plot_bloch_sphere( tol (float, optional): 奇异值的最小容差，低于此容差的奇异值认为是 0，默认为 None，其含义同 ``numpy.linalg.matrix_rank()``
ax, bloch_vectors[:1], show_arrow=True, clear_plt=False,
view_angle=view_angle, view_dist=view_dist, set_color=set_init_color
)
# Show ending vector Returns:
if frame == len(bloch_vectors): int: 给定量子电路对应的有效量子维数
__plot_bloch_sphere(
ax, bloch_vectors[frame - 1:frame], show_arrow=True, clear_plt=False,
view_angle=view_angle, view_dist=view_dist, set_color=set_end_color
)
if save_gif: 代码示例:
# Helper function to plot vectors on a sphere.
fig = plt.figure(figsize=(8, 8), dpi=100)
fig.subplots_adjust(left=0, right=1, bottom=0, top=1)
ax = fig.add_subplot(111, projection='3d')
# Dynamic update and save .. code-block:: python
stop_frames = 15
frames_num = len(bloch_vectors) - 2 + stop_frames
anim = animation.FuncAnimation(fig, update, frames=frames_num, interval=100, repeat=False)
anim.save(filename, dpi=100, writer='pillow')
# close the plt
plt.close(fig)
# Helper function to plot vectors on a sphere. import paddle
fig = plt.figure(figsize=(8, 8), dpi=100) from paddle_quantum.circuit import UAnsatz
fig.subplots_adjust(left=0, right=1, bottom=0, top=1) from paddle_quantum.utils import QuantumFisher
ax = fig.add_subplot(111, projection='3d')
# Draw the penultimate bloch vector cir = UAnsatz(1)
update(len(bloch_vectors) - 3) cir.rz(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False),
# Draw the last bloch vector which_qubit=0)
update(len(bloch_vectors) - 2) cir.ry(theta=paddle.to_tensor(0., dtype="float64", stop_gradient=False),
which_qubit=0)
plt.show() qf = QuantumFisher(cir)
print(cir)
print(f'The number of parameters of -Rz-Ry- is {len(cir.get_param().tolist())}')
print(f'The effective quantum dimension -Rz-Ry- is {qf.get_eff_qdim()}')
::
--Rz(0.000)----Ry(0.000)--
The number of parameters of -Rz-Ry- is 2
The effective quantum dimension -Rz-Ry- is 1
"""
# Get the real-time parameters
list_param = self.cir.get_param().tolist()
num_param = len(list_param)
# Generate random parameters
param_samples = 2 * np.pi * np.random.random(
(num_param_samples, num_param))
# Record the ranks
list_ranks = []
# Here it has been assumed that the set of points that do not maximize the rank of QFIMs, as singularities, form a null set.
# Thus one can find the maximal rank using a few samples.
for param in param_samples:
# Set the random parameters
self.cir.update_param(param.tolist())
# Calculate the ranks
list_ranks.append(self.get_qfisher_rank(tol))
# Recover the original parameters
self.cir.update_param(list_param)
return max(list_ranks)
def get_qfisher_rank(self, tol=None):
r"""计算量子费舍信息矩阵的秩。
def pauli_basis(n):
r"""生成 n 量子比特的泡利基空间
Args: Args:
n (int): 量子比特的数量 tol (float, optional): 奇异值的最小容差，低于此容差的奇异值认为是 0，默认为 None，其含义同 ``numpy.linalg.matrix_rank()``
Return: Returns:
tuple: int: 量子费舍信息矩阵的秩
basis_str: 泡利基空间的一组基底表示（array形式）
label_str: 泡利基空间对应的一组基底表示（标签形式），形如``[ 'X', 'Y', 'Z', 'I']``
""" """
sigma_x = np.array([[0, 1], [1, 0]], dtype=np.complex128) qfisher_rank = np.linalg.matrix_rank(self.get_qfisher_matrix(),
sigma_y = np.array([[0, -1j], [1j, 0]], dtype=np.complex128) tol,
sigma_z = np.array([[1, 0], [0, -1]], dtype=np.complex128) hermitian=True)
sigma_id = np.array([[1, 0], [0, 1]], dtype=np.complex128) return qfisher_rank
pauli = [sigma_x, sigma_y, sigma_z, sigma_id]
labels = ['X', 'Y', 'Z', 'I']
num_qubits = n
num = 1
if num_qubits > 0:
basis_str = pauli[:]
label_str = labels[:]
pauli_basis = pauli[:]
palui_label = labels[:]
while num < num_qubits:
length = len(basis_str)
for i in range(4):
for j in range(length):
basis_str.append(np.kron(basis_str[j], pauli_basis[i]))
label_str.append(label_str[j] + palui_label[i])
basis_str = basis_str[-1:-4**(num+1)-1:-1]
label_str = label_str[-1:-4**(num+1)-1:-1]
num += 1
return basis_str, label_str
class ClassicalFisher:
r"""经典费舍信息及相关量的计算器。
Attributes:
model (paddle.nn.Layer): 经典或量子神经网络模型的实例
num_thetas (int): 参数集合的数量
num_inputs (int): 输入的样本数量
"""
def __init__(self,
model,
num_thetas,
num_inputs,
model_type='quantum',
**kwargs):
r"""ClassicalFisher 的构造函数，用于实例化一个经典费舍信息的计算器。
def decompose(matrix):
r"""生成 n 量子比特的泡利基空间
Args: Args:
matrix (numpy.ndarray): 要分解的矩阵 model (paddle.nn.Layer): 经典或量子神经网络模型的实例
num_thetas (int): 参数集合的数量
num_inputs (int): 输入的样本数量
model_type (str, optional): 模型是经典 "classical" 的还是量子 "quantum" 的，默认是量子的
Return: Note:
pauli_form (list): 返回矩阵分解后的哈密顿量，形如 ``[[1, 'Z0, Z1'], [2, 'I']]`` 这里 ``**kwargs`` 包含如下选项:
- size (list): 经典神经网络各层神经元的数量
- num_qubits (int): 量子神经网络量子比特的数量
- depth (int): 量子神经网络的深度
- encoding (str): 量子神经网络中经典数据的编码方式，目前支持 "IQP" 和 "re-uploading"
Raises:
ValueError: 不被支持的编码方式
ValueError: 不被支持的模型类别
""" """
if np.log2(len(matrix)) % 1 != 0: self.model = model
print("Please input correct matrix!") self.num_thetas = num_thetas
return -1 self.num_inputs = num_inputs
basis_space, label_str = pauli_basis(np.log2(len(matrix))) self._model_type = model_type
coefficients = [] # 对应的系数 if self._model_type == 'classical':
pauli_word = [] # 对应的label layer_dims = kwargs['size']
pauli_form = [] # 输出pauli_str list形式：[[1, 'Z0, Z1'], [2, 'I']] self.model_args = [layer_dims]
for i in range(len(basis_space)): self.input_size = layer_dims[0]
# 求系数 self.output_size = layer_dims[-1]
a_ij = 1/len(matrix) * np.trace(matrix@basis_space[i]) self.num_params = sum(layer_dims[i] * layer_dims[i + 1]
if a_ij != 0: for i in range(len(layer_dims) - 1))
if a_ij.imag != 0: elif self._model_type == 'quantum':
coefficients.append(a_ij) num_qubits = kwargs['num_qubits']
depth = kwargs['depth']
# Supported QNN encoding: ‘IQP' and 're-uploading'
encoding = kwargs['encoding']
self.model_args = [num_qubits, depth, encoding]
self.input_size = num_qubits
# Default dimension of output layer = 1
self.output_size = 1
# Determine the number of model parameters for different encoding types
if encoding == 'IQP':
self.num_params = 3 * depth * num_qubits
elif encoding == 're-uploading':
self.num_params = 3 * (depth + 1) * num_qubits
else: else:
coefficients.append(a_ij.real) raise ValueError('Non-existent encoding method')
pauli_word.append(label_str[i]) else:
for i in range(len(coefficients)): raise ValueError(
pauli_site = [] # 临时存放一个基 'The model type should be equal to either classical or quantum'
pauli_site.append(coefficients[i]) )
word = ''
for j in range(len(pauli_word[0])):
if pauli_word[i] == 'I'*int(np.log2(len(matrix))):
word = 'I' # 和Hamiltonian类似，若全是I就用一个I指代
break
if pauli_word[i][j] == 'I':
continue # 如果是I就不加数字下标
if j != 0 and len(word) != 0:
word += ','
word += pauli_word[i][j]
word += str(j) # 对每一个label加标签，说明是作用在哪个比特
pauli_site.append(word) # 添加上对应作用的门
pauli_form.append(pauli_site)
return pauli_form # Generate random data
np.random.seed(0)
x = np.random.normal(0, 1, size=(num_inputs, self.input_size))
# Use the same input data for each theta set
self.x = np.tile(x, (num_thetas, 1))
def get_gradient(self, x):
r"""计算输出层关于变分参数的梯度。
def plot_density_graph(density_matrix: Union[paddle.Tensor, np.ndarray],
size: Optional[float]=.3) -> plt.Figure:
r"""密度矩阵可视化工具。
Args: Args:
density_matrix (numpy.ndarray or paddle.Tensor): 多量子比特的量子态的状态向量或者密度矩阵,要求量子数大于1 x (numpy.ndarray): 输入样本
size (float): 条宽度，在0到1之间，默认0.3
Returns: Returns:
plt.Figure: 对应的密度矩阵可视化3D直方图 numpy.ndarray: 输出层关于变分参数的梯度，数组形状为（输入样本数量, 输出层维数, 变分参数数量）
""" """
if not isinstance(density_matrix, (np.ndarray, paddle.Tensor)): if not paddle.is_tensor(x):
msg = f'Expected density_matrix to be np.ndarray or paddle.Tensor, but got {type(density_matrix)}' x = paddle.to_tensor(x, stop_gradient=True)
raise TypeError(msg) gradvectors = []
if isinstance(density_matrix, paddle.Tensor): seed = 0
density_matrix = density_matrix.numpy()
if density_matrix.shape[0] != density_matrix.shape[1]: pbar = tqdm(desc="running in get_gradient: ",
msg = f'Expected density matrix dim0 equal to dim1, but got dim0={density_matrix.shape[0]}, dim1={density_matrix.shape[1]}' total=len(x),
raise ValueError(msg) ncols=100,
ascii=True)
for m in range(len(x)):
pbar.update(1)
if m % self.num_inputs == 0:
seed += 1
paddle.seed(seed)
net = self.model(*self.model_args)
output = net(x[m])
logoutput = paddle.log(output)
grad = []
for i in range(self.output_size):
net.clear_gradients()
logoutput[i].backward(retain_graph=True)
grads = []
for param in net.parameters():
grads.append(param.grad.reshape((-1, )))
gr = paddle.concat(grads)
grad.append(gr * paddle.sqrt(output[i]))
jacobian = paddle.concat(grad)
# Jacobian matrix corresponding to each data point
jacobian = paddle.reshape(jacobian,
(self.output_size, self.num_params))
gradvectors.append(jacobian.detach().numpy())
pbar.close()
return gradvectors
def get_cfisher(self, gradients):
r"""利用雅可比矩阵计算经典费舍信息矩阵。
real = density_matrix.real Args:
imag = density_matrix.imag gradients (numpy.ndarray): 输出层关于变分参数的梯度, 数组形状为（输入样本数量, 输出层维数, 变分参数数量）
figure = plt.figure() Returns:
ax_real = figure.add_subplot(121, projection='3d', title="real") numpy.ndarray: 经典费舍信息矩阵，数组形状为（输入样本数量, 变分参数数量, 变分参数数量）
ax_imag = figure.add_subplot(122, projection='3d', title="imag") """
fishers = np.zeros((len(gradients), self.num_params, self.num_params))
for i in range(len(gradients)):
grads = gradients[i]
temp_sum = np.zeros(
(self.output_size, self.num_params, self.num_params))
for j in range(self.output_size):
temp_sum[j] += np.array(
np.outer(grads[j], np.transpose(grads[j])))
fishers[i] += np.sum(temp_sum, axis=0)
xx, yy = np.meshgrid( return fishers
list(range(real.shape[0])), list(range(real.shape[1])))
xx, yy = xx.ravel(), yy.ravel()
real = real.reshape(-1)
imag = imag.reshape(-1)
ax_real.bar3d(xx, yy, np.zeros_like(real), size, size, np.abs(real)) def get_normalized_cfisher(self):
ax_imag.bar3d(xx, yy, np.zeros_like(imag), size, size, np.abs(imag)) r"""计算归一化的经典费舍信息矩阵。
return figure Returns:
numpy.ndarray: 归一化的经典费舍信息矩阵，数组形状为（输入样本数量, 变分参数数量, 变分参数数量）
"""
grads = self.get_gradient(self.x)
fishers = self.get_cfisher(grads)
fisher_trace = np.trace(np.average(fishers, axis=0))
# Average over input data
fisher = np.average(np.reshape(fishers,
(self.num_thetas, self.num_inputs,
self.num_params, self.num_params)),
axis=1)
normalized_cfisher = self.num_params * fisher / fisher_trace
def img_to_density_matrix(img_file): return normalized_cfisher, fisher_trace
r"""将图片编码为密度矩阵
Args:
img_file: 图片文件
Return: def get_eff_dim(self, normalized_cfisher, list_num_samples, gamma=1):
rho:密度矩阵 `` r"""计算经典的有效维数。
"""
img_matrix = matplotlib.image.imread(img_file)
#将图片转为灰度图 Args:
img_matrix = img_matrix.mean(axis=2) normalized_cfisher (numpy.ndarray): 归一化的经典费舍信息矩阵
list_num_samples (list): 不同样本量构成的列表
gamma (int, optional): 有效维数定义中包含的一个人为可调参数，默认为 1
#填充矩阵,使其变为[2**n,2**n]的矩阵 Returns:
length = int(2**np.ceil(np.log2(np.max(img_matrix.shape)))) list: 对于不同样本量的有效维数构成的列表
img_matrix = np.pad(img_matrix,((0,length-img_matrix.shape[0]),(0,length-img_matrix.shape[1])),'constant') """
#trace为1的密度矩阵 eff_dims = []
rho = img_matrix@img_matrix.T for n in list_num_samples:
rho = rho/np.trace(rho) one_plus_F = np.eye(
return rho self.num_params) + normalized_cfisher * gamma * n / (
2 * np.pi * np.log(n))
det = np.linalg.slogdet(one_plus_F)[1]
r = det / 2
eff_dims.append(2 * (logsumexp(r) - np.log(self.num_thetas)) /
np.log(gamma * n / (2 * np.pi * np.log(n))))
return eff_dims
requirements.txt
浏览文件 @ 016af983
paddlepaddle>=2.1.1 paddlepaddle>=2.2.0
scipy scipy
networkx>=2.5 networkx>=2.5
matplotlib>=3.3.0 matplotlib>=3.3.0
interval interval
tqdm tqdm
openfermion
pyscf; platform_system == "Linux" or platform_system == "Darwin"
setup.py
浏览文件 @ 016af983
...@@ -23,7 +23,7 @@ with open("README.md", "r", encoding="utf-8") as fh: ...@@ -23,7 +23,7 @@ with open("README.md", "r", encoding="utf-8") as fh:
setuptools.setup( setuptools.setup(
name='paddle-quantum', name='paddle-quantum',
version='2.1.2', version='2.1.3',
author='Institute for Quantum Computing, Baidu INC.', author='Institute for Quantum Computing, Baidu INC.',
author_email='quantum@baidu.com', author_email='quantum@baidu.com',
description='Paddle Quantum is a quantum machine learning (QML) toolkit developed based on Baidu PaddlePaddle.', description='Paddle Quantum is a quantum machine learning (QML) toolkit developed based on Baidu PaddlePaddle.',
...@@ -48,7 +48,16 @@ setuptools.setup( ...@@ -48,7 +48,16 @@ setuptools.setup(
'paddle_quantum.mbqc.VQSVD.example': ['*.txt'], 'paddle_quantum.mbqc.VQSVD.example': ['*.txt'],
}, },
install_requires=['paddlepaddle>=2.1.2', 'scipy', 'networkx>=2.5', 'matplotlib>=3.3.0', 'interval', 'tqdm'], install_requires=[
'paddlepaddle>=2.2.0',
'scipy',
'networkx>=2.5',
'matplotlib>=3.3.0',
'interval',
'tqdm',
'openfermion',
'pyscf; platform_system == "Linux" or platform_system == "Darwin"'
],
python_requires='>=3.6, <4', python_requires='>=3.6, <4',
classifiers=[ classifiers=[
'Programming Language :: Python :: 3', 'Programming Language :: Python :: 3',
......
test_and_documents/readme.md 已删除 100644 → 0
浏览文件 @ ba95036b
- 通过在UAnsatz类中添加新的成员函数expand来实现扩展
- 增加utils.plot_density_graph密度矩阵可视化工具。
```
Args:
density_matrix (numpy.ndarray or paddle.Tensor): 多量子比特的量子态的状态向量或者密度矩阵,要求量子数大于1
size (float): 条宽度，在0到1之间，默认0.3
Returns:
plt.Figure: 对应的密度矩阵可视化3D直方图
```
\ No newline at end of file
test_and_documents/test.py 已删除 100644 → 0
浏览文件 @ ba95036b
from paddle_quantum.circuit import UAnsatz
import matplotlib.pyplot as plt
from paddle_quantum.utils import plot_density_graph
import numpy as np
import paddle
import unittest
#density_matrix
def test_density_matrix():
cir = UAnsatz(1)
cir.ry(paddle.to_tensor(1,dtype='float64'),0)
state = cir.run_density_matrix()
cir.expand(3)
print(cir.get_state())
cir2 = UAnsatz(3)
cir2.ry(paddle.to_tensor(1,dtype='float64'),0)
cir2.run_density_matrix()
print(cir2.get_state())
#state_vector
def test_state_vector():
cir = UAnsatz(1)
cir.ry(paddle.to_tensor(1,dtype='float64'),0)
state = cir.run_state_vector()
cir.expand(3)
print(cir.get_state())
cir2 = UAnsatz(3)
cir2.ry(paddle.to_tensor(1,dtype='float64'),0)
cir2.run_state_vector()
print(cir2.get_state())
class TestPlotDensityGraph(unittest.TestCase):
def setUp(self):
self.func = plot_density_graph
self.x_np = (np.random.rand(8, 8) + np.random.rand(8, 8) * 1j)-0.5-0.5j
self.x_tensor = paddle.to_tensor(self.x_np)
def test_input_type(self):
self.assertRaises(TypeError, self.func, 1)
self.assertRaises(TypeError, self.func, [1, 2, 3])
def test_input_shape(self):
x = np.zeros((2, 3))
self.assertRaises(ValueError, self.func, x)
def test_ndarray_input_inputs(self):
res = self.func(self.x_np)
res.show()
def test_tensor_input(self):
res = self.func(self.x_tensor)
res.show()
if __name__ == '__main__':
test_density_matrix()
test_state_vector()
unittest.main()
\ No newline at end of file
test_documents/test.py 已删除 100644 → 0
浏览文件 @ ba95036b
from paddle_quantum.utils import img_to_density_matrix
import paddle
import matplotlib.image
import numpy as np
img_file = '/home/aistudio/f1.jpeg'
rho = (img_to_density_matrix(img_file))
#半正定
w,_=np.linalg.eig(rho)
print(all(w>=0))
#迹为1
print(np.trace(rho))
#shape为[2**n,2**n]
print(rho.shape)
test_documents/test_construct_h_matrix.py 已删除 100644 → 0
浏览文件 @ ba95036b
from paddle_quantum.utils import Hamiltonian
h = Hamiltonian([(1, 'Z0, Z1')])
print(h.construct_h_matrix())
print(h.construct_h_matrix(4))
tutorial/combinatorial_optimization/DC-QAOA_CN.ipynb
浏览文件 @ 016af983
...@@ -38,7 +38,7 @@ ...@@ -38,7 +38,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 1, "execution_count": 14,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-16T03:41:44.449329Z", "end_time": "2021-05-16T03:41:44.449329Z",
...@@ -50,6 +50,8 @@ ...@@ -50,6 +50,8 @@
"import networkx as nx # networkx的版本 >= 2.5\n", "import networkx as nx # networkx的版本 >= 2.5\n",
"import matplotlib.pyplot as plt\n", "import matplotlib.pyplot as plt\n",
"from itertools import combinations\n", "from itertools import combinations\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"\n", "\n",
"# 将一个图形分割成两个有重合的分离顶点子图\n", "# 将一个图形分割成两个有重合的分离顶点子图\n",
"def NaiveLGP(g, k):\n", "def NaiveLGP(g, k):\n",
...@@ -103,7 +105,7 @@ ...@@ -103,7 +105,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 2, "execution_count": 15,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-16T03:41:44.839484Z", "end_time": "2021-05-16T03:41:44.839484Z",
...@@ -113,7 +115,7 @@ ...@@ -113,7 +115,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
"image/png": 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\n", 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\n",
"text/plain": [ "text/plain": [
"<Figure size 1080x288 with 3 Axes>" "<Figure size 1080x288 with 3 Axes>"
] ]
...@@ -127,7 +129,7 @@ ...@@ -127,7 +129,7 @@
"n = 10\n", "n = 10\n",
"G = nx.Graph()\n", "G = nx.Graph()\n",
"G.add_nodes_from([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n", "G.add_nodes_from([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])\n",
"G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 4), (4, 5),\n", "G.add_edges_from([(0, 1), (1, 2), (2, 3), (3, 4), (4, 5), (1, 7),\n",
" (5, 6), (6, 7), (7, 8), (8, 9), (9, 0)])\n", " (5, 6), (6, 7), (7, 8), (8, 9), (9, 0)])\n",
" \n", " \n",
"k = 9 # 设定量子比特的最大数量\n", "k = 9 # 设定量子比特的最大数量\n",
...@@ -149,7 +151,7 @@ ...@@ -149,7 +151,7 @@
" a.margins(0.20)\n", " a.margins(0.20)\n",
"nx.draw_networkx(G, pos=nx.circular_layout(G), ax=ax[0], **options, node_color=node_color1)\n", "nx.draw_networkx(G, pos=nx.circular_layout(G), ax=ax[0], **options, node_color=node_color1)\n",
"nx.draw_networkx(S[0], pos=nx.circular_layout(S[0]), ax=ax[1], **options, node_color=node_color2)\n", "nx.draw_networkx(S[0], pos=nx.circular_layout(S[0]), ax=ax[1], **options, node_color=node_color2)\n",
"nx.draw_networkx(S[1], pos=nx.circular_layout(S[1]), ax=ax[2], **options, node_color=node_color3)" "nx.draw_networkx(S[1], pos=nx.circular_layout(S[1]), ax=ax[2], **options, node_color=node_color3)\n"
] ]
}, },
{ {
...@@ -170,7 +172,7 @@ ...@@ -170,7 +172,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 16,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-16T03:41:46.108438Z", "end_time": "2021-05-16T03:41:46.108438Z",
...@@ -214,7 +216,7 @@ ...@@ -214,7 +216,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 17,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-16T03:42:41.303385Z", "end_time": "2021-05-16T03:42:41.303385Z",
...@@ -227,11 +229,11 @@ ...@@ -227,11 +229,11 @@
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"第一个子图的最大割：\n", "第一个子图的最大割：\n",
"{'010xxxxxxx': 0.49999449162430293, '101xxxxxxx': 0.49999449162430293, '000xxxxxxx': 2.4202658690211183e-06, '111xxxxxxx': 2.420265869021086e-06, '110xxxxxxx': 1.544054913842632e-06, '011xxxxxxx': 1.5440549138425979e-06, '001xxxxxxx': 1.5440549138425754e-06, '100xxxxxxx': 1.5440549138424998e-06}\n", "{'01010101xx': 0.07887396513978905, '10010101xx': 0.07887396513978903, '01101010xx': 0.078873965139789, '10101010xx': 0.078873965139789, '10101101xx': 0.040906327139884305, '01010010xx': 0.0409063271398843, '01010110xx': 0.04004434869249364, '10100101xx': 0.04004434869249363, '01011010xx': 0.040044348692493625, '10101001xx': 0.040044348692493625}\n",
"第二个子图的最大割：\n", "第二个子图的最大割：\n",
"{'0x01010101': 0.14011845299520287, '1x10101010': 0.1401184529952028, '1x01010010': 0.04249785377879272, '0x10100101': 0.04249785377879272, '1x01011010': 0.0424978537787927, '0x10101101': 0.0424978537787927, '0x10101001': 0.036328002709709005, '1x01001010': 0.036328002709709, '0x10110101': 0.036328002709709, '1x01010110': 0.03632800270970896}\n", "{'0xxxxxx101': 0.4556003303152275, '1xxxxxx010': 0.45560033031522745, '1xxxxxx100': 0.0254542520553071, '0xxxxxx011': 0.025454252055307092, '0xxxxxx110': 0.010740876742244158, '1xxxxxx001': 0.010740876742244157, '1xxxxxx000': 0.0022930869455346486, '0xxxxxx111': 0.002293086945534646, '0xxxxxx100': 0.002293086945534642, '1xxxxxx011': 0.002293086945534638}\n",
"母图的最大割：\n", "母图的最大割：\n",
"{'0101010101': 0.14011845299520287, '1010101010': 0.1401184529952028, '0001010101': 2.4202658690211183e-06, '1110101010': 2.420265869021086e-06, '1101010110': 1.544054913842632e-06, '1101001010': 1.544054913842632e-06, '1101011010': 1.544054913842632e-06, '1101010010': 1.544054913842632e-06, '0110110101': 1.5440549138425979e-06, '0110101001': 1.5440549138425979e-06}\n" "{'0101010101': 0.07887396513978905, '1010101010': 0.078873965139789, '1010100100': 0.0254542520553071, '1010010100': 0.0254542520553071, '1010110100': 0.0254542520553071, '1001010100': 0.0254542520553071, '0101101011': 0.025454252055307092, '0101011011': 0.025454252055307092, '0101001011': 0.025454252055307092, '0110101011': 0.025454252055307092}\n"
] ]
} }
], ],
...@@ -281,16 +283,16 @@ ...@@ -281,16 +283,16 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"就以上例子来说，对于第一个子图而言，最有可能的几个最大割将包括 {'010xxxxxxx','101xxxxxxx'}，而第二个子图最有可能的最大割将包括 {'1x10101010','0x01010101'}。这些字符串中的 'x' 代表不在这个子图却在母图的顶点。从这个例子中我们看到，分离顶点0和2在第一个子图中可能的最大割，'010xxxxxxx'，中都属于 $S_0$，但它们在第二个子图的最大割，'1x10101010'，中都属于 $S_1$，所以它们无法整合。（虽然因为 $S_0$ 和 $S_1$ 的对称性，我们可以把他们进行反转从而进行整合，但是没有必要这么做。）\n", "就以上例子来说，对于第一个子图而言，最有可能的几个最大割将包括 {'01010101xx', '10010101xx', '01101010xx', '10101010xx'}，而第二个子图最有可能的最大割将包括 {'0xxxxxx101,'1xxxxxx010'}。这些字符串中的 'x' 代表不在这个子图却在母图的顶点。\n",
"\n", "\n",
"我们接着尝试整合第一个子图的第一个最大割 '010xxxxxxx' 和第二个子图的第二个最大割 '0x01010101'，此最大割即是'101xxxxxxx' 的对称组。我们发现在这两个字符串所代表的最大割当中，分离顶点0和2都属于 $S_0$，我们也可以从下图第一张和第二张图中看出。所以我们可以整合这两个最大割并得到母图的最大割，'0101010101'，如下图第三张图所示。\n", "从这个例子中我们看到，分离顶点 0 和 7 在第一个子图中可能的最大割，'01010101xx' 中分别属于 $S_0$ 和 $S_1$，它们在第二个子图的最大割，'0xxxxxx101'，中也分别属于 $S_0$ 和 $S_1$，所以我们可以整合这两个最大割并得到母图的最大割，'0101010101'，如下图第三张图所示。\n",
"\n", "\n",
"以下为图形展示，前两个图为两个子图的最大割实例，最右的图为母图的最大割。红色点和蓝色点分别表示被分在在 $S_0$ 和 $S_1$ 中的顶点，虚线表示被切割的边。" "以下为图形展示，前两个图为两个子图的最大割实例，最右的图为母图的最大割。红色点和蓝色点分别表示被分在在 $S_0$ 和 $S_1$ 中的顶点，虚线表示被切割的边。"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 18,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-16T03:42:41.647686Z", "end_time": "2021-05-16T03:42:41.647686Z",
...@@ -300,7 +302,7 @@ ...@@ -300,7 +302,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
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\n", "image/png": 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\n",
"text/plain": [ "text/plain": [
"<Figure size 1080x288 with 3 Axes>" "<Figure size 1080x288 with 3 Axes>"
] ]
...@@ -311,8 +313,8 @@ ...@@ -311,8 +313,8 @@
], ],
"source": [ "source": [
"# 计算出的两个子图的最大割\n", "# 计算出的两个子图的最大割\n",
"strr1 = '010xxxxxxx'\n", "strr1 = '01010101xx'\n",
"strr2 = '0x01010101' \n", "strr2 = '0xxxxxx101' \n",
"strr = '0101010101'\n", "strr = '0101010101'\n",
"\n", "\n",
"# 图形示例展示\n", "# 图形示例展示\n",
...@@ -353,7 +355,7 @@ ...@@ -353,7 +355,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 6, "execution_count": 19,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-16T03:44:13.784486Z", "end_time": "2021-05-16T03:44:13.784486Z",
...@@ -365,8 +367,8 @@ ...@@ -365,8 +367,8 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"最有可能的 t 个图形 G 的最大割: {'0101010101': 947, '1010101010': 920, '1001010010': 150, '1001010100': 150, '1001010110': 150, '1101010010': 136, '1101010100': 136, '1101010110': 136, '1101010101': 135, '1001010101': 135}\n", "最有可能的 t 个图形 G 的最大割: {'1010101100': 419, '0101010011': 382, '0101011011': 368, '1010100100': 351, '0110101011': 303, '0101001011': 251, '1001010100': 247, '1010101010': 229, '0100101011': 227, '1011010100': 218}\n",
"量子近似优化分治算法找到的图形 G 的（最有可能的）最大割: 0101010101\n" "量子近似优化分治算法找到的图形 G 的（最有可能的）最大割: 1010101100\n"
] ]
} }
], ],
...@@ -413,7 +415,7 @@ ...@@ -413,7 +415,7 @@
" out_cnt = [(k, int(s * v / cnt_sum)) for (k, v) in out_cnt]\n", " out_cnt = [(k, int(s * v / cnt_sum)) for (k, v) in out_cnt]\n",
"\n", "\n",
" return out_cnt[0][0], dict(out_cnt)\n", " return out_cnt[0][0], dict(out_cnt)\n",
" \n", "\n",
"# 设定 量子近似优化算法 中的参数\n", "# 设定 量子近似优化算法 中的参数\n",
"p = 2 # 量子电路的层数\n", "p = 2 # 量子电路的层数\n",
"ITR = 100 # 训练迭代的次数\n", "ITR = 100 # 训练迭代的次数\n",
...@@ -456,7 +458,7 @@ ...@@ -456,7 +458,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 7, "execution_count": 20,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-16T03:44:54.150187Z", "end_time": "2021-05-16T03:44:54.150187Z",
...@@ -468,7 +470,7 @@ ...@@ -468,7 +470,7 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"最有可能的 t 个图形 G 的最大割：{'00101': 549, '10110': 512, '00001': 510, '11110': 501, '01001': 471, '11010': 457}\n" "最有可能的 t 个图形 G 的最大割：{'01001': 531, '00001': 504, '11110': 501, '10110': 494, '00101': 489, '11010': 481}\n"
] ]
} }
], ],
...@@ -494,7 +496,7 @@ ...@@ -494,7 +496,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 21,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-11T07:06:44.690385Z", "end_time": "2021-05-11T07:06:44.690385Z",
...@@ -522,7 +524,7 @@ ...@@ -522,7 +524,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 9, "execution_count": 26,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-11T07:16:56.698522Z", "end_time": "2021-05-11T07:16:56.698522Z",
...@@ -538,29 +540,29 @@ ...@@ -538,29 +540,29 @@
"顶点编号 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n", "顶点编号 = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
"\n", "\n",
"随机图形 1\n", "随机图形 1\n",
"边 = [(0, 1), (0, 2), (0, 3), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (2, 3), (2, 4), (2, 7), (3, 8), (3, 9), (4, 5), (5, 6), (5, 9), (6, 7), (6, 8)]\n", "边 = [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 8), (1, 2), (1, 4), (1, 5), (1, 6), (1, 8), (1, 9), (2, 3), (2, 8), (3, 9), (4, 5), (4, 6), (5, 7), (5, 8), (6, 8), (7, 8)]\n",
"半正定规划找的最大割的上限: 14.773421849579332\n", "半正定规划找的最大割的上限: 16.366014900074795\n",
"量子近似优化分治算法找到的最大割分类: 0011011000, 最大割 = 14.0\n", "量子近似优化分治算法找到的最大割分类: 0010100011, 最大割 = 14.0\n",
"\n", "\n",
"随机图形 2\n", "随机图形 2\n",
"边 = [(0, 1), (0, 2), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 4), (1, 6), (1, 7), (1, 8), (2, 4), (2, 5), (2, 7), (2, 9), (3, 6), (3, 8), (3, 9), (4, 5), (4, 6), (5, 7), (6, 9), (7, 9)]\n", "边 = [(0, 2), (0, 3), (0, 4), (0, 5), (0, 8), (1, 4), (1, 8), (1, 9), (2, 5), (2, 6), (2, 8), (3, 4), (3, 5), (3, 6), (3, 9), (4, 6), (4, 7), (4, 8), (5, 7), (6, 8), (7, 9), (8, 9)]\n",
"半正定规划找的最大割的上限: 17.637249299053625\n", "半正定规划找的最大割的上限: 17.401823913484183\n",
"量子近似优化分治算法找到的最大割分类: 1010011010, 最大割 = 15.0\n", "量子近似优化分治算法找到的最大割分类: 1100111001, 最大割 = 16.0\n",
"\n", "\n",
"随机图形 3\n", "随机图形 3\n",
"边 = [(0, 1), (0, 2), (0, 4), (0, 5), (0, 7), (0, 8), (0, 9), (1, 4), (1, 5), (2, 7), (2, 8), (2, 9), (3, 5), (3, 6), (3, 8), (3, 9), (4, 5), (4, 6), (4, 9), (5, 6), (5, 8), (5, 9), (6, 7), (7, 8), (7, 9)]\n", "边 = [(0, 1), (0, 2), (0, 3), (0, 5), (0, 7), (0, 8), (1, 3), (1, 5), (1, 6), (1, 8), (2, 3), (2, 4), (2, 6), (2, 7), (2, 8), (3, 4), (3, 5), (3, 7), (3, 8), (5, 6), (5, 7), (6, 7), (7, 8), (8, 9)]\n",
"半正定规划找的最大割的上限: 19.048588813917966\n", "半正定规划找的最大割的上限: 17.481389612347442\n",
"量子近似优化分治算法找到的最大割分类: 0010110100, 最大割 = 17.0\n", "量子近似优化分治算法找到的最大割分类: 0111000101, 最大割 = 17.0\n",
"\n", "\n",
"随机图形 4\n", "随机图形 4\n",
"边 = [(0, 3), (0, 6), (0, 7), (0, 8), (0, 9), (1, 2), (1, 5), (1, 7), (2, 6), (2, 7), (3, 4), (3, 7), (3, 8), (3, 9), (4, 5), (4, 8), (4, 9), (5, 6), (5, 9), (6, 7), (7, 9), (8, 9)]\n", "边 = [(0, 1), (0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 4), (1, 5), (1, 7), (2, 3), (2, 4), (2, 6), (2, 7), (2, 8), (2, 9), (3, 6), (3, 8), (3, 9), (4, 5), (5, 6), (5, 7), (5, 9), (6, 9), (8, 9)]\n",
"半正定规划找的最大割的上限: 16.551132643953018\n", "半正定规划找的最大割的上限: 19.247444317293844\n",
"量子近似优化分治算法找到的最大割分类: 1010110100, 最大割 = 16.0\n", "量子近似优化分治算法找到的最大割分类: 1110010000, 最大割 = 18.0\n",
"\n", "\n",
"随机图形 5\n", "随机图形 5\n",
"边 = [(0, 2), (0, 5), (0, 6), (0, 7), (0, 8), (1, 2), (1, 4), (1, 7), (2, 4), (2, 7), (2, 9), (3, 4), (3, 5), (3, 6), (3, 9), (4, 6), (4, 7), (4, 8), (5, 6), (5, 7), (5, 9), (6, 8), (7, 8), (8, 9)]\n", "边 = [(0, 3), (0, 5), (0, 6), (0, 7), (1, 3), (1, 5), (1, 7), (1, 8), (2, 7), (2, 9), (3, 4), (3, 6), (3, 7), (3, 8), (3, 9), (4, 6), (4, 7), (4, 8), (4, 9), (5, 7), (5, 8), (5, 9), (6, 7), (6, 9), (8, 9)]\n",
"半正定规划找的最大割的上限: 18.19997280321202\n", "半正定规划找的最大割的上限: 18.715743968566105\n",
"量子近似优化分治算法找到的最大割分类: 1100110001, 最大割 = 17.0\n" "量子近似优化分治算法找到的最大割分类: 1111110000, 最大割 = 17.0\n"
] ]
} }
], ],
...@@ -609,7 +611,7 @@ ...@@ -609,7 +611,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 10, "execution_count": 27,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-11T07:16:56.935061Z", "end_time": "2021-05-11T07:16:56.935061Z",
...@@ -619,7 +621,7 @@ ...@@ -619,7 +621,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
"image/png": 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\n", "image/png": 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\n",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -693,6 +695,9 @@ ...@@ -693,6 +695,9 @@
], ],
"metadata": { "metadata": {
"celltoolbar": "Raw Cell Format", "celltoolbar": "Raw Cell Format",
"interpreter": {
"hash": "3b61f83e8397e1c9fcea57a3d9915794102e67724879b24295f8014f41a14d85"
},
"kernelspec": { "kernelspec": {
"display_name": "Python 3", "display_name": "Python 3",
"language": "python", "language": "python",
...@@ -708,7 +713,7 @@ ...@@ -708,7 +713,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.7.10" "version": "3.7.11"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/combinatorial_optimization/DC-QAOA_EN.ipynb
浏览文件 @ 016af983
...@@ -54,7 +54,8 @@ ...@@ -54,7 +54,8 @@
"import networkx as nx # version of networkx >= 2.5\n", "import networkx as nx # version of networkx >= 2.5\n",
"import matplotlib.pyplot as plt\n", "import matplotlib.pyplot as plt\n",
"from itertools import combinations\n", "from itertools import combinations\n",
"\n", "import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"# Partition a graph into two subgraphs\n", "# Partition a graph into two subgraphs\n",
"def NaiveLGP(g, k):\n", "def NaiveLGP(g, k):\n",
" E = list(g.edges)\n", " E = list(g.edges)\n",
...@@ -117,7 +118,7 @@ ...@@ -117,7 +118,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
"image/png": 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\n", 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\n",
"text/plain": [ "text/plain": [
"<Figure size 1080x288 with 3 Axes>" "<Figure size 1080x288 with 3 Axes>"
] ]
...@@ -131,7 +132,7 @@ ...@@ -131,7 +132,7 @@
"n = 10\n", "n = 10\n",
"G = nx.Graph()\n", "G = nx.Graph()\n",
"G.add_nodes_from([0,1,2,3,4,5,6,7,8,9])\n", "G.add_nodes_from([0,1,2,3,4,5,6,7,8,9])\n",
"G.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),(8,9),(9,0)])\n", "G.add_edges_from([(0,1),(1,2),(2,3),(3,4),(4,5),(1, 7),(5,6),(6,7),(7,8),(8,9),(9,0)])\n",
" \n", " \n",
"k = 9 # Set qubit (vertex) limit\n", "k = 9 # Set qubit (vertex) limit\n",
"S = NaiveLGP(G,k) # Partition G into two subgrahs once\n", "S = NaiveLGP(G,k) # Partition G into two subgrahs once\n",
...@@ -217,7 +218,7 @@ ...@@ -217,7 +218,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 5,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-11T06:52:48.693469Z", "end_time": "2021-05-11T06:52:48.693469Z",
...@@ -230,11 +231,11 @@ ...@@ -230,11 +231,11 @@
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"Max cut for the first partitioned subgraph: \n", "Max cut for the first partitioned subgraph: \n",
"{'010xxxxxxx': 0.49999449162430293, '101xxxxxxx': 0.49999449162430293, '111xxxxxxx': 2.420265869021529e-06, '000xxxxxxx': 2.42026586902126e-06, '001xxxxxxx': 1.5440549138418965e-06, '011xxxxxxx': 1.544054913841822e-06, '100xxxxxxx': 1.544054913841805e-06, '110xxxxxxx': 1.5440549138414785e-06}\n", "{'01010101xx': 0.07887396513978905, '10010101xx': 0.07887396513978903, '01101010xx': 0.078873965139789, '10101010xx': 0.078873965139789, '10101101xx': 0.040906327139884305, '01010010xx': 0.0409063271398843, '01010110xx': 0.04004434869249364, '10100101xx': 0.04004434869249363, '01011010xx': 0.040044348692493625, '10101001xx': 0.040044348692493625}\n",
"Max cut for the second partitioned subgraph: \n", "Max cut for the second partitioned subgraph: \n",
"{'1x10101010': 0.14011845299520345, '0x01010101': 0.14011845299520342, '1x01010010': 0.04249785377879293, '0x10101101': 0.04249785377879292, '1x01011010': 0.0424978537787929, '0x10100101': 0.042497853778792886, '0x10101001': 0.036328002709709185, '1x01010110': 0.03632800270970918, '0x10110101': 0.03632800270970918, '1x01001010': 0.036328002709709165}\n", "{'0xxxxxx101': 0.4556003303152275, '1xxxxxx010': 0.45560033031522745, '1xxxxxx100': 0.0254542520553071, '0xxxxxx011': 0.025454252055307092, '0xxxxxx110': 0.010740876742244158, '1xxxxxx001': 0.010740876742244157, '1xxxxxx000': 0.0022930869455346486, '0xxxxxx111': 0.002293086945534646, '0xxxxxx100': 0.002293086945534642, '1xxxxxx011': 0.002293086945534638}\n",
"Combined max cut for the original graph: \n", "Combined max cut for the original graph: \n",
"{'1010101010': 0.14011845299520345, '0101010101': 0.14011845299520342, '1110101010': 2.420265869021529e-06, '0001010101': 2.42026586902126e-06, '0010110101': 1.5440549138418965e-06, '0010101001': 1.5440549138418965e-06, '0010100101': 1.5440549138418965e-06, '0010101101': 1.5440549138418965e-06, '0110110101': 1.544054913841822e-06, '0110101001': 1.544054913841822e-06}\n" "{'0101010101': 0.07887396513978905, '1010101010': 0.078873965139789, '1010100100': 0.0254542520553071, '1010010100': 0.0254542520553071, '1010110100': 0.0254542520553071, '1001010100': 0.0254542520553071, '0101101011': 0.025454252055307092, '0101011011': 0.025454252055307092, '0101001011': 0.025454252055307092, '0110101011': 0.025454252055307092}\n"
] ]
} }
], ],
...@@ -282,14 +283,14 @@ ...@@ -282,14 +283,14 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"The top several possible max cuts for the first subgraph include {'010xxxxxxx','101xxxxxxx'} and those for the second subgraph include {'1x10101010','0x01010101'}, where 'x' indicates those missing nodes in the subgraph. Shared nodes $0$ and $2$ are all '0's in the first possibility of the first subgraph, i.e. '010xxxxxxx', while they are all '1's in the first possibility of the second subgraph, i.e. '1x10101010', so they cannot combine. (Note that although we can flip 0s and 1s in this situation by symmetry, it is not necessary). We then try to combine '010xxxxxxx' (first possibility of the first subgraph) and '0x01010101' (second possibility of the second subgraph). It is clear that the shared nodes $0$ and $2$ are all '0's in both subgraphs as shown below in the left and middle figure, so we combine these two max cuts and get '0101010101' for the original cycle of six as shown below in the right.\n", "The top several possible max cuts for the first subgraph include {'01010101xx', '10010101xx', '01101010xx', '10101010xx'} and those for the second subgraph include {'0xxxxxx101,'1xxxxxx010'}, where 'x' indicates those missing nodes in the subgraph. From this example we see that the possible maximal cuts of separated vertices 0 and 7 in the first subgraph, '01010101xx', belong to $S_0$ and $S_1$, respectively. And they also belong to $S_0$ and $S_1$, respectively, in the maximal cut of the second subgraph, '0xxxxxx101'. so we can integrate these two maximal cuts and get the maximal cut of the original graph, ' 0101010101', as shown in the third diagram below.\n",
"\n", "\n",
"Graph illustration is shown below. The left and middle subgraphs are subgraphs with approximate max cuts, where red and blue nodes represent $S_0$ and $S_1$ and dashed lines represent cuts." "Graph illustration is shown below. The left and middle subgraphs are subgraphs with approximate max cuts, where red and blue nodes represent $S_0$ and $S_1$ and dashed lines represent cuts."
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 6,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-11T06:52:49.021611Z", "end_time": "2021-05-11T06:52:49.021611Z",
...@@ -299,7 +300,7 @@ ...@@ -299,7 +300,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
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uQtIhwC9JLb3P976g5ZetSfsncB9wZkQUnt1g7eZiqg3ZqNRKEfGOpNtJGwGPjogOL2Y2MysL6YvA3yhuw/MG4FwiziptqK5D0gGkVsZ/B86KiJdzjmRW8ST1johGSScD90bEv/PO1JVIGgJcBqwL7OubQYvG0/zakLXLfSf71x+S5vKOzTZ3NDPLX9oPadQM6Ogd3ZnAa6Q9+KxIEXEtaU3VE8APACQNzjWUWYXKthz4DjBO0uIRcZ4Lqc6XDQp8g7Sva6OkAV5LVTyPTHWQpKWAFUgbO14J/BG4PyLm5hrMzLouSS/DvevD1mrfCFUD8DqwHe5gWlLZFJp/kQrVsyLiXzlHMqsI2fXTFcCqwAER8WLOkSwj6XjgINLfyz/zTVN9PDLVQRExMfsAEPAIaXrHK5J2yzeZmXVFks4Q7L1BxK5K6zwn0HLz2nmmkTZCvxrY3IVU6WU31r5Emvb3oKTv5RzJLHfZHp9zgGdIG/C6kKosvwEuAB6QdGreYaqNR6YWUbauahvS7tv/Bk4m7Vc1Ps9cZlb7svUGBwPDIuLj7MFupM0rTwI2APoBM4DxpC/MG4mYlkvgLkZSP9JGm92A84FfRMQrHTzJpsCRwDqkv8sppAvSy4h4s6SBzUosG426FGiIiAPyzmNtk7QCsEVE3CxpmYj4KO9M1cDFVAlJWpy0geZ+wD3ATyPi9XxTmVktkrQfcDawdUR4n6gKlhVVRwPfBx4FTmmyHrfgC4BvAWcAKwO9WLBb40xgLvAscCbeiNMqkKThwBjg98AZ7hpXPSQtTZqufAHusrhQLqbKIFt8fCjwIPA+8FXgLu+bYGalkG1uORDoHxHv5p3H2ieb6nQ0cAOpOOoXEa82O6gOuJxUTPVrx2nrgR8S8ZvSprUuLxX1896D02nnBaOkxYDJwG7ApIh4sjwBrZyy/b+uIr0H9u7IjCuJ3qSbQFMjqPmeAl4zVQYR8XnWoeZFYBngNFIXwOOyL1Mzs6JI2h+4LSI+cyFVXSJiWkScGxHvkzbQ/KukGyWtA8y7eB0D7Ev7CilIDUd+gXRkOTJbFyN1Q9oR6QFgFmkfus+BmUj3Im2bvU9bebl2B14BvhoR97iQql7Z6PmOpBbqn0paQelmT0ES60n8TmI6aenLRGCWxL8l9s8KrJrkkalOkK2r2hw4HjiFtH6hR5vTPMzMmpH0TeAiYPuIeC3nOLaIJA0AjiGte9tgBuzVE35H+wuppuqBr+DugVYsaWfSSMRA0nuwedEUpIvkz4EDiHh0/kvVCxhNWkN+cHjqac2RdC2wGnBgRPx3/uOsRupsvR7QA+he4OXzmiL9BLgwgpoqPjwy1Qmy/aqeiohvRsRbwFeAFyX9UdJX8s5nZpUvWxh8EbCLC6naEBFTI+IcYGhENHyYLkZbL6TWWAMaGuD66ws925O0Jsus46QDgT8Dy5GaphQafVL23IrAPUj7ppdqCGkd3/PABi6katbBwG3A05JGAkhsRPp73wToQ+FCCmBA9nM2cLlU8P1VtTwylRNJA0k9/Q8BtiJ9EX7uRX5m1ty8rkqSFouISXnnsTKQNg54os19wu6/H/r0gXfegf33L3REA7AMEVPKFdNqUJqadwvpYrjdAhoOhkeuScXVxt5vs2uQtDbQH/49BYY+C3WDOniK6cBvIvhRGeLlwiNTOYmIKZEWDG8YEZOBY4H/SjopW7xpZoakbYGXJC3lQqqmHaG0YLuwESNg0iR4+OG2zjEX+GaJc1ktk3oA19NWIdXKiKigz0Ww/bqwjQupriMixkbE87D4NRAtCqmjj4Znn4XGRrj66oKn6AecKLFmmaN2GhdTOYtsaDAizgT2ATYGnlLSI9dwZpYrSV8FbgZGRMTEvPNYWa3Ngu3P5xswAM4+G048cWHn6AusUtpYVuP2pPWpWcmll6ar4wIGwaxXYIsy5LIKJrEMLLtpobfO+PHws5/BVVe1eYpuwHFlitfpXExVkIh4LiL2AzbJiqw/Sbpd0jC10T3HzGpP9jv/Q+DbXoPQJbS+VuqnP4Urr4QPFrqdmICOTrmxru0U0lqWwhY+IjoAOLn0sazCHQ6Fm0j8+c9wxx3w6adtvr4ncJDUxrTmKuJiqgI12dhuX+B+Uqvcm/JLZGadSdK6wOLAHhFxf955rFNMLvjohhvCDjvAhRe25xwBtH0JYzZP2hNzw1afb/+I6BZIHVpvZVVvf1jkVudzgGElyJK7tod2LVcRMR0YLelyYLnsTvVDwCPA5RHxSa4Bzazksj2HHgIOjYh78s5jneYZYEuar5vaZhtYZRV4N9tSrH9/qKuDddeFTTdtfo5pgFujW3stSbZVS8Fn2z8iOot082ehB1rNGFyCc3QjvQernkemqkBEzI2I97OpfycAqwPjJB2fbzIzKyVJawAPAqe4kOpyflvw0TFjYPXVYaON0s9vfwv33AM771zo6DnAneWLaDWmG61M1SpiRLTVzVytJpWqfqiJ941HpqpMRLwMHCzpNGBJSb2Bq0kb7T00r6GFmVWlTYCzIqLgRkJWwyLeRXoc2J6me/w0NKSfeaZNS22yPmkxMaERuIyIWeUPazXic9LalZY6NiLaMzuXdR1TgMUW8RxzgM8WPUr+vM9UlZPUE/g2cCLp7tD3IuKRfFOZWUdIWh4YFhE35p3FcpS6Nz5IB/f7yUwFhhIxvrShrGalpQNvAKu1eK5PHxg4cP6/n3RSKq6OPLJQIf8KEV8oX1CrNBKXAIdRYIpoXR107w4//jGssAIceijMng1z5rQ4TSOwQkT1r/P0NL8qFxEzI+IqYH1SQTVR0uKSfiJp6ZzjmdlCZL+nDwMr5J3FchbxJGkqd30HX1kP7OFCyjok3U0/l7TWbkENDfDxx/N/Wh8RnZqdw7qWi4HZhZ44/fT0VjnttLS3eGNjeqyZOcAdtVBIgUemapKkZYAfA98CbidNG3o7z0xm1pKkJYBHgT9FxFl557EKIR0EXEK669vWfoONpMX/exDxWGdEsxoj9Qc+hqJbVE8FhjC/C7F1ERJPAZsX+fLpwLYRFN7ArMp4ZKoGRcRHEXEksAYwDughaWVJe0jy37lZ5ZgDjAbOzjuIVZCIq4FNSWth60kjB/PufM4Fps6CqS/ALcDaLqSsaBHTgFPp+Ggo2WtOdCHVZR1L8e+b+2qlkAKPTHUZkjYjdYvqD/wGuCYiivklMLNFJGkAcAHw/YiYknceq2Bp5GBvYBXShryfAa8Mgp5T4NiI2CrPeFYjpF8DR9D+Eap64AIizihfKKt0EnsAf6Rj75sXge0jmFG2YJ3MxVQXku1TtRXpbsJRpMJqVkS8n2swsy5EUl/gL8BY4HB34LRiSOoOvA3sHhEv5RzHaoF0IvDzuRDdWm+CMp00q+n7RIzuvHBWqSS2Au4gdQgfUPioObOhbjZwK3BIBDM7LWAncDHVhUnanzRK9Rfgwoh4LudIZjUtu6FxLzARODAi5uYcyaqYpDOAfhFxat5ZrEZIg5+H09eGQ/qni+N5TQZ6AJ8CvwKuI2Jybhmt4kj0APYCTgHWg/+NOnWDuQLGQLdLIngrp4hl5WKqi5O0GHAIsC/wVdKu1hMjomUTSzMrmiRFREjaCvh7RBTshGTWXtk+gzNdlFupZDd8ukVao7c6sHj21CfAm/ii0RZCYjlgGaA3MAn4L2g/4K6ImJhntnJxMWULkPQb4GukEaurvJ7DbNFlU7JuBK6NiHvyzmO1Q9L2wFIR8Ye8s1j1k7QxMCoitsw7i9UOSTcCT0TEZXlnKQd3drMFRMT3SKNUm5M2j5y3MbCZFSDRW6Ku9edVB1wDDAQe6qxc1mU0Ame7U6uVyEjgb3mHsJpzI+m9VZP84WstRMQ/ImIEsHX20AOSbpH01WwKgFmXJdFD4hsSz0rMIrWtniUxWWK0xNrNXvIDYHlg74iome5FVjGeInXI2iHvIFbdsoL8W6QLX7NSegAYKmn5vIOUg6f52UJlbZwPBL4HPBIRh+WbyCwfEkcA5wB1FO5aNIu0YPslmDESen8CCJgbaT8Xs5KTdCiwRkSckncWq16SBgNnRMSJeWex2iNpSERMyDtHObiYsnbLpisNIXUiewL4MzAmIj7PNZhZmUkI+DVwOO3aTyPmQMNs2PPBiAeHlzmedXHzmpvkncOqm6Q6N5+ycsm2BTk4Ii7JO0upeZqftVtEzImID7MuZEcBXwDelPTdnKOZldupwGG0e2NC1UHvXnD/lhIrlzOYWdYlcmdJJ+WdxaqTpB7AuGx0yqwcZgCnSlo37yCl5mLKihIRL0TE/qT9BP4qaZCkmyVt63VVVkuyYuhMoF/Tx6dOXfBn9my4+OKmR3QDug0AarJ7kVWcN4GTs3bpZh21IzDeM02sXLJRzz+SmpzVFBdTtkgiYnxEvEG64/AQcCnwgqQt8k1mVjJHkdY9LWDAgPk/yywDDQ1wyy0tXlsHbJ/tu2FWNhExDngR+GbeWawqjQRuyjuE1bwbgW/W2k13F1NWEhHRGBFjSFP/TgMmSFpR0hmSlso5nllRJHoBRwC92jpun31gwgR4/PGCT0d2DrNyuxhYK+8QVpXGAy1vB5mV1gvAVrW2xtPFlJVURMyNiPuy0SqAlYDXJf2uVltiWk1r18aVBxwA113X6tO9gf1LFcisNRFxT0ScnncOqy5Z44mTa7XTmlWOrIjqJ+nreWcpJRdTVjYR8V5EHAqsDbwHzJU0VNIutTbEazVrKQpM8WtqpZVg2DC49to2z+NF3dYpskYUo/LOYVXlZkk75x3CuoyewKisQ3RNcDFlZRcREyLi7Ij4kHRxei7wiqTDJLU5fcosZwv9sN9/f3jiCXj77UU7j1mJvAB8W9ISeQexypd179sB+HveWaxriIixpGml2+QcpWRcTFmniojHgY2AY4DtgR6S1pa0bK7BzAr7HJjb1gHf+c5CR6UAppYqkFlbImIicCdwcN5ZrCrsAzwQEVPyDmJdyo3UULMcF1PW6SJ5JCJGRMQ0YFvgVUnXStoo53hmTf2dNppPbL45LL98wS5+Tc0G7itxLrO2jCKt1TNbmEbg8rxDWJdzOXBC3iFKRTXWUMOqlKTFgUOBPUhDv8sAH3k3dsubxA3ACApM1fvtb6Fv3zQ61YYG4MsR/Ks8Cc0KyxoL+DPUCpLULSLaHHk3KxdJWwEzI+LpvLMsKhdTVpEkXQ1sBVwEXJONYJl1OolNgb/RbNPeDvhnBBuXMJLZQknaHjg+IobnncUqk6TjgSUi4oy8s1jXI+lwYLuIGJF3lkXlaX5WqQ4GDiRNAfwzgJtVWB4ieJ40Ta+hiJfXk9YHmnW2p4CvSFoj7yBWsUYCj+UdwrqsW4FdJA3IO8ii8siUVTxJPYFZwPPAWOCiWhgWtuqRbd77MLAJ0KedL6sHDorg5rIFM2uDpHOB7hHx/byzWGWRtCbwOLBCRMzOO491TZLuBm6IiJvyzrIoPDJlFS8iZmYbvW0DPAP8QdL5+aayriSCGcB2wO2kEaqZbRw+DZgC7OVCynI2Gng/7xBWkQYBP3chZTk7CKr/e9IjU1Z1JHUHFiddtD4FXA9cERGTcw1mXYLEGsBxpC+BuUDApEGwWAPwJmkftVsiaMwxptn/SBro1tc2jySRrv/cfMJyJ+kA4J6I+CTvLMXyyJRVnYiYnW0EXA8cBmwKvCVp35yjWRcQwRsRHAcMAYYBe8GxVwLrRfCFCK53IWWVQtJXgb9mF9BmkPZ6/GvOGczm2QX4Rt4hFoVHpqwmSFqBdHNgFmmPld8AT4Tf4GbWhUnqRlprekBEPJV3HsufpPOAWRHxo7yzmEkaDpwcEVvlnaVYHpmymhAR70fEu8Bk4BHgSuBZSZvkm8y6Aknj885gVkg2lesy4Oi8s1j+suJ6X+DGvLOYZe4H1pW0fN5BiuWRKatJ2RfG7sALwEBgL+DyiPgsz1xWmyRFRHgalVUkSYOBvSPiyryzWL6y98KZEXFC3lnM5pG0TER8lHeOYnlkympSRMyNiLsi4gNgBrA28F9JoyUNyTmemVmniYjPgaslrZJ3FsvdZBdSVoGmSDoy7xDFcjFlNS8i3oyIA4F1gI+BRkkbS9rBi7KtRF7IO4DZQnwBeCzrhmpdkKQewLhsdMqskswATpe0Tt5BiuFiyrqMiPgoIn6StQhektSk4iVJB2VfMmZFiYhN885g1paIeBl4DxiedxbLzY7AR9lIpVnFiIg5wB9I6/mqjosp65Ii4kHSndqTgO0BJK0vaelcg1lVkjQm7wxm7XApbkTRlY0Ebso7hFkrbgJGVOOMIRdT1mVF8kBEfDsiZgE7Af+RdKWk9Uvx35CQRF+JxST/vtWwQ/MOYNYOfwIunvcvEt0lBkv0yjGTlUGT755BTb57PgJuyTOXWRueB4ZFRCAJqT/SAKqguPLFnVkmIn4NrAm8CfxKyUpZZ8AOkdhQ4lqgHphCWqs1S+Jlif188WJmnS0iZsAf/yH943yJd4CZpAvseonJEudLrJxzTFsEEhtJXM/8754JwCwp/gnxPHiKn1WmAB6Abd6TXiDtGfo58CkwC+lhpF0o4nqsM7g1ulkbJN0GrAtcBFwXEfVtH8/apHm/awE9gUKLvadm//xRBKNKl9by4tboVukkugPnw9zDoaEX9Cv0fp1Buqb5G7BfBJ92akgrmsQ6pO+eNYBeQF3Lo2bVQ4/ZwKkRjO7UgGZtkbYFrp0DSwj6tlIxTQWmA98l4p5OTLdQLqbM2pDN3R0GnEDaMf7rkvpEREPLY/kS8BDQj/aN+tYDVwPHRuBfxComabmI8Ma9VpGykfB7ga8AfdvxkpnARGDzCN4rZzZbdBKbAw+Qvnvac1OnHhgDnOjvHsudNIJ0LdSnna9oAL5HxO/KF6pjXEyZtVPW8W8OMBZ4GrgwIp5Pz7EGab7vwA6edjrwywh+Vsqs1rkkDY+Iu/LOYdachIBbgV1p/8UKwGxS979NIphUhmhWAhJrAc9S3HfPTyM4t/SpzNpJ2g64m459NkEqqPYl4o7Sh+q4ipx7aFaJImJWRMwFvgS8BPxZ0hnZs5cD/Zu/5uij4dlnobERrr664Gn7AT/yOoWqd2feAcxasXP20+Ji5frrYfx4mDwZxo6FQw5Z4OnuwHLADzslpRXrCgp89zz6KDQ0wNSp6ec//2nxun7ATyRW6ISMZi2l9U83UKiQGjwYbrsNpk2Dt9+GfVt0TO8DXIvUs+w528HFlFkHRcTnEfErYHXgMumWDWHmthT4fRo/Hn72M7jqqjZPKeCosoQ1s67uZNKFcwvnnAOrrAKDBsHXvpY+qzbZZIFDegGHu2FOZZJYHdiMVq7ljjkGBgxIP0OHtnqaI8oUz2xhdqaVzyYuvRRmzoSll4b99oPRo2HddZsf1Q3Yu8wZ28XFlFmRspGqT+Eb+0GPWYWO+fOf4Y474NO2l3H3Ao6QqIg7LGZWG7IR781be/7VV9P1CkBE+ll99ZanoUIuWKyFY1i067jewNES3rTe8nAyMKDFo337wj77wBlnwPTp8OSTcOedsP/+zY8cAJzSCTkXysWU2aLbF7qVohD6agnOYfk4PO8AZgV8bWEHXHppul4ZOxY+/BDuvbfFIQOAFlcxVhFGQOs34c45ByZOhCeegGHDWj1HN1JjErPOI/UCtir43FprwezZMG7c/MdeegnWW6/Q0esgLVmOiB3hYsps0S1WovPk/oFgxYmIMXlnMCtgKdLoQ6uOPjpNA9tyy7REYcaMgoctXY5wtsgWa+2JU06B1VaD5ZeHMWPgrrvSvxcQ+LvHOt9gUtfQlvr3hylTFnxs8uT0QdXSTCrg/etiymzRler3yL+PVUqS26JaJSqw11BLc+emmTQrrABHHln8eazTtfqd8cwzae3+zJlw3XXp73e33QoeqrbOY1YmrX+mTJsGA5s1pxw4MHVSKSz392/uAcxqwJSFH7JQQdrt28ysVD6ltbu/BXTvXnDN1LzzWOVp9eqyuQhQ4R2o/N1jefiM1qaovv56+jBaY435j224IbzySqGje1AB718XU2aL7i8Qsws9UVcHvXqlfzb93wX0BP5ezpBm1uU8SNovqoWlloIRI6BfP+jWDXbaKXUffvjhFodOB/5U5pxWnPtIex8uYNCg9Pc57/tm5EjYemu4776C5+hB2jfRrPNENAAFqyPq69Oc47PPTs0ottgC9twz7eXQ0kfZT65cTJktAknd4bGroKF7oedPPz3tMXXaaakRTWNjeqyZ2cBNEe2/y2gV5+68A5g1F8G/gHGtPMeRR8L778Pnn8P558Pxx6e1Nc10A35f3qRWpAuBFqvcevRIbe4nToRPPoFjj4W99lpwPX9mFnB9BNPLH9WshXNpbXT1qKOgTx+YMAFuuil9WL36avOjpgPnEZH7NHtVQAazqqK00dzuwAnA0xFxmjTnJajboMhT1gNfyS58zMxKRmJfYAwFNnZth9nAdREcstAjLRcS/wYKtjlrhwZg0wheK2Eks/ZJHf0mAAMXdmgrGoClicj9RrRHpsw6ICukXgB+DFyZ/ROoO4JUFHVUPfAnF1LVTVLL+/lmleFWYCwdWDvVxFTgrNLGsRI7gnRR2VH1pBkRLqQsHxEzgOMo/trph5VQSIFHpswWStKKpM0RB0XEEZJWA96KZr88EnsD1wN923nqeuApYLcICm76a9VBUkRE4eXdZjmTWJy0LmZF0ibhCzMXmAZsG8EL5cxmi07iG8C1QJ92vmQ68ASwR0ThNXVmnUY6k7T5bkeuncYQcUL5QnWMR6bM2iDpYuAl0gXIeQAR8WbzQio9zm3AcGASbXdZmgE0AjcCu7qQMrNyiuAz4IvAExANtP6RE6Qi6l3gSy6kqkMEtwB7stDvnjmzSN891wO7u5CyihBxNvA9oGFu26NU9aT375mVVEiBR6bMFiCpDtgL2Coijpe0BfBKRExu/znoCfwf6U7LOqTpNUG6eTEXGA1cFsF7JY5vOfHIlFUL6aGvwpCzYYPNSWui5pL2GuoFPEa6afRIBHNzjGlFyL579iF996zN/O+eOpgpeOFe+MqJEbyfZ06zgqQBL8LJq8HRg9Ln0by7Pj1INwrOB64hIvdW6M25mDLLSNoP+BkwntQl6U+FRqA6dk6WB5YmtT6fBLwZUdTaBTOzRZKt+VwzIsZK9ANWAQaRpn19EMEneeaz0pFYARhC+u75HHgTNBvoFhEt2qmbVQJJdZFu8KwKLEG60fMZ8CYRFXuDx8WUdWmSVgX2A34BbA9MiQjvuWEdIumwiBiTdw6ztkjaFfhpRHwx7yzW+ST9FngqIq7LO4tZc5LWAm4BNlrUG9mdzWumrEuStLGkPwHPktpy9oqIB11IWZEuzzuAWTscDVyWdwjLzd+AffMOYdaKfYG/VlshBR6Zsi5EUg9gb+B2YGvSnPJrImJanrms+nnNlFW6bBT+GWDliCimFbFVOUn9gA9IUz0n5p3HbB5JAv4DfKcab2p3zzuAWblJGgwcTmpvPo40zeFB4MFcg5mZdZ5PgX1cSHVdETFd0i9Ia1FcTFkl6QvcR7rhU3U8MmU1K5t/OwFYl1RMXRgR/8w1lNUkScMjwhv3WkWS1AfYLCIeyzuL5U9SnZtQWCWp9vek10xZTVGynaS7SZsSrh8RT0XEAS6krIyezzuAWRtGAKfmHcLyl02n+reklfPOYgb/6zL6mqTl885SLBdTVhMk9ZI0CFgNuBi4k7Q24PF8k1kX8UHeAcwKyS6ejwEuzTuL5S9b3P8Y8K28s5hltgIaIqJqv0ddTFlVkzRE0pnAO8C+EfFf0mjUmIhoyDme1TqpN9Iyi6X/7c9Tq0SbAYuT1iOYAdwIjMw7hFlmJOk9WbX85W9VSVJ3SX2Bl4AVge0j4rfwvztvZuUh9UP6LtI40manb36UnmlA+gPSZnnGM2vmn8Bu1bwewUruceAJSb3zDmIGjAf+kHeIReEGFFY1snm1OwMnAP+NiCMl9fEIlHWKNF3qFOAM0g7t/QscNQdoBN4F9iHitc4LaLYgSUsCW0fEbXlnscpT7Yv+rfrVynvQI1NWFbJ5/38DzgFuAI4HcCFlnSK9/64CTie1cC1USAHUAf2AocDTSJt3TkCzgr4L7JF3CKs82b5jL2XfrWZ5uUbSPnmHWFQembKKJWlZ4GhgtYgYmXUfetfT+KzTSb8kLeLv18FXTgE2I+L10ocya52kOuBNYO+IcLdJW0C1b5Jq1a/JJtJrRcSEvPMsCo9MWUXKNhZ8FVgM+DFARLzjQso6nbQG8D0KFVIrrwz33AOffQYffgijRkFdXdMj+gOjOyeo2QJ2AMa7kLJCsu/Sm4B9885iXdZw4B/VXkiBiymrEJLqJO0p6XfZHbPbgNUj4piIGJd3PuvSjqO1z8rLLoMJE2DZZWGjjWDYMDjqqKZHdAO2wHu6WOd7APha3iGsot1A2tjeLA+zgEvyDlEKLqYsd9l82bHAj4CHSdNPn4uIz/JNZl2e1Ac4COhZ8PlVV4Wbb4YZM+Djj+G++2C99VqcBTiqwKvNykJpNPXAiJiYdxarXBExLiJ+kU0JNes02Xvutoi4O+8speBiynIhaSVJP5HUA/gYOAD4ckT8ISLm5hzPbJ4tSZ37CrvoIvjWt6BPH1huOdh111RQLagX3iDTOtcxwJp5h7DKJ2lf4Ld557Au52DgwrxDlIqLKetUktaT9EfgRWAg0CcinoiIJ70eyirQkqSRpcIeeyyNRE2ZAh98AM89B7ffXujIxcoTz2xBkvoD+wOX553FqsJjwN6SeuUdxLqUfUkdmmuCiykru2yD3W9IGggMAv4OrBoRJ0bElJzjmbWl9c9IKY1C3XYb9OsHSywBgwfDuecWPLpsCc0WtAPweES8k3cQq3wR8QHwL2DXvLNY1yBpeWAj4C85RykZF1NWNpIGSfo+8F/SIv6lI+KpiLjIRZRVic9obZrf4ounbn6XXAIzZ6aOfldfDbvtVuhov9+tU0TE7cCIvHNYVfkN4Jkh1lkWB34eEY15BykVF1NWcpJWlzQEWAHYBNgnIrZyVz6rQk/SWvOJTz+FN9+EI49M7dAHDYIDDoCXX25+5CzgzjLnNEPSVyQdExEz8s5i1SMi/gzc6UYU1klejYhf5x2ilFxMWUko2VrS7cA/gE0i4pWI2C8inss5nllx0gjqTcDsgs/vvTfssgtMnAhvvAGzZsEJJzQ/ajbpzq9ZuR0P+ILYinEZMDLvEFbbJK0JPJ9tgVMz5DX/tigk9QQGAN2Bh0gfyNdFxPRcg5mVirQ+6QZB3yLP8A8iNi9hIrMWJC0DvEZajzop5zhWZbKufvtHRMF5ymalIOlMYMmIOC7vLKXkkSkriqQlJP0QeBs4JCI+BjaIiNEupKymRPwLuBmo7/BL02uOLnkms5a+CvzehZQV6U5gC0lL5R3EalM2GjUSuDHvLKXmYso6RFIPSd2B50j7mOwaEecBuLW51bBDSS2E211QzYDZj8MxRLxQvlhmSUT8idTox6zDspugvyRtB2FWDv1IM5iezjtIqXmany1UdjdhB+AEYFJEjJTUu5Y6sZgtVFqcfTFwCKnzVe9WjpwKNAJ7CZ4FDgdGR8ScTslpXY6krwFrRcT5eWex6iapW0S0vlG5WZFq+b3lkSlrj7uBC4A/kXatxoWUdTkRc4g4GlgVOBf4nDRSNYVUQM0kdf/7NrAsEU+R1hL+H3CFJH/eWrmcALyXdwirbtmN05clrZR3Fqst2fffq9keUzXHI1PWgqSlgSOBzSJid0krAu97Gp9ZE2m66wrAYGAGMIGIT1oepn7AfaSNMY/275GVkqT1gAeBVSJiZt55rLpJGgO8MW/6vlkpSNoauCQiNsg7Szn4TqktIGsq8R9gGeAkgIh4zxeAZs1EzCbibSJeJOLVQoVUOiymA7sDr3ZuQOsihgIXuJCyErkRt0i30qvJxhPzeGSqi8uGXncF9gUOBNYFxkcrF4ZmVjxJXwF2ioiz885iZtZctnHvpcDxkUbcB5LWiE7FF4zWDhIC+pDWFU+OYI6ks4GrIuLtXMOViUemujBJu5P2JfkpaRoSEfGyCymzsvkvMELS6XkHseon6UhJp+adw2pHQATcPhfuBWYBE4FPgFlI9yPtgNd/WgES60tcRVpLPBn4EJglxWsQb0J8nG/C8vHIVBeTLf47grSAfiipVeVjnsZn1jmyzVUfAy6KiMvyzmPVKWsW8ApwVET8Nec4Vguk3YCr5kL/bunaoLkAppMulA8k4qFOzWcVSWJ14BbSNWUPUuOlZmY1Qo/ZpJv3v4qgpq45XUx1EZLWAn5MmtL3e+CsiPg031RmXZOkFUjTIN7wjQxrUyqaNgNWIV3gTgFeESxHatW/vt9DtsikQ4BRpM+l9mgADiXihvKFskonsTHwKDCA9s12mw78EfhuLRVUBapHqxXZ3Oc9gadIc1dfJHUTm5RnLrOuLiLeB5B0iaQXI+LKvDNZhZEGktrsnwwsAcwF6oA5QI9P4MNb4e7D051gN5+w4knD6VghRXbsGKSJRDxQnmBWySRWAR4GBnXgZf2AEcAE4LQyxMqF573WIEn9JX0PGAf8AFgqWwt1vgsps4pyMXC2JHfPsvlSG+H3gPOAlYH+pEYA/bJ/9lkCVjscDgL+i7RGblmtukk9gOtorZAaMQJefRWmTYM33oAtt2z6bF/g99mG5tb1jCJ9Hi1g6FB4+GGYNAnGjYO99mrxun7A9yTWKnvCTuJiqoZIWiXbE2pxYHNgZERsHhH/yjmamRUQEa8DOwG/lrRh3nmsAkg7AX9hfvHUlgGk6X7PIq1d7mhWk/YijXi2tMMOcO65cNBBMGAAbL01vPlm86N6k5YPWBcisSywA83eO3V1cMcdcPfdsPjicNhh8Pvfw5prtjhFd+C4zklbfl4zVeWyRcibAycC2wKHRcSf8k1lZh0haTlS56MBETEl7zyWE2ko8BwLL6Kam0uaNjOUiMklz2W1S3oO2LTgc08+CVdeCVddtbCzPE7E1qWOZpVL4ifAKaRi+n/WWw/+8Y9Ue89z//3w9NNw5pktTjMdGBJBfVnDdgKPTFUpST0kDSFN/7gU+Buwigsps+oTEeNJX0ovSdox7zyWm5/Q7OKEnj3hiivg7bdhyhR48UXYZZfmr+tGGsk6uDNCWo2QBgMbFHyuWzf44hdhqaXSXK333oNRo6B370JHb47UkfVWVv2+TfPPqlZI8IUvFHxqDjCshJly42KqykgaLOkU4E3guIiYGhEbR8SoiJiadz4zK05ENAD7AzdKqokvGOsAaQlSw6AFp1x1754uZIcNg0GD4PTT4eabYeWVm5+hL3CS9wCyDliStDFvS0svnQr5r38dttoKNtoINt44vf9amkVaXmBdx+BCD44dCxMmwA9+kD66dtwxfXT17VvwHN1I78Gq5w/dKiGpVzal73FgPWDPiPDGn2Y1JCKeAL4FXCgv6u5qDiZN11tQfT2cdRa8807aTvWee+Ctt2DTgjOzBgLblTmn1Y5u0Ep76oaG9M9Ro+Cjj+DTT+GCC2C33QodHfh6sqsp+Pc9e3ZqOLH77ult8/3vp3s/77/fsfNUG7dGr2BZ8bQNcAJQFxG7S9o0IgrfSTKzqhcRD0v6MlAnafWsSYXVvu1Jo0ttGzIE1loLXnml0LN9SWtovZmqtcdnQM+Cz0yalEZEm66rb32NfU/g89JGswo3BVis0BP/+hdss838f3/ySbj22oLnmEuNvG9qoiKsYTcClwH3AN8AcCFlVvsiYhbwJeAxSYVnm1utWfg0qe7d4YYb0pXJ2LGFjugGLFXqYFazPgFaHzO4+mo49ti0bmqxxeCEE1Kbtpb+Q8S0MmW0ynQnaXpnC+uvD716QZ8+aWRq2WXhmmsKnqMn8ET5InYeF1MVRNKSkk6X9LdsVOr7wHoRcXlEVH23EzNrv2zK3/HAA3Lb666g7RtlElx/PcycCccc09aR/q6w9kntnM8FChdCP/0pPPssvP46vPZaan7y8583P2pqdg7rWi4GZhd6Yv/94cMP09qp7bdP66ZmttxWfA5wewSflTlnp3Br9AqRbbL7E+BPwEUR8e98E5lZJZB0ALB0RJyXdxYrI+n3wEhABZ+/6ipYZZW0ZqWxsbWzNACnEDGqLBmt9kj9SG31Fz7FtIBZ0NgDBhPR6pvSapM04TUYMrTIl9cDwyJ4rpSZ8uKRqZwo2VnSzUotRe8H1o6I77qQMrN5IuLaiDhP0taSVso7j5XNlaR9V1oaPRrWWQeGD2+rkIJUiN1ShmxWqyKmAydTxIjmXGh4AX6htL6z5basVrMk/RL27A9ziimi64F7a6WQAhdTuZC0HfAK8CvgXmBORPwnIibkm8zMKthGwCPZBr9We/4KTGrx6EorwRFHpNbUH30EU6emn5Ejmx8ZwENEfFTuoFZjIi4l7VfZkYKqvhv86ssRPwW+CPxd0vfk1vw1TdK2knoA18E/hkLdPnTwfQM8D+xXloA58TS/TiJpGeAoYBRpgfCywCPhvwAzaydJPyTtRTXMN19qkHQs8EuKm3JVD+xKxGOlDWVdhnQc6f03F+jXylHTSTfijydizPyXak3gGtLav50iouB6GqtOkgYBF5C2XtgxIt6Y/xxfBe4gNZQY0MopZpBu+PwRODSicPOKauU7CGUmaRVJ1wKvkTYnq4uIVyPiYRdSZtYREfEL4He0/oVl1W008AzQ0akz04HfuZCyRRJxMelG7w9JXf7qgcnZTz3wDvADYOmmhVR6aYwDtgbOjojZkr6cNdKyKidpMPAyqeHEBk0LKYAIniS9bw5k/ufXvPfNVFIb9YuAtSM4sNYKKfDIVFlkw9x7AP/KHhoBjImImuhaYmb5yqZZ/BQ4JyIm553HSkjqD/wF2IT2jVBNB/4AHEZEy01/zYqRCqFVmd+y/1Pgbdpx0SipO/AY6b15SES8W7acVjZKn0VfiYiHJH2hvev5JZYBlgF6kaYuvxVBy35+NcTFVAlJ6gscRGpnPAk4KiKezTOTmdWe7I7vKGBjYOfwHi+1JRXLZwHzeqAXGomcShot+AlweXsucs06S1ZQnQycAPxfttWDVQlJw4Crgfsj4si881Q6F1MlIGlF5u8AfhlwCfCkp/GZWblkI+BjgNWAXSJi5vznWB04GtgcGES66B5Hmkb2eAT+bKoGUi/g66QbdCsDvUl/l/8Gzgce8GiUVTJJ6wNvk6aBTYuI8fkmsoWR9B3gHOCIiLgr7zzVwMXUIpD0JeBEYCfg+Ii4LudIZtaFSKoD9gT+HBEhMYw0/W8z0prYnk0OD9K0m0+BXwBXROALcTMrO0nfJX3unAjc4JvNlUfS5sBHpDVORMSn+SaqHi6mOigbuh4CfEKaE/xH4MqImJJrMDPrsiRtAj+/HE5bD9SnHS+ZTtrbbmQEM8ocz8ws+5ziWuAJTx2rHJJ6A2eTOsXuGxF/zTdR9XEx1U5ZW8hDgOOAOyPiuJwjmZkBIDUcChoNves68LJ6UkH1dY9QmVlnUJq6ujowFtghIu7POVKXlq2/fZw0InVkREzMOVJVcjG1EJJ6R0SjpKdI834vdFMJM6sUEmsCLwHtGZFqbjpwUgS/LW0qM7PWSVoBeJDUcvvoiPgk50hdiqSewEjSSOGKwHueelk87zNVgJKtJN0GPJQ9vE1EjHQhZWYV5ntA90JPDB0KDz8MkybBuHGw114tDukHnCbh/WDMrNNExPuk9v/vAf+StGzOkboMSRsBzwJ7A30j4l0XUovGxVRho4ErgYeBXQCadsoyM6sEEn1JGyX2aP5cXR3ccQfcfTcsvjgcdhj8/vew5potTrM4abNNM7NOExENEXESsF1EfChpx2yDWCuTbN3aA8AFwJ4RMT3nSDXB0/wASYsDhwH7AFuQLi4mhlvOmlkFk9gXuJwC+xCttx784x8woMkz998PTz8NZ565wKEB3BrBN8ub1sysdZJ+CXwbODwi7sk7Ty2RtB6wAqmQGhIRH+ccqaZ0+ZEpSYcA/wWGAodGxKyI+NiFlJlVgZXpwFopCb7whZYPkxaEm5nlJiJOJXWUu0TS0XnnqQWS6iSdAvwVWCoSF1IlVnCefcVIm1JuTbpg6AtMBl4i4pXiTykB2wFHAd8FHgXWiYiPFj2wmVmn6ksrn+Njx8KECfCDH8CFF8K228KwYfDoo62ep/pJawGbkjYqbgQ+AB4lYnauucysXSLiUUkbAL2zJhXrRMSDC3udxJLANqSZRXNJ29c8EkF1b1uTtuPZFlietGn3ZOA5Isa18wwXAesBm0XE2+WIaJVaTElLktqQn0i66yrSKNocoA5pHHAucBsR7d4jRdIWwG+BOtIbrCEiPi9teDOzTjMZmMmCm/MCMHt2ajgxahSccgo89xzcfDPMKPiJ+V5fWHHexpqfkdoWvxEd+HzNTbrYGA6cDGwIzCZ9xs/NfmYjjQIuJ+LD3HKaWbtExFRgqqQvAVdKugf4QURMa3pc1jjny8D3gT1In4XdSVOX5wA9JG4CLorgX535Z1hk0nLA4cCxpM+zbsy/Du6O9E/gPODu5jeLlAYijgT+APwYmOTZVuVVeWumpN1JG+GKtu+WTgUmAdsQ8Wbrp9MQ0pvqWtIbcU3gAXcuMbNqJ7Ej8CcKrJkq5Mkn4dprYcyYpo/GLJh0XcTg70o6G9gIWBv4OCK2lnQssCrwH1KR9WRUykhPuuB4BFiOtv8/aCRdYB1CxE2dEc3MFp2kxYALgY2BTeYVBRK9gBtITcL60PqyldnALOAK4Piq2FNP2p+0Flak0ajWTAXeB7Yjm10laXXg6uy1IyPivTKnNSqtmJK+AVxD+6eczCXdmf0SEW8seCotT9rReW/gFuCnflOZWS2R6Eb6Mi3YVnj99eH116FbNzjqKDj66NQufeaCvUkbgQ0iWGDaiCRFREjaktSYZ23SzajtgBGkDczHkoqs64HxQI+IaCzpH7I1qZB6gTStp0U3w1bUAycScXnZcplZyWXXdOOBg+GgW+Gqu0mt1dt7vTgduAsYGUEFXfg2Ix0F/Ir2/7lmAZ8CmwimAa8BvwYujog55QlpzVVOAwppUzpWSEHKPxD4G1J/Sd0k7ZZ1LZkFvAWsFRGHuZAys1qT3WX9NalIaGH//eHDD9Paqe23hx13bFFIAbzQvJBK50532iLiiYg4LyIOiYits1Gpu4ATSIuaB5Hunq4FTJL0pqS/SNoLQNKXJC2brVctjbTh5KPAErS/kIL0/XIh0nYly2JmZRcRH5CmM28Lu7wLc75Ix64X+5GmA5+5sANzI+0InE/H/lw95sKSn8I/I90YWzciLnQh1bkqZ2RKug/YCZpsHtmzJ1x2GeywQ9oo5b//hdNOg/vuW+ClAdOvhzsOSHcpGoHjIuLxzoxvZpYHicHAG8Bg6PDmuw3AHhE8Upos6kGaErg2aTPOl0iteDciXQjdHBGHShpOKsDGAuMioqGD/6FvkvYC7N/iucGD4corYaed4JNP0nfGTS1m9j1PxBc79N80s9xJrARz3oC6BW6iTJ264HF9+qTLx+OOa3GKemBIBJW3v1JaB7Vhi8dXXjn9YTbfPC16vfVWOP54mDO/XpoBM7vDvnURt3VaXvufymhAkTq2DKP5hUD37vDee6kF1bvvwm67pRXU668P77wz/+XQb2fYsw72mAN/83ooM+sqIvg8Wzv1NwoVF62rB04rVSGVssQs4PXsZ54d4X/7+S2WPbYcaa3D2sCykpbI/n0nUoE1Fni6jQ0lT6G1P+ull6bht6WXho02gnvugZdegldfbXrUukjrEvFqwXOYWaU6CuparHtqup9ev37w0Udwyy0FXz8XGAn8rkz5ipM6GLbcUh1SITVhAiy7LCy2GDz4YJq3PWrU/w7plW5WnQK4mMpBpUzzO4JCd1Tr6+Gss1LhFJG+FN96CzbdtMWhS0PMhtkupMysq4ngBdINqc9pZcpfE7NJI1LHR3BxubPNExGfRdYsKCIuj4j/i4h1gSWzReXvkkazNgF+AqwiaUNJz0m6QdKZkjZCWjdgnYL/kb59YZ994IwzYPr01HHjzjvTfMcF9QCOL8+f1MzKQaIHqaFYr7aO22efVHs8Xnh+Un9S0VFpTqBAV1YAVl11fivWjz9Os7PWW6/QkesjrV3OkFZYpRRT27GQXw4AhgyBtdaCVwpuM9WT1CLTzKzLyQqqNYCzgI9JnZ5mZU/PIS1Orid1tdokojLuzM6b2x8R/46IX0fEodnarFdII1zHkKYK9gaWnA1fnt7aRsVrrZV6wo9rsgTspZcKXXh0JxWfZlY9VqYd160HHADXXdfmIatKrRQu+dmK1maLXXQRfOtbae7icsvBrru2WO6SmQ1sVr6I1prKmOY3f+pH67p3hxtuSH19x44tdESPdp3HzKxGRfAZcJ7E+cAOwAaktVTTSKM+f67ItQKtyNZS/SP7SaTv9YMZFLoB178/TGm2R+fkyQvOAZpvYAmjmln5DSLdGGrVSiullSGHHNLmeWaSrhcnlCzZomt9a4fHHoPDDkufbd27wzXXwO23FzrS18E5qZSRqbZb6Upw/fVpHvwxx7R21NyFnsfMrAuIYG4ED0RwfgQ/iuCcCH5fTYVUG2aIVvaKmTYNBjarkQYObLk6PTtPyZOZWTnNYCHXrfvvD088AW+/3dZRM3vD8icASBovKbKf57PHxjR5LCQtJ2l4s8cOy45t+thd2WN3NX08e+ywZscOz84bkuI9GFIwqpRGoW67LS0GW2KJ1GTn3HMLHT0HXwfnolKKqXfbfPbKK9Ni4n32SVM4Cmsg7UFgZma1azzzpy8u6PXX053bNdaY/9iGG7Y2NdzfF2bV5SNaW1eU+c530gSmtvWcAR/8ECAilosIZT+bZo8d1uQxRcT4iLir2WNjsmObPjY8e2x408ezx8Y0O/au7LyKCK0IzxSMuvjiqZvfJZekAYXPPoOrr04N2Vqagz/XclEpxdTlpGkoLY0eDeusA8OHQ2ObBXd34M9lyGZmZpXjAVprAV9fn+7gnn12akaxxRaw555pZsOCpgKXljmnmZVQBJ/QWtFB6hy+/PKtdvGbZzZwUwVu3HsZha6DP/0U3nwTjjwS6upg0KC0KOzll1s7z0PlDGmFVUoxdT+FOlCttBIccURqb/vRR2mqxtSpMHJk8yPnALcQMansSc3MLD8RjaS2xi23H4bUMrhPn9TO66ab0kXIqwU7oN9axpRmVh7nkW6GtHDAAeleyrTCt+bnmQlcWIZci+rmVp/Ze2/YZReYOBHeeANmzYITTmh+1AxgNBGFPxetrCpp094fkNrhdmTn53nqga8S8c9SRjIzswokrQq8Qmtd/drWCFxCxA9KG8rMyk2iDvgAWLqIl88FXopgk9KmKhHpQtJWQb2LeHUDMJSItpfNWFlUysgUwEXAC3R88dx04BwXUmZmXUTEW8CJLHxPreZmktqtn1nyTGZWdhHMAYbT8d/9AKYAXy95qNL5EfAGrY26t64eOM6FVH4qp5iKmAXsRiqo2vtLUk+a9/7zcsUyM7MKFPFb0p5a7f2+aATGAtuTWq6bWRWK4FlgT9Iao/ZMr5oDTAK2i+DNMkZbNBH1pH1Xx9H+gYUG4EwirihbLluoyimmACKmAtuSRqmmUHhe7FzSL9BbwCFEnELFzFU0M7NOE3Ee8C1SkTSdwnvQTMueuxz4ChGfdF5AMyuHCB4CtgAeJRUehUZzGkhrie4GNo7gxc5LWKSIicCXSetCp1O4Odsc0k2k14BvEPHrzgtohVTOmqnmpJ7A3sBxwEqkOaTTgBeBXwNPuogyMzMApM1IU/++QtoAcwbwIXAJ8EePRpnVJolVgKOA/yNt7DsX+Bz4PfC7iIranLf9pL6km0VHAcuSNiqfCvwduICI53JMZ01UbjFlZmZmZmZWwSprmp+ZmZmZmVmVcDFlZmZmZmZWBBdTZmZmZmZmRXAxZWZmZmZmVgQXU2ZmZmZmZkVwMWVmZmZmZlYEF1NmZmZmZmZFcDFlZmZmZmZWBBdTZmZmZmZmRXAxZWZmZmZmVgQXU2ZmZmZmZkVwMWVmZmZmZlYEF1NmZmZmZmZFcDFlZmZmZmZWBBdTZmZmZmZmRXAxZWZmZmZmVgQXU2ZmZmZmZkVwMWVmZmZmZlYEF1NmZmZmZmZFcDFlZmZmZmZWBBdTZmZmZmZmRXAxZWZmZmZmVgQXU2ZmZmZmZkVwMWVmZmZmZlYEF1NmZmZmZmZFcDFlZmZmZmZWBBdTZmZmZmZmRXAxZWZmZmZmVoT/B76BecCGbBsWAAAAAElFTkSuQmCC\n", "image/png": 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\n",
"text/plain": [ "text/plain": [
"<Figure size 1080x288 with 3 Axes>" "<Figure size 1080x288 with 3 Axes>"
] ]
...@@ -310,8 +311,8 @@ ...@@ -310,8 +311,8 @@
], ],
"source": [ "source": [
"# Computed max cut for two subgraphs\n", "# Computed max cut for two subgraphs\n",
"strr1 = '010xxxxxxx'\n", "strr1 = '01010101xx'\n",
"strr2 = '0x01010101' \n", "strr2 = '0xxxxxx101' \n",
"strr = '0101010101'\n", "strr = '0101010101'\n",
"\n", "\n",
"# Show graph illustration\n", "# Show graph illustration\n",
...@@ -352,7 +353,7 @@ ...@@ -352,7 +353,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 6, "execution_count": 7,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-11T06:54:04.788730Z", "end_time": "2021-05-11T06:54:04.788730Z",
...@@ -364,8 +365,8 @@ ...@@ -364,8 +365,8 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"First t possible approximate maxcut for graph G: {'1010101010': 938, '0101010101': 878, '0110101001': 160, '0110101011': 160, '1001010110': 152, '1001010100': 152, '1001010010': 145, '1101010010': 137, '1101010110': 137, '1101010100': 137}\n", "First t possible approximate maxcut for graph G: {'0101011011': 408, '0101010011': 393, '1010101100': 386, '1010100100': 350, '1001010100': 257, '0101010101': 250, '1011010100': 248, '0101001011': 244, '0110101011': 235, '0100101011': 225}\n",
"Max cut found by DC-QAOA algorithms: 1010101010\n" "Max cut found by DC-QAOA algorithms: 0101011011\n"
] ]
} }
], ],
...@@ -461,7 +462,7 @@ ...@@ -461,7 +462,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 7, "execution_count": 8,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-11T06:54:45.016920Z", "end_time": "2021-05-11T06:54:45.016920Z",
...@@ -473,7 +474,7 @@ ...@@ -473,7 +474,7 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"First t possible approximate maxcut for graph G: {'00001': 532, '00101': 501, '11110': 496, '01001': 496, '10110': 492, '11010': 483}\n" "First t possible approximate maxcut for graph G: {'11010': 535, '01001': 515, '00001': 495, '11110': 495, '10110': 488, '00101': 472}\n"
] ]
} }
], ],
...@@ -499,7 +500,7 @@ ...@@ -499,7 +500,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 10,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-11T06:54:47.679276Z", "end_time": "2021-05-11T06:54:47.679276Z",
...@@ -527,7 +528,7 @@ ...@@ -527,7 +528,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 9, "execution_count": 15,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-11T07:02:35.277145Z", "end_time": "2021-05-11T07:02:35.277145Z",
...@@ -543,29 +544,29 @@ ...@@ -543,29 +544,29 @@
"Node = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n", "Node = [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]\n",
"\n", "\n",
"Random graph 1\n", "Random graph 1\n",
"Edges = [(0, 2), (0, 6), (0, 7), (0, 8), (1, 3), (1, 5), (1, 6), (1, 8), (1, 9), (2, 3), (2, 4), (2, 6), (2, 8), (2, 9), (3, 4), (3, 6), (3, 7), (3, 8), (3, 9), (4, 9), (5, 8), (7, 9), (8, 9)]\n", "Edges = [(0, 1), (0, 5), (0, 6), (0, 7), (1, 3), (1, 4), (1, 6), (1, 8), (1, 9), (2, 3), (2, 4), (2, 6), (2, 8), (3, 5), (3, 6), (3, 8), (4, 5), (4, 7), (4, 8), (5, 8), (5, 9), (6, 7), (6, 8), (6, 9), (7, 8), (7, 9)]\n",
"SDP upper bound: 17.750789460578076\n", "SDP upper bound: 21.03787674994891\n",
"DC-QAOA node partition: 1001011001, max cut = 17.0\n", "DC-QAOA node partition: 1001100011, max cut = 21.0\n",
"\n", "\n",
"Random graph 2\n", "Random graph 2\n",
"Edges = [(0, 1), (0, 3), (0, 6), (1, 2), (1, 3), (2, 5), (2, 6), (2, 7), (3, 5), (3, 6), (3, 8), (3, 9), (4, 6), (4, 7), (4, 8), (4, 9), (5, 7), (5, 8), (6, 7), (6, 8), (7, 9)]\n", "Edges = [(0, 1), (0, 2), (0, 4), (0, 8), (0, 9), (1, 2), (1, 3), (1, 5), (1, 6), (1, 7), (1, 8), (2, 3), (2, 6), (2, 8), (3, 8), (4, 8), (4, 9), (5, 9), (6, 8), (6, 9)]\n",
"SDP upper bound: 16.64755118085844\n", "SDP upper bound: 16.028382190698274\n",
"DC-QAOA node partition: 1100111001, max cut = 15.0\n", "DC-QAOA node partition: 1011011100, max cut = 14.0\n",
"\n", "\n",
"Random graph 3\n", "Random graph 3\n",
"Edges = [(0, 2), (0, 3), (0, 4), (0, 5), (0, 6), (0, 7), (0, 8), (0, 9), (1, 5), (1, 6), (1, 7), (1, 8), (1, 9), (2, 3), (2, 4), (2, 6), (2, 7), (2, 8), (4, 5), (4, 7), (4, 9), (5, 7), (5, 8), (5, 9), (6, 7), (7, 8), (8, 9)]\n", "Edges = [(0, 2), (0, 5), (0, 6), (0, 7), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (1, 7), (1, 9), (2, 3), (2, 5), (2, 6), (2, 9), (3, 4), (3, 6), (3, 7), (4, 6), (4, 7), (4, 8), (5, 6), (5, 7), (6, 7)]\n",
"SDP upper bound: 19.402766322145684\n", "SDP upper bound: 17.0971057189657\n",
"DC-QAOA node partition: 1101100010, max cut = 18.0\n", "DC-QAOA node partition: 0010111100, max cut = 15.0\n",
"\n", "\n",
"Random graph 4\n", "Random graph 4\n",
"Edges = [(0, 1), (0, 2), (0, 5), (0, 6), (0, 7), (0, 9), (1, 5), (1, 6), (1, 7), (1, 9), (2, 3), (2, 6), (2, 8), (3, 5), (3, 6), (3, 8), (3, 9), (4, 5), (4, 6), (4, 7), (4, 9), (5, 6), (5, 7), (5, 8), (6, 7), (6, 8), (7, 8)]\n", "Edges = [(0, 1), (0, 2), (0, 3), (0, 4), (0, 6), (0, 7), (0, 8), (0, 9), (1, 7), (1, 8), (1, 9), (2, 3), (2, 6), (2, 7), (2, 9), (3, 4), (3, 5), (3, 7), (3, 8), (3, 9), (4, 7), (4, 8), (5, 6), (5, 8), (5, 9), (6, 7), (6, 9), (7, 8), (7, 9)]\n",
"SDP upper bound: 20.999869854784496\n", "SDP upper bound: 20.153931079390457\n",
"DC-QAOA node partition: 0010011011, max cut = 18.0\n", "DC-QAOA node partition: 1111101000, max cut = 17.0\n",
"\n", "\n",
"Random graph 5\n", "Random graph 5\n",
"Edges = [(0, 1), (0, 4), (0, 7), (1, 2), (1, 3), (1, 6), (1, 7), (1, 8), (1, 9), (2, 4), (2, 7), (2, 9), (3, 7), (3, 9), (4, 5), (4, 6), (4, 8), (5, 6), (5, 7), (5, 8), (6, 7), (6, 8), (6, 9), (7, 9), (8, 9)]\n", "Edges = [(0, 1), (0, 2), (0, 6), (1, 2), (1, 4), (1, 5), (1, 7), (1, 8), (2, 3), (2, 4), (2, 5), (2, 6), (2, 8), (2, 9), (3, 6), (3, 7), (3, 8), (4, 7), (4, 9), (5, 7), (5, 8), (6, 7), (6, 9), (7, 9), (8, 9)]\n",
"SDP upper bound: 19.454398132157152\n", "SDP upper bound: 18.82486962324589\n",
"DC-QAOA node partition: 1011011001, max cut = 18.0\n" "DC-QAOA node partition: 1010000110, max cut = 18.0\n"
] ]
} }
], ],
...@@ -612,7 +613,7 @@ ...@@ -612,7 +613,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 11, "execution_count": 16,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-05-11T07:02:35.547590Z", "end_time": "2021-05-11T07:02:35.547590Z",
...@@ -622,7 +623,7 @@ ...@@ -622,7 +623,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
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e2WlaCdZulHkKwM3vQvfJgMKItrBvvdtRhQRL/Nk0Z84cJk2axMKFC1myZAm//PILFSpUOLN89OjRLFmyhCVLlpA3b95zSjfky5ePxMREli1bRp48eRg0aJAbL+EcvtT+MWEsJcUZJGXwlZAwApI2OfNzhUCKiL0Ces2COz5zvqwAkja7G1OQC4G/anDavn07JUuWJG9e50JTyZIlKVv2/BtY8uTJw7vvvsumTZtYvHjxecuvvPJK1qxZc978ggXP9lUeN24c3bt3B6B79+706tWL+Ph4atSowaRJkwAYMWIE7du3p1WrVlSvXp3XXnvtzPajRo2iSZMmxMXF8fDDD59J8gULFuTpp5+mQYMGzJkz57wYvvjiizO/TObPnw/Avn37uO2226hfvz7NmjVjyZIlALz66qu89957Z7atW7cuGzZsYMOGDVx22WU8+OCD1KlThzZt2nDs2DGAM/WJGjRowCeffJLJu2386sBWGNXBGSQl9kroMxeKVXI7qguTtyDUuc15vPlP6BcHP7/gXJw25wmfxP9Z2/On+Z86y04eTX/5otHO8iN7z1+WhTZt2rB582Zq1KhBnz59+O233zJcNyoqigYNGrBq1apz5p8+fZqffvrpTBE1X23YsIH58+czefJkevXqdWYw8vnz5zN+/HiWLFnCN998w4IFC1i5ciVjx45l1qxZJCYmEhUVxejRzus+cuQITZs2ZfHixVxxxfn9oo8ePUpiYiIDBgygZ8+eALzyyis0bNiQJUuW8Oabb9K1a9a9PFavXs0jjzzC8uXLKVq0KOPHjwegR48efPzxx+l+IZoASUlxCqNtng/t/gtdvoFCl7od1cW5pBY06gZzP4FBV8Amnwf+ixjhk/gDrGDBgiQkJDBkyBBKlSrFXXfdxYgRIzJc37s0xrFjx4iLiyM+Pp6KFSty//33X9CxO3XqRK5cuahevTpVqlQ584Vy/fXXU6JECfLly8ftt9/OzJkzmTZtGgkJCVx++eXExcUxbdo01q1bBzhfSB07dszwOJ07dwbgqquu4uDBgyQlJTFz5kzuu+8+AK699lr27t3LwYOZj4VQuXJl4uLiAGjcuDEbNmwgKSmJpKQkrrrqKoAz+zQBcnQfJJ92mnJu+dC5SSq+p//uwA2kvIWg3QfQ9XtIPgXDb4Bpr7sdVVAJn+6cPSZnvCxP/syXFyiR+fIMREVF0apVK1q1akW9evUYOXLkmSYZb8nJySxduvRMvZnUNv7MiNcHMPWMPr1l3s/Tm6+qdOvWjbfeeuu8Y8TExJwziEtmMaT33Fvu3LnPGdPXO+bU5jBw3rPUph7jktW/OHV2Ln8Arn4WKrVwOyL/qNIK+syG/71kJZ7TsDP+bPrrr79YvXr1meeJiYlUqnR+u+ipU6d4/vnnqVChAvXr1/d5/6VLl2blypWkpKTw3XfnDl/wzTffkJKSwtq1a1m3bh01a9YEYOrUqezbt49jx44xYcIEWrZsSevWrRk3bhy7du0CnDb6jRs3+hTD2LFjAZg5cyZFihShSJEiXHnllWeain799VdKlixJ4cKFiY2NZeHChQAsXLiQ9esz711RtGhRihYtysyZMwHO7NP40ckjzoDnoztCvqJQo43bEflf3kLOL5oWjzvPV0x0vghOHc90s3AXPmf8AXb48GEee+wxkpKSyJ07N9WqVWPIkCFnlnfp0oW8efNy4sQJrrvuOr7//vsL2v/bb79Nu3btKFWqFPHx8Rw+fPjMsooVK9KkSRMOHjzIoEGDiIlxbmpp0qQJHTt2ZMuWLdx7771nBnJ54403aNOmDSkpKURHR/PJJ5+k+yWVVkxMDA0bNuTUqVMMHz4ccC7i9uzZk/r165M/f35GjhwJQMeOHfn888+pU6cOTZs2pUaNGlnu/7PPPqNnz56ICG3aREASctO2Rc4oV/vWQfNH4dqXzt4MFQlSf61uWwSz+8HfP8NtA6H8eYUrI4KVZQ4x3bt3p127dtxxxx3nzB8xYgQLFiygf//+LkXmP5H6t85RWxOcxH/rx1D5SrejcdeaaTDxcTi0DVo8Bq1eCNsvwYzKMltTjzHhatcqmP2x87hcY3h0gSV9gGqtnbb/hvfCrI9gzS9uRxRwdsZvgp79rS9QSopTxuCXV5027kfmOx0YzPm2LoSyDZ2moE1znce582a9XYgIyzP+UPjSMhfH/sYXKGkzfNEepjwPVa+B3rMt6WemXCMn6R/eDZ/fBoOvdr4MwlzIJv6YmBj27t1riSGMqSp79+49c/HaZOH0CRjWxklct/SDzl9BodJuRxUaCpaCu76A40kw9Dqn3//pE25H5Tch29Rz6tQptmzZcl4fdxNeYmJiKF++PNHR0W6HEryOH4C8hZ0z179+glK1ztasMRfmWBJMeQESR0PpuvDAtJC+8Bt2Y+5GR0dTubL95zYRbvVU52as1i87Fytr3uR2RKEtX1FnaMfa7WH7Yq/6/ymhUbDOR357JSJSQURmiMgKEVkuIk945hcXkakistrzbzF/xWBM2DpxGH7oC6PvgPwl4FLfbw40PqhxA1z9D+fxpnkw5GrniyBMZJn4ReROX+al4zTwtKrWBpoBj4hIbeA5YJqqVgemeZ4bY3y1+U+n+FjCCKcf+oMzoIwlfr85dRQO74RPr4UZb8Lpk25HdNF8OeN/3sd551DV7aq60PP4ELASKAe0B0Z6VhsJ3OZTpMYYx9E9oMnOACRt3gjpNuiQUPUap1R13Y7w2zvOF8D2JW5HdVEybOMXkZuAm4FyItLPa1FhnLN5n4lILNAQmAeUVtXtnkU7gHS7HYjIQ8BD4JQoMCai7Vrp9NZp2MVpx69yjSX8QMpfHG4f4rT9/9AX1oX2r6zMLu5uAxYAtwIJXvMPAU/6egARKQiMB/qq6kHvCo+qqiKSbrciVR0CDAGnV4+vxzMmrKSkwNwBMO3fTlt+nQ5OtVlL+u6o1RYqNoeYIs7ztdOhwCVwaWgNG5ph4lfVxcBiERmtqhd0hp9KRKJxkv5oVf3WM3uniJRR1e0iUgbYlZ19GxP2kjbBd71h40yo2RZu+chJ+sZd+Ys7/6akwJR/wZ7VcPU/4Yq+EBUa3Y59aeNfLSLr0k5ZbSTOqf0wYKWqfuC1aCLQzfO4G3BhZSuNiQTHD8CgK52eJO0/gbtHOzcZmeCRKxd0mwS1b4UZb8DQ1rBzhdtR+STLG7hExPt+7xjgTqC4qr6cxXZXAH8AS4HUETpewGnn/xqoCGwEOqnqvsz2ld4NXMaEpZNHz57VJ34JlVqG3vi3kWjFRJj0pPOF3XsWlKrpdkRAxjdwZevOXc/OGudIZD6wxG8iwl8/ww+POzcQVbvO7WjMhTqyF5aMhWa9nbuojx90feSvbN+5KyKNvJ7mAuJ92c4Y46MTh5wyAQs/d8oEFCrjdkQmOwqUgOZ9nMd71sDQa6HlE9DiCYgKrpTpSzTvez0+DWwAOvklGmMizaa58O1DzoXcln3hmhfCqixwxMpX1Bnzd9q/YeUkZ7SvS2q5HdUZWSZ+Vb0mEIEYE5F2Lnf+7fETVGrubiwm5xQoCZ0+h2XfwuSnYfCVcO2Lzi+AIJDZDVxPAQdUdVia+fcDhVT1Qz/HZkx42rkc9m+EWjdDfE9ocDfkKeB2VMYf6t4OsVfA5Kfg4Da3ozkjszP+Ljg1dtL6AufGrg/9EZAxYSslGeb0h+lvQJEKUL2N0/ZrST+8FbwEOn3h/P3BKfq2eR40fwRyRbkSUmb9+HOr6qm0M1X1JCDprG+Mycj+jTCiHUx92Un49/8v6C74GT8SOfv3XjEBpr4Ew290bv5yQWaJP5eInFdHJ715xphMHNwGA1vCzmVw2yC4a5TTBmwi0w1vwu1DYc/fTpXV2R+f/TUQIJkl/v8DJovI1SJSyDO1AiYB7wUiOGNCWmr53sJl4ZrnnRt74jo7Z38mcolA/TvhkflQtTX870VY8nVgQ8jsBi5Phc7ngLqAAsuBt1X1p8CE57AbuEzIWTUZJj8D94wN6SqOxs9U4e+fnea/XFFO///ilXOs7T9bN3B5EnxAk7wxIe34QZjyPCwaBZfWsz75JnMiZ4fLPLYfht8AJao5d2+XqOq3w4bPIJLGuG3DLBjU0qmxc+XT8MD0oKnZYkJATFFnYJ1dK51rQnMHOhVA/cC6FRiTU9bNAMkFPX6Gik3djsaEGhHnGlCVq+GHJ+Dn55w7uzuNzHrbCz1Udoq0BZq18ZugtWOpM/B5peaQfApOn4C8Bd2OyoQ6VeeXY4GSzsDv2ZRRG78vg61/ISJFvJ5XEpFp2Y7EmHCxfAIMucZp01d1BuGwpG9ygogzzOZFJP3M+NLGPxOYJyI3i8iDwFTsrl0T6bYmwHcPQ9mG0GW8ddE0IcWXIm2DRWQ5MAPYAzRU1R1+j8yYYHVgK4y5x7kVv/MYpxyvMSHEl6ae+4DhQFdgBPCjiDTwc1zGBK+5A+DkEeg81u7ANSHJl149HYErVHUXMEZEvgNGAnH+DMyYoHXdaxB3D5Su7XYkxmRLlmf8qnqbJ+mnPp8PNPFrVMYEowWfwaEdTrGt0nXcjsaYbPNl6MUY4H6gDs5g66l6+isoY4LO4q9gUl/YvwGuf83taIy5KL706vkCuBS4AfgNKA8c8mdQxgSVTXNh4mMQ6xlFyZgQ50vir6aqLwFHVHUk0Baw2xJNZNi/Eb7qAkXKO0PpRUW7HZExF82XxJ86GEuSiNQFigCX+C8kY4LI/1507si952vIX9ztaIzJEb706hkiIsWAl4CJQEHgZb9GZUywuPVj2LsGSlZ3OxJjcowvvXqGqup+Vf1NVauo6iWqOiir7URkuIjsEpFlXvMaiMgcEVkqIj+ISOGLfQHG+MXScXDqOOQrCuXPK3ViTEjL8IxfRJ7KbENV/SCLfY8A+gOfe80bCjyjqr+JSE/gWZxfEsYEj4WfOxdz2/wHWjzqdjTG5LjMzvjfA+4FSuA07xRKM2VKVX8H9qWZXQP43fN4Ks7NYcYEj/V/wKQnnSHxmvZyOxpj/CKzNv6GQGecXjwJwBhgml5cHeflQHtgAnAnUCGjFUXkIeAhgIoVK17EIY3x0d618PV9ULwq3PmZc6OWMWEowzN+VV2sqs+pahwwDCdhrxCRWy/ieD2BPiKSgPOr4WQmxx+iqvGqGl+qVKmLOKQxPlB1qm0icM9XEFMky02MCVW+3LlbCufsvx6wBdiV+RYZU9VVQBvPfmvg/Jowxn0i0H4AHNsHxau4HY0xfpXZxd2eQCecMg3jgE7eNXuyQ0QuUdVdIpILeBHIsneQMX63djpUuQZK1XA7EmMCIrOLu0OBsjjlGW4AhorIxNQpqx2LyBhgDlBTRLaIyP1AZxH5G1gFbAM+u+hXYMzFmP8pfNEBln/rdiTGBExmTT3XXMyOVbVzBos+upj9GpNj1kyDn/4JNW6E2re5HY0xAZNh4lfV3wIZiDEBtfsv+KYHlKoFHYdCrii3IzImYHyp1WNMeEk+BV/dA7nzOD148mZ5W4oxYcU6KpvIExUNN77tdNksaveImMhjid9EDlXYuRwurQvVr3c7GmNck1l3zh+ADO/SVdWLuZHLmMCb8wlMfQl6/AwVbUgJE7kyO+N/L2BRGONvf/3s1NavfSuUv9ztaIxxlfXqMeFv53IYfz+UaQC3DYJc1qfBRDZfSjZUB94CauM12Lqq2n3tJvgdPwBf3u303Ok8BvLkdzsiY1zny8Xdz4BXgP/i3NTVA+sGakJF3sLQ9CGIvQIKl3U7GmOCgi8JPJ+qTgNEVTeq6qtYcTUT7FThwFan+FqLx6BsQ7cjMiZo+JL4T3iKqq0WkUdFpAPOwCzGBK8/3ocBzZ0a+8aYc/iS+J8A8gOPA42B+4Bu/gzKmIuy4nuY/jrUaGMllo1JR5Zt/Kr6p+fhYZz2fWOC17ZE+PZhp8vmrf2dph5jzDl86dUTD/wLqOS9vqrW92Ncxly4QzthTGfIXwLu/hKiY7LexpgI5EuvntHAs8BSIMW/4RhzEWKKOM07lz8ABS9xOxpjgpYviX+3qmY58IoxrklJgZOHIaYw3GLDPRiTFV8S/ysiMhSYBpxInamqNmSRCQ6/vQ3LxsP9UyF/cbejMSbo+ZL4ewC1gGjONvUoYInfuG/pOPjtHYi7F/IVczsaY0KCL4n/clWt6fdIjLlQm/+ECX2gUkto91/rwWOMj3zpxz9bRGr7PRJjLkTSZmcUrUKXQqcvnNG0jDE+8eWMvxmQKCLrcdr4BVDrzmlcFRUNpes4I2kVKOF2NMaEFF8S/41+j8IYX6WkgKY4Z/pdJ7gdjTEhKcOmHhEp7Hl4KIPJmMCb9hqMuQtOn8h6XWNMujI74/8SaAck4PTi8b5ypoAVQTGBtWg0zPoQ4ntClLXpG5NdmY3A1c7zb+Xs7FhEhuN8cexS1bqeeXHAIJwBXU4DfVR1fnb2byLMxtnwwxNQ+Wq46V3rwWPMRciyV4+ITPNlXjpGcP71gXeB11Q1DnjZ89yYzO1bD191gWKVoNNI58KuMSbbMjzjF5EYnHLMJUWkGGebegoD5bLasar+LiKxaWd7tgcoAmy70IBNBDpx0LmYe9eooLpJa/XOQ/SfsYaTp62ElfGfR66pRt1yRXJ0n5m18T8M9AXKAgu95h8E+mfzeH2BKSLyHs6vjRYZrSgiDwEPAVSsWDGbhzMhTdVp0inTAHrNCqpB0g8cO8X9Ixew/8hJyhS1KqDGf46dSs7xfWbWxv8R8JGIPKaqH+fQ8XoDT6rqeBHpBAwDrsvg+EOAIQDx8fGaQ8c3oeTn5yFXFLR5I6iSfkqK8vTXi9mWdIyxDzencaXg+RVijC98+TQNFZGnRORbERkvIn09zUDZ0Y2zNX6+AZpkcz8m3C0YDvMGnj3rDyKDf1/HLyt38q+2l1nSNyHJl8Q/EqgDfIzTxFMH+CKbx9sGXO15fC2wOpv7MeFs3a8w+Rmo3gbavO52NOeYs3Yv/zdlFW3rl6F7i1i3wzEmW3y5c7euqnrX6pkhIiuy2khExgCtcC4ObwFeAR7EaT7KDRzH04ZvzBl7VsPXXaFkDeg4zGnqCRI7Dx7nsTELqVyyAO90rI8E2S8RY3zlS+JfKCLNVHUugIg0BRZktZGqds5gUeMLiM9Emj1/Q55CcM9XzsAqQeJUcgqPfrmQIyeS+fLBZhTM68tHx5jg5Mv/3sY4FTo3eZ5XBP4SkaVYsTaT02q1haqtg2683Hd/XsWfG/bz0d1x1ChdyO1wjLko4V+kbecKKFHNyvYGM1X4+TkoEwdxnYMu6f+8bDuf/rGe+5pVon1clrewGBP0fEn8VXAu6AIsV9UZfownZ506Dp+3d+70bPE4NOoKefK7HZVJa94gZ2rZ1+1IzrN+zxGe/WYJDSoU5cV2l7kdjjE5IrPqnOVEZB7wKk7yrwK8KiLzRSQ0Tnty54UOA6FYLPz8T/iwHvzxPhw/4HZkJtXqqTDlBajVDlq/4nY05zh2MpneoxKIihI+uacheXMHz4VmYy5GZmf8/YGBqjrCe6aIdAUGAO39GFfOEIFq1znTxjlO0p/2byjXGKq0cjs6s2slfNPDGVClw+CguklLVXlxwjL+2nmIz7pfTvli9kvRhI/MEn9tVe2Qdqaqfi4i//JjTP5RqTlUGge7VkEpzxDC0/4NJ49Ci0ehSHl344tEa6Y5TW+dv4K8Bd2O5hxf/bmZ8Qu38Hjr6rSqeYnb4RiTozI7xUp3mYjkAkL3N+8ltc7eCXr8IPz5KXwUB98/CnvXuhpaxGnxKPSZG3Rfusu2HuCVicu5snpJnmhd3e1wjMlxmSX+SSLyqYgUSJ3heTwI+NHvkQVC2/fg8UXQuDss+Rr6x8P8T92OKrypwpR/wRbPrSD5i7sbTxoHjp6i16gEShTIw0d3NyQql92kZcJPZon/H8ABYKOIJIhIArABpzrnMwGILTCKVnS+APoudXr+xF7hzN+zGjbbGDE5btZHMKe/08wTZFJSlKe+TmTnweN80qURxQtYF2ATnjKrznkKeEZEXgKqeWavVdWjAYks0AqVhutfO/t85oeQOApir4Qrn3YuBtst+hdn1WT45VWo0wGuetbtaM4z8Le1TFu1i9durUOjilZ8zYSvLLtRqOoxVV3qmcIz6afnpnegzX+cM/8vboNPr4W/p7gdVejavgTGPwhlG8JtA4OqBw/ArDV7eP9/f3FLg7J0bV7J7XCM8avg+vQFk7wFnYuPfZdAuw/h2D7YMNNZpgrJp10NL+QsGAYxRaDzGIjO53Y059hx4DiPj1lElVIFefv2elZ8zYQ9qzSVldx5Ib4HNLwPkk8489ZMgx+fdu40jbvHWcdkru0HcOVWZwjFIJJafO3YqWTG3tuIAlZ8zUSAzMbcbZTZhqq6MLPlYScqtzOB0/c8X3GY1Bd+ewdaPOb0DMpTILM9RB5V+PVtaNwNCpd1LqQHmbd/WsWCjfvp17kh1S6x4msmMmR2evO+598YIB5YjDPgen2csszN/RtaEKvUAh6cDut/g9/fc0oOJI6BXn/YBWBvv/8f/PY25CsKzXq7Hc15fly6nWEz19OteSVubVDW7XCMCZjMevVcAyAi3wKNVHWp53ldnPo9kU3E6elTpZXT7fPIHmfe6ZMw60PnF0DBCL7jc9m3MOM/0KAzNO3ldjTnWbf7MP8Yt4S4CkX5V9vaWW9gTBjx5eJuzdSkD6CqywArU+itQhOodbPzePNc+PUtpyDc5GcgaVPm24ajrQkwoTdUaAa3fBR0v4KOnjxN71ELiY4SPunSiDy5rY+DiSy+/I9fIiJDRaSVZ/oUWOLvwEJW5avg0QVQvxMkjIB+DWFCHzhx2O3IAueX15xfO3ePDroL36rKi98t4+9dh/jo7oaUKxpcPYyMCQRfujD0AHoDT3ie/w4M9FtE4aBEVbj1Y7j6nzC7v3MGnHrh9/BuKFjK3fj87a4vnKavAiXdjuQ8X87fxLeLttL3uupcVSPM/w7GZCDLxK+qx0VkEPCjqv4VgJjCR5HycNPbkJLiNHcc2w8fN4IKTZ27gSuF0fXxlBSYP9i5thFTxJmCzJItSbw2cQVX1SjF49da8TUTubJs6hGRW4FE4GfP8zgRmejnuMJL6l2quaLhir6wbRF8diMMvwnW/OJ0ewx10193hk9cEZz/NZKOnqT3qIWUKpSXD++KI5cVXzMRzJc2/leAJkASgKomApX9F1IYy1vQOdPvuxRufAeSNsKojs6AJKFs8Vcw8wNo1M25thFkUlKUJ8cmsuuQFV8zBnxr4z+lqgfS3MYeBqeoLsqTH5r1gviesO5XKO3pTjjjTShWGerd4YwTHAo2zYOJjznF7Nq+H3Q9eAA+mbGGGX/t5vX2dYirUNTtcIxxnS9n/MtF5B4gSkSqi8jHwGw/xxUZcueBGm2cx8mnnCJwE3pBv0bOuACnjrsbX1ZSkmGiZ/SyTp8H5ZfVzNV7+OCXv2kfV5Z7m1nxNWPAt8T/GFAHOAF8iVOj/4lMtwBEZLiI7BKRZV7zxopIomfaICKJ2Yw7/ERFw0O/wj1fO/VsfnzGuRdg3a9uR5axXFFw9xgn5iAbUAVg+4FjPP7VIqqVKshbVnzNmDN8SfxtVfVfqnq5Z3oRuNWH7UYAN3rPUNW7VDVOVeOA8cC3FxrwhdJQunAqAjVugPv/B90mQZn6ULyqs2zvWji6z934UqUkw7LxzkXpktWgZPD1kDl5OoVHRi/kxKlkBt7bmPx5rPiaMal8SfzP+zjvHKr6O5BuphLn1KsTMMaH42fbNws203vUQo6dTPbnYXKeCFS+Eu4dD0UrOPMmPw3/resMW3hoh7vxTX0ZxvUM6l8jb/20koWbknjnjvpUuyS4BnI3xm0ZJn4RucnTnl9ORPp5TSOAiy1GfyWwU1VXZ3L8h0RkgYgs2L17d7YOcvjEaaas2MHdn85lz+ET2Y01ONzwJtRqC3MHOE1Ak56E/RsCH0fCSGfoxCYPQ9VrAn98H0xaso3PZm2ge4tY2tW34mvGpJXZGf82nCqcx4EEr2kicMNFHrczWZztq+oQVY1X1fhSpbJ3h2WPlpUZ2KUxf+04SIcBs1izK4TLJpSuDR0/hccSIK4LLBrlNLcE0vo/YPJTUPVa54soCK3ZdZh/jltCo4pFeeFmKyllTHokqzZwEYn2jL974TsXiQUmqWpdr3m5ga1AY1Xd4st+4uPjdcGCBdkJAYBFm/bzwMgFnEpOYUjXeJpVKZHtfQWNg9ud+wLyFoKl42D5d849AuUyHUYh+04egY8aQL5icP9Up9RykDl68jS3fTKLPYdPMvnxKyhTxOrwmMgmIgmqGp92vi9t/LEiMk5EVojIutTpImK5Dljla9LPCQ0rFuO7Pi0pVSgv9w2bx3eLAnZo/ylcxkn6ACcOwYY/4NNr4IsOzhCROX1RO08B6DAY7hkblElfVXnh26Ws3nWYj+6Os6RvTCZ8Sfyf4RRlOw1cA3wOjMpqIxEZA8wBaorIFhG537Pobvx8UTc9FUvk59veLWlcqRhPjl1Mv2mrQ6vHT2bie0DfZXDda7BjGYxo61QEzQnJp2HjHOdxtdZQvErO7DeHjZq3iQmJ23jyuhpcWd2KrxmTGV+aehJUtbGILFXVet7zAhIhF9/U4+3E6WSeG7+U7xZt5Y7G5XmzQ73wqsd+6pjT/l+oDFzWzikHvWYqXHar0+/+Qk1+Bv4cCn3mwCXB2Wa+eHMSdw6aQ4tqJRje7XKrw2OMR0ZNPb50bj4hIrmA1SLyKE77fMj2j8ubO4oPOjWgQvH89Ju2mm1Jxxh4b2OK5Au+u06zJTofNHnw7POlXzs9gIpXhSuehPp3OXcM+2L+p/Dnp9Di8aBN+vuPnKTPaCu+ZsyF8OVU9wkgP/A40Bi4D+jmz6D8TUR46voavHdnA+av38cdA2ezZf9Rt8Pyj0bd4M6RThv9xEedgWHmDXbKKGdm7XT46Z9Q82a47tWAhHqhUlKUvmMT2X3oBAPvbUTR/FZ8zRhfZNnUEwxysqknrdlr9vDwqARioqMY1i2e+uWL+uU4rlN1SkD//p5THqL7JGd+8qnza+wc2gH9mzg3j/X8+exF5CDz0S+r+e8vf/PGbXWtDo8x6cioqSfDxC8iP5BJFU5V9aVsQ47wZ+IHWL3zEN0/+5N9R07Sr3NDrq9d2m/HCgonDjnJ/OB2GHwVNO4GTXtDAU83V1WnXb/GDVC0oruxZuD3v3fT7bP53BZXjg86NbA6PMakIzuJ/+rMdqiqv+VQbFnyd+IH2HXoOA+MXMDSrQd4pV1tureMgCEH9m9wyi+smOhcG4i7B+rcDrEt3Y4sU9uSjtG23x+UKpSXCY+0tDo8xmTgghN/MAlE4gfnBqDHxyTyy8qd9GxZmX+1vYyoSLhYuPsvmPkhLP4SovPDE4udwdKD0MnTKXQaPIc1uw7z/aMtqVoqZPsZGON32e7VIyLrSafJR1WDs0P3RcifJzeD72vMG5NXMHzWerbsP8pHdzckX55sdIMMJaVqQoeB0Oo5SNoUtEkf4M0fV5K4OYkBXRpZ0jcmm3z5jez9bRED3AkEX/H1HBKVS3jlljpUKJaf1yev4O4hcxja7XJKFcrrdmj+V6ySMwWpiYu3MWL2Bnq2rMzN9cq4HY4xISvL7pyqutdr2qqqHwJt/R+au3peUZnB9zbmr52H6DBgFqt3HnI7pIi2Ztchnhu/hMaVivH8zbXcDseYkJZl4heRRl5TvIj0wrdfCiGvTZ1LGftQc46fSuH2gbOZvXaP2yFFpCMnTtNr1ELyRUfxyT2NiI4KozutjXGBL5+g972mt4BGOIOoRIQGFYryXZ8WlC4cQ7fh8xmfEAYF3kKIqvL8t0tZt/sw/To35NIiMW6HZEzIy/LMXVWDc7SNAKpQPD/je7eg96gEnv5mMZv2HaXvddWt73gAfDF3IxMXb+PZG2rSslpJt8MxJiz40tTzpogU9XpeTETe8GtUQahIvmhG9GhCx0bl+Wjaap7+ejEnT2dR9sBclEWb9vP6pBW0rnUJva+u6nY4xoQNX5p6blLVpNQnqrofuNlvEQWxPLlz8d6d9Xnq+hp8u2gr3YbP58DRbI1RY7Kw78hJHhm9kNKFY/igkxVfMyYn+ZL4o0TkTF9GEckHREDfxvSJCI+3rs4HnRqwYOM+Og6azeZ9YVrgzSXJKcoTXy1iz+GTDOzSmCL5w6RyqjFBwpfEPxqYJiL3ewZTmQqM9G9Ywe/2RuX5vGdTdh08TocBs0jcnOR2SGGj37TV/LF6D6/eWod65Yu4HY4xYceXfvzvAP8BLvNMr6vqu/4OLBQ0r1qCb/u0ICY6iruHzGHK8h1uhxTyfv1rF/2mr+b2RuXo3KSC2+EYE5asVk8O2H3oBA98voAlW5J4sW1t7r8iAgq8+cFWT/G1SwvH8F2fluFfKsMYP7vgwdZF5JCIHExnOiQiB/0bbmgpVSgvXz3YjDa1S/P6pBW8OnE5ySnB/4UaTE6cTqbP6IWcTlYGdGlkSd8YP8qwH7+qBufoG0EqX54oBnRpzJs/rmTYTKfAW7/ODa1ksI/+M3klizcnMejeRlSx4mvG+JXP976LyCUiUjF18mdQoSoql/BSu9r8u30dpq/axV2D57Lr0HG3wwp63ydu5fM5G3ngisrcWNeKrxnjb77cwHWriKwG1gO/ARuAn/wcV0jr2jyWT7vGs2bXYTp8Mpu/rcBbhlbvPMRz45dyeWwx/nmTFV8zJhB8OeN/HWgG/K2qlYHWwFy/RhUGWl9Wmq8fbs7J5BQ6DpjNrDVW4C2twydO02tUAgXyRtHfiq8ZEzC+fNJOqepeIJeI5FLVGZxbo99koF75Ikx4pCVlijoF3r5ZsNntkIKGqvLc+CWs33OEfp0bUrqwFV8zJlB8SfxJIlIQ+B0YLSIfAUey2khEhovILhFZlmb+YyKySkSWi0jY3w9Qrmg+xvVuQbMqJXh23BI++N9fhEIXWn8bOXsDk5Zs55kbatKiqhVfMyaQfEn87YGjwJPAz8Ba4BYfthsB3Og9Q0Su8eyvgarWAd67kGBDVeGYaD7rcTmd4svTb/oanvp6MSdOJ7sdlmsSNu7njckrue6yS+h1lRVfMybQMuxrKCLVgNKqOsszKwUYKSJXAEWBvZntWFV/F5HYNLN7A2+r6gnPOruyGXfIiY7KxTsd61OxeH7e+9/fbE06xpD7GlM0fx63QwuovYdP8OiXCylTNIb377Tia8a4IbMz/g+B9G7UOuBZlh01gCtFZJ6I/CYil2e0oog8JCILRGTB7t27s3m44CIiPHptdT66O47ETUncPnA2m/ZGToE3p/haInuPWPE1Y9yUWeIvrapL0870zIvN5vFy4wzU3gx4FvhaMhjNRFWHqGq8qsaXKlUqm4cLTu3jyvHF/U3Ye/gkHQbMYtGm/W6HFBAf/fI3M9fs4d+31qFuOSu+ZoxbMkv8RTNZli+bx9sCfKuO+TjNRxF5Za9pFafAW4G8ubl7yFx+Wrrd7ZD8asZfu+g3fQ13NC7PXZdb8TVj3JRZ4l8gIg+mnSkiDwAJ2TzeBOAaz35qAHmAiO3gXrVUQb7r04LaZQvT58uFDP1jXVj2+Nmy/yhPjk2k1qWFeL19XRuy0hiXZVZIpi/wnYh04Wyij8dJ1h2y2rGIjAFaASVFZAvwCjAcGO7p4nkS6KbhmOkuQImCeRnzYDOeHJvIG5NXsnHvUV65pTa5w+RmptTia8nJyqB7G1vxNWOCQGZF2nYCLTxdMOt6Zk9W1em+7FhVO2ew6N4LCzH8xURH8ck9jXjn51UM/n0dW5OO8XHnhhTIG/oF3l6ftIIlWw4w6N7GxJYs4HY4xhgyP+MHwHOn7owAxBLRcuUSnr/5MsoXz88r3y+j0+A5DO9+eUjf0Tph0VZGzd3EQ1dV4ca6l7odjjHGIzzaE8LIfc0qMazb5azfc4QOn8xi1Y7QHPrg752HeP7bpTSJLc4/bqjpdjjGGC+W+IPQNbUu4euHm3M6Rblj4Bz+WB1a9zGcLb6Wm/73NAyb6xXGhAv7RAapuuWcAm/li+Wjx2d/MvbPTW6H5BNV5Z/jlrBx71H639OQS0K4qcqYcGWJP4iVLZqPb3o1p3nVEvxz/FLemxL8Bd6Gz9rA5KXbefaGmjSrUsLtcIwx6bDEH+QKxUQzvPvl3H15BfrPWMMTXyUGbYG3BRv28daPK7m+dmkevqqK2+EYYzIQ+v0FI0B0VC7eur0eFUvk592f/2LHgeMMvq8xxQoET4G3PYdP8MiXCylXLB/v3dnAbtIyJojZGX+IEBH6tKrGx50bkrjZKfC2cW+WwyIEhFN8bRFJR08xoEsjiuSz4mvGBDNL/CHmlgZlGf1gU/YfPUmHAbNJ2Oh+gbf/Tv2bWWv28nr7utQpa8XXjAl2lvhD0OWxxfmuT0sKx+Sm86dzmbzEvQJv01ftpP+MNXSKL08nK75mTEiwxB+iKpcswLd9WlKvXBEe+XIhg39bG/AeP5v3HeXJsYupXaYw/25fN+sNjDFBwRJ/CCteIA+jH2hK2/pleOunVbw4YRmnk1MCcuzjp5ziaymqDLy3ETHRVnzNmFBhvXpCXEx0FB/f3ZAKxfIz6Le1bE06Rv97GlHQzwXe/j1pBUu3HmDIfY2pVMKKrxkTSuyMPwzkyiU8d1Mt3uxQjz9W76HToDnsOHDcb8f7duEWvpy3iV5XV6VNHSu+ZkyoscQfRu5pWpFh3eLZuPcIt30yixXbcr7A26odB3nhu6U0q1KcZ9rUyPH9G2P8zxJ/mGlV8xK+6dUCgDsHzea3v3OuwNuh46foPWohhWOi6dfZiq8ZE6rskxuGapctzHePtKBiiQL0HPEnX867+AJvqsqz3yxh076j9L+nEZcUsuJrxoQqS/xhqkwRp8DbFdVK8sJ3S3nn51WkpGS/u+ewmev5efkO/nljTZpULp6DkRpjAs0SfxgrmDc3w7rFc0/Tigz8dS2Pf7WI46cuvMDbnxv28dZPq7ihTmkevNKKrxkT6qw7Z5jLHZWL/9xWl0rF8/PWT6vYceA4Q7rGU9zHAm+7D53gkdELqVAsH/9nxdeMCQt2xh8BRISHr67KJ/c0YsnWA9w+YBbr92Rd4O10cgqPj1nEgWOnGNClMYVjrPiaMeHAEn8EaVu/DGMebMqBY6e4fcAsFmzYl+n6H0z9mznr9vLGbXWpXbZwgKI0xvibJf4I07iSU+CtaP483DN0Hj8s3pbuer+s2MmAX9dy9+UVuDPeiq8ZE04s8Ueg2JIF+LZ3CxqUL8JjYxYx8NdzC7xt2nuUp75OpE7Zwrx6ax0XIzXG+IPfEr+IDBeRXSKyzGveqyKyVUQSPdPN/jq+yVyxAnn44v6m3NKgLO/8vIoXvlvKqeQUp/jalwkADOzS2IqvGROG/NmrZwTQH/g8zfz/qup7fjyu8VFMdBQf3RVHxeL5+GTGWrYmHadUwbws23qQoV3jqVgiv9shGmP8wG+JX1V/F5FYf+3f5IxcuYRnb6hFhWL5+deEZSSnKH1aVeW62qXdDs0Y4ydu9ON/VES6AguAp1U13bEDReQh4CGAihUrBjC8yHR3k4pULJ6f2Wv30ve66m6HY4zxI/HnqE2eM/5JqlrX87w0sAdQ4HWgjKr2zGo/8fHxumDBAr/FaYwx4UhEElQ1Pu38gPbqUdWdqpqsqinAp0CTQB7fGGNMgBO/iJTxetoBWJbRusYYY/zDb238IjIGaAWUFJEtwCtAKxGJw2nq2QA87K/jG2OMSZ8/e/V0Tmf2MH8dzxhjjG/szl1jjIkwlviNMSbCWOI3xpgIY4nfGGMijF9v4MopIrIb2JjNzUvi3DQWbCyuC2NxXRiL68IEa1xwcbFVUtVSaWeGROK/GCKyIL0719xmcV0Yi+vCWFwXJljjAv/EZk09xhgTYSzxG2NMhImExD/E7QAyYHFdGIvrwlhcFyZY4wI/xBb2bfzGGGPOFQln/MYYY7xY4jfGmAgTNolfRG4Ukb9EZI2IPJfO8rwiMtazfF6ghoX0Ia7uIrLbawD6BwIQ03AR2SUi6ZbFFkc/T8xLRKSRv2PyMa5WInLA6716OUBxVRCRGSKyQkSWi8gT6awT8PfMx7gC/p6JSIyIzBeRxZ64XktnnYB/Hn2MK+CfR69jR4nIIhGZlM6ynH2/VDXkJyAKWAtUAfIAi4HaadbpAwzyPL4bGBskcXUH+gf4/boKaAQsy2D5zcBPgADNgHlBElcrnBHdAv3/qwzQyPO4EPB3On/HgL9nPsYV8PfM8x4U9DyOBuYBzdKs48bn0Ze4Av559Dr2U8CX6f29cvr9Cpcz/ibAGlVdp6onga+A9mnWaQ+M9DweB7QWEQmCuAJOVX8H9mWySnvgc3XMBYqmGUTHrbhcoarbVXWh5/EhYCVQLs1qAX/PfIwr4DzvwWHP02jPlLYXScA/jz7G5QoRKQ+0BYZmsEqOvl/hkvjLAZu9nm/h/A/AmXVU9TRwACgRBHEBdPQ0D4wTkQp+jskXvsbthuaen+o/iUidQB/c8xO7Ic7ZojdX37NM4gIX3jNPs0UisAuYqqoZvl8B/Dz6Ehe483n8EPgHkJLB8hx9v8Il8YeyH4BYVa0PTOXst7o530Kc2iMNgI+BCYE8uIgUBMYDfVX1YCCPnZks4nLlPVNnbO04oDzQRETqBuK4WfEhroB/HkWkHbBLVRP8faxU4ZL4twLe38zlPfPSXUdEcgNFgL1ux6Wqe1X1hOfpUKCxn2PyhS/vZ8Cp6sHUn+qq+iMQLSIlA3FsEYnGSa6jVfXbdFZx5T3LKi433zPPMZOAGcCNaRa58XnMMi6XPo8tgVtFZANOc/C1IjIqzTo5+n6FS+L/E6guIpVFJA/OxY+JadaZCHTzPL4DmK6eKyVuxpWmHfhWnHZat00Eunp6qjQDDqjqdreDEpFLU9s1RaQJzv9fvycLzzGHAStV9YMMVgv4e+ZLXG68ZyJSSkSKeh7nA64HVqVZLeCfR1/icuPzqKrPq2p5VY3FyRHTVfXeNKvl6PvltzF3A0lVT4vIo8AUnJ40w1V1uYj8G1igqhNxPiBfiMganAuIdwdJXI+LyK3AaU9c3f0dl4iMwentUVJEtgCv4FzoQlUHAT/i9FJZAxwFevg7Jh/jugPoLSKngWPA3QH48gbnjOw+YKmnfRjgBaCiV2xuvGe+xOXGe1YGGCkiUThfNF+r6iS3P48+xhXwz2NG/Pl+WckGY4yJMOHS1GOMMcZHlviNMSbCWOI3xpgIY4nfGGMijCV+Y4yJMJb4TUgRkWRP1cRlIvJDar/sHNhvdxHpnxP7SrPf3CLypois9qr4+K8c3P8IEbkjp/ZnIoMlfhNqjqlqnKrWxenP/IjbAWXhDaAsUM9TKuBKPPcmePPc+GWfRxMQ9h/NhLI5eAqhiUgTEZkjTj3z2SJS0zO/u4h8KyI/e866303dWER6iMjfIjIf52ao1PmxIjLdU6hrmohU9MwfISIDRWSuiKwTp9b9cBFZKSIj0gYnIvmBB4HHVPU4OFU0VfVVr+P8JSKfA8uACp79L5A09eJFZIOIvCsiS8WpKV/N61BXeV7zOjv7N76wxG9Ckufuy9acLYGxCrhSVRsCLwNveq0eB9wF1APuEmcAkzLAazgJ/wqgttf6HwMjPYW6RgP9vJYVA5oDT3qO/V+gDlBPROLShFkN2OQpmZyR6sAAVa2jqhuBf6lqPFAfuFpE6nute0BV6wH9cao5pirjeQ3tgLczOZYxgCV+E3ryecoT7ABK41RQBKdo1TfijN6VmoxTTVPVA56z7hVAJaAp8Kuq7vaMlTDWa/3mOANiAHyBk1RT/eApebAU2KmqS1U1BVgOxGYWuOcXRqKIbJaz5X43eur3p+okIguBRZ7X4P2FNMbr3+Ze8yeoaoqqrvC8J8ZkyhK/CTXHPG3llXBGVEpt438dmOFp+78FiPHa5oTX42QurkZV6r5S0uw3JZ39rgEqikghAFX9zBP7AZzaTQBHUlcWkcrAM0Brz6+NyWleh2bw2DsOfw8uZMKAJX4TklT1KPA48LScLVObWga5uw+7mIfTlFJCnNLGd3otm83ZIlhdgD8uIsZhQH8RiYEzTVR5MtikMM4XwQERKQ3clGb5XV7/zslOTMZAmFTnNJFJVReJyBKgM/AuTuXFF3HOlLPadruIvIqTQJOARK/FjwGficizwG4urtLmv3B+jSwTkUM4FTJHAttwevt4x7RYRBbhXK/YDMxKs69intd7Auc1G5MtVp3TmBAgziAd8aq6x+1YTOizph5jjIkwdsZvjDERxs74jTEmwljiN8aYCGOJ3xhjIowlfmOMiTCW+I0xJsL8P9+jczLRXmOgAAAAAElFTkSuQmCC\n", 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\n",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -698,6 +699,9 @@ ...@@ -698,6 +699,9 @@
], ],
"metadata": { "metadata": {
"celltoolbar": "Raw Cell Format", "celltoolbar": "Raw Cell Format",
"interpreter": {
"hash": "3b61f83e8397e1c9fcea57a3d9915794102e67724879b24295f8014f41a14d85"
},
"kernelspec": { "kernelspec": {
"display_name": "Python 3", "display_name": "Python 3",
"language": "python", "language": "python",
...@@ -713,7 +717,7 @@ ...@@ -713,7 +717,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.7.10" "version": "3.7.11"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/combinatorial_optimization/MAXCUT_CN.ipynb
浏览文件 @ 016af983
...@@ -136,7 +136,7 @@ ...@@ -136,7 +136,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 2, "execution_count": 4,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:11:08.078417Z", "end_time": "2021-04-30T09:11:08.078417Z",
...@@ -153,7 +153,10 @@ ...@@ -153,7 +153,10 @@
"# 加载额外需要用到的包\n", "# 加载额外需要用到的包\n",
"import numpy as np\n", "import numpy as np\n",
"import matplotlib.pyplot as plt\n", "import matplotlib.pyplot as plt\n",
"import networkx as nx" "import networkx as nx\n",
"\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")"
] ]
}, },
{ {
...@@ -165,7 +168,7 @@ ...@@ -165,7 +168,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 5,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:11:08.411878Z", "end_time": "2021-04-30T09:11:08.411878Z",
...@@ -175,7 +178,7 @@ ...@@ -175,7 +178,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
"image/png": 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\n", 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\n",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -190,7 +193,7 @@ ...@@ -190,7 +193,7 @@
"G = nx.Graph()\n", "G = nx.Graph()\n",
"V = range(n)\n", "V = range(n)\n",
"G.add_nodes_from(V)\n", "G.add_nodes_from(V)\n",
"E = [(0, 1), (1, 2), (2, 3), (3, 0)]\n", "E = [(0, 1), (1, 2), (2, 3), (3, 0), (1, 3)]\n",
"G.add_edges_from(E)\n", "G.add_edges_from(E)\n",
"\n", "\n",
"# 将生成的图 G 打印出来\n", "# 将生成的图 G 打印出来\n",
...@@ -221,7 +224,7 @@ ...@@ -221,7 +224,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 6,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:11:08.426170Z", "end_time": "2021-04-30T09:11:08.426170Z",
...@@ -233,7 +236,7 @@ ...@@ -233,7 +236,7 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"[[-1.0, 'z0,z1'], [-1.0, 'z1,z2'], [-1.0, 'z2,z3'], [-1.0, 'z3,z0']]\n" "[[-1.0, 'z0,z1'], [-1.0, 'z1,z2'], [-1.0, 'z2,z3'], [-1.0, 'z3,z0'], [-1.0, 'z1,z3']]\n"
] ]
} }
], ],
...@@ -261,7 +264,7 @@ ...@@ -261,7 +264,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 7,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:11:08.792299Z", "end_time": "2021-04-30T09:11:08.792299Z",
...@@ -273,8 +276,8 @@ ...@@ -273,8 +276,8 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"[-4. 0. 0. 0. 0. 4. 0. 0. 0. 0. 4. 0. 0. 0. 0. -4.]\n", "[-5. 1. -1. 1. 1. 3. 1. -1. -1. 1. 3. 1. 1. -1. 1. -5.]\n",
"H_max: 4.0\n" "H_max: 3.0\n"
] ]
} }
], ],
...@@ -319,7 +322,7 @@ ...@@ -319,7 +322,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 6, "execution_count": 8,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:11:10.245237Z", "end_time": "2021-04-30T09:11:10.245237Z",
...@@ -373,7 +376,7 @@ ...@@ -373,7 +376,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 7, "execution_count": 9,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:11:11.218109Z", "end_time": "2021-04-30T09:11:11.218109Z",
...@@ -419,7 +422,7 @@ ...@@ -419,7 +422,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 10,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:11:12.968989Z", "end_time": "2021-04-30T09:11:12.968989Z",
...@@ -443,7 +446,7 @@ ...@@ -443,7 +446,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 9, "execution_count": 11,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:11:54.550338Z", "end_time": "2021-04-30T09:11:54.550338Z",
...@@ -455,32 +458,32 @@ ...@@ -455,32 +458,32 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"iter: 10 loss: -3.8886\n", "iter: 10 loss: -1.8359\n",
"iter: 20 loss: -3.9134\n", "iter: 20 loss: -2.5392\n",
"iter: 30 loss: -3.9659\n", "iter: 30 loss: -2.7250\n",
"iter: 40 loss: -3.9906\n", "iter: 40 loss: -2.8061\n",
"iter: 50 loss: -3.9979\n", "iter: 50 loss: -2.8748\n",
"iter: 60 loss: -3.9993\n", "iter: 60 loss: -2.9134\n",
"iter: 70 loss: -3.9998\n", "iter: 70 loss: -2.9302\n",
"iter: 80 loss: -3.9999\n", "iter: 80 loss: -2.9321\n",
"iter: 90 loss: -4.0000\n", "iter: 90 loss: -2.9321\n",
"iter: 100 loss: -4.0000\n", "iter: 100 loss: -2.9325\n",
"iter: 110 loss: -4.0000\n", "iter: 110 loss: -2.9327\n",
"iter: 120 loss: -4.0000\n", "iter: 120 loss: -2.9328\n",
"\n", "\n",
"训练后的电路：\n", "训练后的电路：\n",
"--H----*-----------------*--------------------------------------------------X----Rz(3.140)----X----Rx(0.824)----*-----------------*--------------------------------------------------X----Rz(0.737)----X----Rx(2.506)----*-----------------*--------------------------------------------------X----Rz(4.999)----X----Rx(4.854)----*-----------------*--------------------------------------------------X----Rz(0.465)----X----Rx(1.900)--\n", "--H----*-----------------*--------------------------------------------------x----Rz(2.379)----x----Rx(2.503)-----------------------------------*-----------------*--------------------------------------------------x----Rz(1.230)----x----Rx(0.792)-----------------------------------*-----------------*--------------------------------------------------x----Rz(4.375)----x----Rx(5.180)-----------------------------------*-----------------*--------------------------------------------------x----Rz(0.711)----x----Rx(2.353)---------------------------------\n",
" | | | | | | | | | | | | | | | | \n",
"--H----X----Rz(3.140)----X----*-----------------*---------------------------|-----------------|----Rx(0.824)----X----Rz(0.737)----X----*-----------------*---------------------------|-----------------|----Rx(2.506)----X----Rz(4.999)----X----*-----------------*---------------------------|-----------------|----Rx(4.854)----X----Rz(0.465)----X----*-----------------*---------------------------|-----------------|----Rx(1.900)--\n",
" | | | | | | | | | | | | | | | | \n", " | | | | | | | | | | | | | | | | \n",
"--H---------------------------X----Rz(3.140)----X----*-----------------*----|-----------------|----Rx(0.824)---------------------------X----Rz(0.737)----X----*-----------------*----|-----------------|----Rx(2.506)---------------------------X----Rz(4.999)----X----*-----------------*----|-----------------|----Rx(4.854)---------------------------X----Rz(0.465)----X----*-----------------*----|-----------------|----Rx(1.900)--\n", "--H----x----Rz(2.379)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(2.503)----x----Rz(1.230)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(0.792)----x----Rz(4.375)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(5.180)----x----Rz(0.711)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(2.353)--\n",
" | | | | | | | | | | | | | | | | \n", " | | | | | | | | | | | | | | | | | | | | | | | | \n",
"--H--------------------------------------------------X----Rz(3.140)----X----*-----------------*----Rx(0.824)--------------------------------------------------X----Rz(0.737)----X----*-----------------*----Rx(2.506)--------------------------------------------------X----Rz(4.999)----X----*-----------------*----Rx(4.854)--------------------------------------------------X----Rz(0.465)----X----*-----------------*----Rx(1.900)--\n", "--H---------------------------x----Rz(2.379)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(2.503)---------------------------x----Rz(1.230)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(0.792)---------------------------x----Rz(4.375)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(5.180)---------------------------x----Rz(0.711)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(2.353)--\n",
" | | | | | | | | | | | | | | | | | | | | | | | | \n",
"--H--------------------------------------------------x----Rz(2.379)----x----*-----------------*--------x--------Rz(2.379)----x----Rx(2.503)--------------------------------------------------x----Rz(1.230)----x----*-----------------*--------x--------Rz(1.230)----x----Rx(0.792)--------------------------------------------------x----Rz(4.375)----x----*-----------------*--------x--------Rz(4.375)----x----Rx(5.180)--------------------------------------------------x----Rz(0.711)----x----*-----------------*--------x--------Rz(0.711)----x----Rx(2.353)--\n",
" \n", " \n",
"优化后的参数 gamma:\n", "优化后的参数 gamma:\n",
" [3.14046713 0.73681226 4.99897226 0.46481489]\n", " [2.37918879 1.22914743 4.37582352 0.71142941]\n",
"优化后的参数 beta:\n", "优化后的参数 beta:\n",
" [0.82379898 2.50618308 4.85422542 1.90024859]\n" " [2.50287593 0.79179726 5.17941547 2.35294027]\n"
] ]
} }
], ],
...@@ -529,7 +532,7 @@ ...@@ -529,7 +532,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 10, "execution_count": 20,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:11:55.548009Z", "end_time": "2021-04-30T09:11:55.548009Z",
...@@ -539,7 +542,7 @@ ...@@ -539,7 +542,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
"image/png": 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\n", "image/png": 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\n",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -569,7 +572,7 @@ ...@@ -569,7 +572,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 11, "execution_count": 21,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:11:55.906817Z", "end_time": "2021-04-30T09:11:55.906817Z",
...@@ -586,7 +589,7 @@ ...@@ -586,7 +589,7 @@
}, },
{ {
"data": { "data": {
"image/png": 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\n", "image/png": 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\n",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -603,10 +606,15 @@ ...@@ -603,10 +606,15 @@
"# 在图上画出上面得到的比特串对应的割\n", "# 在图上画出上面得到的比特串对应的割\n",
"node_cut = [\"blue\" if cut_bitstring[v] == \"1\" else \"red\" for v in V]\n", "node_cut = [\"blue\" if cut_bitstring[v] == \"1\" else \"red\" for v in V]\n",
"\n", "\n",
"edge_cut = [\n", "edge_cut = []\n",
" \"solid\" if cut_bitstring[u] == cut_bitstring[v] else \"dashed\"\n", "for u in range(n):\n",
" for (u, v) in E\n", " for v in range(u+1,n):\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", "nx.draw(\n",
" G,\n", " G,\n",
" pos,\n", " pos,\n",
...@@ -640,6 +648,9 @@ ...@@ -640,6 +648,9 @@
} }
], ],
"metadata": { "metadata": {
"interpreter": {
"hash": "3b61f83e8397e1c9fcea57a3d9915794102e67724879b24295f8014f41a14d85"
},
"kernelspec": { "kernelspec": {
"display_name": "Python 3", "display_name": "Python 3",
"language": "python", "language": "python",
...@@ -655,7 +666,7 @@ ...@@ -655,7 +666,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.7.10" "version": "3.7.11"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/combinatorial_optimization/MAXCUT_EN.ipynb
浏览文件 @ 016af983
...@@ -139,7 +139,7 @@ ...@@ -139,7 +139,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 2, "execution_count": 3,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:07:40.001750Z", "end_time": "2021-04-30T09:07:40.001750Z",
...@@ -157,7 +157,10 @@ ...@@ -157,7 +157,10 @@
"import numpy as np\n", "import numpy as np\n",
"from numpy import pi as PI\n", "from numpy import pi as PI\n",
"import matplotlib.pyplot as plt\n", "import matplotlib.pyplot as plt\n",
"import networkx as nx" "import networkx as nx\n",
"\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")"
] ]
}, },
{ {
...@@ -169,7 +172,7 @@ ...@@ -169,7 +172,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 4,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:07:40.192343Z", "end_time": "2021-04-30T09:07:40.192343Z",
...@@ -179,7 +182,7 @@ ...@@ -179,7 +182,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
"image/png": 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\n", 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\n",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -194,7 +197,7 @@ ...@@ -194,7 +197,7 @@
"G = nx.Graph()\n", "G = nx.Graph()\n",
"V = range(n)\n", "V = range(n)\n",
"G.add_nodes_from(V)\n", "G.add_nodes_from(V)\n",
"E = [(0, 1), (1, 2), (2, 3), (3, 0)]\n", "E = [(0, 1), (1, 2), (2, 3), (3, 0), (1, 3)]\n",
"G.add_edges_from(E)\n", "G.add_edges_from(E)\n",
"\n", "\n",
"# Print out the generated graph G\n", "# Print out the generated graph G\n",
...@@ -225,7 +228,7 @@ ...@@ -225,7 +228,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 5,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:07:40.206426Z", "end_time": "2021-04-30T09:07:40.206426Z",
...@@ -237,7 +240,7 @@ ...@@ -237,7 +240,7 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"[[-1.0, 'z0,z1'], [-1.0, 'z1,z2'], [-1.0, 'z2,z3'], [-1.0, 'z3,z0']]\n" "[[-1.0, 'z0,z1'], [-1.0, 'z1,z2'], [-1.0, 'z2,z3'], [-1.0, 'z3,z0'], [-1.0, 'z1,z3']]\n"
] ]
} }
], ],
...@@ -265,7 +268,7 @@ ...@@ -265,7 +268,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 6,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:07:40.501135Z", "end_time": "2021-04-30T09:07:40.501135Z",
...@@ -277,8 +280,8 @@ ...@@ -277,8 +280,8 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"[-4. 0. 0. 0. 0. 4. 0. 0. 0. 0. 4. 0. 0. 0. 0. -4.]\n", "[-5. 1. -1. 1. 1. 3. 1. -1. -1. 1. 3. 1. 1. -1. 1. -5.]\n",
"H_max: 4.0\n" "H_max: 3.0\n"
] ]
} }
], ],
...@@ -322,7 +325,7 @@ ...@@ -322,7 +325,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 6, "execution_count": 7,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:07:41.987233Z", "end_time": "2021-04-30T09:07:41.987233Z",
...@@ -381,7 +384,7 @@ ...@@ -381,7 +384,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 7, "execution_count": 8,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:07:43.856891Z", "end_time": "2021-04-30T09:07:43.856891Z",
...@@ -424,7 +427,7 @@ ...@@ -424,7 +427,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 9,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:07:44.907375Z", "end_time": "2021-04-30T09:07:44.907375Z",
...@@ -460,32 +463,32 @@ ...@@ -460,32 +463,32 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"iter: 10 loss: -3.8886\n", "iter: 10 loss: -1.8359\n",
"iter: 20 loss: -3.9134\n", "iter: 20 loss: -2.5392\n",
"iter: 30 loss: -3.9659\n", "iter: 30 loss: -2.7250\n",
"iter: 40 loss: -3.9906\n", "iter: 40 loss: -2.8061\n",
"iter: 50 loss: -3.9979\n", "iter: 50 loss: -2.8748\n",
"iter: 60 loss: -3.9993\n", "iter: 60 loss: -2.9134\n",
"iter: 70 loss: -3.9998\n", "iter: 70 loss: -2.9302\n",
"iter: 80 loss: -3.9999\n", "iter: 80 loss: -2.9321\n",
"iter: 90 loss: -4.0000\n", "iter: 90 loss: -2.9321\n",
"iter: 100 loss: -4.0000\n", "iter: 100 loss: -2.9325\n",
"iter: 110 loss: -4.0000\n", "iter: 110 loss: -2.9327\n",
"iter: 120 loss: -4.0000\n", "iter: 120 loss: -2.9328\n",
"\n", "\n",
"The trained circuit:\n", "The trained circuit:\n",
"--H----*-----------------*--------------------------------------------------X----Rz(3.140)----X----Rx(0.824)----*-----------------*--------------------------------------------------X----Rz(0.737)----X----Rx(2.506)----*-----------------*--------------------------------------------------X----Rz(4.999)----X----Rx(4.854)----*-----------------*--------------------------------------------------X----Rz(0.465)----X----Rx(1.900)--\n", "--H----*-----------------*--------------------------------------------------x----Rz(2.379)----x----Rx(2.503)-----------------------------------*-----------------*--------------------------------------------------x----Rz(1.230)----x----Rx(0.792)-----------------------------------*-----------------*--------------------------------------------------x----Rz(4.375)----x----Rx(5.180)-----------------------------------*-----------------*--------------------------------------------------x----Rz(0.711)----x----Rx(2.353)---------------------------------\n",
" | | | | | | | | | | | | | | | | \n",
"--H----X----Rz(3.140)----X----*-----------------*---------------------------|-----------------|----Rx(0.824)----X----Rz(0.737)----X----*-----------------*---------------------------|-----------------|----Rx(2.506)----X----Rz(4.999)----X----*-----------------*---------------------------|-----------------|----Rx(4.854)----X----Rz(0.465)----X----*-----------------*---------------------------|-----------------|----Rx(1.900)--\n",
" | | | | | | | | | | | | | | | | \n", " | | | | | | | | | | | | | | | | \n",
"--H---------------------------X----Rz(3.140)----X----*-----------------*----|-----------------|----Rx(0.824)---------------------------X----Rz(0.737)----X----*-----------------*----|-----------------|----Rx(2.506)---------------------------X----Rz(4.999)----X----*-----------------*----|-----------------|----Rx(4.854)---------------------------X----Rz(0.465)----X----*-----------------*----|-----------------|----Rx(1.900)--\n", "--H----x----Rz(2.379)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(2.503)----x----Rz(1.230)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(0.792)----x----Rz(4.375)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(5.180)----x----Rz(0.711)----x----*-----------------*---------------------------|-----------------|--------*---------------------*----Rx(2.353)--\n",
" | | | | | | | | | | | | | | | | \n", " | | | | | | | | | | | | | | | | | | | | | | | | \n",
"--H--------------------------------------------------X----Rz(3.140)----X----*-----------------*----Rx(0.824)--------------------------------------------------X----Rz(0.737)----X----*-----------------*----Rx(2.506)--------------------------------------------------X----Rz(4.999)----X----*-----------------*----Rx(4.854)--------------------------------------------------X----Rz(0.465)----X----*-----------------*----Rx(1.900)--\n", "--H---------------------------x----Rz(2.379)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(2.503)---------------------------x----Rz(1.230)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(0.792)---------------------------x----Rz(4.375)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(5.180)---------------------------x----Rz(0.711)----x----*-----------------*----|-----------------|--------|---------------------|----Rx(2.353)--\n",
" | | | | | | | | | | | | | | | | | | | | | | | | \n",
"--H--------------------------------------------------x----Rz(2.379)----x----*-----------------*--------x--------Rz(2.379)----x----Rx(2.503)--------------------------------------------------x----Rz(1.230)----x----*-----------------*--------x--------Rz(1.230)----x----Rx(0.792)--------------------------------------------------x----Rz(4.375)----x----*-----------------*--------x--------Rz(4.375)----x----Rx(5.180)--------------------------------------------------x----Rz(0.711)----x----*-----------------*--------x--------Rz(0.711)----x----Rx(2.353)--\n",
" \n", " \n",
"Optimized parameters gamma:\n", "Optimized parameters gamma:\n",
" [3.14046713 0.73681226 4.99897226 0.46481489]\n", " [2.37918879 1.22914743 4.37582352 0.71142941]\n",
"Optimized parameters beta:\n", "Optimized parameters beta:\n",
" [0.82379898 2.50618308 4.85422542 1.90024859]\n" " [2.50287593 0.79179726 5.17941547 2.35294027]\n"
] ]
} }
], ],
...@@ -545,7 +548,7 @@ ...@@ -545,7 +548,7 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
"image/png": 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\n", 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\n",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -587,12 +590,12 @@ ...@@ -587,12 +590,12 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"The bit string form of the cut found: 1010\n" "The bit string form of the cut found: 0101\n"
] ]
}, },
{ {
"data": { "data": {
"image/png": 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\n", "image/png": 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\n",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -609,10 +612,14 @@ ...@@ -609,10 +612,14 @@
"# Draw the cut corresponding to the bit string obtained above on the graph\n", "# Draw the cut corresponding to the bit string obtained above on the graph\n",
"node_cut = [\"blue\" if cut_bitstring[v] == \"1\" else \"red\" for v in V]\n", "node_cut = [\"blue\" if cut_bitstring[v] == \"1\" else \"red\" for v in V]\n",
"\n", "\n",
"edge_cut = [\n", "edge_cut = []\n",
" \"solid\" if cut_bitstring[u] == cut_bitstring[v] else \"dashed\"\n", "for u in range(n):\n",
" for (u, v) in E\n", " for v in range(u+1,n):\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", "nx.draw(\n",
" G,\n", " G,\n",
" pos,\n", " pos,\n",
...@@ -646,6 +653,9 @@ ...@@ -646,6 +653,9 @@
} }
], ],
"metadata": { "metadata": {
"interpreter": {
"hash": "3b61f83e8397e1c9fcea57a3d9915794102e67724879b24295f8014f41a14d85"
},
"kernelspec": { "kernelspec": {
"display_name": "Python 3", "display_name": "Python 3",
"language": "python", "language": "python",
...@@ -661,7 +671,7 @@ ...@@ -661,7 +671,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.3" "version": "3.7.11"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/locc/LOCCNET_Tutorial_CN.ipynb
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...@@ -91,7 +91,7 @@ ...@@ -91,7 +91,7 @@
"source": [ "source": [
"在 `__init__()` 函数中，我们需要初始化所有的参与方、量子态以及 QNN 的参数。\n", "在 `__init__()` 函数中，我们需要初始化所有的参与方、量子态以及 QNN 的参数。\n",
"\n", "\n",
"- `self.add_new_party(qubits_number, party_name=None)` 是用于添加一个新的参与方的函数，第一个参数代表该参与方有几个量子比特；第二个参数是可选参数，代表着参与者的名字。在协议中，我们可以选择是用过名字来指定参与方，也可以选择用编号来指定。如果我们希望使用名字，那么只需要在 `add_new_party` 函数中给 `party_name` 命名；如果希望使用编号，那么我们就不用给第二个参数赋值，第一个参与方会自动编号为 0，每增加一个参与方，其编号都会加一，同时该函数会将所添加的 party 的 ID 返回，其值根据定义会是 `int` 或者 `str`。\n", "- `self.add_new_party(qubits_number, party_name=None)` 是用于添加一个新的参与方的函数，第一个参数代表该参与方有几个量子比特；第二个参数是可选参数，代表着参与者的名字。在协议中，我们可以选择使用名字来指定参与方，也可以选择用编号来指定。如果我们希望使用名字，那么只需要在 `add_new_party` 函数中给 `party_name` 命名；如果希望使用编号，那么我们就不用给第二个参数赋值，第一个参与方会自动编号为 0，每增加一个参与方，其编号都会加一，同时该函数会将所添加的 party 的 ID 返回，其值根据定义会是 `int` 或者 `str`。\n",
"\n", "\n",
"- `self.set_init_state(state, which_qubits)` 是用于设置协议的初始态的函数。第一个参数 `state` 是量子态，必须是密度矩阵的形式；第二个参数 `which_qubits` 是定位量子比特（哪一参与方的第几个量子比特，如 `(\"Alice\", 0)`）。需要说明的是，我们必须初始化所有的量子比特，否则程序将出现错误。" "- `self.set_init_state(state, which_qubits)` 是用于设置协议的初始态的函数。第一个参数 `state` 是量子态，必须是密度矩阵的形式；第二个参数 `which_qubits` 是定位量子比特（哪一参与方的第几个量子比特，如 `(\"Alice\", 0)`）。需要说明的是，我们必须初始化所有的量子比特，否则程序将出现错误。"
] ]
...@@ -100,7 +100,7 @@ ...@@ -100,7 +100,7 @@
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
"source": [ "source": [
"在 `forward()` 函数中，我们需要定义协议的流程。如果我们想要训练一个模型，那么需要定义损失函数，并设置为 `forward()` 的返回值，这样才能不断更新参数使得损失函数最小化。如果我们仅仅是想要验证某个协议的结果，我们就做上述的事情，只需要把协议的流程定义清除，就可以把我们感兴趣的值设为返回值。在 `forward()` 函数中，我们主要做两件事情--量子操作和测量，我们为他们提供了相应的函数：\n", "在 `forward()` 函数中，我们需要定义协议的流程。如果我们想要训练一个模型，那么需要定义损失函数，并设置为 `forward()` 的返回值，这样才能不断更新参数使得损失函数最小化。如果我们仅仅是想要验证某个协议的结果，我们就做上述的事情，只需要把协议的流程定义清楚，就可以把我们感兴趣的值设为返回值。在 `forward()` 函数中，我们主要做两件事情--量子操作和测量，我们为他们提供了相应的函数：\n",
"\n", "\n",
"- `self.create_ansatz(party_id)` 是为某一参与方创建本地量子电路的函数。所以参数 `party_id` 用来指定参与方。举个例子 `cir1 = self.create_ansatz(\"Alice\")` 为 Alice 创建了电路。之后，我们可以在电路中添加不同的操作比如 X 门， CNOT 门等，也可以在添加门之后通过 `run()` 函数来运行电路，得到运行后的结果，如 `status_out = cir1.run(status)`。\n", "- `self.create_ansatz(party_id)` 是为某一参与方创建本地量子电路的函数。所以参数 `party_id` 用来指定参与方。举个例子 `cir1 = self.create_ansatz(\"Alice\")` 为 Alice 创建了电路。之后，我们可以在电路中添加不同的操作比如 X 门， CNOT 门等，也可以在添加门之后通过 `run()` 函数来运行电路，得到运行后的结果，如 `status_out = cir1.run(status)`。\n",
"\n", "\n",
...@@ -141,7 +141,7 @@ ...@@ -141,7 +141,7 @@
"\n", "\n",
"[1] Chitambar, Eric, et al. \"Everything you always wanted to know about LOCC (but were afraid to ask).\" [Communications in Mathematical Physics 328.1 (2014): 303-326.](https://link.springer.com/article/10.1007/s00220-014-1953-9)\n", "[1] Chitambar, Eric, et al. \"Everything you always wanted to know about LOCC (but were afraid to ask).\" [Communications in Mathematical Physics 328.1 (2014): 303-326.](https://link.springer.com/article/10.1007/s00220-014-1953-9)\n",
"\n", "\n",
"[2] Zhao, Xuanqiang, et al. \"LOCCNet: a machine learning framework for distributed quantum information processing.\" [arXiv:2101.12190 (2021).](https://arxiv.org/abs/2101.12190)\n", "[2] Zhao, Xuanqiang, et al. \"Practical distributed quantum information processing with LOCCNet.\" [npj Quantum Information 7, 159 (2021).](https://www.nature.com/articles/s41534-021-00496-x)\n",
"\n", "\n",
"[3] Bennett, Charles H., et al. \"Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.\" [Physical Review Letters 70.13 (1993): 1895.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1895)\n", "[3] Bennett, Charles H., et al. \"Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.\" [Physical Review Letters 70.13 (1993): 1895.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1895)\n",
"\n", "\n",
......
tutorial/locc/LOCCNET_Tutorial_EN.ipynb
浏览文件 @ 016af983
...@@ -133,7 +133,7 @@ ...@@ -133,7 +133,7 @@
"\n", "\n",
"[1] Chitambar, Eric, et al. \"Everything you always wanted to know about LOCC (but were afraid to ask).\" [Communications in Mathematical Physics 328.1 (2014): 303-326.](https://link.springer.com/article/10.1007/s00220-014-1953-9)\n", "[1] Chitambar, Eric, et al. \"Everything you always wanted to know about LOCC (but were afraid to ask).\" [Communications in Mathematical Physics 328.1 (2014): 303-326.](https://link.springer.com/article/10.1007/s00220-014-1953-9)\n",
"\n", "\n",
"[2] Zhao, Xuanqiang, et al. \"LOCCNet: a machine learning framework for distributed quantum information processing.\" [arXiv:2101.12190 (2021).](https://arxiv.org/abs/2101.12190)\n", "[2] Zhao, Xuanqiang, et al. \"Practical distributed quantum information processing with LOCCNet.\" [npj Quantum Information 7, 159 (2021).](https://www.nature.com/articles/s41534-021-00496-x)\n",
"\n", "\n",
"[3] Bennett, Charles H., et al. \"Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.\" [Physical Review Letters 70.13 (1993): 1895.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1895)\n", "[3] Bennett, Charles H., et al. \"Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels.\" [Physical Review Letters 70.13 (1993): 1895.](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.70.1895)\n",
"\n", "\n",
...@@ -167,7 +167,7 @@ ...@@ -167,7 +167,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.7.9" "version": "3.7.10"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/machine_learning/QClassifier_CN.ipynb
浏览文件 @ 016af983
...@@ -15,7 +15,7 @@ ...@@ -15,7 +15,7 @@
"source": [ "source": [
"## 概览\n", "## 概览\n",
"\n", "\n",
"本教程我们将讨论量子分类器（quantum classifier）的原理，以及如何利用量子神经网络（quantum neural network, QNN）来完成**两分类**任务。这类方法早期工作的主要代表是 Mitarai et al.(2018) 的量子电路学习 [(Quantum Circuit Learning, QCL)](https://arxiv.org/abs/1803.00745) [1], Farhi & Neven (2018) [2] 和 Schuld et al.(2018) 的中心电路量子分类器 [Circuit-Centric Quantum Classifiers](https://arxiv.org/abs/1804.00633) [3]。这里我们以第一类的 QCL 框架应用于监督学习（Supervised learning）为例进行介绍，通常我们需要先将经典数据编码成量子数据，然后通过训练量子神经网络的参数，最终得到一个最优的分类器。" "本教程我们将讨论量子分类器（quantum classifier）的原理，以及如何利用量子神经网络（quantum neural network, QNN）来完成**二分类**任务。这类方法早期工作的主要代表是 Mitarai et al.(2018) 的量子电路学习 [(Quantum Circuit Learning, QCL)](https://arxiv.org/abs/1803.00745) [1], Farhi & Neven (2018) [2] 和 Schuld et al.(2018) 的中心电路量子分类器 [Circuit-Centric Quantum Classifiers](https://arxiv.org/abs/1804.00633) [3]。这里我们以第一类的 QCL 框架应用于监督学习（Supervised learning）为例进行介绍，通常我们需要先将经典数据编码成量子数据，然后通过训练量子神经网络的参数，最终得到一个最优的分类器。"
] ]
}, },
{ {
...@@ -40,7 +40,7 @@ ...@@ -40,7 +40,7 @@
"\n", "\n",
"这里我们给出实现量子电路学习 (QCL) 框架下量子分类器的一个流程。\n", "这里我们给出实现量子电路学习 (QCL) 框架下量子分类器的一个流程。\n",
"\n", "\n",
"1. 将经典数据编码$x^k$为量子数据$\\lvert \\psi_{\\rm in}\\rangle^k$。本教材采用角度编码。关于编码方式的具体操作，见[量子态编码经典数据](./DataEncoding_EN.ipynb)。用户也可以尝试其他编码，如振幅编码，体验不同编码方式学习效率的区别。\n", "1. 将经典数据编码$x^k$为量子数据$\\lvert \\psi_{\\rm in}\\rangle^k$。本教程采用角度编码。关于编码方式的具体操作，见[量子态编码经典数据](./DataEncoding_CN.ipynb)。用户也可以尝试其他编码，如振幅编码，体验不同编码方式对分类器学习效率的影响。\n",
"2. 构建可调参数量子电路，对应幺正变换(unitary gate)$U(\\theta)$。\n", "2. 构建可调参数量子电路，对应幺正变换(unitary gate)$U(\\theta)$。\n",
"3. 对每一个量子数据$\\lvert\\psi_{\\rm in}\\rangle^k$，通过参数化量子电路$U(\\theta)$，得到输出态$\\lvert \\psi_{\\rm out}\\rangle^k = U(\\theta)\\lvert \\psi_{\\rm in} \\rangle^k$。\n", "3. 对每一个量子数据$\\lvert\\psi_{\\rm in}\\rangle^k$，通过参数化量子电路$U(\\theta)$，得到输出态$\\lvert \\psi_{\\rm out}\\rangle^k = U(\\theta)\\lvert \\psi_{\\rm in} \\rangle^k$。\n",
"4. 对每一个量子数据得到的输出量子态$\\lvert \\psi_{\\rm out}\\rangle^k$，通过测量与数据后处理，得到标签 $\\tilde{y}^{k}$。\n", "4. 对每一个量子数据得到的输出量子态$\\lvert \\psi_{\\rm out}\\rangle^k$，通过测量与数据后处理，得到标签 $\\tilde{y}^{k}$。\n",
...@@ -69,9 +69,18 @@ ...@@ -69,9 +69,18 @@
"start_time": "2021-03-02T09:15:03.413324Z" "start_time": "2021-03-02T09:15:03.413324Z"
} }
}, },
"outputs": [], "outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\yeruilin\\Anaconda3\\envs\\paddle_quantum_env\\lib\\site-packages\\matplotlib_inline\\config.py:66: DeprecationWarning: InlineBackend._figure_formats_changed is deprecated in traitlets 4.1: use @observe and @unobserve instead.\n",
" def _figure_formats_changed(self, name, old, new):\n"
]
}
],
"source": [ "source": [
"# 导入numpy与paddle\n", "# 导入 numpy 与 paddle\n",
"import numpy as np\n", "import numpy as np\n",
"import paddle\n", "import paddle\n",
"\n", "\n",
...@@ -79,8 +88,8 @@ ...@@ -79,8 +88,8 @@
"from paddle_quantum.circuit import UAnsatz\n", "from paddle_quantum.circuit import UAnsatz\n",
"# 一些用到的函数\n", "# 一些用到的函数\n",
"from numpy import pi as PI\n", "from numpy import pi as PI\n",
"from paddle import matmul, transpose # paddle矩阵乘法与转置\n", "from paddle import matmul, transpose, reshape # paddle 矩阵乘法与转置\n",
"from paddle_quantum.utils import pauli_str_to_matrix,dagger # 得到N量子比特泡利矩阵,复共轭\n", "from paddle_quantum.utils import pauli_str_to_matrix,dagger # 得到 N 量子比特泡利矩阵,复共轭\n",
"\n", "\n",
"# 作图与计算时间\n", "# 作图与计算时间\n",
"from matplotlib import pyplot as plt\n", "from matplotlib import pyplot as plt\n",
...@@ -100,18 +109,19 @@ ...@@ -100,18 +109,19 @@
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"# 训练参数设置\n", "# 数据集参数设置\n",
"Ntrain = 200 # 规定训练集大小\n", "Ntrain = 200 # 规定训练集大小\n",
"Ntest = 100 # 规定测试集大小\n", "Ntest = 100 # 规定测试集大小\n",
"gap = 0.5 # 设定决策边界的宽度\n", "boundary_gap = 0.5 # 设置决策边界的宽度\n",
"seed_data = 2 # 固定随机种子\n",
"# 训练参数设置\n",
"N = 4 # 所需的量子比特数量\n", "N = 4 # 所需的量子比特数量\n",
"DEPTH = 1 # 采用的电路深度\n", "DEPTH = 1 # 采用的电路深度\n",
"BATCH = 20 # 训练时 batch 的大小\n", "BATCH = 20 # 训练时 batch 的大小\n",
"EPOCH = int(200 * BATCH / Ntrain) \n", "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", " # 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", "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 = 19 # 设置随机种子用以初始化各种参数"
"seed_data = 2 # 固定生成数据集所需要的随机种子"
] ]
}, },
{ {
...@@ -120,7 +130,7 @@ ...@@ -120,7 +130,7 @@
"source": [ "source": [
"### 数据集的生成\n", "### 数据集的生成\n",
"\n", "\n",
"对于监督学习来说，我们绕不开的一个问题就是——采用的数据集是什么样的？在这个教程中我们按照论文 [1] 里所提及方法生成简单的圆形决策边界二分数据集 $\\{(x^{k}, y^{k})\\}$。其中数据点 $x^{k}\\in \\mathbb{R}^{2}$，标签 $y^{k} \\in \\{0,1\\}$。\n", "对于监督学习来说，我们绕不开的一个问题就是——采用什么样的数据集呢？在这个教程中我们按照论文 [1] 里所提及方法生成简单的圆形决策边界二分数据集 $\\{(x^{k}, y^{k})\\}$。其中数据点 $x^{k}\\in \\mathbb{R}^{2}$，标签 $y^{k} \\in \\{0,1\\}$。\n",
"\n", "\n",
"<img src=\"./figures/qclassifier-fig-data-cn.png\" width=\"400px\" /> \n", "<img src=\"./figures/qclassifier-fig-data-cn.png\" width=\"400px\" /> \n",
"<center> 图 2：生成的数据集和对应的决策边界 </center>\n", "<center> 图 2：生成的数据集和对应的决策边界 </center>\n",
...@@ -137,7 +147,7 @@ ...@@ -137,7 +147,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 4,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-03-02T09:15:04.631031Z", "end_time": "2021-03-02T09:15:04.631031Z",
...@@ -183,7 +193,7 @@ ...@@ -183,7 +193,7 @@
" print(\"训练集的维度大小 x {} 和 y {}\".format(np.shape(train_x[0:Ntrain]), np.shape(train_y[0:Ntrain])))\n", " print(\"训练集的维度大小 x {} 和 y {}\".format(np.shape(train_x[0:Ntrain]), np.shape(train_y[0:Ntrain])))\n",
" print(\"测试集的维度大小 x {} 和 y {}\".format(np.shape(train_x[Ntrain:]), np.shape(train_y[Ntrain:])), \"\\n\")\n", " print(\"测试集的维度大小 x {} 和 y {}\".format(np.shape(train_x[Ntrain:]), np.shape(train_y[Ntrain:])), \"\\n\")\n",
"\n", "\n",
" return train_x[0:Ntrain], train_y[0:Ntrain], train_x[Ntrain:], train_y[Ntrain:]\n" " return train_x[0:Ntrain], train_y[0:Ntrain], train_x[Ntrain:], train_y[Ntrain:]"
] ]
}, },
{ {
...@@ -195,7 +205,7 @@ ...@@ -195,7 +205,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 6,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -225,7 +235,7 @@ ...@@ -225,7 +235,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 7,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-03-02T09:15:06.422981Z", "end_time": "2021-03-02T09:15:06.422981Z",
...@@ -245,7 +255,7 @@ ...@@ -245,7 +255,7 @@
}, },
{ {
"data": { "data": {
"image/png": 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", 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",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -264,7 +274,7 @@ ...@@ -264,7 +274,7 @@
}, },
{ {
"data": { "data": {
"image/png": 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VuQVS2UNju3K6cWauLJa0HHgc+AjwHHAv8OnsLScl/THwexFxiaRNwMcj4lOSzgK+C2wA3grcDrwtIl4f9Z2uLLZa8m3uEq6crq0iK4s3APsi4smIeAW4HtjYt85GYGf6/Cbgw5KUzr8+Il6OiKeAfennmTWPb3OXqHN9iQ2URyA4BXg28/q5dN7AddKb3f8SWDPhewGQtFXSoqTFAwcO5JBsswZoYll7netLbKDGVBZHxI6ImI+I+bVr11adHLPiNbWsvc71JTZQHoFgP3Ba5vWp6byB60g6DvhN4OCE77Wua2KuOA917pswSlPv29xheVQWH0dSWfxhkpP4vcAfRsSezDpfBt6ZqSz+txHxSUm/A/wvjlQW3wGc6cpi+5U699gt2rJlg2+YIyX1EGZTKqyyOC3zvxS4FXgUuDEi9ki6UtKF6WrfBNZI2gd8FdiWvncPcCPwCPB/gC+PCwLWMU3NFefBZe1WEo81ZPXW5Vxxl6+GrBAea8iaqcu5Ype1W0kcCKzeBrVA+bVfg8OHu1F57L4JVgIHAqu3/lzxmjXJ48GDzWpSaTaBqhrIORBY/WVzxSecAK+8cvTyulQed7WZq+Wiym4jDgTWLHUbvqB38pfgs59tXuevaTjQFarKBnIOBNYsdao8zmbh4NjWTXW5UslDU3s5N8igcfpGzc+TAwHO6DRKnYYvGJSF69eWgda63J+jJMuXTzc/T50PBM7oNMywJpVQfjSf5CTflmaudSuSa6HXh3SlHTY/T50PBM7oNFB/k0qoJpqPO8m3aaC1OhXJtdTc3HTz89T5QOCMTgtUFc0HFVNJyWPbOn/VqUiupS644Mjh01PWJu58IHBGpwWqiuaDiqmuuy65Kmlb5y/3ci7UwgLs3Hl0ewMJtmwpZxN3fqwhD+fSAr41ojVcWYewxxoawhmdFnCxhTVc1UXUnQ8E4OFcGs/R3Bqu6iJqBwJrB0dza7CqL2pnCgSSVku6TdLe9HHVgHXOlvRDSXskPSjpU5ll10p6StL96XT2LOkxK5V7IlpOqr6onamyWNKfAoci4ipJ24BVEXFZ3zpvAyIi9kp6K3Af8I6I+IWka4H/HRE3TfO9vjGNVc6tDKyBiqos3gjsTJ/vBC7qXyEiHo+IvenzfwReANbO+L1m1XJPRGuRWQPBSRHxfPr8J8BJo1aWtAFYATyRmb09LTK6WtLxM6bHrBxVN/Mwy9HYQCDpdkkPD5g2ZteLpIxpaDmTpJOB64DPR0TvZrOXA28H/iWwGrhsyNuRtFXSoqTFAwcOjP9lZkWqupmHWY7GBoKIODcifnfAdDPw0/QE3zvRvzDoMyT9BvB94IqIuCfz2c9H4mXg28CGEenYERHzETG/dq1LlqxiVTfzMMvRrEVDu4Et6fMtwM39K0haAXwP+E5/pXAmiIikfuHhGdNjVo6qm3lYq5XdIG3WVkNrgBuBdcDTwCcj4pCkeeCSiPiipM+Q5Pb3ZN76uYi4X9KdJBXHAu5P33N43Pe61ZCZtVWRDdKGtRrq/FhD4ywsJA1BnnkmKf7dvt2ZPjMrTpHjDnmsoSXwTWtawh2/rEGqaJDmQDCCm4q3gKO5NUwVDdIcCEZwU/EWcDS3hqmiQZoDwQhuKl5zkxT5tCmau4irE6pokOZAMIKbitfYpEU+bYnmLuLqlLIH03UgGMFNxWts0iKftkRzF3FZgdx81Jpp2bKjb/DaIyXZqKw2tAGe5veaDTGs+ehxVSTGbGbr1g1ubD2oyGfz5uad+PtN83vNpuSiIWumthT5TKprv9dK5UBgzdS1Cpyu/V4rlesIctCGImgzaz8PMdEnrybZbtVnZk3XyUCQ58nbrfrMrOk6GQjyPHm3qeOqmXVTJwNBnifvtnRcNbPu6mQgyPPk7VZ9ZtZ0MwUCSasl3SZpb/q4ash6r0u6P512Z+afLulHkvZJuiG9rWXh8jx5u1WfmTXdrFcE24A7IuJM4I709SAvRcTZ6XRhZv6fAFdHxG8BPwe+MGN6JpL3ybvsAaLMzPI06z2LHwM+EBHPpzeivzsifnvAeocj4oS+eQIOAG+JiNckvQ/4ekScN+5769aPwMysCYrqR3BSRDyfPv8JcNKQ9d4kaVHSPZIuSuetAX4REa+lr58DTpkxPWZmNqWxg85Juh14y4BFRzW2jIiQNOzyYi4i9ks6A7hT0kPAL6dJqKStwFaAdW6SY2aWm7GBICLOHbZM0k8lnZwpGnphyGfsTx+flHQ38C7gb4A3SzouvSo4Fdg/Ih07gB2QFA2NS7eZmU1m1qKh3cCW9PkW4Ob+FSStknR8+vxE4P3AI5FUTtwFXDzq/WZmVqxZA8FVwEck7QXOTV8jaV7SNek67wAWJT1AcuK/KiIeSZddBnxV0j6SOoNvzpgeMzOb0kyBICIORsSHI+LMiDg3Ig6l8xcj4ovp87+PiHdGxL9IH7+Zef+TEbEhIn4rIj4RES/P9nOqMckAdr7vuJnVle9QNqPeAHa9sYt6A9jBkf4Ek6xjZlaVzgwxUVSOfJIB7DxCqZnVWSeuCIrMkU8ygJ1HKDWzOuvEFUGROfJJBrDzCKVm7dWG+r9OBIIic+TjBrBbWIDDh499n0coNWu+ttyhsBOBoMgc+agB7HoHycGDR79nzRqPUGrWBm2p/+vEzev76wggyZEXfTJevz7JIfSbm0tGKTWzZlu2LLkS6CcloxHXTadvXl/VPQNcSWzWbm2p/+tEIIBq7hnQloPEzAab9iZXS61YLrpCujOBoAq+jaVZu01T2rDUiuUyKqQ7UUdQpYWFpOLomWeSK4Ht211JbNZFS60zzLOucVgdgQOBmVkJllqxnGeFdKcri9ukDZ1XzLpoqXWGZdQ1OhA0SFs6r5h10VLrDMuoa3QgaJC2dF4x66KlNmMvo/m76wgapGmdV8ysXgqpI5C0WtJtkvamj6sGrPNBSfdnpn+SdFG67FpJT2WWnT1LetrO/RLMrAizFg1tA+6IiDOBO9LXR4mIuyLi7Ig4G/gQ8CLwfzOr/Ofe8oi4f8b0tJr7JZhZEWYNBBuBnenzncBFY9a/GPhBRLw4Zj0boKqhMsys3WYNBCdFxPPp858AJ41ZfxPw3b552yU9KOlqScfPmJ7Wq2KoDDNrt7F3KJN0O/CWAYuOaqsSESFpaM2zpJOBdwK3ZmZfThJAVgA7gMuAK4e8fyuwFWCdC8XNzHIz9oogIs6NiN8dMN0M/DQ9wfdO9C+M+KhPAt+LiFczn/18JF4Gvg1sGJGOHRExHxHza9eunfT3mZktWVc6cM5aNLQb2JI+3wLcPGLdT9NXLJQJIiKpX3h4xvSYmU1s1Im+Sx04Zw0EVwEfkbQXODd9jaR5Sdf0VpK0HjgN+H9971+Q9BDwEHAi8N9mTI+N0JXcjdkkxp3ou9SB0x3KxuiNHvr007B8Obz+etJap2mjiFZ1lzazuho3qmcbO3B60LklyOYYIAkC0MxLxC7lbswmMeoOggsLSSAYpKi2KlVesfuKYIRhOYaeJt17uI25G7NZDPt/r1kDL710bMYJiruKLuuK3VcESzDu3sJNuvewh6cwS/Ry3k8/nWSEsno99wcFgeXLiwsCW7ZUe8XuQDDCUscJryMPT2F2bHFvxJFg0Oupf+jQ4Pe+8cZ0QWCSop5eenrFzv1Ky2xGROOmc845J8qwa1fEypURyeFy9LRyZbK8SXbtipibi5CSx6al32xWc3OD/89zc9OtM86gc8egc8aw71rKd04CWIwB59TKT+pLmcoKBBFHTp4QsXz5kZ1T1UnUJ3OzpZMGn3ClI+tMehIfZdJgMiw9RWU2HQhaII8DtGoOZFalSU/Qsx6nkwScUelZvryY/4YDQQvkccmaVfZJuQ2BzJqtrGNwmoBT5n/CgaAFJs1lTKKKk3LegcxsKcrIAE3z/yozQzYsELgfQYOM6wlZ1WdNyn0ZrEt6oxI880zSwrAOoxG4H0EL5NkEdFSvyqK4L4N1SZPuHeJA0CB53qGsipPyoEAmwQUXFPedZjaeA0HD5JXLGHd1UcS4J5s3Jz0os705I2DnzmaN29QGHonWjjKo4qDuU1cri/M2rJKqyIrkulQYd7kZaxtbb3V5f04DtxoqXlsOxiJP1nm2fFqqNp4Ip1GXYJyXru/PaQwLBC4aykmb7mZUZEVyHSqMuz4k97T7t+7FSG3cn6Vv80HRYdIJ+ASwB3gDmB+x3vnAY8A+YFtm/unAj9L5NwArJvneOl4RtCmXVeRvqUPurQ5XJVWaZv/WYX+N07b9WeQ2p4iiIeAdwG8Ddw8LBMBy4AngDGAF8ABwVrrsRmBT+vyvgC9N8r11DARtOhiL/vNXXYTWpqC9FNPs3yZsqyakcRpF/p5CAsGvPmR0IHgfcGvm9eXpJOBnwHGD1hs11TEQtO1grPpkXaQm5HKLNun+bUIGp237s8htPiwQlFFHcArwbOb1c+m8NcAvIuK1vvmN1Lbx/pvUGWZaefbHaKpJ928d6nTGadv+rGKbjw0Ekm6X9PCAaWNxyRqYjq2SFiUtHjhwoMyvnkjbDsa2a3Ogy1NTMjht2p9VbPPjxq0QEefO+B37gdMyr09N5x0E3izpuPSqoDd/WDp2ADsgGWtoxjQVYvPmZh+AZv16x3Pdxsxpsyq2+dhAkIN7gTMlnU5yot8E/GFSFqa7gIuB64EtwM0lpMfMpuAMTvnK3uYz1RFI+rik50gqer8v6dZ0/lsl3QKQ5vYvBW4FHgVujIg96UdcBnxV0j6SOoNvzpIeMzObnoehNjPrCA9DbWZmAzkQmJl1nAOBmVnHNbKOQNIBYMCNFidyIkmP5rpxuqZT13RBfdPmdE2vrmlbarrmImJt/8xGBoJZSFocVFlSNadrOnVNF9Q3bU7X9OqatrzT5aIhM7OOcyAwM+u4LgaCHVUnYAinazp1TRfUN21O1/TqmrZc09W5OgIzMztaF68IzMwsw4HAzKzjWhkIJH1C0h5Jb0ga2sRK0vmSHpO0T9K2zPzTJf0onX+DpBU5pWu1pNsk7U0fVw1Y54OS7s9M/yTponTZtZKeyiw7u6x0peu9nvnu3Zn5VW6vsyX9MN3fD0r6VGZZrttr2PGSWX58+vv3pdtjfWbZ5en8xySdN0s6lpCur0p6JN0+d0iayywbuE9LTNvnJB3IpOGLmWVb0n2/V9KWktN1dSZNj0v6RWZZYdtM0rckvSDp4SHLJenP03Q/KOndmWVL316DblvW9ImK7qU8Qbr+FNiWPt8G/MmY9VcDh4CV6etrgYsL2F4TpQs4PGR+ZdsLeBtwZvr8rcDzwJvz3l6jjpfMOn8M/FX6fBNwQ/r8rHT944HT089ZXmK6Ppg5hr7US9eofVpi2j4H/MWA964GnkwfV6XPV5WVrr71vwJ8q6Rt9q+BdwMPD1l+AfADklv9vhf4UR7bq5VXBBHxaEQ8Nma1DcC+iHgyIl4huSfCRkkCPgTclK63E7gop6RtTD9v0s+9GPhBRLyY0/cPM226fqXq7RURj0fE3vT5PwIvAMf0nMzBwONlRHpvAj6cbp+NwPUR8XJEPAXsSz+vlHRFxF2ZY+gekptAlWGSbTbMecBtEXEoIn4O3AacX1G6Pg18N6fvHiki/o4k8zfMRuA7kbiH5OZeJzPj9mplIJhQFfdSPikink+f/wQ4acz6mzj2ANyeXhJeLen4ktP1JiW3C72nV1xFjbaXpA0kObwnMrPz2l7DjpeB66Tb45ck22eS9xaZrqwvkOQoewbt07xMmrY/SPfRTZJ6dzOsxTZLi9FOB+7MzC5ym40zLO0zba8y7lBWCEm3A28ZsOiKiKjsTmej0pV9EREhaWjb3TTKv5Pkhj49l5OcEFeQtCO+DLiyxHTNRcR+SWcAd0p6iORkt2Q5b6/rgC0R8UY6e8nbq40kfQaYB34/M/uYfRoRTwz+hEL8LfDdiHhZ0r8nuaL6UInfP84m4KaIeD0zr+ptlrvGBoKoyb2Up0mXpJ9KOjkink9PXC+M+KhPAt+LiFczn93LHb8s6dvAfyozXRGxP318UtLdwLuAv6Hi7SXpN4Dvk2QC7sl89pK31wDDjpdB6zwn6TjgN0mOp0neW2S6kHQuSXD9/Yh4uTd/yD7N66Q2Nm0RcTDz8hqSeqHeez/Q9967y0pXxibgy9kZBW+zcYalfabt1eWioV/dS1lJK5dNwO5Ial5691KGfO+lvDv9vEk+95hyyfRk2CuXvwgY2LKgiHRJWtUrWpF0IvB+4JGqt1e6775HUm56U9+yPLfXwONlRHovBu5Mt89uYJOSVkWnA2cC/zBDWqZKl6R3Af8TuDAiXsjMH7hPc0rXpGk7OfPyQpLb2UJyJfzRNI2rgI9y9NVxoelK0/Z2korXH2bmFb3NxtkN/Lu09dB7gV+mGZ7ZtldRtd9VTsDHScrIXgZ+Ctyazn8rcEtmvQuAx0mi+RWZ+WeQ/FH3AX8NHJ9TutYAdwB7gduB1en8eeCazHrrSSL8sr733wk8RHJC2wWcUFa6gH+VfvcD6eMX6rC9gM8ArwL3Z6azi9heg44XkqKmC9Pnb0p//750e5yRee8V6fseAz6W8/E+Ll23p/+D3vbZPW6flpi2/w7sSdNwF/D2zHv/KN2W+4DPl5mu9PXXgav63lfoNiPJ/D2fHtPPkdTpXAJcki4X8I003Q+RaRU5y/byEBNmZh3X5aIhMzPDgcDMrPMcCMzMOs6BwMys4xwIzMw6zoHAzKzjHAjMzDru/wPTby8hcT1iEgAAAABJRU5ErkJggg==", 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",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -284,12 +294,6 @@ ...@@ -284,12 +294,6 @@
} }
], ],
"source": [ "source": [
"# 数据集参数设置\n",
"Ntrain = 200 # 规定训练集大小\n",
"Ntest = 100 # 规定测试集大小\n",
"boundary_gap = 0.5 # 设置决策边界的宽度\n",
"seed_data = 2 # 固定随机种子\n",
"\n",
"# 生成自己的数据集\n", "# 生成自己的数据集\n",
"train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain, Ntest, boundary_gap, seed_data)\n", "train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain, Ntest, boundary_gap, seed_data)\n",
"\n", "\n",
...@@ -434,7 +438,7 @@ ...@@ -434,7 +438,7 @@
}, },
"outputs": [], "outputs": [],
"source": [ "source": [
"# 构建绕Y轴，绕Z轴旋转theta角度矩阵\n", "# 构建绕 Y 轴，绕 Z 轴旋转 theta 角度矩阵\n",
"def Ry(theta):\n", "def Ry(theta):\n",
" \"\"\"\n", " \"\"\"\n",
" :param theta: 参数\n", " :param theta: 参数\n",
...@@ -466,20 +470,20 @@ ...@@ -466,20 +470,20 @@
" zero_state = np.array([[1, 0]])\n", " zero_state = np.array([[1, 0]])\n",
" # 角度编码\n", " # 角度编码\n",
" for i in range(n_qubits):\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", " # 对偶数编号量子态作用 Rz(arccos(x0^2)) Ry(arcsin(x0))\n",
" if i % 2 == 0:\n", " if i % 2 == 0:\n",
" state_tmp=np.dot(zero_state, Ry(np.arcsin(data[sam][0])).T)\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", " state_tmp=np.dot(state_tmp, Rz(np.arccos(data[sam][0] ** 2)).T)\n",
" res_state=np.kron(res_state, state_tmp)\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", " # 对奇数编号量子态作用 Rz(arccos(x1^2)) Ry(arcsin(x1))\n",
" elif i % 2 == 1:\n", " elif i % 2 == 1:\n",
" state_tmp=np.dot(zero_state, Ry(np.arcsin(data[sam][1])).T)\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", " 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_state=np.kron(res_state, state_tmp)\n",
" res.append(res_state)\n", " res.append(res_state)\n",
"\n",
" res = np.array(res)\n", " res = np.array(res)\n",
" return res.astype(\"complex128\")\n" "\n",
" return res.astype(\"complex128\")"
] ]
}, },
{ {
...@@ -573,7 +577,7 @@ ...@@ -573,7 +577,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 13,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-03-02T09:15:06.795398Z", "end_time": "2021-03-02T09:15:06.795398Z",
...@@ -592,7 +596,7 @@ ...@@ -592,7 +596,7 @@
" \"\"\"\n", " \"\"\"\n",
" # 初始化网络\n", " # 初始化网络\n",
" cir = UAnsatz(n)\n", " cir = UAnsatz(n)\n",
" \n", "\n",
" # 先搭建广义的旋转层\n", " # 先搭建广义的旋转层\n",
" for i in range(n):\n", " for i in range(n):\n",
" cir.rz(theta[i][0], i)\n", " cir.rz(theta[i][0], i)\n",
...@@ -699,7 +703,7 @@ ...@@ -699,7 +703,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 9, "execution_count": 8,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-03-02T09:15:07.667491Z", "end_time": "2021-03-02T09:15:07.667491Z",
...@@ -716,12 +720,13 @@ ...@@ -716,12 +720,13 @@
" :return: 局部可观测量: Z \\otimes I \\otimes ...\\otimes I\n", " :return: 局部可观测量: Z \\otimes I \\otimes ...\\otimes I\n",
" \"\"\"\n", " \"\"\"\n",
" Ob = pauli_str_to_matrix([[1.0, 'z0']], n)\n", " Ob = pauli_str_to_matrix([[1.0, 'z0']], n)\n",
"\n",
" return Ob" " return Ob"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 10, "execution_count": 9,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -735,7 +740,6 @@ ...@@ -735,7 +740,6 @@
" super(Opt_Classifier, self).__init__()\n", " super(Opt_Classifier, self).__init__()\n",
" self.n = n\n", " self.n = n\n",
" self.depth = depth\n", " self.depth = depth\n",
" \n",
" # 初始化参数列表 theta，并用 [0, 2*pi] 的均匀分布来填充初始值\n", " # 初始化参数列表 theta，并用 [0, 2*pi] 的均匀分布来填充初始值\n",
" self.theta = self.create_parameter(\n", " self.theta = self.create_parameter(\n",
" shape=[n, depth + 3], # 此处使用量子电路有初始一层广义旋转门，故+3\n", " shape=[n, depth + 3], # 此处使用量子电路有初始一层广义旋转门，故+3\n",
...@@ -759,22 +763,22 @@ ...@@ -759,22 +763,22 @@
" \"\"\"\n", " \"\"\"\n",
" # 将 Numpy array 转换成 tensor\n", " # 将 Numpy array 转换成 tensor\n",
" Ob = paddle.to_tensor(Observable(self.n))\n", " Ob = paddle.to_tensor(Observable(self.n))\n",
" label_pp = paddle.to_tensor(label)\n", " label_pp = reshape(paddle.to_tensor(label), [-1, 1])\n",
"\n", "\n",
" # 按照随机初始化的参数 theta \n", " # 按照随机初始化的参数 theta \n",
" cir = cir_Classifier(self.theta, n=self.n, depth=self.depth)\n", " cir = cir_Classifier(self.theta, n=self.n, depth=self.depth)\n",
" Utheta = cir.U\n", " Utheta = cir.U\n",
" \n", "\n",
" # 因为 Utheta是学习到的，我们这里用行向量运算来提速而不会影响训练效果\n", " # 因为 Utheta是学习到的，我们这里用行向量运算来提速而不会影响训练效果\n",
" state_out = matmul(state_in, Utheta) # [-1, 1, 2 ** n]形式，第一个参数在此教程中为BATCH\n", " state_out = matmul(state_in, Utheta) # [-1, 1, 2 ** n]形式，第一个参数在此教程中为BATCH\n",
" \n", "\n",
" # 测量得到泡利 Z 算符的期望值 <Z> -- shape [-1,1,1]\n", " # 测量得到泡利 Z 算符的期望值 <Z> -- shape [-1,1,1]\n",
" E_Z = matmul(matmul(state_out, Ob), transpose(paddle.conj(state_out), perm=[0, 2, 1]))\n", " E_Z = matmul(matmul(state_out, Ob), transpose(paddle.conj(state_out), perm=[0, 2, 1]))\n",
" \n", "\n",
" # 映射 <Z> 处理成标签的估计值 \n", " # 映射 <Z> 处理成标签的估计值 \n",
" state_predict = paddle.real(E_Z)[:, 0] * 0.5 + 0.5 + self.bias # 计算每一个y^{i,k}与真实值得平方差\n", " state_predict = paddle.real(E_Z)[:, 0] * 0.5 + 0.5 + self.bias # 计算每一个y^{i,k}与真实值得平方差\n",
" loss = paddle.mean((state_predict - label_pp) ** 2) # 对BATCH个得到的平方差取平均，得到L_i：shape:[1,1]\n", " loss = paddle.mean((state_predict - label_pp) ** 2) # 对BATCH个得到的平方差取平均，得到L_i：shape:[1,1]\n",
" \n", "\n",
" # 计算交叉验证正确率\n", " # 计算交叉验证正确率\n",
" is_correct = (paddle.abs(state_predict - label_pp) < 0.5).nonzero().shape[0]\n", " is_correct = (paddle.abs(state_predict - label_pp) < 0.5).nonzero().shape[0]\n",
" acc = is_correct / label.shape[0]\n", " acc = is_correct / label.shape[0]\n",
...@@ -842,7 +846,7 @@ ...@@ -842,7 +846,7 @@
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"def QClassifier(Ntrain, Ntest, gap, N, DEPTH, EPOCH, LR, BATCH, seed_paras, seed_data,):\n", "def QClassifier(Ntrain, Ntest, gap, N, DEPTH, EPOCH, LR, BATCH, seed_paras, seed_data):\n",
" \"\"\"\n", " \"\"\"\n",
" 量子二分类器\n", " 量子二分类器\n",
" 输入参数：\n", " 输入参数：\n",
...@@ -861,7 +865,7 @@ ...@@ -861,7 +865,7 @@
" train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain=Ntrain, Ntest=Ntest, boundary_gap=gap, seed_data=seed_data)\n", " train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain=Ntrain, Ntest=Ntest, boundary_gap=gap, seed_data=seed_data)\n",
" # 读取训练集的维度\n", " # 读取训练集的维度\n",
" N_train = train_x.shape[0]\n", " N_train = train_x.shape[0]\n",
" \n", "\n",
" paddle.seed(seed_paras)\n", " paddle.seed(seed_paras)\n",
" # 初始化寄存器存储正确率 acc 等信息\n", " # 初始化寄存器存储正确率 acc 等信息\n",
" summary_iter, summary_test_acc = [], []\n", " summary_iter, summary_test_acc = [], []\n",
...@@ -904,7 +908,7 @@ ...@@ -904,7 +908,7 @@
" loss.backward()\n", " loss.backward()\n",
" opt.minimize(loss)\n", " opt.minimize(loss)\n",
" opt.clear_grad()\n", " opt.clear_grad()\n",
" \n", "\n",
" # 得到训练后电路\n", " # 得到训练后电路\n",
" print(\"训练后的电路：\")\n", " print(\"训练后的电路：\")\n",
" print(cir)\n", " print(cir)\n",
...@@ -960,7 +964,7 @@ ...@@ -960,7 +964,7 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"主程序段总共运行了 7.24103569984436 秒\n" "主程序段总共运行了 6.890974283218384 秒\n"
] ]
} }
], ],
...@@ -998,6 +1002,379 @@ ...@@ -998,6 +1002,379 @@
"通过打印训练结果可以看到不断优化后分类器在测试集和数据集的正确率都达到了 $100\\%$。" "通过打印训练结果可以看到不断优化后分类器在测试集和数据集的正确率都达到了 $100\\%$。"
] ]
}, },
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 研究不同的编码方式\n",
"\n",
"监督学习的编码方式对分类结果有很大影响 [4]。在量桨中，我们集成了常用的编码方式，包括振幅编码、角度编码、IQP编码等。 用户可以用内置的 ``SimpleDataset`` 类实例对简单分类数据（不需要降维的数据）进行编码；也可以用内置的 ``VisionDataset`` 类实例对图片数据进行编码。编码的方法都是调用类对象的 ``encode`` 方法。"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'numpy.ndarray'>\n",
"(100, 4)\n"
]
}
],
"source": [
"# 使用前面构建的圆形数据集研究编码\n",
"from paddle_quantum.dataset import *\n",
"\n",
"# 用两个量子比特编码二维数据\n",
"quantum_train_x = SimpleDataset(2).encode(train_x, 'angle_encoding', 2)\n",
"quantum_test_x = SimpleDataset(2).encode(test_x, 'angle_encoding', 2)\n",
"\n",
"print(type(quantum_test_x)) # ndarray\n",
"print(quantum_test_x.shape) # (100, 4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"这里我们对上面的分类器进行化简，之后的所有分类都采用这个分类器。"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [],
"source": [
"# 简化的分类器\n",
"def QClassifier2(quantum_train_x, train_y,quantum_test_x,test_y, N, DEPTH, EPOCH, LR, BATCH):\n",
" \"\"\"\n",
" 量子二分类分类器\n",
" 输入：\n",
" quantum_train_x # 训练特征\n",
" train_y # 训练标签\n",
" quantum_test_x # 测试特征\n",
" test_y # 测试标签\n",
" N # 使用的量子比特数目\n",
" DEPTH # 分类器电路的深度\n",
" EPOCH # 迭代次数\n",
" LR # 学习率\n",
" 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",
" # 测试准确率列表\n",
" summary_iter, summary_test_acc = [], []\n",
"\n",
" # 这里用 Adam，但是也可以是 SGD 或者 RMSprop\n",
" opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())\n",
"\n",
" # 进行优化\n",
" for ep in range(EPOCH):\n",
" for itr in range(Ntrain // BATCH):\n",
" # 导入数据\n",
" input_state = quantum_train_x[itr * BATCH:(itr + 1) * BATCH] # paddle.tensor类型\n",
" input_state = reshape(input_state, [-1, 1, 2 ** N])\n",
" label = train_y[itr * BATCH:(itr + 1) * BATCH]\n",
" test_input_state = reshape(quantum_test_x, [-1, 1, 2 ** N])\n",
"\n",
" loss, train_acc, state_predict_useless, cir = net(state_in=input_state, label=label)\n",
"\n",
" if itr % 5 == 0:\n",
" # 获取测试准确率\n",
" loss_useless, test_acc, state_predict_useless, t_cir = net(state_in=test_input_state, label=test_y)\n",
" print(\"epoch:\", ep, \"iter:\", itr,\n",
" \"loss: %.4f\" % loss.numpy(),\n",
" \"train acc: %.4f\" % train_acc,\n",
" \"test acc: %.4f\" % test_acc)\n",
" summary_test_acc.append(test_acc)\n",
"\n",
" loss.backward()\n",
" opt.minimize(loss)\n",
" opt.clear_grad()\n",
"\n",
" return summary_test_acc"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"现在可以开始用不同编码方式对上面产生的圆形数据进行编码。这里我们采用五种编码方法：振幅编码、角度编码、泡利旋转编码、IQP编码、复杂纠缠编码。然后我们绘制出测试精度曲线以便分析。"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Encoding method: amplitude_encoding\n",
"epoch: 0 iter: 0 loss: 0.3066 train acc: 0.4000 test acc: 0.5400\n",
"epoch: 0 iter: 5 loss: 0.2378 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 10 loss: 0.2308 train acc: 0.8000 test acc: 0.6700\n",
"epoch: 0 iter: 15 loss: 0.2230 train acc: 0.8000 test acc: 0.6100\n",
"Encoding method: angle_encoding\n",
"epoch: 0 iter: 0 loss: 0.2949 train acc: 0.5000 test acc: 0.3600\n",
"epoch: 0 iter: 5 loss: 0.1770 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 10 loss: 0.1654 train acc: 0.8000 test acc: 0.7000\n",
"epoch: 0 iter: 15 loss: 0.1966 train acc: 0.7000 test acc: 0.5800\n",
"Encoding method: pauli_rotation_encoding\n",
"epoch: 0 iter: 0 loss: 0.2433 train acc: 0.6000 test acc: 0.7000\n",
"epoch: 0 iter: 5 loss: 0.2142 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 10 loss: 0.2148 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 15 loss: 0.2019 train acc: 0.8000 test acc: 0.7600\n",
"Encoding method: IQP_encoding\n",
"epoch: 0 iter: 0 loss: 0.2760 train acc: 0.6000 test acc: 0.4200\n",
"epoch: 0 iter: 5 loss: 0.1916 train acc: 0.6000 test acc: 0.6200\n",
"epoch: 0 iter: 10 loss: 0.1355 train acc: 0.9000 test acc: 0.7300\n",
"epoch: 0 iter: 15 loss: 0.1289 train acc: 0.9000 test acc: 0.6700\n",
"Encoding method: complex_entangled_encoding\n",
"epoch: 0 iter: 0 loss: 0.3274 train acc: 0.3000 test acc: 0.2900\n",
"epoch: 0 iter: 5 loss: 0.2120 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 10 loss: 0.2237 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 15 loss: 0.2095 train acc: 0.8000 test acc: 0.7200\n"
]
}
],
"source": [
"# 测试不同编码方式\n",
"encoding_list = ['amplitude_encoding', 'angle_encoding', 'pauli_rotation_encoding', 'IQP_encoding', 'complex_entangled_encoding']\n",
"num_qubit = 2 # 这里需要小心，如果量子比特数目取 1，可能会报错，因为有 CNOT 门\n",
"dimension = 2\n",
"acc_list = []\n",
"\n",
"for i in range(len(encoding_list)):\n",
" encoding = encoding_list[i]\n",
" print(\"Encoding method:\", encoding)\n",
" # 用 SimpleDataset 类来编码数据，这里数据维度为 2，编码量子比特数目也是 2\n",
" quantum_train_x= SimpleDataset(dimension).encode(train_x, encoding, num_qubit)\n",
" quantum_test_x= SimpleDataset(dimension).encode(test_x, encoding, num_qubit)\n",
" quantum_train_x = paddle.to_tensor(quantum_train_x)\n",
" quantum_test_x = paddle.to_tensor(quantum_test_x)\n",
"\n",
" acc = QClassifier2(\n",
" quantum_train_x, # 训练特征\n",
" train_y, # 训练标签\n",
" quantum_test_x, # 测试特征\n",
" test_y, # 测试标签\n",
" N = num_qubit, # 使用的量子比特数目\n",
" DEPTH = 1, # 分类器电路的深度\n",
" EPOCH = 1, # 迭代次数\n",
" LR = 0.1, # 学习率\n",
" BATCH = 10, # 一个批量的大小\n",
" )\n",
" acc_list.append(acc)"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# 绘制五种编码方法的训练曲线\n",
"x=[2*i for i in range(len(acc_list[0]))]\n",
"for i in range(len(encoding_list)):\n",
" plt.plot(x,acc_list[i])\n",
"plt.legend(encoding_list)\n",
"plt.title(\"Benchmarking different encoding methods\")\n",
"plt.xlabel(\"Iteration\")\n",
"plt.ylabel(\"Test accuracy\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## 用内置的 MNIST 和 Iris 数据集实现量子分类\n",
"\n",
"量桨将常用的分类数据集进行了编码，用户可以使用 `paddle_quantum.dataset` 模块获取编码的量子电路或者量子态。目前集成了4个数据集，包括 MNIST, FashionMNIST, Iris 和 BreastCancer。下面展示如何用这些内置数据集快速实现量子监督学习。\n",
"\n",
"我们从 Iris 数据集开始。Iris 数据集包括三种类别，每种类别有50个样本。数据集中只有四个特征，是比较简单且容易编码的数据集。"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"epoch: 0 iter: 0 loss: 0.3543 train acc: 0.0000 test acc: 0.0000\n",
"epoch: 0 iter: 5 loss: 0.2697 train acc: 0.5000 test acc: 0.5000\n",
"epoch: 0 iter: 10 loss: 0.2139 train acc: 1.0000 test acc: 0.9000\n",
"epoch: 0 iter: 15 loss: 0.1989 train acc: 0.7500 test acc: 0.9000\n",
"epoch: 1 iter: 0 loss: 0.0859 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 1 iter: 5 loss: 0.0432 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 1 iter: 10 loss: 0.0432 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 1 iter: 15 loss: 0.0531 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 2 iter: 0 loss: 0.0374 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 2 iter: 5 loss: 0.0356 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 2 iter: 10 loss: 0.0377 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 2 iter: 15 loss: 0.0440 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 3 iter: 0 loss: 0.0317 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 3 iter: 5 loss: 0.0344 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 3 iter: 10 loss: 0.0384 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 3 iter: 15 loss: 0.0412 train acc: 1.0000 test acc: 1.0000\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Iris 数据集二分类\n",
"\n",
"test_rate=0.2\n",
"num_qubit=4\n",
"\n",
"# 获取 Iris 数据集的量子态\n",
"iris =Iris (encoding='angle_encoding', num_qubits=num_qubit, test_rate=test_rate,classes=[0, 1], return_state=True)\n",
"\n",
"quantum_train_x, train_y = iris.train_x, iris.train_y\n",
"quantum_test_x, test_y = iris.test_x, iris.test_y\n",
"testing_data_num = len(test_y)\n",
"training_data_num = len(train_y)\n",
"\n",
"acc = QClassifier2(\n",
" quantum_train_x, # 训练特征\n",
" train_y, # 训练标签\n",
" quantum_test_x, # 测试特征\n",
" test_y, # 测试标签\n",
" N = num_qubit, # 使用的量子比特数目\n",
" DEPTH = 1, # 分类器电路的深度\n",
" EPOCH = 4, # 迭代次数\n",
" LR = 0.1, # 学习率\n",
" BATCH = 4, # 一个批量的大小\n",
" )\n",
"plt.plot(acc)\n",
"plt.title(\"Classify Iris 0&1 using angle encoding\")\n",
"plt.xlabel(\"Iteration\")\n",
"plt.ylabel(\"Testing accuracy\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"第二个例子为 MNIST 数据集。 MNIST 是手写数字数据集，有 0-9 十个类别（每一类训练集中有 6000 个样本，测试集中有 1000 个样本）。所有的图片都是 $28\\times28$ 的灰度图，所以需要使用 ``resize`` 或 ``PCA`` 降维到目标维度 ``target_dimension`` 。"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"epoch: 0 iter: 0 loss: 0.3237 train acc: 0.3250 test acc: 0.5450\n",
"epoch: 0 iter: 5 loss: 0.2124 train acc: 0.7500 test acc: 0.6500\n",
"epoch: 0 iter: 10 loss: 0.2294 train acc: 0.6500 test acc: 0.6850\n",
"epoch: 1 iter: 0 loss: 0.1970 train acc: 0.7250 test acc: 0.7850\n",
"epoch: 1 iter: 5 loss: 0.1521 train acc: 0.8500 test acc: 0.8150\n",
"epoch: 1 iter: 10 loss: 0.1726 train acc: 0.7750 test acc: 0.8900\n",
"epoch: 2 iter: 0 loss: 0.1742 train acc: 0.7250 test acc: 0.8650\n",
"epoch: 2 iter: 5 loss: 0.1167 train acc: 0.9000 test acc: 0.8900\n",
"epoch: 2 iter: 10 loss: 0.1654 train acc: 0.8000 test acc: 0.8950\n",
"epoch: 3 iter: 0 loss: 0.1609 train acc: 0.8000 test acc: 0.8850\n",
"epoch: 3 iter: 5 loss: 0.1148 train acc: 0.9250 test acc: 0.8850\n",
"epoch: 3 iter: 10 loss: 0.1649 train acc: 0.8000 test acc: 0.8750\n",
"epoch: 4 iter: 0 loss: 0.1629 train acc: 0.8250 test acc: 0.8750\n",
"epoch: 4 iter: 5 loss: 0.1112 train acc: 0.9000 test acc: 0.8700\n",
"epoch: 4 iter: 10 loss: 0.1630 train acc: 0.8500 test acc: 0.8850\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# 使用 MNIST 进行分类\n",
"\n",
"# 主要参数\n",
"training_data_num = 500\n",
"testing_data_num = 200\n",
"qubit_num = 4\n",
"\n",
"# 选择3和6两个类，将 MNIST 从 28*28 重采样为 4*4，再用振幅编码方式进行编码 \n",
"train_dataset = MNIST(mode='train', encoding='amplitude_encoding', num_qubits=qubit_num, classes=[3,6],\n",
" data_num=training_data_num,need_cropping=True,\n",
" downscaling_method='resize', target_dimension=16, return_state=True)\n",
"\n",
"val_dataset = MNIST(mode='test', encoding='amplitude_encoding', num_qubits=qubit_num, classes=[3,6],\n",
" data_num=testing_data_num,need_cropping=True,\n",
" downscaling_method='resize', target_dimension=16,return_state=True)\n",
"\n",
"quantum_train_x, train_y = train_dataset.quantum_image_states, train_dataset.labels\n",
"quantum_test_x, test_y = val_dataset.quantum_image_states, val_dataset.labels\n",
"\n",
"acc = QClassifier2(\n",
" quantum_train_x, # 训练特征\n",
" train_y, # 训练标签\n",
" quantum_test_x, # 测试特征\n",
" test_y, # 测试标签\n",
" N = num_qubit, # 使用的量子比特数目\n",
" DEPTH = 3, # 分类器电路的深度\n",
" EPOCH = 5, # 迭代次数\n",
" LR = 0.1, # 学习率\n",
" BATCH = 40, # 一个批量的大小\n",
" )\n",
"plt.plot(acc)\n",
"plt.title(\"Classify MNIST 3&6 using amplitude encoding\")\n",
"plt.xlabel(\"Iteration\")\n",
"plt.ylabel(\"Testing accuracy\")\n",
"plt.show()"
]
},
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
...@@ -1010,7 +1387,9 @@ ...@@ -1010,7 +1387,9 @@
"\n", "\n",
"[2] Farhi, Edward, and Hartmut Neven. Classification with quantum neural networks on near term processors. [arXiv preprint arXiv:1802.06002 (2018).](https://arxiv.org/abs/1802.06002)\n", "[2] Farhi, Edward, and Hartmut Neven. Classification with quantum neural networks on near term processors. [arXiv preprint arXiv:1802.06002 (2018).](https://arxiv.org/abs/1802.06002)\n",
"\n", "\n",
"[3] Schuld, Maria, et al. Circuit-centric quantum classifiers. [Physical Review A 101.3 (2020): 032308.](https://arxiv.org/abs/1804.00633)" "[3] Schuld, Maria, et al. Circuit-centric quantum classifiers. [Physical Review A 101.3 (2020): 032308.](https://arxiv.org/abs/1804.00633)\n",
"\n",
"[4] Schuld, Maria. Supervised quantum machine learning models are kernel methods. [arXiv preprint arXiv:2101.11020 (2021).](https://arxiv.org/pdf/2101.11020)"
] ]
} }
], ],
...@@ -1030,7 +1409,7 @@ ...@@ -1030,7 +1409,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.7.11" "version": "3.8.12"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/machine_learning/QClassifier_EN.ipynb
浏览文件 @ 016af983
...@@ -15,7 +15,7 @@ ...@@ -15,7 +15,7 @@
"source": [ "source": [
"## Overview\n", "## Overview\n",
"\n", "\n",
"In this tutorial, we will discuss the workflow of Variational Quantum Classifiers (VQC) and how to use quantum neural networks (QNN) to accomplish a **binary classification** task. The main representatives of this approach include the [Quantum Circuit Learning (QCL)](https://arxiv.org/abs/1803.00745) [1] by Mitarai et al. (2018), Farhi & Neven ( 2018) [2] and [Circuit-Centric Quantum Classifiers](https://arxiv.org/abs/1804.00633) [3] by Schuld et al. (2018). Here, we mainly talk about classification in the language of supervised learning. Unlike classical methods, quantum classifiers require pre-processing to encode classical data into quantum data, and then train the parameters in the quantum neural network. Finally, we benchmark the optimal classification performance through test data.\n", "In this tutorial, we will discuss the workflow of Variational Quantum Classifiers (VQC) and how to use quantum neural networks (QNN) to accomplish a **binary classification** task. The main representatives of this approach include the [Quantum Circuit Learning (QCL)](https://arxiv.org/abs/1803.00745) [1] by Mitarai et al. (2018), Farhi & Neven (2018) [2] and [Circuit-Centric Quantum Classifiers](https://arxiv.org/abs/1804.00633) [3] by Schuld et al. (2018). Here, we mainly talk about classification in the language of supervised learning. Unlike classical methods, quantum classifiers require pre-processing to encode classical data into quantum data, and then train the parameters in the quantum neural network. Using different encoding methods, we can benchmark the optimal classification performance through test data. Finally, we demonstrate how to use built-in quantum datasets to accomplish quantum classification.\n",
"\n", "\n",
"### Background\n", "### Background\n",
"\n", "\n",
...@@ -53,7 +53,16 @@ ...@@ -53,7 +53,16 @@
"cell_type": "code", "cell_type": "code",
"execution_count": 1, "execution_count": 1,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\yeruilin\\Anaconda3\\envs\\paddle_quantum_env\\lib\\site-packages\\matplotlib_inline\\config.py:66: DeprecationWarning: InlineBackend._figure_formats_changed is deprecated in traitlets 4.1: use @observe and @unobserve instead.\n",
" def _figure_formats_changed(self, name, old, new):\n"
]
}
],
"source": [ "source": [
"# Import numpy and paddle\n", "# Import numpy and paddle\n",
"import numpy as np\n", "import numpy as np\n",
...@@ -63,8 +72,8 @@ ...@@ -63,8 +72,8 @@
"from paddle_quantum.circuit import UAnsatz\n", "from paddle_quantum.circuit import UAnsatz\n",
"# Some functions\n", "# Some functions\n",
"from numpy import pi as PI\n", "from numpy import pi as PI\n",
"from paddle import matmul, transpose # paddle matrix multiplication and transpose\n", "from paddle import matmul, transpose, reshape # paddle matrix multiplication and transpose\n",
"from paddle_quantum.utils import pauli_str_to_matrix,dagger # N qubits Pauli matrix, complex conjugate\n", "from paddle_quantum.utils import pauli_str_to_matrix, dagger # N qubits Pauli matrix, complex conjugate\n",
"\n", "\n",
"# Plot figures, calculate the run time\n", "# Plot figures, calculate the run time\n",
"from matplotlib import pyplot as plt\n", "from matplotlib import pyplot as plt\n",
...@@ -84,17 +93,19 @@ ...@@ -84,17 +93,19 @@
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
"# Parameters for generating the data set\n",
"Ntrain = 200 # Specify the training set size\n", "Ntrain = 200 # Specify the training set size\n",
"Ntest = 100 # Specify the test set size\n", "Ntest = 100 # Specify the test set size\n",
"gap = 0.5 # Set the width of the decision boundary\n", "boundary_gap = 0.5 # Set the width of the decision boundary\n",
"seed_data = 2 # Fixed random seed required to generate the data set\n",
"# Parameters for training\n",
"N = 4 # Number of qubits required\n", "N = 4 # Number of qubits required\n",
"DEPTH = 1 # Circuit depth\n", "DEPTH = 1 # Circuit depth\n",
"BATCH = 20 # Batch size during training\n", "BATCH = 20 # Batch size during training\n",
"EPOCH = int(200 * BATCH / Ntrain)\n", "EPOCH = int(200 * BATCH / Ntrain)\n",
" # Number of training epochs, the total iteration number \"EPOCH * (Ntrain / BATCH)\" is chosen to be about 200\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", "LR = 0.01 # Set the learning rate\n",
"seed_paras = 19 # Set random seed to initialize various parameters\n", "seed_paras = 19 # Set random seed to initialize various parameters"
"seed_data = 2 # Fixed random seed required to generate the data set\n"
] ]
}, },
{ {
...@@ -167,7 +178,7 @@ ...@@ -167,7 +178,7 @@
" print(\"The dimensions of the training set x {} and y {}\".format(np.shape(train_x[0:Ntrain]), np.shape(train_y[0:Ntrain])))\n", " print(\"The dimensions of the training set x {} and y {}\".format(np.shape(train_x[0:Ntrain]), np.shape(train_y[0:Ntrain])))\n",
" print(\"The dimensions of the test set x {} and y {}\".format(np.shape(train_x[Ntrain:]), np.shape(train_y[Ntrain:])), \"\\n\")\n", " print(\"The dimensions of the test set x {} and y {}\".format(np.shape(train_x[Ntrain:]), np.shape(train_y[Ntrain:])), \"\\n\")\n",
"\n", "\n",
" return train_x[0:Ntrain], train_y[0:Ntrain], train_x[Ntrain:], train_y[Ntrain:]\n" " return train_x[0:Ntrain], train_y[0:Ntrain], train_x[Ntrain:], train_y[Ntrain:]"
] ]
}, },
{ {
...@@ -228,7 +239,7 @@ ...@@ -228,7 +239,7 @@
}, },
{ {
"data": { "data": {
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", 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",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -247,7 +258,7 @@ ...@@ -247,7 +258,7 @@
}, },
{ {
"data": { "data": {
"image/png": 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", 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",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 432x288 with 1 Axes>"
] ]
...@@ -267,12 +278,6 @@ ...@@ -267,12 +278,6 @@
} }
], ],
"source": [ "source": [
"# Set parameters\n",
"Ntrain = 200 # Specify the training set size\n",
"Ntest = 100 # Specify the test set size\n",
"boundary_gap = 0.5 # Set the width of the decision boundary\n",
"seed_data = 2 # Fixed random seed\n",
"\n",
"# Generate data set\n", "# Generate data set\n",
"train_x, train_y, test_x, test_y = circle_data_point_generator(\n", "train_x, train_y, test_x, test_y = circle_data_point_generator(\n",
" Ntrain, Ntest, boundary_gap, seed_data)\n", " Ntrain, Ntest, boundary_gap, seed_data)\n",
...@@ -463,9 +468,9 @@ ...@@ -463,9 +468,9 @@
" state_tmp=np.dot(state_tmp, Rz(np.arccos(data[sam][1] ** 2)).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_state=np.kron(res_state, state_tmp)\n",
" res.append(res_state)\n", " res.append(res_state)\n",
"\n",
" res = np.array(res)\n", " res = np.array(res)\n",
" return res.astype(\"complex128\")\n" "\n",
" return res.astype(\"complex128\")"
] ]
}, },
{ {
...@@ -509,7 +514,7 @@ ...@@ -509,7 +514,7 @@
"<center> Figure 3: Parameterized Quantum Circuit </center>\n", "<center> Figure 3: Parameterized Quantum Circuit </center>\n",
"\n", "\n",
"\n", "\n",
"For convenience, we call the parameterized quantum neural network as $U(\\boldsymbol{\\theta})$. $U(\\boldsymbol{\\theta})$ is a key component of our classifier, and it needs a certain complex structure to fit our decision boundary. Similar to traditional neural networks, the structure of a quantum neural network is not unique. The structure shown above is just one case. You could design your own structure. Let’s take the previously mentioned data point $x = (x_0, x_1)= (1,0)$ as an example. After encoding, we have obtained a quantum state $|\\psi_{\\rm in}\\rangle$,\n", "For convenience, we call the parameterized quantum neural network as $U(\\boldsymbol{\\theta})$. $U(\\boldsymbol{\\theta})$ is a key component of our classifier, and it needs a certain complex structure to fit our decision boundary. Similar to traditional neural networks, the structure of a quantum neural network is not unique. The structure shown above is just one case. You could design your own structure. Let's take the previously mentioned data point $x = (x_0, x_1)= (1,0)$ as an example. After encoding, we have obtained a quantum state $|\\psi_{\\rm in}\\rangle$,\n",
"\n", "\n",
"$$\n", "$$\n",
"|\\psi_{\\rm in}\\rangle =\n", "|\\psi_{\\rm in}\\rangle =\n",
...@@ -562,7 +567,7 @@ ...@@ -562,7 +567,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 11,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-03-09T04:03:37.426687Z", "end_time": "2021-03-09T04:03:37.426687Z",
...@@ -572,7 +577,7 @@ ...@@ -572,7 +577,7 @@
"outputs": [], "outputs": [],
"source": [ "source": [
"# Simulation of building a quantum neural network\n", "# Simulation of building a quantum neural network\n",
"def cir_Classifier(theta, n, depth): \n", "def cir_Classifier(theta, n, depth):\n",
" \"\"\"\n", " \"\"\"\n",
" :param theta: dim: [n, depth + 3], \"+3\" because we add an initial generalized rotation gate to each qubit\n", " :param theta: dim: [n, depth + 3], \"+3\" because we add an initial generalized rotation gate to each qubit\n",
" :param n: number of qubits\n", " :param n: number of qubits\n",
...@@ -599,7 +604,7 @@ ...@@ -599,7 +604,7 @@
" for i in range(n):\n", " for i in range(n):\n",
" cir.ry(theta[i][d], i)\n", " cir.ry(theta[i][d], i)\n",
"\n", "\n",
" return cir\n" " return cir"
] ]
}, },
{ {
...@@ -677,6 +682,7 @@ ...@@ -677,6 +682,7 @@
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Loss function\n", "### Loss function\n",
"\n",
"To calculate the loss function in Eq. (1), we need to measure all training data in each iteration. In real practice, we devide the training data into \"Ntrain/BATCH\" groups, where each group contains \"BATCH\" data pairs.\n", "To calculate the loss function in Eq. (1), we need to measure all training data in each iteration. In real practice, we devide the training data into \"Ntrain/BATCH\" groups, where each group contains \"BATCH\" data pairs.\n",
"\n", "\n",
"The loss function for the i-th group is \n", "The loss function for the i-th group is \n",
...@@ -690,7 +696,7 @@ ...@@ -690,7 +696,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 9, "execution_count": 6,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-03-09T04:03:37.439183Z", "end_time": "2021-03-09T04:03:37.439183Z",
...@@ -707,12 +713,13 @@ ...@@ -707,12 +713,13 @@
" :return: local observable: Z \\otimes I \\otimes ...\\otimes I\n", " :return: local observable: Z \\otimes I \\otimes ...\\otimes I\n",
" \"\"\"\n", " \"\"\"\n",
" Ob = pauli_str_to_matrix([[1.0,'z0']], n)\n", " Ob = pauli_str_to_matrix([[1.0,'z0']], n)\n",
"\n",
" return Ob" " return Ob"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 10, "execution_count": 7,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-03-09T04:03:37.503213Z", "end_time": "2021-03-09T04:03:37.503213Z",
...@@ -731,7 +738,6 @@ ...@@ -731,7 +738,6 @@
" super(Opt_Classifier, self).__init__()\n", " super(Opt_Classifier, self).__init__()\n",
" self.n = n\n", " self.n = n\n",
" self.depth = depth\n", " self.depth = depth\n",
" \n",
" # Initialize the parameters theta with a uniform distribution of [0, 2*pi]\n", " # Initialize the parameters theta with a uniform distribution of [0, 2*pi]\n",
" self.theta = self.create_parameter(\n", " self.theta = self.create_parameter(\n",
" shape=[n, depth + 3], # \"+3\" because we add an initial generalized rotation gate to each qubit\n", " shape=[n, depth + 3], # \"+3\" because we add an initial generalized rotation gate to each qubit\n",
...@@ -757,28 +763,27 @@ ...@@ -757,28 +763,27 @@
" \"\"\"\n", " \"\"\"\n",
" # Convert Numpy array to tensor\n", " # Convert Numpy array to tensor\n",
" Ob = paddle.to_tensor(Observable(self.n))\n", " Ob = paddle.to_tensor(Observable(self.n))\n",
" label_pp = paddle.to_tensor(label)\n", " label_pp = reshape(paddle.to_tensor(label), [-1, 1])\n",
"\n", "\n",
" # Build the quantum circuit\n", " # Build the quantum circuit\n",
" cir = cir_Classifier(self.theta, n=self.n, depth=self.depth)\n", " cir = cir_Classifier(self.theta, n=self.n, depth=self.depth)\n",
" Utheta = cir.U\n", " Utheta = cir.U\n",
" \n", "\n",
" # Because Utheta is achieved by learning, we compute with row vectors to speed up without affecting the training effect\n", " # Because Utheta is achieved by learning, we compute with row vectors to speed up without affecting the training effect\n",
" state_out = matmul(state_in, Utheta) # shape:[-1, 1, 2 ** n], the first parameter is BATCH in this tutorial\n", " state_out = matmul(state_in, Utheta) # shape:[-1, 1, 2 ** n], the first parameter is BATCH in this tutorial\n",
" \n", "\n",
" # Measure the expected value of Pauli Z operator <Z> -- shape [-1,1,1]\n", " # Measure the expectation value of Pauli Z operator <Z> -- shape [-1,1,1]\n",
" E_Z = matmul(matmul(state_out, Ob), transpose(paddle.conj(state_out), perm=[0, 2, 1]))\n", " E_Z = matmul(matmul(state_out, Ob), transpose(paddle.conj(state_out), perm=[0, 2, 1]))\n",
" \n", "\n",
" # Mapping <Z> to the estimated value of the label\n", " # Mapping <Z> to the estimated value of the label\n",
" state_predict = paddle.real(E_Z)[:, 0] * 0.5 + 0.5 + self.bias # |y^{i,k} - \\tilde{y}^{i,k}|^2\n", " state_predict = paddle.real(E_Z)[:, 0] * 0.5 + 0.5 + self.bias # |y^{i,k} - \\tilde{y}^{i,k}|^2\n",
" loss = paddle.mean((state_predict - label_pp) ** 2) # Get average for \"BATCH\" |y^{i,k} - \\tilde{y}^{i,k}|^2: L_i：shape:[1,1]\n", " loss = paddle.mean((state_predict - label_pp) ** 2) # Get average for \"BATCH\" |y^{i,k} - \\tilde{y}^{i,k}|^2: L_i：shape:[1,1]\n",
" \n", "\n",
" # Calculate the accuracy of cross-validation\n", " # Calculate the accuracy of cross-validation\n",
" is_correct = (paddle.abs(state_predict - label_pp) < 0.5).nonzero().shape[0]\n", " is_correct = (paddle.abs(state_predict - label_pp) < 0.5).nonzero().shape[0]\n",
" acc = is_correct / label.shape[0]\n", " acc = is_correct / label.shape[0]\n",
"\n", "\n",
" return loss, acc, state_predict.numpy(), cir\n", " return loss, acc, state_predict.numpy(), cir"
" "
] ]
}, },
{ {
...@@ -846,10 +851,10 @@ ...@@ -846,10 +851,10 @@
}, },
"outputs": [], "outputs": [],
"source": [ "source": [
"def QClassifier(Ntrain, Ntest, gap, N, DEPTH, EPOCH, LR, BATCH, seed_paras, seed_data,):\n", "def QClassifier(Ntrain, Ntest, gap, N, DEPTH, EPOCH, LR, BATCH, seed_paras, seed_data):\n",
" \"\"\"\n", " \"\"\"\n",
" Quantum Binary Classifier\n", " Quantum Binary Classifier\n",
" Input：\n", " Input:\n",
" Ntrain # Specify the training set size\n", " Ntrain # Specify the training set size\n",
" Ntest # Specify the test set size\n", " Ntest # Specify the test set size\n",
" gap # Set the width of the decision boundary\n", " gap # Set the width of the decision boundary\n",
...@@ -860,6 +865,7 @@ ...@@ -860,6 +865,7 @@
" LR # Set the learning rate\n", " LR # Set the learning rate\n",
" seed_paras # Set random seed to initialize various parameters\n", " seed_paras # Set random seed to initialize various parameters\n",
" seed_data # Fixed random seed required to generate the data set\n", " seed_data # Fixed random seed required to generate the data set\n",
" plot_heat_map # Whether to plot heat map, default True\n",
" \"\"\"\n", " \"\"\"\n",
" # Generate data set\n", " # Generate data set\n",
" train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain=Ntrain, Ntest=Ntest, boundary_gap=gap, seed_data=seed_data)\n", " train_x, train_y, test_x, test_y = circle_data_point_generator(Ntrain=Ntrain, Ntest=Ntest, boundary_gap=gap, seed_data=seed_data)\n",
...@@ -916,7 +922,7 @@ ...@@ -916,7 +922,7 @@
" # Draw the decision boundary represented by heatmap\n", " # Draw the decision boundary represented by heatmap\n",
" heatmap_plot(myLayer, N=N)\n", " heatmap_plot(myLayer, N=N)\n",
"\n", "\n",
" return summary_test_acc\n" " return summary_test_acc"
] ]
}, },
{ {
...@@ -970,7 +976,7 @@ ...@@ -970,7 +976,7 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"The main program finished running in 7.169757127761841 seconds.\n" "The main program finished running in 8.05081820487976 seconds.\n"
] ]
} }
], ],
...@@ -996,6 +1002,7 @@ ...@@ -996,6 +1002,7 @@
" \n", " \n",
" time_span = time.time()-time_start\n", " time_span = time.time()-time_start\n",
" print('The main program finished running in ', time_span, 'seconds.')\n", " print('The main program finished running in ', time_span, 'seconds.')\n",
"\n",
"if __name__ == '__main__':\n", "if __name__ == '__main__':\n",
" main()" " main()"
] ]
...@@ -1007,6 +1014,387 @@ ...@@ -1007,6 +1014,387 @@
"By printing out the training results, you can see that the classification accuracy in the test set and the data set after continuous optimization has reached $100\\%$." "By printing out the training results, you can see that the classification accuracy in the test set and the data set after continuous optimization has reached $100\\%$."
] ]
}, },
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Benchmarking Different Encoding Methods\n",
"\n",
"Encoding methods are fundemental in supervised quantum machine learning [4]. In paddle quantum, commonly used encoding methods such as amplitude encoding, angle encoding, IQP encoding, etc., are integrated. Simple classification data of users (without reducing dimensions) can be encoded by an instance of the ``SimpleDataset`` class and image data can be encoded by an instance of the ``VisionDataset`` class both using the method ``encode``."
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"<class 'numpy.ndarray'>\n",
"(100, 4)\n"
]
}
],
"source": [
"# Use circle data above to accomplish classification\n",
"from paddle_quantum.dataset import *\n",
"\n",
"# The data are two-dimensional and are encoded by two qubits\n",
"quantum_train_x = SimpleDataset(2).encode(train_x, 'angle_encoding', 2)\n",
"quantum_test_x = SimpleDataset(2).encode(test_x, 'angle_encoding', 2)\n",
"\n",
"print(type(quantum_test_x)) # ndarray\n",
"print(quantum_test_x.shape) # (100, 4)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Here we define an ordinary classifier, and it will be used by different data afterwards."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [],
"source": [
"# A simpler classifier\n",
"def QClassifier2(quantum_train_x, train_y,quantum_test_x,test_y, N, DEPTH, EPOCH, LR, BATCH):\n",
" \"\"\"\n",
" Quantum Binary Classifier\n",
" Input：\n",
" quantum_train_x # training x\n",
" train_y # training y\n",
" quantum_test_x # testing x\n",
" test_y # testing y\n",
" N # Number of qubits required\n",
" DEPTH # Circuit depth\n",
" EPOCH # Number of training epochs\n",
" LR # Set the learning rate\n",
" BATCH # Batch size during training\n",
" \"\"\"\n",
" Ntrain = len(quantum_train_x)\n",
" \n",
" paddle.seed(1)\n",
"\n",
" net = Opt_Classifier(n=N, depth=DEPTH)\n",
"\n",
" # Test accuracy list\n",
" summary_iter, summary_test_acc = [], []\n",
"\n",
" # Adam can also be replaced by SGD or RMSprop\n",
" opt = paddle.optimizer.Adam(learning_rate=LR, parameters=net.parameters())\n",
"\n",
" # Optimize\n",
" for ep in range(EPOCH):\n",
" for itr in range(Ntrain // BATCH):\n",
" # Import data\n",
" input_state = quantum_train_x[itr * BATCH:(itr + 1) * BATCH] # paddle.tensor\n",
" input_state = reshape(input_state, [-1, 1, 2 ** N])\n",
" label = train_y[itr * BATCH:(itr + 1) * BATCH]\n",
" test_input_state = reshape(quantum_test_x, [-1, 1, 2 ** N])\n",
"\n",
" loss, train_acc, state_predict_useless, cir = net(state_in=input_state, label=label)\n",
"\n",
" if itr % 5 == 0:\n",
" # get accuracy on test dataset (test_acc)\n",
" loss_useless, test_acc, state_predict_useless, t_cir = net(state_in=test_input_state, label=test_y)\n",
" print(\"epoch:\", ep, \"iter:\", itr,\n",
" \"loss: %.4f\" % loss.numpy(),\n",
" \"train acc: %.4f\" % train_acc,\n",
" \"test acc: %.4f\" % test_acc)\n",
" summary_test_acc.append(test_acc)\n",
"\n",
" loss.backward()\n",
" opt.minimize(loss)\n",
" opt.clear_grad()\n",
"\n",
" return summary_test_acc"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now we can test different encoding methods on the circle data generated above. Here we choose five encoding methods: amplitude encoding, angle encoding, pauli rotation encoding, IQP encoding, and complex entangled encoding. Then the curves of the testing accuracy are shown below."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Encoding method: amplitude_encoding\n",
"epoch: 0 iter: 0 loss: 0.3066 train acc: 0.4000 test acc: 0.5400\n",
"epoch: 0 iter: 5 loss: 0.2378 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 10 loss: 0.2308 train acc: 0.8000 test acc: 0.6700\n",
"epoch: 0 iter: 15 loss: 0.2230 train acc: 0.8000 test acc: 0.6100\n",
"Encoding method: angle_encoding\n",
"epoch: 0 iter: 0 loss: 0.2949 train acc: 0.5000 test acc: 0.3600\n",
"epoch: 0 iter: 5 loss: 0.1770 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 10 loss: 0.1654 train acc: 0.8000 test acc: 0.7000\n",
"epoch: 0 iter: 15 loss: 0.1966 train acc: 0.7000 test acc: 0.5800\n",
"Encoding method: pauli_rotation_encoding\n",
"epoch: 0 iter: 0 loss: 0.2433 train acc: 0.6000 test acc: 0.7000\n",
"epoch: 0 iter: 5 loss: 0.2142 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 10 loss: 0.2148 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 15 loss: 0.2019 train acc: 0.8000 test acc: 0.7600\n",
"Encoding method: IQP_encoding\n",
"epoch: 0 iter: 0 loss: 0.2760 train acc: 0.6000 test acc: 0.4200\n",
"epoch: 0 iter: 5 loss: 0.1916 train acc: 0.6000 test acc: 0.6200\n",
"epoch: 0 iter: 10 loss: 0.1355 train acc: 0.9000 test acc: 0.7300\n",
"epoch: 0 iter: 15 loss: 0.1289 train acc: 0.9000 test acc: 0.6700\n",
"Encoding method: complex_entangled_encoding\n",
"epoch: 0 iter: 0 loss: 0.3274 train acc: 0.3000 test acc: 0.2900\n",
"epoch: 0 iter: 5 loss: 0.2120 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 10 loss: 0.2237 train acc: 0.7000 test acc: 0.7000\n",
"epoch: 0 iter: 15 loss: 0.2095 train acc: 0.8000 test acc: 0.7200\n"
]
}
],
"source": [
"# Testing different encoding methods\n",
"encoding_list = ['amplitude_encoding', 'angle_encoding', 'pauli_rotation_encoding', 'IQP_encoding', 'complex_entangled_encoding']\n",
"num_qubit = 2 # If qubit number is 1, CNOT gate in cir_classifier can not be used\n",
"dimension = 2\n",
"acc_list = []\n",
"\n",
"for i in range(len(encoding_list)):\n",
" encoding = encoding_list[i]\n",
" print(\"Encoding method:\", encoding)\n",
" # Use SimpleDataset to encode the data\n",
" quantum_train_x= SimpleDataset(dimension).encode(train_x, encoding, num_qubit)\n",
" quantum_test_x= SimpleDataset(dimension).encode(test_x, encoding, num_qubit)\n",
" quantum_train_x = paddle.to_tensor(quantum_train_x)\n",
" quantum_test_x = paddle.to_tensor(quantum_test_x)\n",
" \n",
" acc = QClassifier2(\n",
" quantum_train_x, # Training x\n",
" train_y, # Training y\n",
" quantum_test_x, # Testing x\n",
" test_y, # Testing y\n",
" N = num_qubit, # Number of qubits required\n",
" DEPTH = 1, # Circuit depth\n",
" EPOCH = 1, # Number of training epochs\n",
" LR = 0.1, # Set the learning rate\n",
" BATCH = 10, # Batch size during training\n",
" )\n",
" acc_list.append(acc)"
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {},
"outputs": [
{
"data": {
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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Benchmarking different encoding methods\n",
"x=[2*i for i in range(len(acc_list[0]))]\n",
"for i in range(len(encoding_list)):\n",
" plt.plot(x,acc_list[i])\n",
"plt.legend(encoding_list)\n",
"plt.title(\"Benchmarking different encoding methods\")\n",
"plt.xlabel(\"Iteration\")\n",
"plt.ylabel(\"Test accuracy\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Quantum Classification on Built-In MNIST and Iris Datasets\n",
"\n",
"Paddle Quantum provides datasets commonly used in quantum classification tasks, and users can use the `paddle_quantum.dataset` module to get the encoding circuits or encoded states. There are four built-in datasets in Paddle Quantum at present, including MNIST, FashionMNIST, Iris and BreastCancer. We can easily accomplishing quantum classification using these quantum datasets.\n",
"\n",
"The first case is Iris. It has three types of labels and 50 samples of each type. There are only four features in Iris data, and it is very easy to fulfill its classification."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\Users\\yeruilin\\Anaconda3\\envs\\paddle_quantum_env\\lib\\site-packages\\paddle\\fluid\\dygraph\\math_op_patch.py:237: UserWarning: The dtype of left and right variables are not the same, left dtype is paddle.float64, but right dtype is paddle.int32, the right dtype will convert to paddle.float64\n",
" warnings.warn(\n"
]
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"epoch: 0 iter: 0 loss: 0.3113 train acc: 0.0000 test acc: 0.0000\n",
"epoch: 0 iter: 5 loss: 0.4818 train acc: 0.0000 test acc: 0.3500\n",
"epoch: 0 iter: 10 loss: 0.2171 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 0 iter: 15 loss: 0.1688 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 1 iter: 0 loss: 0.1350 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 1 iter: 5 loss: 0.1110 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 1 iter: 10 loss: 0.0879 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 1 iter: 15 loss: 0.0490 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 2 iter: 0 loss: 0.0733 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 2 iter: 5 loss: 0.0740 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 2 iter: 10 loss: 0.0660 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 2 iter: 15 loss: 0.0394 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 3 iter: 0 loss: 0.0654 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 3 iter: 5 loss: 0.0557 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 3 iter: 10 loss: 0.0602 train acc: 1.0000 test acc: 1.0000\n",
"epoch: 3 iter: 15 loss: 0.0397 train acc: 1.0000 test acc: 1.0000\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Using Iris\n",
"test_rate = 0.2\n",
"num_qubit = 4\n",
"\n",
"# acquire Iris data as quantum states\n",
"iris =Iris (encoding='angle_encoding', num_qubits=num_qubit, test_rate=test_rate,classes=[0, 1], return_state=True)\n",
"\n",
"quantum_train_x, train_y = iris.train_x, iris.train_y\n",
"quantum_test_x, test_y = iris.test_x, iris.test_y\n",
"testing_data_num = len(test_y)\n",
"training_data_num = len(train_y)\n",
"\n",
"acc = QClassifier2(\n",
" quantum_train_x, # training x\n",
" train_y, # training y\n",
" quantum_test_x, # testing x\n",
" test_y, # testing y\n",
" N = num_qubit, # Number of qubits required\n",
" DEPTH = 1, # Circuit depth\n",
" EPOCH = 4, # Number of training epochs, the total iteration number \"EPOCH * (Ntrain / BATCH)\" is chosen to be about 200\n",
" LR = 0.1, # Set the learning rate\n",
" BATCH = 4, # Batch size during training\n",
" )\n",
"plt.plot(acc)\n",
"plt.title(\"Classify Iris 0&1 using angle encoding\")\n",
"plt.xlabel(\"Iteration\")\n",
"plt.ylabel(\"Testing accuracy\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The second case is MNIST. It is a handwritten digit dataset and has 10 classes. Each figure has $28\\times28$ pixels, and downscaling methods such as ``resize`` and ``PCA`` should be used to transform it into the target dimension."
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"epoch: 0 iter: 0 loss: 0.3237 train acc: 0.3250 test acc: 0.5450\n",
"epoch: 0 iter: 5 loss: 0.2124 train acc: 0.7500 test acc: 0.6500\n",
"epoch: 0 iter: 10 loss: 0.2294 train acc: 0.6500 test acc: 0.6850\n",
"epoch: 1 iter: 0 loss: 0.1970 train acc: 0.7250 test acc: 0.7850\n",
"epoch: 1 iter: 5 loss: 0.1521 train acc: 0.8500 test acc: 0.8150\n",
"epoch: 1 iter: 10 loss: 0.1726 train acc: 0.7750 test acc: 0.8900\n",
"epoch: 2 iter: 0 loss: 0.1742 train acc: 0.7250 test acc: 0.8650\n",
"epoch: 2 iter: 5 loss: 0.1167 train acc: 0.9000 test acc: 0.8900\n",
"epoch: 2 iter: 10 loss: 0.1654 train acc: 0.8000 test acc: 0.8950\n",
"epoch: 3 iter: 0 loss: 0.1609 train acc: 0.8000 test acc: 0.8850\n",
"epoch: 3 iter: 5 loss: 0.1148 train acc: 0.9250 test acc: 0.8850\n",
"epoch: 3 iter: 10 loss: 0.1649 train acc: 0.8000 test acc: 0.8750\n",
"epoch: 4 iter: 0 loss: 0.1629 train acc: 0.8250 test acc: 0.8750\n",
"epoch: 4 iter: 5 loss: 0.1112 train acc: 0.9000 test acc: 0.8700\n",
"epoch: 4 iter: 10 loss: 0.1630 train acc: 0.8500 test acc: 0.8850\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# using MNIST\n",
"\n",
"# main parameters\n",
"training_data_num = 500\n",
"testing_data_num = 200\n",
"qubit_num = 4\n",
"\n",
"# MNIST data with amplitude encoding, resized to 4*4\n",
"train_dataset = MNIST(mode='train', encoding='amplitude_encoding', num_qubits=qubit_num, classes=[3, 6],\n",
" data_num=training_data_num, need_cropping=True,\n",
" downscaling_method='resize', target_dimension=16, return_state=True)\n",
"\n",
"val_dataset = MNIST(mode='test', encoding='amplitude_encoding', num_qubits=qubit_num, classes=[3, 6],\n",
" data_num=testing_data_num, need_cropping=True,\n",
" downscaling_method='resize', target_dimension=16,return_state=True)\n",
"\n",
"quantum_train_x, train_y = train_dataset.quantum_image_states, train_dataset.labels\n",
"quantum_test_x, test_y = val_dataset.quantum_image_states, val_dataset.labels\n",
"\n",
"acc = QClassifier2(\n",
" quantum_train_x, # Training x\n",
" train_y, # Training y\n",
" quantum_test_x, # Testing x\n",
" test_y, # Testing y\n",
" N = qubit_num, # Number of qubits required\n",
" DEPTH = 3, # Circuit depth\n",
" EPOCH = 5, # Number of training epochs, the total iteration number \"EPOCH * (Ntrain / BATCH)\" is chosen to be about 200\n",
" LR = 0.1, # Set the learning rate\n",
" BATCH = 40, # Batch size during training\n",
" )\n",
"\n",
"plt.plot(acc)\n",
"plt.title(\"Classify MNIST 3&6 using amplitude encoding\")\n",
"plt.xlabel(\"Iteration\")\n",
"plt.ylabel(\"Testing accuracy\")\n",
"plt.show()"
]
},
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {}, "metadata": {},
...@@ -1020,7 +1408,9 @@ ...@@ -1020,7 +1408,9 @@
"\n", "\n",
"[2] Farhi, Edward, and Hartmut Neven. Classification with quantum neural networks on near term processors. [arXiv preprint arXiv:1802.06002 (2018).](https://arxiv.org/abs/1802.06002)\n", "[2] Farhi, Edward, and Hartmut Neven. Classification with quantum neural networks on near term processors. [arXiv preprint arXiv:1802.06002 (2018).](https://arxiv.org/abs/1802.06002)\n",
"\n", "\n",
"[3] Schuld, Maria, et al. Circuit-centric quantum classifiers. [Physical Review A 101.3 (2020): 032308.](https://arxiv.org/abs/1804.00633)\n" "[3] Schuld, Maria, et al. Circuit-centric quantum classifiers. [Physical Review A 101.3 (2020): 032308.](https://arxiv.org/abs/1804.00633)\n",
"\n",
"[4] Schuld, Maria. Supervised quantum machine learning models are kernel methods. [arXiv preprint arXiv:2101.11020 (2021).](https://arxiv.org/pdf/2101.11020)"
] ]
} }
], ],
...@@ -1040,7 +1430,7 @@ ...@@ -1040,7 +1430,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.7.11" "version": "3.8.12"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/machine_learning/VQSVD_CN.ipynb
浏览文件 @ 016af983
...@@ -919,7 +919,7 @@ ...@@ -919,7 +919,7 @@
"\n", "\n",
"## 参考文献\n", "## 参考文献\n",
"\n", "\n",
"[1] Wang, X., Song, Z. & Wang, Y. Variational Quantum Singular Value Decomposition. [arXiv:2006.02336 (2020).](https://arxiv.org/abs/2006.02336)" "[1] Wang, X., Song, Z., & Wang, Y. Variational Quantum Singular Value Decomposition. [Quantum, 5, 483 (2021).](https://quantum-journal.org/papers/q-2021-06-29-483/)"
] ]
} }
], ],
......
tutorial/machine_learning/VQSVD_EN.ipynb
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"\n", "\n",
"## References\n", "## References\n",
"\n", "\n",
"[1] Wang, X., Song, Z. & Wang, Y. Variational Quantum Singular Value Decomposition. [arXiv:2006.02336 (2020).](https://arxiv.org/abs/2006.02336)" "[1] Wang, X., Song, Z., & Wang, Y. Variational Quantum Singular Value Decomposition. [Quantum, 5, 483 (2021).](https://quantum-journal.org/papers/q-2021-06-29-483/)"
] ]
} }
], ],
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tutorial/machine_learning/VSQL_CN.ipynb
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"\n", "\n",
"## 参考文献\n", "## 参考文献\n",
"\n", "\n",
"[1] Li, Guangxi, et al. \"VSQL: Variational Shadow Quantum Learning for Classification.\" [arXiv:2012.08288 (2020).](https://arxiv.org/abs/2012.08288)\n", "[1] Li, Guangxi, Zhixin Song, and Xin Wang. \"VSQL: Variational Shadow Quantum Learning for Classification.\" [Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. No. 9. 2021.](https://ojs.aaai.org/index.php/AAAI/article/view/17016)\n",
"\n", "\n",
"[2] Goodfellow, Ian, et al. Deep learning. Vol. 1. No. 2. Cambridge: MIT press, 2016.\n", "[2] Goodfellow, Ian, et al. Deep learning. Vol. 1. No. 2. Cambridge: MIT press, 2016.\n",
"\n", "\n",
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tutorial/machine_learning/VSQL_EN.ipynb
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"\n", "\n",
"## References\n", "## References\n",
"\n", "\n",
"[1] Li, Guangxi, et al. \"VSQL: Variational Shadow Quantum Learning for Classification.\" [arXiv:2012.08288 (2020).](https://arxiv.org/abs/2012.08288)\n", "[1] Li, Guangxi, Zhixin Song, and Xin Wang. \"VSQL: Variational Shadow Quantum Learning for Classification.\" [Proceedings of the AAAI Conference on Artificial Intelligence. Vol. 35. No. 9. 2021.](https://ojs.aaai.org/index.php/AAAI/article/view/17016)\n",
"\n", "\n",
"[2] Goodfellow, Ian, et al. Deep learning. Vol. 1. No. 2. Cambridge: MIT press, 2016.\n", "[2] Goodfellow, Ian, et al. Deep learning. Vol. 1. No. 2. Cambridge: MIT press, 2016.\n",
"\n", "\n",
......
tutorial/qnn_research/BarrenPlateaus_CN.ipynb
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因为 它太大了无法显示 source diff 。你可以改为 查看blob。
tutorial/qnn_research/BarrenPlateaus_EN.ipynb
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因为 它太大了无法显示 source diff 。你可以改为 查看blob。
tutorial/qnn_research/Fisher_CN.ipynb 0 → 100644
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{
"cells": [
{
"cell_type": "markdown",
"source": [
"# 量子费舍信息\n",
"\n",
"<em> Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. </em>"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## 概览\n",
"\n",
"本教程简要介绍经典费舍信息（classical Fisher information, CFI）和量子费舍信息（quantum Fisher information, QFI）的概念及其在量子机器学习中的应用，并展示如何调用量桨来计算它们。"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## 背景\n",
"\n",
"量子费舍信息这一概念源自量子传感领域，现已逐渐成为研究参数化量子系统的通用工具 [[1]](https://arxiv.org/abs/2103.15191)，例如描述过参数化现象 [[2]](https://arxiv.org/abs/2102.01659)，量子自然梯度下降 [[3]](https://arxiv.org/abs/1909.02108) 等。量子费舍信息是经典费舍信息在量子系统中的自然类比。经典费舍信息刻画了一个参数化的『概率分布』对其参数变化的灵敏度，而量子费舍信息刻画了一个参数化的『量子态』对其参数变化的灵敏度。\n",
"\n",
"按照传统的介绍方式，经典费舍信息会作为数理统计中参数估计的一部分内容出现，但对于初学者来说可能是复杂且不直观的。本教程将从几何的角度出发来介绍经典费舍信息，这不仅有助于直观理解，且更容易由此看出其与量子费舍信息之间的联系。"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### 经典费舍信息\n",
"\n",
"首先介绍经典费舍信息。对于一个参数化的概率分布 $p(\\boldsymbol{x};\\boldsymbol{\\theta})$，考虑如下问题\n",
"\n",
"- 一个轻微的参数改变会在多大程度上造成概率分布的改变？\n",
"\n",
"这是个关于微扰的问题，所以自然地想到做类似泰勒展开的操作。但在此之前，我们需要知道展开哪个函数，即我们需要量化『概率分布的改变』。更正式的说法是，我们需要定义任意两个概率分布之间的『距离』，记为 $d(p(\\boldsymbol{x};\\boldsymbol{\\theta}),p(\\boldsymbol{x};\\boldsymbol{\\theta}'))$，或简记为 $d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')$。\n",
"\n",
"一般地，一个合法的距离定义应该是非负的，当且仅当两点重合时为零，即\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')\\geq 0,\\\\\n",
"&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')=0~\\Leftrightarrow~\\boldsymbol{\\theta}=\\boldsymbol{\\theta}'.\n",
"\\end{aligned}\n",
"\\tag{1}\n",
"$$\n",
"\n",
"考虑一个很短的距离函数的展开 $d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})$，以上条件会导致\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta})=0~\\Rightarrow~\\text{零阶项}=0,\\\\\n",
"&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\geq 0~\\Rightarrow~\\boldsymbol{\\delta}=0~\\text{取极小值}\n",
"~\\Rightarrow~\\text{一阶项}=0.\n",
"\\end{aligned}\n",
"\\tag{2}\n",
"$$\n",
"\n",
"因此，在这个展开中最低阶的非零贡献来自二阶。因此它可被写为\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\n",
"=\\frac{1}{2}\\sum_{ij}\\delta_iM_{ij}\\delta_j+O(\\|\\boldsymbol{\\delta}\\|^3) \n",
"=\\frac{1}{2} \\boldsymbol{\\delta}^T M \\boldsymbol{\\delta} + O(\\|\\boldsymbol{\\delta}\\|^3),\n",
"\\end{aligned}\n",
"\\tag{3}\n",
"$$\n",
"\n",
"此处\n",
"\n",
"$$\n",
"M_{ij}(\\boldsymbol{\\theta})=\\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0},\n",
"\\tag{4}\n",
"$$\n",
"\n",
"正是这个距离函数展开的海森矩阵。在微分几何的框架下，这称作流形的[度规](http://en.wikipedia.org/wiki/Metric_tensor)。以上简单的推导说明，我们总是可以用参数的一个二次型来近似表示一小段距离（如图1）。而二次型的系数矩阵，除了有一个 $1/2$ 因子的差别外，正是距离函数展开的海森矩阵。\n",
"\n",
"![feature map](./figures/FIM-fig-Sphere-metric.png \"Figure 1. Approximate a small distance on the 2-sphere as a quadratic form\")\n",
"<div style=\"text-align:center\">图 1. 将一小段距离近似为二次型，此处以二维球面为例绘制 </div>\n",
"\n",
"如果我们定义概率分布之间的距离为相对熵或称 KL 散度\n",
"\n",
"$$\n",
"d_{\\mathrm{KL}}(\\boldsymbol{\\theta}, \\boldsymbol{\\theta}^{\\prime})=\\sum_{\\boldsymbol{x}} p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\log \\frac{p(\\boldsymbol{x};\\boldsymbol{\\theta})}{p(\\boldsymbol{x};\\boldsymbol{\\theta}^{\\prime})}.\n",
"\\tag{5}\n",
"$$\n",
"\n",
"对应的海森矩阵为\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\mathcal{I}_{ij}(\\boldsymbol{\\theta})&= \\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d_{\\mathrm{KL}}(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0}\\\\\n",
"&=-\\sum_{\\boldsymbol{x}} p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\partial_{i} \\partial_{j} \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})\n",
"=\\mathbb{E}_{\\boldsymbol{x}}[-\\partial_{i} \\partial_{j} \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})] \\\\\n",
"&=\\sum_{\\boldsymbol{x}} \\frac{1}{p(\\boldsymbol{x};\\boldsymbol{\\theta})} \\partial_i p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\cdot \\partial_j p(\\boldsymbol{x};\\boldsymbol{\\theta})\n",
"=\\mathbb{E}_{\\boldsymbol{x}}[\\partial_i\\log p(\\boldsymbol{x};\\boldsymbol{\\theta})\\cdot \\partial_j \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})].\n",
"\\end{aligned}\n",
"\\tag{6}\n",
"$$\n",
"\n",
"这就是所谓的经典费舍信息矩阵（classical Fisher information matrix, CFIM），矩阵元越大说明概率分布对相应的参数变化越灵敏。上式中我们使用了偏导数符号的简记 $\\partial_i=\\partial/\\partial \\theta_i$。\n",
"\n",
"为什么 $\\mathcal{I}(\\boldsymbol{\\theta})$ 称为『信息』？这是因为，CFIM 刻画了概率分布在对应参数一个领域内的灵敏度，或称锐度。对参数变化越灵敏，说明我们越容易将其同其它概率分布区分开来，进一步地，说明我们需要越少的样本就可以完成这种区分，那么每个样本中平均所含的信息量就越多。\n",
"\n",
"参数化量子电路（parameterized quantum circuit, PQC）的测量结果会形成一个概率分布，因此可以对不同的测量基定义不同的 CFIM。目前在 NISQ 设备上计算 CFIM 的主要挑战是，可能出现的测量结果的数量会随着量子比特数的增加而指数地增加，这意味着可能有很多小概率的测量结果从未出现过，导致 CFIM 的计算出现发散。一些可能的解决方案包括直接忽略小的概率事件，以及贝叶斯更新等 [[1]](https://arxiv.org/abs/2103.15191)。"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### 量子费舍信息\n",
"\n",
"量子费舍信息是经典费舍信息的自然类比，只是距离函数不再定义在两个概率分布之间，而是定义在两个量子态之间。我们通常选用保真度距离\n",
"\n",
"$$\n",
"d_f(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')=2-2|\\langle\\psi(\\boldsymbol{\\theta})|\\psi(\\boldsymbol{\\theta}')\\rangle|^2.\n",
"\\tag{7}\n",
"$$\n",
"\n",
"此处因子 $2$ 是人为乘上去的，为的是让后续的结果与 CFIM 对应上。一个参数化量子纯态 $|\\psi(\\boldsymbol{\\theta})\\rangle, \\boldsymbol{\\theta}\\in\\mathbb{R}^m$ 的量子费舍信息矩阵（quantum Fisher information matrix, QFIM）就是保真度距离展开的海森矩阵，即\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\mathcal{F}_{ij}(\\boldsymbol{\\theta})\n",
"&= \\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d_{f}(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0} \\\\\n",
"&=4 \\operatorname{Re}\\left[\\left\\langle\\partial_{i} \\psi \\mid \\partial_{j} \\psi\\right\\rangle - \\left\\langle\\partial_{i} \\psi \\mid \\psi\\right\\rangle\\left\\langle\\psi \\mid \\partial_{j} \\psi\\right\\rangle\\right],\n",
"\\end{aligned}\n",
"\\tag{8}\n",
"$$\n",
"\n",
"上式中简洁起见我们略写了自变量 $\\boldsymbol{\\theta}$。与 CFIM 类似，QFIM 刻画了参数化量子态对参数微小变化的灵敏度。此外值得一提的是，QFIM 可以被视为另一个被称作量子几何张量的复数矩阵的实部，或称为 Fubini-Study 度规 [[1]](https://arxiv.org/abs/2103.15191)。\n",
"\n",
"目前，人们已经提出了一些在 NISQ 设备上计算纯态 QFIM 的方法，其中最直接的两个方法是\n",
"\n",
"- 利用二阶参数平移规则计算每个矩阵元 [[4]](https://arxiv.org/abs/2008.06517)\n",
"$$\n",
"\\begin{aligned}\n",
"\\mathcal{F}_{i j}=-\\frac{1}{2} \\Big(&|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}+(\\boldsymbol{e}_{i}+\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\n",
"-|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}+(\\boldsymbol{e}_{i}-\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\\\\\n",
"-&|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}-(\\boldsymbol{e}_{i}-\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\n",
"+|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}-(\\boldsymbol{e}_{i}+\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\\Big),\n",
"\\end{aligned}\n",
"\\tag{9}\n",
"$$\n",
"其中 $\\boldsymbol{e}_{i}$ 是 $\\theta_i$ 对应方向的单位向量。\n",
"\n",
"- 利用有限差分计算 QFIM 沿一个确定方向的投影 [[1]](https://arxiv.org/abs/2103.15191)\n",
"$$\n",
"\\boldsymbol{v}^{T} \\mathcal{F} \\boldsymbol{v} \\approx \\frac{4 d_{f}(\\boldsymbol{\\theta}, \\boldsymbol{\\theta}+\\epsilon \\boldsymbol{v})}{\\epsilon^{2}}.\n",
"\\tag{10}\n",
"$$\n",
"这个量可以被视为著名的 Fisher-Rao 模在量子态空间的类比。\n",
"\n",
"对于混态，QFIM 可以类似地通过 Bures 保真度距离的展开来定义\n",
"\n",
"$$\n",
"d_B(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')\\equiv \n",
"2-2\\left[\\text{Tr}\\left([\\sqrt{\\rho(\\boldsymbol{\\theta})} \\rho(\\boldsymbol{\\theta}')\\sqrt{\\rho(\\boldsymbol{\\theta})}]^{1/2}\\right)\\right]^2,\n",
"\\tag{11}\n",
"$$\n",
"\n",
"或者等价地（$\\log x\\sim x-1$），通过如下形式的 $\\alpha=1/2$ 的 Rényi 相对熵的展开来定义 [[5]](https://arxiv.org/abs/1308.5961)\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"d_R(\\boldsymbol{\\theta},\\boldsymbol{\\theta}') &\\equiv 2\\widetilde{D}_{\\alpha=1/2}(\\rho(\\boldsymbol{\\theta'}) \\| \\rho(\\boldsymbol{\\theta})), \\\\\n",
"\\widetilde{D}_{\\alpha}(\\rho \\| \\sigma) \n",
"&\\equiv \n",
"\\frac{1}{\\alpha-1} \\log \\operatorname{Tr}\\left[\\left(\\sigma^{\\frac{1-\\alpha}{2 \\alpha}} \\rho \\sigma^{\\frac{1-\\alpha}{2 \\alpha}}\\right)^{\\alpha}\\right].\\\\\n",
"\\end{aligned}\n",
"\\tag{12}\n",
"$$\n",
"\n",
"更多细节请参考这篇综述 [[1]](https://arxiv.org/abs/2103.15191) 。"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### 经典与量子费舍信息的关系\n",
"\n",
"根据定义，对于一个参数化的量子电路，CFIM 依赖于测量基，而 QFIM 不依赖。事实上可以证明，一个量子态 $\\rho(\\boldsymbol{\\theta})$ 的 QFIM 是其在任意测量基下对应 CFIM 的一个上限，即\n",
"\n",
"$$\n",
"\\mathcal{I}[\\mathcal{E}[\\rho(\\boldsymbol{\\theta})]]\\leq \\mathcal{F}[\\rho(\\boldsymbol{\\theta})],~\\forall\\mathcal{E},\n",
"\\tag{13}\n",
"$$\n",
"\n",
"此处 $\\mathcal{E}$ 表示测量对应的量子操作。正定矩阵间不等式的含义是，大的减去小的结果仍然是一个正定矩阵。由于对量子态的测量永远无法提取出比量子态本身更多的信息，因此上式的成立是很自然的。数学上这根源于保真度距离对于保迹量子操作的单调性 [[1]](https://arxiv.org/abs/2103.15191)。"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### 应用：有效维数\n",
"\n",
"经典/量子费舍信息矩阵的秩在参数空间的最大值可以用来衡量神经网络表达能力，称为经典/量子有效维数\n",
"\n",
"$$\n",
"d_{\\text{eff}}=\\underset{\\boldsymbol{\\theta}\\in\\Theta} {\\max}\n",
"\\operatorname{rank}{\\mathcal{F}}(\\boldsymbol{\\theta}).\n",
"\\tag{14}\n",
"$$\n",
"\n",
"秩的大小刻画了参数变化会造成概率分布/量子态变化的方向的数量。非满秩意味着有一些特定方向的参数变化不能实际地导致概率分布/量子态发生变化，或者说有一些参数自由度是冗余的，可以把它们从模型中投影掉，因此这种现象被称作过参数化。另一方面，有效维数越大，对应着更多可以延伸的方向，这意味着模型对应的函数空间更大，即表达能力更强。\n",
"\n",
"在机器学习的语境下，『经验费舍信息矩阵』[[6]](https://arxiv.org/abs/2011.00027) 的使用更为广泛，它与 CFIM 的区别是用对样本的求和代替了求期望\n",
"\n",
"$$\n",
"\\tilde{\\mathcal{I}}_{ij}(\\boldsymbol{\\theta})\n",
"=\\frac{1}{n}\\sum_{k=1}^{n}\n",
"\\partial_i\\log p(x_k,y_k;\\boldsymbol{\\theta})\n",
"\\partial_j\\log p(x_k,y_k;\\boldsymbol{\\theta}),\n",
"\\tag{15}\n",
"$$\n",
"\n",
"此处 $(x_k,y_k)^{n}_{k=1}$ 是独立同分布的样本，分布为 $p(x,y;\\boldsymbol{\\theta})=p(y|x;\\boldsymbol{\\theta})p(x)$。显然，经验费舍信息矩阵在无限样本的极限下可以回到 CFIM，只要满足（1）模型被训练到全局最优；（2）模型拥有足够的表达能力来表达底层的数据分布。使用经验费舍信息矩阵的优势在于，它可以利用现成的样本直接计算，而不是为了计算公式中的积分而生成新的样本。\n",
"\n",
"利用经验费舍信息矩阵，我们可以定义有效维数的一个变体 \n",
"\n",
"$$\n",
"d_{\\text{eff}}(\\gamma, n)=\n",
"2 \\frac{\\log \\left(\\frac{1}{V_{\\Theta}} \\int_{\\Theta} \\sqrt{\\operatorname{det}\\left( 1 + \\frac{\\gamma n}{2 \\pi \\log n} \\hat{\\mathcal{I}}( \\boldsymbol{\\theta})\\right)} \\mathrm{d} \\boldsymbol{\\theta} \\right)}\n",
"{\\log \\left(\\frac{\\gamma n}{2 \\pi \\log n}\\right)},\n",
"\\tag{16}\n",
"$$\n",
"\n",
"其中 $V_{\\Theta}:=\\int_{\\Theta} \\mathrm{d} \\boldsymbol{\\theta} \\in \\mathbb{R}_{+}$ 是参数空间的体积。$\\gamma\\in(0,1]$ 是一个人为可调参数。$\\hat{\\mathcal{I}} (\\boldsymbol{\\theta}) \\in \\mathbb{R}^{d\\times d}$ 是归一化的经验费舍信息矩阵\n",
"\n",
"$$\n",
"\\hat{\\mathcal{I}}_{i j}(\\boldsymbol{\\theta}):= \\frac{V_{\\Theta} d }{\\int_{\\Theta} \\operatorname{Tr}(F( \\boldsymbol{\\theta} ) \\mathrm{d} \\theta} \\tilde{\\mathcal{I}}_{i j}(\\boldsymbol{\\theta}).\n",
"\\tag{17}\n",
"$$\n",
"\n",
"这个定义乍看起来可能很迷惑，因为它比上文通过秩来定义要复杂得多。然而，它实际上可以在无限样本的极限下 $n\\rightarrow \\infty$ 回到 CFIM 最大秩的定义 [[6]](https://arxiv.org/abs/2011.00027)。若忽略定义中的一些系数和取对数的操作，此处定义的有效维数可以粗略地看作归一化 CFIM 加上一个单位矩阵的本征谱的几何平均。依据几何平均与算术平均间的不等式关系，可知本征谱分布越均匀，有效维数越大。这和我们的直觉是一致的。在这个意义上，它可以看作是一个软化版本的有效维数。\n",
"\n",
"另外，费舍信息不仅可以用来计算模型的表达能力，还可以用来表征模型的可训练性。如果费舍信息矩阵的矩阵元在参数空间的平均随体系规模的增大而指数地趋于零，即概率分布/量子态对参数变化的灵敏度指数地趋于零，那么我们将无法高效地区分它们，也就意味着贫瘠高原现象的存在 [[6]](https://arxiv.org/abs/2011.00027)。"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## 调用量桨计算费舍信息"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### 计算量子费舍信息\n",
"\n",
"利用量桨工具，通过以下步骤我们就可以方便地算出 QFIM。\n",
"\n",
"1. 调用 `UAnsatz` 类定义一个量子电路。\n",
"2. 调用 `QuantumFisher` 类定义一个 QFIM 计算器。\n",
"3. 调用 `get_qfisher_matrix()` 方法计算 QFIM。\n",
"\n",
"其中计算器 `QuantumFisher` 会追踪量子电路 `UAnsatz` 的实时变化。\n",
"\n",
"现在来着手写代码。首先导入一些必要的包。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 1,
"source": [
"import paddle\n",
"from paddle_quantum.circuit import UAnsatz\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from paddle_quantum.utils import QuantumFisher, ClassicalFisher\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"然后定义量子电路。作为一个简单的例子，我们采用布洛赫角表示的单个量子比特\n",
"\n",
"$$\n",
"|\\psi(\\theta,\\phi)\\rangle=R_z(\\phi)R_y(\\theta)|0\\rangle=e^{-i\\phi/2}\\cos\\frac{\\theta}{2}|0\\rangle+e^{i\\phi/2}\\sin\\frac{\\theta}{2}|1\\rangle.\n",
"\\tag{18}\n",
"$$\n",
"\n",
"利用 (8) 式可以计算出对应 QFIM 的解析表达式为\n",
"\n",
"$$\n",
"\\mathcal{F}(\\theta,\\phi)=\\left(\\begin{matrix}\n",
"1&0\\\\\n",
"0&\\sin^2\\theta\n",
"\\end{matrix}\\right).\n",
"\\tag{19}\n",
"$$"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 2,
"source": [
"def circuit_bloch():\n",
" cir = UAnsatz(1)\n",
" theta = 2 * np.pi * np.random.random(2)\n",
" theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n",
" cir.ry(theta[0], which_qubit=0)\n",
" cir.rz(theta[1], which_qubit=0)\n",
" \n",
" return cir"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 3,
"source": [
"cir = circuit_bloch()\n",
"print(cir)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"--Ry(1.888)----Rz(2.181)--\n",
" \n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"定义 QFIM 计算器然后计算不同 $\\theta$ 对应的 QFIM 矩阵元 $\\mathcal{F}_{\\phi\\phi}$ 。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 4,
"source": [
"qf = QuantumFisher(cir)\n",
"# 记录 QFIM 的矩阵元 F_{phi,phi}\n",
"list_qfisher_elements = []\n",
"num_thetas = 21\n",
"thetas = np.linspace(0, np.pi, num_thetas)\n",
"for theta in thetas:\n",
" list_param = cir.get_param().tolist()\n",
" list_param[0] = theta\n",
" cir.update_param(list_param)\n",
" # 计算 QFIM\n",
" qfim = qf.get_qfisher_matrix()\n",
" print(f'The QFIM at {np.array(list_param)} is \\n {qfim.round(14)}.')\n",
" list_qfisher_elements.append(qfim[1][1])"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"The QFIM at [0. 2.18107874] is \n",
" [[1. 0.]\n",
" [0. 0.]].\n",
"The QFIM at [0.15707963 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.02447174]].\n",
"The QFIM at [0.31415927 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.0954915]].\n",
"The QFIM at [0.4712389 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.20610737]].\n",
"The QFIM at [0.62831853 2.18107874] is \n",
" [[ 1. -0. ]\n",
" [-0. 0.3454915]].\n",
"The QFIM at [0.78539816 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.5]].\n",
"The QFIM at [0.9424778 2.18107874] is \n",
" [[ 1. -0. ]\n",
" [-0. 0.6545085]].\n",
"The QFIM at [1.09955743 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.79389263]].\n",
"The QFIM at [1.25663706 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.9045085]].\n",
"The QFIM at [1.41371669 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.97552826]].\n",
"The QFIM at [1.57079633 2.18107874] is \n",
" [[1. 0.]\n",
" [0. 1.]].\n",
"The QFIM at [1.72787596 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.97552826]].\n",
"The QFIM at [1.88495559 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.9045085]].\n",
"The QFIM at [2.04203522 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.79389263]].\n",
"The QFIM at [2.19911486 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.6545085]].\n",
"The QFIM at [2.35619449 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.5]].\n",
"The QFIM at [2.51327412 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.3454915]].\n",
"The QFIM at [2.67035376 2.18107874] is \n",
" [[ 1. -0. ]\n",
" [-0. 0.20610737]].\n",
"The QFIM at [2.82743339 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.0954915]].\n",
"The QFIM at [2.98451302 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.02447174]].\n",
"The QFIM at [3.14159265 2.18107874] is \n",
" [[1. 0.]\n",
" [0. 0.]].\n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"画出 $\\mathcal{F}_{\\phi\\phi}$ 随 $\\theta$ 变化的图像。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 5,
"source": [
"# 创建图像\n",
"fig = plt.figure(figsize=(9, 6))\n",
"ax = fig.add_subplot(111)\n",
"# 绘制 QFIM\n",
"ax.plot(thetas, list_qfisher_elements, 's', markersize=11, markerfacecolor='none')\n",
"# 绘制 sin^2 theta\n",
"ax.plot(thetas, np.sin(thetas) ** 2, linestyle=(0, (5, 3)))\n",
"# 设置图例，标签，刻度\n",
"label_font_size = 18\n",
"ax.legend(['get_qfisher_matrix()[1][1]', '$\\\\sin^2\\\\theta$'], \n",
" prop= {'size': label_font_size}, frameon=False) \n",
"ax.set_xlabel('$\\\\theta$', fontsize=label_font_size)\n",
"ax.set_ylabel('QFIM element $\\\\mathcal{F}_{\\\\phi\\\\phi}$', fontsize=label_font_size)\n",
"ax.tick_params(labelsize=label_font_size)"
],
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
],
"image/png": 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"
},
"metadata": {
"needs_background": "light"
}
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"可以看到程序输出和解析结果是一致的。\n",
"\n",
"此外，我们还可以调用 `get_qfisher_norm()` 方法来计算式 (10) 中的量子费舍信息矩阵在某个方向的投影。\n",
"\n",
"举一个和上面不同的例子，两个量子比特上的一个典型的 hardware-efficient 拟设\n",
"\n",
"$$\n",
"|\\psi(\\boldsymbol{\\theta})\\rangle=\\left[R_{y}\\left( \\theta_{3}\\right) \\otimes R_{y}\\left( \\theta_{4}\\right)\\right] \\text{CNOT}_{0,1}\\left[ R_{y}\\left( \\theta_{1}\\right) \\otimes R_{y}\\left( \\theta_{2}\\right)\\right]|00\\rangle.\n",
"\\tag{20}\n",
"$$\n",
"\n",
"对应的 QFIM 为\n",
"\n",
"$$\n",
"\\mathcal{F}(\\theta_1,\\theta_2,\\theta_3,\\theta_4)=\\left(\\begin{array}{cc|cc}\n",
"1 & 0 & \\sin \\theta_{2} & 0 \\\\\n",
"0 & 1 & 0 & \\cos \\theta_{1} \\\\\n",
"\\hline \n",
"\\sin \\theta_{2} & 0 & 1 & -\\sin\\theta_1\\cos\\theta_2 \\\\\n",
"0 & \\cos \\theta_{1} & -\\sin\\theta_1\\cos\\theta_2 & 1\n",
"\\end{array}\\right).\n",
"\\tag{21}\n",
"$$\n",
"\n",
"定义相应的量子电路。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 6,
"source": [
"def circuit_hardeff_2qubit():\n",
" cir = UAnsatz(2)\n",
" theta = 2 * np.pi * np.random.random(4)\n",
" theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n",
" cir.ry(theta[0], which_qubit=0)\n",
" cir.ry(theta[1], which_qubit=1)\n",
" cir.cnot(control=[0, 1])\n",
" cir.ry(theta[2], which_qubit=0)\n",
" cir.ry(theta[3], which_qubit=1)\n",
"\n",
" return cir"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 7,
"source": [
"cir = circuit_hardeff_2qubit()\n",
"print(cir)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"--Ry(2.614)----*----Ry(3.253)--\n",
" | \n",
"--Ry(2.906)----x----Ry(5.027)--\n",
" \n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"定义 QFIM 计算器并计算不同 $\\theta$ 对应的 QFIM 在 $\\boldsymbol{v}=(1,1,1,1)$ 方向上的投影 $\\boldsymbol{v}^T\\mathcal{F}\\boldsymbol{v}$ （固定 $\\theta_1=\\theta_2=\\theta$）。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 8,
"source": [
"qf = QuantumFisher(cir)\n",
"v = [1, 1, 1, 1]\n",
"# 记录 QFIM 投影\n",
"list_qfisher_norm = []\n",
"num_thetas = 41\n",
"thetas = np.linspace(0, np.pi * 4, num_thetas)\n",
"for theta in thetas:\n",
" list_param = cir.get_param().tolist()\n",
" list_param[0] = theta\n",
" list_param[1] = theta\n",
" cir.update_param(list_param)\n",
" # 计算 QFIM 投影\n",
" qfisher_norm = qf.get_qfisher_norm(v)\n",
" print(\n",
" f'The QFI norm along {v} at {np.array(list_param)} is {qfisher_norm:.8f}.'\n",
" )\n",
" list_qfisher_norm.append(qfisher_norm)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"The QFI norm along [1, 1, 1, 1] at [0. 0. 3.2533421 5.02652273] is 5.99962501.\n",
"The QFI norm along [1, 1, 1, 1] at [0.31415927 0.31415927 3.2533421 5.02652273] is 5.93033916.\n",
"The QFI norm along [1, 1, 1, 1] at [0.62831853 0.62831853 3.2533421 5.02652273] is 5.84133590.\n",
"The QFI norm along [1, 1, 1, 1] at [0.9424778 0.9424778 3.2533421 5.02652273] is 5.84309143.\n",
"The QFI norm along [1, 1, 1, 1] at [1.25663706 1.25663706 3.2533421 5.02652273] is 5.93367838.\n",
"The QFI norm along [1, 1, 1, 1] at [1.57079633 1.57079633 3.2533421 5.02652273] is 5.99962501.\n",
"The QFI norm along [1, 1, 1, 1] at [1.88495559 1.88495559 3.2533421 5.02652273] is 5.86697827.\n",
"The QFI norm along [1, 1, 1, 1] at [2.19911486 2.19911486 3.2533421 5.02652273] is 5.38230779.\n",
"The QFI norm along [1, 1, 1, 1] at [2.51327412 2.51327412 3.2533421 5.02652273] is 4.49128513.\n",
"The QFI norm along [1, 1, 1, 1] at [2.82743339 2.82743339 3.2533421 5.02652273] is 3.28287364.\n",
"The QFI norm along [1, 1, 1, 1] at [3.14159265 3.14159265 3.2533421 5.02652273] is 1.97995933.\n",
"The QFI norm along [1, 1, 1, 1] at [3.45575192 3.45575192 3.2533421 5.02652273] is 0.87758767.\n",
"The QFI norm along [1, 1, 1, 1] at [3.76991118 3.76991118 3.2533421 5.02652273] is 0.25010151.\n",
"The QFI norm along [1, 1, 1, 1] at [4.08407045 4.08407045 3.2533421 5.02652273] is 0.26070618.\n",
"The QFI norm along [1, 1, 1, 1] at [4.39822972 4.39822972 3.2533421 5.02652273] is 0.90660775.\n",
"The QFI norm along [1, 1, 1, 1] at [4.71238898 4.71238898 3.2533421 5.02652273] is 2.01995733.\n",
"The QFI norm along [1, 1, 1, 1] at [5.02654825 5.02654825 3.2533421 5.02652273] is 3.32425271.\n",
"The QFI norm along [1, 1, 1, 1] at [5.34070751 5.34070751 3.2533421 5.02652273] is 4.52539873.\n",
"The QFI norm along [1, 1, 1, 1] at [5.65486678 5.65486678 3.2533421 5.02652273] is 5.40406149.\n",
"The QFI norm along [1, 1, 1, 1] at [5.96902604 5.96902604 3.2533421 5.02652273] is 5.87599852.\n",
"The QFI norm along [1, 1, 1, 1] at [6.28318531 6.28318531 3.2533421 5.02652273] is 5.99962501.\n",
"The QFI norm along [1, 1, 1, 1] at [6.59734457 6.59734457 3.2533421 5.02652273] is 5.93033916.\n",
"The QFI norm along [1, 1, 1, 1] at [6.91150384 6.91150384 3.2533421 5.02652273] is 5.84133590.\n",
"The QFI norm along [1, 1, 1, 1] at [7.2256631 7.2256631 3.2533421 5.02652273] is 5.84309143.\n",
"The QFI norm along [1, 1, 1, 1] at [7.53982237 7.53982237 3.2533421 5.02652273] is 5.93367838.\n",
"The QFI norm along [1, 1, 1, 1] at [7.85398163 7.85398163 3.2533421 5.02652273] is 5.99962501.\n",
"The QFI norm along [1, 1, 1, 1] at [8.1681409 8.1681409 3.2533421 5.02652273] is 5.86697827.\n",
"The QFI norm along [1, 1, 1, 1] at [8.48230016 8.48230016 3.2533421 5.02652273] is 5.38230779.\n",
"The QFI norm along [1, 1, 1, 1] at [8.79645943 8.79645943 3.2533421 5.02652273] is 4.49128513.\n",
"The QFI norm along [1, 1, 1, 1] at [9.1106187 9.1106187 3.2533421 5.02652273] is 3.28287364.\n",
"The QFI norm along [1, 1, 1, 1] at [9.42477796 9.42477796 3.2533421 5.02652273] is 1.97995933.\n",
"The QFI norm along [1, 1, 1, 1] at [9.73893723 9.73893723 3.2533421 5.02652273] is 0.87758767.\n",
"The QFI norm along [1, 1, 1, 1] at [10.05309649 10.05309649 3.2533421 5.02652273] is 0.25010151.\n",
"The QFI norm along [1, 1, 1, 1] at [10.36725576 10.36725576 3.2533421 5.02652273] is 0.26070618.\n",
"The QFI norm along [1, 1, 1, 1] at [10.68141502 10.68141502 3.2533421 5.02652273] is 0.90660775.\n",
"The QFI norm along [1, 1, 1, 1] at [10.99557429 10.99557429 3.2533421 5.02652273] is 2.01995733.\n",
"The QFI norm along [1, 1, 1, 1] at [11.30973355 11.30973355 3.2533421 5.02652273] is 3.32425271.\n",
"The QFI norm along [1, 1, 1, 1] at [11.62389282 11.62389282 3.2533421 5.02652273] is 4.52539873.\n",
"The QFI norm along [1, 1, 1, 1] at [11.93805208 11.93805208 3.2533421 5.02652273] is 5.40406149.\n",
"The QFI norm along [1, 1, 1, 1] at [12.25221135 12.25221135 3.2533421 5.02652273] is 5.87599852.\n",
"The QFI norm along [1, 1, 1, 1] at [12.56637061 12.56637061 3.2533421 5.02652273] is 5.99962501.\n"
]
}
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 9,
"source": [
"# 创建图像\n",
"fig = plt.figure(figsize=(9, 6))\n",
"ax = fig.add_subplot(111)\n",
"# 绘制 QFIM 投影\n",
"ax.plot(thetas, list_qfisher_norm, 's', markersize=11, markerfacecolor='none')\n",
"analytical_qfi_norm = 4 + 2 * np.sin(thetas) + 2 * np.cos(thetas) - 2 * np.cos(thetas) * np.sin(thetas)\n",
"ax.plot(thetas, analytical_qfi_norm, linestyle=(0, (5, 3)))\n",
"# 设置图例，标签，刻度\n",
"ax.legend(\n",
" ['get_qfisher_norm()', '$4+2\\\\sin\\\\theta+2\\\\cos\\\\theta-2\\\\sin\\\\theta\\\\cos\\\\theta$'], \n",
" loc='best', prop= {'size': label_font_size}, frameon=False,\n",
")\n",
"ax.set_xlabel('$\\\\theta$', fontsize=label_font_size)\n",
"ax.set_ylabel('QFI norm along $v=(1,1,1,1)$', fontsize=label_font_size)\n",
"ax.set_ylim([-1, 9])\n",
"ax.tick_params(labelsize=label_font_size)"
],
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
],
"image/png": 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"
},
"metadata": {
"needs_background": "light"
}
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"可以看到程序的输出和解析结果是一致的。"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### 计算有效量子维数\n",
"\n",
"利用量桨，我们可以通过调用 `get_eff_qdim()` 方法方便地计算有效量子维数（effective quantum dimension, EQD）。以下是上面提到的 hardware-efficient 拟设的 EQD 计算示例。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 10,
"source": [
"cir = circuit_hardeff_2qubit()\n",
"qf = QuantumFisher(cir)\n",
"print(cir)\n",
"print(f'The number of parameters is {len(cir.get_param().tolist())}.')\n",
"print(f'The EQD is {qf.get_eff_qdim()}. \\n')"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"--Ry(4.248)----*----Ry(1.233)--\n",
" | \n",
"--Ry(6.121)----x----Ry(4.717)--\n",
" \n",
"The number of parameters is 4.\n",
"The EQD is 3. \n",
"\n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"在这个例子中，EQD 比参数个数要少，这实际上可以通过控制电路上两个 $R_y$ 可以直接合并这一点上看出来。这可以通过替换其中一个 $R_y$ 门为 $R_x$ 门来修复，这会使得 EQD 增长 1。\n",
"\n",
"如果继续在电路上增加门，EQD 会无限增长吗？答案显然是不会，这是因为对于 $n$ 个量子比特，量子态的实数自由度为 $2\\cdot 2^n-2$，其中减 $2$ 是由于归一化和全局相位无关性这两条约束。这说明无论门的数量为多少，EQD 都不会超过 $2\\cdot 2^n-2$。我们可以通过下面的例子做一简单的验证。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 11,
"source": [
"def circuit_hardeff_overparam():\n",
" cir = UAnsatz(2)\n",
" theta = 2 * np.pi * np.random.random(8)\n",
" theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n",
" cir.ry(theta[0], which_qubit=0)\n",
" cir.ry(theta[1], which_qubit=1)\n",
" cir.rx(theta[2], which_qubit=0)\n",
" cir.rx(theta[3], which_qubit=1)\n",
" cir.cnot(control=[0, 1])\n",
" cir.ry(theta[4], which_qubit=0)\n",
" cir.ry(theta[5], which_qubit=1)\n",
" cir.rx(theta[6], which_qubit=0)\n",
" cir.rx(theta[7], which_qubit=1)\n",
"\n",
" return cir\n",
"\n",
"\n",
"cir = circuit_hardeff_overparam()\n",
"qf = QuantumFisher(cir)\n",
"print(cir)\n",
"print(f'The number of parameters is {len(cir.get_param().tolist())}.')\n",
"print(f'The EQD is {qf.get_eff_qdim()}. \\n')"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"--Ry(0.173)----Rx(5.837)----*----Ry(3.082)----Rx(3.997)--\n",
" | \n",
"--Ry(1.354)----Rx(0.536)----x----Ry(5.267)----Rx(5.647)--\n",
" \n",
"The number of parameters is 8.\n",
"The EQD is 6. \n",
"\n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### 计算经典费舍信息和有效维数\n",
"\n",
"这里我们举一个简单的例子来展示如何利用量桨对于一个量子神经网络计算式 (16) 中的有效维数。\n",
"\n",
"首先，定义经典数据到量子数据的编码方式。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 12,
"source": [
"def U_theta(x, theta, num_qubits, depth, encoding):\n",
" cir = UAnsatz(num_qubits)\n",
" if encoding == 'IQP':\n",
" S = [[i, i + 1] for i in range(num_qubits - 1)]\n",
" cir.iqp_encoding(x, num_repeats=1, pattern=S)\n",
" cir.complex_entangled_layer(theta, depth)\n",
" elif encoding == 're-uploading':\n",
" for i in range(depth):\n",
" cir.complex_entangled_layer(theta[i:i + 1], depth=1)\n",
" for j in range(num_qubits):\n",
" cir.rx(x[j], which_qubit=j)\n",
" cir.complex_entangled_layer(theta[-1:], depth=1)\n",
" else:\n",
" raise RuntimeError('Non-existent encoding method')\n",
" return cir"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"然后调用飞桨定义量子神经网络和相应的损失函数。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 13,
"source": [
"import paddle.nn as nn\n",
"\n",
"class QuantumNeuralNetwork(nn.Layer):\n",
" def __init__(self, num_qubits, depth, encoding):\n",
" super().__init__()\n",
" self.num_qubits, self.depth, self.encoding = num_qubits, depth, encoding\n",
" if self.encoding == 'IQP':\n",
" self.theta = self.create_parameter(\n",
" shape=[self.depth, self.num_qubits, 3],\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0.0,\n",
" high=2 *\n",
" np.pi),\n",
" dtype='float64',\n",
" is_bias=False)\n",
" elif self.encoding == 're-uploading':\n",
" self.theta = self.create_parameter(\n",
" shape=[self.depth + 1, self.num_qubits, 3],\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0.0,\n",
" high=2 *\n",
" np.pi),\n",
" dtype='float64',\n",
" is_bias=False)\n",
" else:\n",
" raise RuntimeError('Non-existent encoding method')\n",
"\n",
" def forward(self, x):\n",
" if not paddle.is_tensor(x):\n",
" x = paddle.to_tensor(x)\n",
" cir = U_theta(x, self.theta, self.num_qubits, self.depth,\n",
" self.encoding)\n",
" cir.run_state_vector()\n",
" return cir.expecval([[1.0, 'z0']]) * paddle.to_tensor(\n",
" [0.5], dtype='float64') + paddle.to_tensor([0.5], dtype='float64')"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"最后，定义 CFIM 计算器并计算不同大小的训练集对应的有效维数。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 17,
"source": [
"# 配置模型参数\n",
"num_qubits = 4\n",
"depth = 2\n",
"num_inputs = 100\n",
"num_thetas = 10\n",
"# 定义 CFIM 计算器\n",
"cfim = ClassicalFisher(model=QuantumNeuralNetwork,\n",
" num_thetas=num_thetas,\n",
" num_inputs=num_inputs,\n",
" num_qubits=num_qubits,\n",
" depth=depth,\n",
" encoding='IQP')\n",
"# 计算归一化的 CFIM\n",
"fim, _ = cfim.get_normalized_cfisher()\n",
"# 计算不同样本大小对应的有效维数\n",
"n = [5000, 8000, 10000, 40000, 60000, 100000, 150000, 200000, 500000, 1000000]\n",
"effdim = cfim.get_eff_dim(fim, n)"
],
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"running in get_gradient: 100%|##################################| 1000/1000 [02:05<00:00, 7.94it/s]\n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"画出有效维数与参数个数之比随训练集大小的变化规律。"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 19,
"source": [
"fig = plt.figure(figsize=(9, 6))\n",
"ax = fig.add_subplot(111)\n",
"print('the number of parameters：%s' % cfim.num_params)\n",
"ax.plot(n, np.array(effdim) / cfim.num_params)\n",
"label_font_size = 14\n",
"ax.set_xlabel('sample size', fontsize=label_font_size)\n",
"ax.set_ylabel('effective dimension / number of parameters', fontsize=label_font_size)\n",
"ax.tick_params(labelsize=label_font_size)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"the number of parameters：24\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
],
"image/png": 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"
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{
"cell_type": "markdown",
"source": [
"## 总结\n",
"\n",
"本教程从几何的角度简要介绍了经典费舍信息和量子费舍信息的概念及二者之间的关系，并以有效维数为例阐述了它们在量子机器学习中的应用，最后展示了如何调用量桨来具体地计算它们。"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"_______\n",
"\n",
"## 参考文献\n",
"\n",
"[1] Meyer, Johannes Jakob. \"Fisher information in noisy intermediate-scale quantum applications.\" [arXiv preprint arXiv:2103.15191 (2021).](https://arxiv.org/abs/2103.15191)\n",
"\n",
"[2] Haug, Tobias, Kishor Bharti, and M. S. Kim. \"Capacity and quantum geometry of parametrized quantum circuits.\" [arXiv preprint arXiv:2102.01659 (2021).](https://arxiv.org/abs/2102.01659)\n",
"\n",
"[3] Stokes, James, et al. \"Quantum natural gradient.\" [Quantum 4 (2020): 269.](https://quantum-journal.org/papers/q-2020-05-25-269/)\n",
"\n",
"[4] Mari, Andrea, Thomas R. Bromley, and Nathan Killoran. \"Estimating the gradient and higher-order derivatives on quantum hardware.\" [Physical Review A 103.1 (2021): 012405.](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.012405)\n",
"\n",
"[5] Datta, Nilanjana, and Felix Leditzky. \"A limit of the quantum Rényi divergence.\" [Journal of Physics A: Mathematical and Theoretical 47.4 (2014): 045304.](https://iopscience.iop.org/article/10.1088/1751-8113/47/4/045304)\n",
"\n",
"[6] Abbas, Amira, et al. \"The power of quantum neural networks.\" [Nature Computational Science 1.6 (2021): 403-409.](https://www.nature.com/articles/s43588-021-00084-1)"
],
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tutorial/qnn_research/Fisher_EN.ipynb 0 → 100644
浏览文件 @ 016af983
{
"cells": [
{
"cell_type": "markdown",
"source": [
"# Quantum Fisher Information\n",
"\n",
"<em> Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. </em>"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Overview\n",
"\n",
"In this tutorial, we briefly introduce the concepts of the classical and quantum Fisher information, along with their applications in quantum machine learning, and show how to compute them with Paddle Quantum."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Background\n",
"\n",
"The quantum Fisher information (QFI) originates from the field of quantum sensing and have been versatile tools to study parameterized quantum systems [[1]](https://arxiv.org/abs/2103.15191), such as characterizing the overparameterization [[2]](https://arxiv.org/abs/2102.01659) and performing the quantum natural gradient descent [[3]](https://arxiv.org/abs/1909.02108). The QFI is a quantum analogue of the classical Fisher information (CFI). The CFI characterizes the sensibility of a parameterized **probability distribution** to parameter changes, while the QFI characterizes the sensibility of a parameterized **quantum state** to parameter changes.\n",
"\n",
"In a traditional introduction, the CFI will appear as a quantity of parameter estimation in mathematical statistics, which might be complicated and confusing for the beginners. This tutorial will introduce the CFI from a geometric point of view, which is not only helpful for intuitive understanding, but also easier to see the relationship between the CFI and QFI."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Classical Fisher information\n",
"\n",
"Let's consider the classical Fisher information first. Suppose we now have a parameterized probability distribution $p(\\boldsymbol{x};\\boldsymbol{\\theta})$. Here comes a question:\n",
"\n",
"- How much does a small parameter change result in the probability distribution change ?\n",
"\n",
"Since the question sounds like a perturbation problem, an intuition is to perform something like the Taylor expansion. But before expansion, we need to know which function to expand, i.e. we need to quantify the probability distribution change first. More formally, we need to define a distance measure between any two probability distributions, denoted by $d(p(\\boldsymbol{x};\\boldsymbol{\\theta}),p(\\boldsymbol{x};\\boldsymbol{\\theta}'))$, or $d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')$ for short.\n",
"\n",
"Generally, a legal distance measure is supposed to be non-negative and equal to zero if and only if two points are identical, i.e.\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')\\geq 0,\\\\\n",
"&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')=0~\\Leftrightarrow~\\boldsymbol{\\theta}=\\boldsymbol{\\theta}'.\n",
"\\end{aligned}\n",
"\\tag{1}\n",
"$$\n",
"\n",
"Considering the expansion of a small distance $d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})$, the conditions above lead to\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta})=0~\\Rightarrow~\\text{the zero order}=0,\\\\\n",
"&d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\geq 0~\\Rightarrow~\\boldsymbol{\\delta}=0~\\text{takes minimum}\n",
"~\\Rightarrow~\\text{the first order}=0.\n",
"\\end{aligned}\n",
"\\tag{2}\n",
"$$\n",
"\n",
"Thus, the second order is the lowest order that does not vanish in the expansion. So the expansion can be written as\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\n",
"=\\frac{1}{2}\\sum_{ij}\\delta_iM_{ij}\\delta_j+O(\\|\\boldsymbol{\\delta}\\|^3) \n",
"=\\frac{1}{2} \\boldsymbol{\\delta}^T M \\boldsymbol{\\delta} + O(\\|\\boldsymbol{\\delta}\\|^3),\n",
"\\end{aligned}\n",
"\\tag{3}\n",
"$$\n",
"\n",
"where\n",
"\n",
"$$\n",
"M_{ij}(\\boldsymbol{\\theta})=\\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0},\n",
"\\tag{4}\n",
"$$\n",
"\n",
"is exactly the Hessian matrix of the distance expansion, which is called [metric](http://en.wikipedia.org/wiki/Metric_tensor) of manifold in the context of differentiable geometry. The brief derivation above tells us that we can approximate a small distance as a quadratic form of the corresponding parameters, as shown in Fig.1, and the coefficient matrix of the quadratic form is exactly the Hessian matrix from the distance expansion, up to a $1/2$ factor.\n",
"\n",
"![feature map](./figures/FIM-fig-Sphere-metric.png \"Figure 1. Approximate a small distance on the 2-sphere as a quadratic form\")\n",
"<div style=\"text-align:center\">Figure 1. Approximate a small distance on the 2-sphere as a quadratic form </div>\n",
"\n",
"If the distance measure is specified to be the relative entropy / KL divergence, i.e.\n",
"$$\n",
"d_{\\mathrm{KL}}(\\boldsymbol{\\theta}, \\boldsymbol{\\theta}^{\\prime})=\\sum_{\\boldsymbol{x}} p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\log \\frac{p(\\boldsymbol{x};\\boldsymbol{\\theta})}{p(\\boldsymbol{x};\\boldsymbol{\\theta}^{\\prime})}.\n",
"\\tag{5}\n",
"$$\n",
"\n",
"The corresponding Hessian matrix\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\mathcal{I}_{ij}(\\boldsymbol{\\theta})&= \\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d_{\\mathrm{KL}}(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0}\\\\\n",
"&=-\\sum_{\\boldsymbol{x}} p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\partial_{i} \\partial_{j} \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})\n",
"=\\mathbb{E}_{\\boldsymbol{x}}[-\\partial_{i} \\partial_{j} \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})] \\\\\n",
"&=\\sum_{\\boldsymbol{x}} \\frac{1}{p(\\boldsymbol{x};\\boldsymbol{\\theta})} \\partial_i p(\\boldsymbol{x};\\boldsymbol{\\theta}) \\cdot \\partial_j p(\\boldsymbol{x};\\boldsymbol{\\theta})\n",
"=\\mathbb{E}_{\\boldsymbol{x}}[\\partial_i\\log p(\\boldsymbol{x};\\boldsymbol{\\theta})\\cdot \\partial_j \\log p(\\boldsymbol{x};\\boldsymbol{\\theta})].\n",
"\\end{aligned}\n",
"\\tag{6}\n",
"$$\n",
"\n",
"is the so-called classical Fisher information matrix (CFIM), with large entries indicating large sensibility to the corresponding parameter changes. Here we use the notation $\\partial_i=\\partial/\\partial \\theta_i$.\n",
"\n",
"Why is $\\mathcal{I}(\\boldsymbol{\\theta})$ called \"information\"? Geometrically, the CFIM characterizes the sensitivity / sharpness of a probability distribution in the vicinity of $\\boldsymbol{\\theta}$. The more sensitive it is to a parameter change, the easier one can discriminate it from others, the fewer samples are needed to discriminate it, the more information per sample can give.\n",
"\n",
"The measurement outcomes from a parameterized quantum circuit (PQC) form a parameterized probability distribution. So one can define a CFIM for each kind of measurement on a PQC. Currently, the main challenge of calculating CFIM on NISQ devices is that the number of possible measurement outputs increases exponentially with the number of qubits, which means that there may be many measurement outputs with low probabilities that never appear, leading to divergence in CFIM calculations. Possible solutions includes neglecting small probabilities (cause diverge) and Bayesian updating [[1]](https://arxiv.org/abs/2103.15191)."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Quantum Fisher information\n",
"\n",
"The quantum Fisher information is a natural quantum analogue of the classical notion above, where the expanded distance is not defined between two probability distributions, but two quantum states. A common choice is the fidelity distance \n",
"\n",
"$$\n",
"d_f(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')=2-2|\\langle\\psi(\\boldsymbol{\\theta})|\\psi(\\boldsymbol{\\theta}')\\rangle|^2.\n",
"\\tag{7}\n",
"$$\n",
"\n",
"where an additional factor $2$ here is manually multiplied to make the subsequent results resemble the CFIM. Hence formally, the quantum Fisher information matrix (QFIM) at a parameterized pure quantum state $|\\psi(\\boldsymbol{\\theta})\\rangle, \\boldsymbol{\\theta}\\in\\mathbb{R}^m$ is the Hessian matrix of the fidelity distance expansion, i.e.\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"\\mathcal{F}_{ij}(\\boldsymbol{\\theta})\n",
"&= \\left.\\frac{\\partial^2}{\\partial\\delta_i\\partial\\delta_j}d_{f}(\\boldsymbol{\\theta},\\boldsymbol{\\theta}+\\boldsymbol{\\delta})\\right|_{\\boldsymbol{\\delta}=0} \\\\\n",
"&=4 \\operatorname{Re}\\left[\\left\\langle\\partial_{i} \\psi \\mid \\partial_{j} \\psi\\right\\rangle - \\left\\langle\\partial_{i} \\psi \\mid \\psi\\right\\rangle\\left\\langle\\psi \\mid \\partial_{j} \\psi\\right\\rangle\\right],\n",
"\\end{aligned}\n",
"\\tag{8}\n",
"$$\n",
"\n",
"where we have omitted the argument $\\boldsymbol{\\theta}$ for simplicity. Similar to the CFIM, the QFIM characterizes the sensibility of a parameterized quantum state to a small change of parameters. In addition, it is worth mentioning that the QFIM can be seen as the real part of a complex matrix called the quantum geometric tensor, or say the Fubini-Study metric [[1]](https://arxiv.org/abs/2103.15191).\n",
"\n",
"Currently, the community has developed some techniques to calculate the QFIM for pure states on NISQ devices, among which the two most straight methods are\n",
"\n",
"- applying the second order parameter shift rule [[4]](https://arxiv.org/abs/2008.06517)\n",
"$$\n",
"\\begin{aligned}\n",
"\\mathcal{F}_{i j}=-\\frac{1}{2} \\Big(&|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}+(\\boldsymbol{e}_{i}+\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\n",
"-|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}+(\\boldsymbol{e}_{i}-\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\\\\\n",
"-&|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}-(\\boldsymbol{e}_{i}-\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\n",
"+|\\langle\\psi(\\boldsymbol{\\theta}) \\mid \\psi(\\boldsymbol{\\theta}-(\\boldsymbol{e}_{i}+\\boldsymbol{e}_{j}) \\frac{\\pi}{2})\\rangle|^{2}\\Big),\n",
"\\end{aligned}\n",
"\\tag{9}\n",
"$$\n",
"where $\\boldsymbol{e}_{i}$ denotes the unit vector corresponding to $\\theta_i$.\n",
"\n",
"- applying the finite difference expression to calculate the projection along a certain direction [[1]](https://arxiv.org/abs/2103.15191)\n",
"$$\n",
"\\boldsymbol{v}^{T} \\mathcal{F} \\boldsymbol{v} \\approx \\frac{4 d_{f}(\\boldsymbol{\\theta}, \\boldsymbol{\\theta}+\\epsilon \\boldsymbol{v})}{\\epsilon^{2}}.\n",
"\\tag{10}\n",
"$$\n",
"which can be regarded as the quantum analogue of the famed Fisher-Rao norm.\n",
"\n",
"For mixed states, the QFIM can be defined by the expansion of the Bures fidelity distance\n",
"\n",
"$$\n",
"d_B(\\boldsymbol{\\theta},\\boldsymbol{\\theta}')\\equiv \n",
"2-2\\left[\\text{Tr}\\left([\\sqrt{\\rho(\\boldsymbol{\\theta})} \\rho(\\boldsymbol{\\theta}')\\sqrt{\\rho(\\boldsymbol{\\theta})}]^{1/2}\\right)\\right]^2,\n",
"\\tag{11}\n",
"$$\n",
"\n",
"or equivalently ($\\log x\\sim x-1$), the $\\alpha=1/2$ \"sandwiched\" Rényi relative entropy [[5]](https://arxiv.org/abs/1308.5961)\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"d_R(\\boldsymbol{\\theta},\\boldsymbol{\\theta}') &\\equiv 2\\widetilde{D}_{\\alpha=1/2}(\\rho(\\boldsymbol{\\theta'}) \\| \\rho(\\boldsymbol{\\theta})), \\\\\n",
"\\widetilde{D}_{\\alpha}(\\rho \\| \\sigma) \n",
"&\\equiv \n",
"\\frac{1}{\\alpha-1} \\log \\operatorname{Tr}\\left[\\left(\\sigma^{\\frac{1-\\alpha}{2 \\alpha}} \\rho \\sigma^{\\frac{1-\\alpha}{2 \\alpha}}\\right)^{\\alpha}\\right].\\\\\n",
"\\end{aligned}\n",
"\\tag{12}\n",
"$$\n",
"\n",
"Please see the review [[1]](https://arxiv.org/abs/2103.15191) for more details."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### The relation between CFIM and QFIM\n",
"\n",
"By definition, for a parameterized quantum circuit, the CFIM depends on the measurement bases while the QFIM does not. In fact, one can prove that the QFIM of a quantum state $\\rho(\\boldsymbol{\\theta})$ is an upper bound of the CFIM obtained by arbitrary measurement from the same quantum state, i.e.\n",
"\n",
"$$\n",
"\\mathcal{I}[\\mathcal{E}[\\rho(\\boldsymbol{\\theta})]]\\leq \\mathcal{F}[\\rho(\\boldsymbol{\\theta})],~\\forall\\mathcal{E},\n",
"\\tag{13}\n",
"$$\n",
"\n",
"where $\\mathcal{E}$ denotes the quantum operation corresponding to the measurement, and the inequality between two positive matrices means that the large minus the small is still a positive matrix. This is a natural result since measurements can not extract more information than the quantum state itself, which mathematically stems from the monotonicity of the fidelity distance with respect to trace-preserving quantum operations [[1]](https://arxiv.org/abs/2103.15191)."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Application: effective dimension\n",
"\n",
"The maximal rank of the CFIM / QFIM over the parameter space $\\Theta$ is a quantity to characterize the **capacity** of a classical / quantum neural network, called effective classical / quantum dimension\n",
"\n",
"$$\n",
"d_{\\text{eff}}=\\underset{\\boldsymbol{\\theta}\\in\\Theta} {\\max}\n",
"\\operatorname{rank}{\\mathcal{F}}(\\boldsymbol{\\theta}).\n",
"\\tag{14}\n",
"$$\n",
"\n",
"The rank captures in how many directions parameter changes will result in the probability distribution / quantum state changes. A not-full rank means that some changes of parameters can not actually change the probability distribution / quantum state, or say there are redundant degrees of freedom of parameters that can be projected out and the model is therefore overparameterized. On the other hand, a larger effective dimension corresponds to more directions that can be extended, suggesting a more extensive space occupied by the model, i.e. a larger capacity.\n",
"\n",
"In the context of machine learning, the so-called empirical CFIM [[6]](https://arxiv.org/abs/2011.00027) is more widely used, which is defined by a summation over samples instead of the expectation in the original definition\n",
"\n",
"$$\n",
"\\tilde{\\mathcal{I}}_{ij}(\\boldsymbol{\\theta})\n",
"=\\frac{1}{n}\\sum_{k=1}^{n}\n",
"\\partial_i\\log p(x_k,y_k;\\boldsymbol{\\theta})\n",
"\\partial_j\\log p(x_k,y_k;\\boldsymbol{\\theta}),\n",
"\\tag{15}\n",
"$$\n",
"\n",
"where $(x_k,y_k)^{n}_{k=1}$ are identical independent distributed training data drawn from the distribution $p(x,y;\\boldsymbol{\\theta})=p(y|x;\\boldsymbol{\\theta})p(x)$. Clearly, the empirical CFIM can converge to the CFIM in the limit of infinite samples if (1) the model has been well-trained and (2) the model has enough capacity to cover the underlying data distribution. The advantage of the empirical CFIM is that it can be calculated directly using the training data at hand, instead of calculating the original integral by generating new samples. \n",
"\n",
"By use of the empirical CFIM, a variant of the effective dimension can be defined as\n",
"\n",
"$$\n",
"d_{\\text{eff}}(\\gamma, n)=\n",
"2 \\frac{\\log \\left(\\frac{1}{V_{\\Theta}} \\int_{\\Theta} \\sqrt{\\operatorname{det}\\left( 1 + \\frac{\\gamma n}{2 \\pi \\log n} \\hat{\\mathcal{I}}( \\boldsymbol{\\theta})\\right)} \\mathrm{d} \\boldsymbol{\\theta} \\right)}\n",
"{\\log \\left(\\frac{\\gamma n}{2 \\pi \\log n}\\right)},\n",
"\\tag{16}\n",
"$$\n",
"\n",
"where $V_{\\Theta}:=\\int_{\\Theta} \\mathrm{d} \\boldsymbol{\\theta} \\in \\mathbb{R}_{+}$ is the volume of the parameter space. $\\gamma\\in(0,1]$ is an artificial tunable parameter. $\\hat{\\mathcal{I}} (\\boldsymbol{\\theta}) \\in \\mathbb{R}^{d\\times d}$ is the normalized empirical CFIM\n",
"\n",
"$$\n",
"\\hat{\\mathcal{I}}_{i j}(\\boldsymbol{\\theta}):= \\frac{V_{\\Theta} d }{\\int_{\\Theta} \\operatorname{Tr}(F( \\boldsymbol{\\theta} ) \\mathrm{d} \\theta} \\tilde{\\mathcal{I}}_{i j}(\\boldsymbol{\\theta}).\n",
"\\tag{17}\n",
"$$\n",
"\n",
"This definition might be strange and confusing at first glance, which is far more complicated than the maximal rank of the CFIM. However, it can converge to the maximal rank of the CFIM in the limit of infinite samples $n\\rightarrow \\infty$ [[6]](https://arxiv.org/abs/2011.00027). Regardless of the coefficients and the logarithm, the effective dimension here can be seen roughly as the geometric mean of the spectrum of the normalized CFIM plus an identity, then averaging over the parameter space. Associated with the inequality between the geometric mean and the arithmetic mean, we may expect that a more uniform empirical CFIM spectrum leads to a larger effective dimension, which is consistent with our natural impression. In this sense, it is a \"soft\" version of the effective dimension.\n",
"\n",
"In addition, the Fisher information can not only provide an capacity measure, but also can serve as an indicator of trainability. If the entries of the Fisher information vanish exponentially with the system size averaging over the parameter space, i.e. the sensitivity becomes exponentially small, we can not distinguish them efficiently, which indicates the existence of barrens plateaus [[6]](https://arxiv.org/abs/2011.00027)."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"## Paddle Quantum Implementation"
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Calculate the QFIM\n",
"\n",
"With Paddle Quantum, one can obtain the QFIM conveniently by the following steps.\n",
"\n",
"1. Define a quantum circuit using `UAnsatz`.\n",
"2. Define a `QuantumFisher` class as a calculator of the QFIM.\n",
"3. Use the method `get_qfisher_matrix()` to calculate the QFIM.\n",
"\n",
"The calculator `QuantumFisher` will keep track of the change of the circuit `UAnsatz`.\n",
"\n",
"Now let's code. Firstly, import packages."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 1,
"source": [
"import paddle\n",
"from paddle_quantum.circuit import UAnsatz\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from paddle_quantum.utils import QuantumFisher, ClassicalFisher\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Then, define a quantum circuit. As a simple example, we exploit a single qubit parameterized by two Bloch angles\n",
"\n",
"$$\n",
"|\\psi(\\theta,\\phi)\\rangle=R_z(\\phi)R_y(\\theta)|0\\rangle=e^{-i\\phi/2}\\cos\\frac{\\theta}{2}|0\\rangle+e^{i\\phi/2}\\sin\\frac{\\theta}{2}|1\\rangle.\n",
"\\tag{18}\n",
"$$\n",
"\n",
"The corresponding QFIM can be directly calculated using Eq.(8). The analytical result reads\n",
"\n",
"$$\n",
"\\mathcal{F}(\\theta,\\phi)=\\left(\\begin{matrix}\n",
"1&0\\\\\n",
"0&\\sin^2\\theta\n",
"\\end{matrix}\\right).\n",
"\\tag{19}\n",
"$$"
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 2,
"source": [
"def circuit_bloch():\n",
" cir = UAnsatz(1)\n",
" theta = 2 * np.pi * np.random.random(2)\n",
" theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n",
" cir.ry(theta[0], which_qubit=0)\n",
" cir.rz(theta[1], which_qubit=0)\n",
" \n",
" return cir"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 3,
"source": [
"cir = circuit_bloch()\n",
"print(cir)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"--Ry(1.888)----Rz(2.181)--\n",
" \n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Define a QFIM calculator and calculate the QFIM element $\\mathcal{F}_{\\phi\\phi}$ corresponding to different $\\theta$."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 4,
"source": [
"qf = QuantumFisher(cir)\n",
"# Record the QFIM element F_{phi,phi}\n",
"list_qfisher_elements = []\n",
"num_thetas = 21\n",
"thetas = np.linspace(0, np.pi, num_thetas)\n",
"for theta in thetas:\n",
" list_param = cir.get_param().tolist()\n",
" list_param[0] = theta\n",
" cir.update_param(list_param)\n",
" # Calculate the QFIM\n",
" qfim = qf.get_qfisher_matrix()\n",
" print(f'The QFIM at {np.array(list_param)} is \\n {qfim.round(14)}.')\n",
" list_qfisher_elements.append(qfim[1][1])"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"The QFIM at [0. 2.18107874] is \n",
" [[1. 0.]\n",
" [0. 0.]].\n",
"The QFIM at [0.15707963 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.02447174]].\n",
"The QFIM at [0.31415927 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.0954915]].\n",
"The QFIM at [0.4712389 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.20610737]].\n",
"The QFIM at [0.62831853 2.18107874] is \n",
" [[ 1. -0. ]\n",
" [-0. 0.3454915]].\n",
"The QFIM at [0.78539816 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.5]].\n",
"The QFIM at [0.9424778 2.18107874] is \n",
" [[ 1. -0. ]\n",
" [-0. 0.6545085]].\n",
"The QFIM at [1.09955743 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.79389263]].\n",
"The QFIM at [1.25663706 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.9045085]].\n",
"The QFIM at [1.41371669 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.97552826]].\n",
"The QFIM at [1.57079633 2.18107874] is \n",
" [[1. 0.]\n",
" [0. 1.]].\n",
"The QFIM at [1.72787596 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.97552826]].\n",
"The QFIM at [1.88495559 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.9045085]].\n",
"The QFIM at [2.04203522 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.79389263]].\n",
"The QFIM at [2.19911486 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.6545085]].\n",
"The QFIM at [2.35619449 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.5]].\n",
"The QFIM at [2.51327412 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.3454915]].\n",
"The QFIM at [2.67035376 2.18107874] is \n",
" [[ 1. -0. ]\n",
" [-0. 0.20610737]].\n",
"The QFIM at [2.82743339 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.0954915]].\n",
"The QFIM at [2.98451302 2.18107874] is \n",
" [[1. 0. ]\n",
" [0. 0.02447174]].\n",
"The QFIM at [3.14159265 2.18107874] is \n",
" [[1. 0.]\n",
" [0. 0.]].\n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Plot the outputs of the QFIM element $\\mathcal{F}_{\\phi\\phi}$ as function of $\\theta$."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 5,
"source": [
"# Create a figure\n",
"fig = plt.figure(figsize=(9, 6))\n",
"ax = fig.add_subplot(111)\n",
"# Plot the QFIM\n",
"ax.plot(thetas, list_qfisher_elements, 's', markersize=11, markerfacecolor='none')\n",
"# Plot sin^2 theta\n",
"ax.plot(thetas, np.sin(thetas) ** 2, linestyle=(0, (5, 3)))\n",
"# Set legends, labels, ticks\n",
"label_font_size = 18\n",
"ax.legend(['get_qfisher_matrix()[1][1]', '$\\\\sin^2\\\\theta$'], \n",
" prop= {'size': label_font_size}, frameon=False) \n",
"ax.set_xlabel('$\\\\theta$', fontsize=label_font_size)\n",
"ax.set_ylabel('QFIM element $\\\\mathcal{F}_{\\\\phi\\\\phi}$', fontsize=label_font_size)\n",
"ax.tick_params(labelsize=label_font_size)"
],
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
],
"image/png": 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"
},
"metadata": {
"needs_background": "light"
}
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We can see that the outputs are consistent with the analytical results.\n",
"\n",
"Moreover, one can use the method `get_qfisher_norm()` to calculate the quantum Fisher-Rao norm in Eq.(10), i.e. the QFIM projection along a certain direction.\n",
"\n",
"As a different example, we exploit two qubits with a typical hardware-efficient ansatz\n",
"\n",
"$$\n",
"|\\psi(\\boldsymbol{\\theta})\\rangle=\\left[R_{y}\\left( \\theta_{3}\\right) \\otimes R_{y}\\left( \\theta_{4}\\right)\\right] \\text{CNOT}_{0,1}\\left[ R_{y}\\left( \\theta_{1}\\right) \\otimes R_{y}\\left( \\theta_{2}\\right)\\right]|00\\rangle.\n",
"\\tag{20}\n",
"$$\n",
"\n",
"The corresponding QFIM reads\n",
"\n",
"$$\n",
"\\mathcal{F}(\\theta_1,\\theta_2,\\theta_3,\\theta_4)=\\left(\\begin{array}{cc|cc}\n",
"1 & 0 & \\sin \\theta_{2} & 0 \\\\\n",
"0 & 1 & 0 & \\cos \\theta_{1} \\\\\n",
"\\hline \n",
"\\sin \\theta_{2} & 0 & 1 & -\\sin\\theta_1\\cos\\theta_2 \\\\\n",
"0 & \\cos \\theta_{1} & -\\sin\\theta_1\\cos\\theta_2 & 1\n",
"\\end{array}\\right).\n",
"\\tag{21}\n",
"$$\n",
"\n",
"Define the corresponding quantum circuit."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 6,
"source": [
"def circuit_hardeff_2qubit():\n",
" cir = UAnsatz(2)\n",
" theta = 2 * np.pi * np.random.random(4)\n",
" theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n",
" cir.ry(theta[0], which_qubit=0)\n",
" cir.ry(theta[1], which_qubit=1)\n",
" cir.cnot(control=[0, 1])\n",
" cir.ry(theta[2], which_qubit=0)\n",
" cir.ry(theta[3], which_qubit=1)\n",
"\n",
" return cir"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 7,
"source": [
"cir = circuit_hardeff_2qubit()\n",
"print(cir)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"--Ry(2.614)----*----Ry(3.253)--\n",
" | \n",
"--Ry(2.906)----x----Ry(5.027)--\n",
" \n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Define a QFIM calculator and calculate the quantum Fisher-Rao norm $\\boldsymbol{v}^T\\mathcal{F}\\boldsymbol{v}$ along the direction $\\boldsymbol{v}=(1,1,1,1)$ corresponding to different $\\theta$ (set $\\theta_1=\\theta_2=\\theta$)."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 8,
"source": [
"qf = QuantumFisher(cir)\n",
"v = [1, 1, 1, 1]\n",
"# Record the QFI norm\n",
"list_qfisher_norm = []\n",
"num_thetas = 41\n",
"thetas = np.linspace(0, np.pi * 4, num_thetas)\n",
"for theta in thetas:\n",
" list_param = cir.get_param().tolist()\n",
" list_param[0] = theta\n",
" list_param[1] = theta\n",
" cir.update_param(list_param)\n",
" # Calculate the QFI norm\n",
" qfisher_norm = qf.get_qfisher_norm(v)\n",
" print(\n",
" f'The QFI norm along {v} at {np.array(list_param)} is {qfisher_norm:.8f}.'\n",
" )\n",
" list_qfisher_norm.append(qfisher_norm)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"The QFI norm along [1, 1, 1, 1] at [0. 0. 3.2533421 5.02652273] is 5.99962501.\n",
"The QFI norm along [1, 1, 1, 1] at [0.31415927 0.31415927 3.2533421 5.02652273] is 5.93033916.\n",
"The QFI norm along [1, 1, 1, 1] at [0.62831853 0.62831853 3.2533421 5.02652273] is 5.84133590.\n",
"The QFI norm along [1, 1, 1, 1] at [0.9424778 0.9424778 3.2533421 5.02652273] is 5.84309143.\n",
"The QFI norm along [1, 1, 1, 1] at [1.25663706 1.25663706 3.2533421 5.02652273] is 5.93367838.\n",
"The QFI norm along [1, 1, 1, 1] at [1.57079633 1.57079633 3.2533421 5.02652273] is 5.99962501.\n",
"The QFI norm along [1, 1, 1, 1] at [1.88495559 1.88495559 3.2533421 5.02652273] is 5.86697827.\n",
"The QFI norm along [1, 1, 1, 1] at [2.19911486 2.19911486 3.2533421 5.02652273] is 5.38230779.\n",
"The QFI norm along [1, 1, 1, 1] at [2.51327412 2.51327412 3.2533421 5.02652273] is 4.49128513.\n",
"The QFI norm along [1, 1, 1, 1] at [2.82743339 2.82743339 3.2533421 5.02652273] is 3.28287364.\n",
"The QFI norm along [1, 1, 1, 1] at [3.14159265 3.14159265 3.2533421 5.02652273] is 1.97995933.\n",
"The QFI norm along [1, 1, 1, 1] at [3.45575192 3.45575192 3.2533421 5.02652273] is 0.87758767.\n",
"The QFI norm along [1, 1, 1, 1] at [3.76991118 3.76991118 3.2533421 5.02652273] is 0.25010151.\n",
"The QFI norm along [1, 1, 1, 1] at [4.08407045 4.08407045 3.2533421 5.02652273] is 0.26070618.\n",
"The QFI norm along [1, 1, 1, 1] at [4.39822972 4.39822972 3.2533421 5.02652273] is 0.90660775.\n",
"The QFI norm along [1, 1, 1, 1] at [4.71238898 4.71238898 3.2533421 5.02652273] is 2.01995733.\n",
"The QFI norm along [1, 1, 1, 1] at [5.02654825 5.02654825 3.2533421 5.02652273] is 3.32425271.\n",
"The QFI norm along [1, 1, 1, 1] at [5.34070751 5.34070751 3.2533421 5.02652273] is 4.52539873.\n",
"The QFI norm along [1, 1, 1, 1] at [5.65486678 5.65486678 3.2533421 5.02652273] is 5.40406149.\n",
"The QFI norm along [1, 1, 1, 1] at [5.96902604 5.96902604 3.2533421 5.02652273] is 5.87599852.\n",
"The QFI norm along [1, 1, 1, 1] at [6.28318531 6.28318531 3.2533421 5.02652273] is 5.99962501.\n",
"The QFI norm along [1, 1, 1, 1] at [6.59734457 6.59734457 3.2533421 5.02652273] is 5.93033916.\n",
"The QFI norm along [1, 1, 1, 1] at [6.91150384 6.91150384 3.2533421 5.02652273] is 5.84133590.\n",
"The QFI norm along [1, 1, 1, 1] at [7.2256631 7.2256631 3.2533421 5.02652273] is 5.84309143.\n",
"The QFI norm along [1, 1, 1, 1] at [7.53982237 7.53982237 3.2533421 5.02652273] is 5.93367838.\n",
"The QFI norm along [1, 1, 1, 1] at [7.85398163 7.85398163 3.2533421 5.02652273] is 5.99962501.\n",
"The QFI norm along [1, 1, 1, 1] at [8.1681409 8.1681409 3.2533421 5.02652273] is 5.86697827.\n",
"The QFI norm along [1, 1, 1, 1] at [8.48230016 8.48230016 3.2533421 5.02652273] is 5.38230779.\n",
"The QFI norm along [1, 1, 1, 1] at [8.79645943 8.79645943 3.2533421 5.02652273] is 4.49128513.\n",
"The QFI norm along [1, 1, 1, 1] at [9.1106187 9.1106187 3.2533421 5.02652273] is 3.28287364.\n",
"The QFI norm along [1, 1, 1, 1] at [9.42477796 9.42477796 3.2533421 5.02652273] is 1.97995933.\n",
"The QFI norm along [1, 1, 1, 1] at [9.73893723 9.73893723 3.2533421 5.02652273] is 0.87758767.\n",
"The QFI norm along [1, 1, 1, 1] at [10.05309649 10.05309649 3.2533421 5.02652273] is 0.25010151.\n",
"The QFI norm along [1, 1, 1, 1] at [10.36725576 10.36725576 3.2533421 5.02652273] is 0.26070618.\n",
"The QFI norm along [1, 1, 1, 1] at [10.68141502 10.68141502 3.2533421 5.02652273] is 0.90660775.\n",
"The QFI norm along [1, 1, 1, 1] at [10.99557429 10.99557429 3.2533421 5.02652273] is 2.01995733.\n",
"The QFI norm along [1, 1, 1, 1] at [11.30973355 11.30973355 3.2533421 5.02652273] is 3.32425271.\n",
"The QFI norm along [1, 1, 1, 1] at [11.62389282 11.62389282 3.2533421 5.02652273] is 4.52539873.\n",
"The QFI norm along [1, 1, 1, 1] at [11.93805208 11.93805208 3.2533421 5.02652273] is 5.40406149.\n",
"The QFI norm along [1, 1, 1, 1] at [12.25221135 12.25221135 3.2533421 5.02652273] is 5.87599852.\n",
"The QFI norm along [1, 1, 1, 1] at [12.56637061 12.56637061 3.2533421 5.02652273] is 5.99962501.\n"
]
}
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 9,
"source": [
"# Create a figure\n",
"fig= plt.figure(figsize=(9, 6))\n",
"ax = fig.add_subplot(111)\n",
"# Plot the QFI norm\n",
"ax.plot(thetas, list_qfisher_norm, 's', markersize=11, markerfacecolor='none')\n",
"analytical_qfi_norm = 4 + 2 * np.sin(thetas) + 2 * np.cos(thetas) - 2 * np.cos(thetas) * np.sin(thetas)\n",
"ax.plot(thetas, analytical_qfi_norm, linestyle=(0, (5, 3)))\n",
"# Set legends, labels, ticks\n",
"ax.legend(\n",
" ['get_qfisher_norm()', '$4+2\\\\sin\\\\theta+2\\\\cos\\\\theta-2\\\\sin\\\\theta\\\\cos\\\\theta$'], \n",
" loc='best', prop= {'size': label_font_size}, frameon=False,\n",
")\n",
"ax.set_xlabel('$\\\\theta$', fontsize=label_font_size)\n",
"ax.set_ylabel('QFI norm along $v=(1,1,1,1)$', fontsize=label_font_size)\n",
"ax.set_ylim([-1, 9])\n",
"ax.tick_params(labelsize=label_font_size)"
],
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
],
"image/png": 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"
},
"metadata": {
"needs_background": "light"
}
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"We can see that the outputs are consistent with the analytical results."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Calculate the effective quantum dimension\n",
"\n",
"With Paddle Quantum, one can obtain the effective quantum dimension (EQD) by simply using the method `get_eff_qdim()`. For example, the EQD of the hardware-efficient ansatz shown above can be calculated as follows."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 10,
"source": [
"cir = circuit_hardeff_2qubit()\n",
"qf = QuantumFisher(cir)\n",
"print(cir)\n",
"print(f'The number of parameters is {len(cir.get_param().tolist())}.')\n",
"print(f'The EQD is {qf.get_eff_qdim()}. \\n')"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"--Ry(4.248)----*----Ry(1.233)--\n",
" | \n",
"--Ry(6.121)----x----Ry(4.717)--\n",
" \n",
"The number of parameters is 4.\n",
"The EQD is 3. \n",
"\n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"In this example, the EQD is smaller than the number of parameters, which can be easily seen from the fact that the two $R_y$ gates on the control wire can be merged without changing anything. This inefficiency can be fixed by simply replacing one of the $R_y$ gates with a $R_x$ gate, and then the EQD will increase by one.\n",
"\n",
"If we continue to add gates to the circuit, can we make the EQD grow indefinitely? The answer is clearly no. Provided $n$ qubits, an obvious upper bound can be given by the real number degrees of freedom in a general quantum state, which is equal to $2\\cdot 2^n-2$. The minus two reflect the two constraints of normalization and global phase independence. This can be verified by the following example."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 11,
"source": [
"def circuit_hardeff_overparam():\n",
" cir = UAnsatz(2)\n",
" theta = 2 * np.pi * np.random.random(8)\n",
" theta = paddle.to_tensor(theta, stop_gradient=False, dtype='float64')\n",
" cir.ry(theta[0], which_qubit=0)\n",
" cir.ry(theta[1], which_qubit=1)\n",
" cir.rx(theta[2], which_qubit=0)\n",
" cir.rx(theta[3], which_qubit=1)\n",
" cir.cnot(control=[0, 1])\n",
" cir.ry(theta[4], which_qubit=0)\n",
" cir.ry(theta[5], which_qubit=1)\n",
" cir.rx(theta[6], which_qubit=0)\n",
" cir.rx(theta[7], which_qubit=1)\n",
"\n",
" return cir\n",
"\n",
"\n",
"cir = circuit_hardeff_overparam()\n",
"qf = QuantumFisher(cir)\n",
"print(cir)\n",
"print(f'The number of parameters is {len(cir.get_param().tolist())}.')\n",
"print(f'The EQD is {qf.get_eff_qdim()}. \\n')"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"--Ry(0.173)----Rx(5.837)----*----Ry(3.082)----Rx(3.997)--\n",
" | \n",
"--Ry(1.354)----Rx(0.536)----x----Ry(5.267)----Rx(5.647)--\n",
" \n",
"The number of parameters is 8.\n",
"The EQD is 6. \n",
"\n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"### Calculate the CFIM and effective dimension\n",
"\n",
"Here we exploit a brief example to show how to calculate the effective dimension defined in Eq.(16) with respect to a quantum neural network with Paddle Quantum.\n",
"\n",
"Firstly, define the encoding method from classical data to quantum data."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 12,
"source": [
"def U_theta(x, theta, num_qubits, depth, encoding):\n",
" cir = UAnsatz(num_qubits)\n",
" if encoding == 'IQP':\n",
" S = [[i, i + 1] for i in range(num_qubits - 1)]\n",
" cir.iqp_encoding(x, num_repeats=1, pattern=S)\n",
" cir.complex_entangled_layer(theta, depth)\n",
" elif encoding == 're-uploading':\n",
" for i in range(depth):\n",
" cir.complex_entangled_layer(theta[i:i + 1], depth=1)\n",
" for j in range(num_qubits):\n",
" cir.rx(x[j], which_qubit=j)\n",
" cir.complex_entangled_layer(theta[-1:], depth=1)\n",
" else:\n",
" raise RuntimeError('Non-existent encoding method')\n",
" return cir"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Then, define our quantum neural network along with the loss function using PaddlePaddle."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 13,
"source": [
"import paddle.nn as nn\n",
"\n",
"class QuantumNeuralNetwork(nn.Layer):\n",
" def __init__(self, num_qubits, depth, encoding):\n",
" super().__init__()\n",
" self.num_qubits, self.depth, self.encoding = num_qubits, depth, encoding\n",
" if self.encoding == 'IQP':\n",
" self.theta = self.create_parameter(\n",
" shape=[self.depth, self.num_qubits, 3],\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0.0,\n",
" high=2 *\n",
" np.pi),\n",
" dtype='float64',\n",
" is_bias=False)\n",
" elif self.encoding == 're-uploading':\n",
" self.theta = self.create_parameter(\n",
" shape=[self.depth + 1, self.num_qubits, 3],\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0.0,\n",
" high=2 *\n",
" np.pi),\n",
" dtype='float64',\n",
" is_bias=False)\n",
" else:\n",
" raise RuntimeError('Non-existent encoding method')\n",
"\n",
" def forward(self, x):\n",
" if not paddle.is_tensor(x):\n",
" x = paddle.to_tensor(x)\n",
" cir = U_theta(x, self.theta, self.num_qubits, self.depth,\n",
" self.encoding)\n",
" cir.run_state_vector()\n",
" return cir.expecval([[1.0, 'z0']]) * paddle.to_tensor(\n",
" [0.5], dtype='float64') + paddle.to_tensor([0.5], dtype='float64')"
],
"outputs": [],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Finally, define a CFIM calculator and calculate the effective dimension corresponding to different size of training samples."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 17,
"source": [
"# Configure model parameters\n",
"num_qubits = 4\n",
"depth = 2\n",
"num_inputs = 100\n",
"num_thetas = 10\n",
"# Define the CFIM calculator\n",
"cfim = ClassicalFisher(model=QuantumNeuralNetwork,\n",
" num_thetas=num_thetas,\n",
" num_inputs=num_inputs,\n",
" num_qubits=num_qubits,\n",
" depth=depth,\n",
" encoding='IQP')\n",
"# Compute the normalized classical Fisher information\n",
"fim, _ = cfim.get_normalized_cfisher()\n",
"# Compute the effective dimension for different size of samples\n",
"n = [5000, 8000, 10000, 40000, 60000, 100000, 150000, 200000, 500000, 1000000]\n",
"effdim = cfim.get_eff_dim(fim, n)"
],
"outputs": [
{
"output_type": "stream",
"name": "stderr",
"text": [
"running in get_gradient: 100%|##################################| 1000/1000 [02:05<00:00, 7.94it/s]\n"
]
}
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"Plot the ratio of the effective dimension over number of parameters vs. sample size."
],
"metadata": {}
},
{
"cell_type": "code",
"execution_count": 19,
"source": [
"fig = plt.figure(figsize=(9, 6))\n",
"ax = fig.add_subplot(111)\n",
"print('the number of parameters：%s' % cfim.num_params)\n",
"ax.plot(n, np.array(effdim) / cfim.num_params)\n",
"label_font_size = 14\n",
"ax.set_xlabel('sample size', fontsize=label_font_size)\n",
"ax.set_ylabel('effective dimension / number of parameters', fontsize=label_font_size)\n",
"ax.tick_params(labelsize=label_font_size)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"the number of parameters：24\n"
]
},
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
],
"image/png": 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"
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"needs_background": "light"
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{
"cell_type": "markdown",
"source": [
"## Conclusion\n",
"\n",
"This tutorial briefly introduces the concept of classical and quantum Fisher information and their relationship from a geometric point of view. Then, we illustrates their applications in quantum machine learning by taking effective dimension as an example. Finally, we show how to actually perform calculations of these quantities with Paddle Quantum."
],
"metadata": {}
},
{
"cell_type": "markdown",
"source": [
"_______\n",
"\n",
"## References\n",
"\n",
"[1] Meyer, Johannes Jakob. \"Fisher information in noisy intermediate-scale quantum applications.\" [arXiv preprint arXiv:2103.15191 (2021).](https://arxiv.org/abs/2103.15191)\n",
"\n",
"[2] Haug, Tobias, Kishor Bharti, and M. S. Kim. \"Capacity and quantum geometry of parametrized quantum circuits.\" [arXiv preprint arXiv:2102.01659 (2021).](https://arxiv.org/abs/2102.01659)\n",
"\n",
"[3] Stokes, James, et al. \"Quantum natural gradient.\" [Quantum 4 (2020): 269.](https://quantum-journal.org/papers/q-2020-05-25-269/)\n",
"\n",
"[4] Mari, Andrea, Thomas R. Bromley, and Nathan Killoran. \"Estimating the gradient and higher-order derivatives on quantum hardware.\" [Physical Review A 103.1 (2021): 012405.](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.103.012405)\n",
"\n",
"[5] Datta, Nilanjana, and Felix Leditzky. \"A limit of the quantum Rényi divergence.\" [Journal of Physics A: Mathematical and Theoretical 47.4 (2014): 045304.](https://iopscience.iop.org/article/10.1088/1751-8113/47/4/045304)\n",
"\n",
"[6] Abbas, Amira, et al. \"The power of quantum neural networks.\" [Nature Computational Science 1.6 (2021): 403-409.](https://www.nature.com/articles/s43588-021-00084-1)"
],
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"display_name": "Python 3",
"language": "python",
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\ No newline at end of file
tutorial/qnn_research/Noise_CN.ipynb
浏览文件 @ 016af983
...@@ -2,6 +2,7 @@ ...@@ -2,6 +2,7 @@
"cells": [ "cells": [
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "dedicated-alexander",
"metadata": {}, "metadata": {},
"source": [ "source": [
"# 在 Paddle Quantum 中模拟含噪量子电路\n", "# 在 Paddle Quantum 中模拟含噪量子电路\n",
...@@ -11,6 +12,7 @@ ...@@ -11,6 +12,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "weird-functionality",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## 噪声简介\n", "## 噪声简介\n",
...@@ -54,7 +56,7 @@ ...@@ -54,7 +56,7 @@
"\\tag{4}\n", "\\tag{4}\n",
"$$\n", "$$\n",
"\n", "\n",
"其中 $X,I$ 是泡利矩阵。 对应的 *Kruas* 算符为：\n", "其中 $X,I$ 是泡利矩阵。 对应的 *Kraus* 算符为：\n",
"\n", "\n",
"$$\n", "$$\n",
"E_0 = \\sqrt{1-p}\n", "E_0 = \\sqrt{1-p}\n",
...@@ -77,6 +79,7 @@ ...@@ -77,6 +79,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "transsexual-hayes",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Paddle Quantum 中添加信道的方式\n", "### Paddle Quantum 中添加信道的方式\n",
...@@ -87,6 +90,7 @@ ...@@ -87,6 +90,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 1, "execution_count": 1,
"id": "scheduled-attraction",
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-08T05:16:08.247239Z", "end_time": "2021-04-08T05:16:08.247239Z",
...@@ -136,6 +140,7 @@ ...@@ -136,6 +140,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "indian-slave",
"metadata": {}, "metadata": {},
"source": [ "source": [
"之后，我们加上一个 $p=0.1$ 的比特反转噪声，并测量通过信道之后的量子比特。 \n", "之后，我们加上一个 $p=0.1$ 的比特反转噪声，并测量通过信道之后的量子比特。 \n",
...@@ -145,6 +150,7 @@ ...@@ -145,6 +150,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 2, "execution_count": 2,
"id": "fiscal-literature",
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-08T05:16:09.221527Z", "end_time": "2021-04-08T05:16:09.221527Z",
...@@ -193,6 +199,7 @@ ...@@ -193,6 +199,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "bibliographic-undergraduate",
"metadata": {}, "metadata": {},
"source": [ "source": [
"可以看到，经过了比特反转信道（概率为 $p=0.1$）之后的量子态变成了混合态 $0.9 | 0 \\rangle \\langle 0 | + 0.1 | 1 \\rangle \\langle 1 |$。\n", "可以看到，经过了比特反转信道（概率为 $p=0.1$）之后的量子态变成了混合态 $0.9 | 0 \\rangle \\langle 0 | + 0.1 | 1 \\rangle \\langle 1 |$。\n",
...@@ -201,6 +208,7 @@ ...@@ -201,6 +208,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "million-diagnosis",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### 常用噪声信道\n", "### 常用噪声信道\n",
...@@ -307,6 +315,7 @@ ...@@ -307,6 +315,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "alert-senator",
"metadata": {}, "metadata": {},
"source": [ "source": [
"### 自定义信道\n", "### 自定义信道\n",
...@@ -317,6 +326,7 @@ ...@@ -317,6 +326,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 3,
"id": "mobile-death",
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-08T05:17:30.681411Z", "end_time": "2021-04-08T05:17:30.681411Z",
...@@ -375,6 +385,7 @@ ...@@ -375,6 +385,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "proper-director",
"metadata": {}, "metadata": {},
"source": [ "source": [
"按照上述例子，用户可以通过自定义 *Kraus* 算符的方式实现特定的信道。" "按照上述例子，用户可以通过自定义 *Kraus* 算符的方式实现特定的信道。"
...@@ -382,6 +393,7 @@ ...@@ -382,6 +393,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "tested-elder",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## 拓展：Paddle Quantum 模拟含噪纠缠资源\n", "## 拓展：Paddle Quantum 模拟含噪纠缠资源\n",
...@@ -393,6 +405,7 @@ ...@@ -393,6 +405,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 4,
"id": "spread-monkey",
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-08T05:24:35.552425Z", "end_time": "2021-04-08T05:24:35.552425Z",
...@@ -450,6 +463,7 @@ ...@@ -450,6 +463,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "comparable-athletics",
"metadata": {}, "metadata": {},
"source": [ "source": [
"**注释：** 在 [纠缠蒸馏](../locc/EntanglementDistillation_LOCCNET_CN.ipynb) 的教程中我们介绍了如何利用 Paddle Quantm 中的 LoccNet 模块来研究纠缠蒸馏，即利用多个含噪声的纠缠对来提取高保真度的纠缠对，感兴趣的读者可以前往阅读。" "**注释：** 在 [纠缠蒸馏](../locc/EntanglementDistillation_LOCCNET_CN.ipynb) 的教程中我们介绍了如何利用 Paddle Quantm 中的 LoccNet 模块来研究纠缠蒸馏，即利用多个含噪声的纠缠对来提取高保真度的纠缠对，感兴趣的读者可以前往阅读。"
...@@ -457,6 +471,7 @@ ...@@ -457,6 +471,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "elegant-bikini",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## 应用： Paddle Quantum 模拟含噪变分量子本征求解器（VQE）\n", "## 应用： Paddle Quantum 模拟含噪变分量子本征求解器（VQE）\n",
...@@ -477,6 +492,7 @@ ...@@ -477,6 +492,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 5,
"id": "unavailable-october",
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-08T05:34:47.301281Z", "end_time": "2021-04-08T05:34:47.301281Z",
...@@ -508,6 +524,7 @@ ...@@ -508,6 +524,7 @@
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 6, "execution_count": 6,
"id": "protected-difficulty",
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-08T05:34:51.742273Z", "end_time": "2021-04-08T05:34:51.742273Z",
...@@ -666,6 +683,7 @@ ...@@ -666,6 +683,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "important-testing",
"metadata": {}, "metadata": {},
"source": [ "source": [
"可以看到，含噪的变分量子本征求解器的效果要差于不含噪的版本，无法达到化学精度的要求 $\\varepsilon = 0.0016$ Ha。" "可以看到，含噪的变分量子本征求解器的效果要差于不含噪的版本，无法达到化学精度的要求 $\\varepsilon = 0.0016$ Ha。"
...@@ -673,6 +691,7 @@ ...@@ -673,6 +691,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "extensive-forge",
"metadata": {}, "metadata": {},
"source": [ "source": [
"## 总结\n", "## 总结\n",
...@@ -682,6 +701,7 @@ ...@@ -682,6 +701,7 @@
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"id": "inappropriate-board",
"metadata": {}, "metadata": {},
"source": [ "source": [
"---\n", "---\n",
...@@ -716,7 +736,7 @@ ...@@ -716,7 +736,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.3" "version": "3.7.10"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/quantum_simulation/DistributedVQE_CN.ipynb 0 → 100644
浏览文件 @ 016af983
{
"cells": [
{
"cell_type": "markdown",
"id": "c1a5f1e6",
"metadata": {},
"source": [
"# 基于施密特分解的分布式变分量子本征求解器\n",
"\n",
"*Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*"
]
},
{
"cell_type": "markdown",
"id": "cf44390c",
"metadata": {
"tags": []
},
"source": [
"## 概览\n",
"\n",
"在物理和化学等学科中，一个非常重要的问题就是提取分子、原子等物理系统的基态信息。系统的基态是由系统对应的哈密顿量决定的。目前普遍认为量子计算机在求解哈密顿量基态问题上具有优势。[变分量子本征求解器](https://qml.baidu.com/tutorials/quantum-simulation/variational-quantum-eigensolver.html)（variational quantum eigensolver, VQE），作为有望在近期展现量子优势的算法之一，为研究者们提供了可以在含噪的中等规模量子（NISQ）设备上研究量子化学的可能。然而，目前 NISQ 设备仍存在许多局限性，阻碍了大规模量子算法的运行。例如，受限于现有量子设备所能提供的量子比特数，研究者们无法利用 VQE 在 NISQ 设备上模拟真实的大分子。为了突破这一限制，许多分布式方案 [1-3] 相继被提出。\n",
"在本教程中，我们以 [4] 提出的基于施密特分解的 VQE 为例，向读者展示如何利用 Paddle Quantum 实现分布式量子算法。"
]
},
{
"cell_type": "markdown",
"id": "f3fcc1b4",
"metadata": {},
"source": [
"## 施密特分解\n",
"\n",
"对于任意处于复合系统 $AB$ 上的纯态 $|\\psi\\rangle$，我们有如下平凡分解:\n",
"\n",
"$$\n",
"|\\psi\\rangle=\\sum_{ij}a_{ij}|i\\rangle\\otimes|j\\rangle,\n",
"\\tag{1}\n",
"$$\n",
"\n",
"其中 $|i\\rangle$ 和 $|j\\rangle$ 分别是子系统 $A$、$B$ 上的计算基底，$a_{ij}$ 是某复矩阵 $a$ 的元素。接下来，我们对矩阵 $a$ 运用[奇异值分解](https://zh.wikipedia.org/wiki/奇异值分解)（singular value decomposition, SVD），即，$a = udv$，其中 $u,v$ 是酉矩阵，$d$ 是对角矩阵。那么，$a_{ij}=\\sum_ku_{ik}d_{kk}v_{kj}$。\n",
"\n",
"通过定义 \n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"|k_A\\rangle\\equiv & \\sum_iu_{ik}|i\\rangle=u|k\\rangle,\\\\\n",
"|k_B\\rangle\\equiv & \\sum_jv_{kj}|j\\rangle=v^T|k\\rangle,\\\\\n",
"\\lambda_k\\equiv & d_{kk},\\end{aligned}\n",
"\\tag{2}\n",
"$$\n",
"\n",
"我们可以把（1）式重写为\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
" |\\psi\\rangle &= \\sum_{ijk}u_{ik}d_{kk}v_{kj}|i\\rangle\\otimes|j\\rangle \\\\\n",
" &= \\sum_{k}\\lambda_{k}\\Big(\\sum_iu_{ik}|i\\rangle\\Big)\\otimes\\Big(\\sum_jv_{kj}|j\\rangle\\Big) \\\\\n",
" &=\\sum_{k}\\lambda_k(u|k\\rangle\\otimes v^T|k\\rangle)\\\\\n",
" &=\\sum_{k}\\lambda_k|k_A\\rangle\\otimes|k_B\\rangle.\n",
"\\end{aligned}\n",
"\\tag{3}\n",
"$$\n",
"\n",
"形如 $|\\psi\\rangle=\\sum_k\\lambda_k|k_A\\rangle\\otimes|k_B\\rangle$ 的分解方式就称为 **施密特分解** [5]。同时，$\\{\\lambda_k\\}_k$ 被称作施密特系数，非零 $\\lambda_k$ 的数量被称为 $|\\psi\\rangle$ 的施密特秩。事实上，奇异值分解的性质还保证了 $\\lambda_k\\in\\mathbb{R}^+$ 及 $\\sum_k\\lambda_k^2=1$。"
]
},
{
"cell_type": "markdown",
"id": "620e053c",
"metadata": {
"tags": []
},
"source": [
"## 基于施密特分解的分布式 VQE\n",
"\n",
"作为标准 VQE [6] 的一个变种，分布式 VQE 同样试图寻找一个 $N$ 量子比特哈密顿量 $\\hat{H}=\\sum_tc_t\\hat{H}_t^{(A)}\\otimes\\hat{H}_t^{(B)}$ 的基态及其能量，其中 $\\hat{H}_t^{(A)},\\hat{H}_t^{(B)}$ 是分别作用于子系统 $A$、$B$ 上的哈密顿量分量（我们假设 $A$、$B$ 都包含 $N/2$ 量子比特）。\n",
"\n",
"我们从如下试探波函数开始：\n",
"\n",
"$$\n",
"|\\psi\\rangle\\equiv\\sum_{k=1}^S\\lambda_k\\Big(U(\\boldsymbol{\\theta})|k\\rangle\\Big)\\otimes\\Big(V(\\boldsymbol{\\phi})|k\\rangle\\Big)\n",
"\\tag{4},\n",
"$$\n",
"\n",
"其中 $\\boldsymbol{\\lambda}\\equiv(\\lambda_1, \\lambda_2,...,\\lambda_S)^T$，$1\\leq S\\leq 2^{N/2}$ 是一个用户定义的常数。根据施密特分解，目标基态同样可写成（4）式的形式。因此，通过寻找合适的参数向量 $\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}$ 和 $\\boldsymbol{\\phi}$，我们可以在任意误差内近似目标基态。\n",
"\n",
"接下来，对于所有 $i,j=1,...,S$，我们在一台 $N/2$ 量子比特的量子计算机上计算如下项：\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"E_{ijt}^A(\\boldsymbol{\\theta}) &\\equiv \\langle i|U^\\dagger(\\boldsymbol{\\theta}) \\hat{H}_t^{(A)} U(\\boldsymbol{\\theta})|j\\rangle,\\\\\n",
"E_{ijt}^B(\\boldsymbol{\\phi}) &\\equiv \\langle i|V^\\dagger(\\boldsymbol{\\phi}) \\hat{H}_t^{(B)} V(\\boldsymbol{\\phi}))|j\\rangle.\n",
"\\end{aligned}\n",
"\\tag{5}\n",
"$$\n",
"\n",
"然后，在一台经典计算机上，我们根据如下定义构造一个 $S\\times S$ 维的矩阵 $M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$：\n",
"\n",
"$$\n",
"[M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})]_{ij}\\equiv\\sum_tc_tE_{ijt}^A(\\boldsymbol{\\theta})E_{ijt}^B(\\boldsymbol{\\phi}).\n",
"\\tag{6}\n",
"$$\n",
"\n",
"这样，目标基态能量就可以写为 \n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"E_{tar} &= \\min_{\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}, \\boldsymbol{\\phi}} \\langle{\\psi}|\\hat{H}|\\psi\\rangle \\\\\n",
" &= \\min_{\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}, \\boldsymbol{\\phi}}\\Big(\\sum_{i,j=1}^S\\lambda_i\\lambda_j[M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})]_{ij}\\Big)\\\\\n",
" &= \\min_{\\boldsymbol{\\theta}, \\boldsymbol{\\phi}} E(\\boldsymbol{\\theta},\\boldsymbol{\\phi}),\n",
"\\end{aligned}\n",
"\\tag{7}\n",
"$$\n",
"\n",
"其中 $E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})\\equiv\\min_{\\boldsymbol{\\lambda}} \\boldsymbol{\\lambda}^T M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})\\boldsymbol{\\lambda}$。根据线性代数的内容，不难发现，$E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$ 正是矩阵 $M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$ 的最小特征值，可以通过经典算法求得。\n",
"\n",
"最终，我们重复如上过程，并使用基于梯度下降的优化方法最小化 $E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$，使其趋近于 $E_{tar}$。\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "f79d3333",
"metadata": {
"tags": []
},
"source": [
"## 量桨实现\n",
"\n",
"首先，我们导入必要的包。由于我们要使用飞桨和量桨的最新功能，请确保您的 *PaddlePaddle* >= 2.2.0 且 *Paddle Quantum* >= 2.1.3。"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "bb7c0db4",
"metadata": {},
"outputs": [],
"source": [
"import time\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"\n",
"import paddle\n",
"from paddle_quantum.circuit import UAnsatz\n",
"from paddle_quantum.utils import pauli_str_to_matrix, schmidt_decompose"
]
},
{
"cell_type": "markdown",
"id": "c84dd264",
"metadata": {},
"source": [
"定义一些全局常数："
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "27e4ce36",
"metadata": {},
"outputs": [],
"source": [
"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",
"D = 3 # 设置量子神经网络的层数"
]
},
{
"cell_type": "markdown",
"id": "3db38f56",
"metadata": {},
"source": [
"下面这一函数经典地计算出哈密顿量 $H$ 的基态信息（基态对能量和施密特秩），以作为后面量子模型的基准参照。"
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "32b310ed",
"metadata": {},
"outputs": [],
"source": [
"def get_ground_state_info(H):\n",
"\n",
" # 计算 H 的特征值与特征向量\n",
" vals, vecs = paddle.linalg.eigh(H)\n",
" # 获取基态\n",
" ground_state = vecs[:, 0].numpy()\n",
" # 获取基态能量\n",
" ground_state_energy = vals.tolist()[0]\n",
" print(f'The ground state energy is {ground_state_energy:.5f} Ha.')\n",
" # 对基态运用施密特分解\n",
" l, _, _ = schmidt_decompose(ground_state)\n",
" print(f'Schmidt rank of the ground state is {l.size}.')\n",
"\n",
" return ground_state_energy"
]
},
{
"cell_type": "markdown",
"id": "8c2c88d3",
"metadata": {},
"source": [
"现在，我们生成一个哈密顿量并计算其基态信息。"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "6149b4d4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The ground state energy is -0.99783 Ha.\n",
"Schmidt rank of the ground state is 3.\n"
]
}
],
"source": [
"# 固定随机种子\n",
"np.random.seed(SEED)\n",
"\n",
"# 硬编码一个哈密顿量\n",
"coefs = [-0.8886258, 0.453882]\n",
"pauli_str = ['x0,z1,z2,z4,x5,y6,y7,x8,x9', 'y0,x1,x2,x3,y4,x5,z6,z7,y8,x9']\n",
"pauli_str_A = ['x0,z1,z2,z4', 'y0,x1,x2,x3,y4'] # 子系统 A 的泡利字符串\n",
"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",
"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",
"H_B = [pauli_str_to_matrix([[1., pstr]], n=N-N//2) for pstr in pauli_str_B]\n",
"H_B = paddle.to_tensor(np.stack(H_B))\n",
"\n",
"# 计算该哈密顿量的基态信息\n",
"ground_state_energy = get_ground_state_info(H_mtr)"
]
},
{
"cell_type": "markdown",
"id": "9abf331c",
"metadata": {},
"source": [
"准备好一个哈密顿量后，我们可以构建一个分布式 VQE 来求解它。"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "32cacc67",
"metadata": {},
"outputs": [],
"source": [
"# 构造参数化量子电路\n",
"def U_theta(param, N, D):\n",
" \n",
" cir = UAnsatz(N) # 初始化一个宽度为 N 量子比特的电路\n",
" cir.complex_entangled_layer(param, D) # 添加量子门\n",
" return cir.U # 获取参数化电路的矩阵\n",
"\n",
"# 把参数化电路作用在计算基底上\n",
"# 并返回一个形状为 [2**N, num_states] 的张量\n",
"def output_states(theta, num_states, N, D):\n",
" # 创建 num_states 个计算基底\n",
" basis = paddle.eye(2**N, num_states)\n",
" \n",
" # 获得参数化电路\n",
" U = U_theta(theta, N, D)\n",
" \n",
" # 把参数化电路作用在这些基底上\n",
" vec = U @ basis \n",
" \n",
" return vec"
]
},
{
"cell_type": "markdown",
"id": "0ca5787c",
"metadata": {},
"source": [
"以下代码是本教程的核心。请读者仔细阅读，并与前文的公式叙述做比较。"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "6ebf5159",
"metadata": {},
"outputs": [],
"source": [
"# 构造分布式模型\n",
"class DistributedVQE(paddle.nn.Layer):\n",
" def __init__(self, N, D, S):\n",
" super().__init__()\n",
" paddle.seed(SEED)\n",
"\n",
" # 定义常数 S\n",
" self.S = S\n",
" self.N, self.D = N, D\n",
" # 初始化参数列表 theta, phi，并用 [0, 2*pi] 的均匀分布来填充初始值\n",
" self.theta = self.create_parameter(shape=[D, N//2, 3], dtype=\"float64\",\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n",
" self.phi = self.create_parameter(shape=[D, N - N//2, 3], dtype=\"float64\",\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n",
" \n",
" # 分布式 VQE 的核心逻辑\n",
" def forward(self):\n",
" # 分别获得子系统 A、B 上的 U|k> 和 V|k> \n",
" vec_A = output_states(self.theta, self.S, self.N//2, self.D)\n",
" vec_B = output_states(self.phi, self.S, self.N - self.N//2, self.D)\n",
" \n",
" # 计算由前文定义的 E_{ijt}^A 和 E_{ijt}^B 组成的张量 E_A, E_B\n",
" E_A = vec_A.conj().t() @ H_A @ vec_A\n",
" E_B = vec_B.conj().t() @ H_B @ vec_B\n",
" M = (coefs.reshape([-1, 1, 1]) * E_A * E_B).sum(0)\n",
"\n",
" # 计算矩阵 M 的最小特征值\n",
" eigval = paddle.linalg.eigvalsh(M)\n",
" loss = eigval[0]\n",
" \n",
" return loss"
]
},
{
"cell_type": "markdown",
"id": "d04669ff",
"metadata": {},
"source": [
"定义训练函数。"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "066f5e72",
"metadata": {},
"outputs": [],
"source": [
"def train(model):\n",
" start_time = time.time() # 用以计算该函数的运行时长\n",
" \n",
" # 我们使用基于梯度下降的优化器 Adam 来优化 theta 和 phi\n",
" opt = paddle.optimizer.Adam(learning_rate=LR, parameters=model.parameters())\n",
" summary_loss = [] # 记录损失历史\n",
"\n",
" # 迭代优化\n",
" for itr in range(ITR):\n",
"\n",
" # 前向传播，计算损失函数\n",
" loss = model()\n",
"\n",
" # 后向传播，优化损失函数\n",
" loss.backward()\n",
" opt.minimize(loss)\n",
" opt.clear_grad()\n",
"\n",
" # 更新优化结果\n",
" summary_loss.append(loss.numpy())\n",
"\n",
" # 打印中间结果\n",
" if (itr+1) % 20 == 0:\n",
" print(f\"iter: {itr+1}, loss: {loss.tolist()[0]: .4f} Ha\")\n",
"\n",
" print(f'Ground truth is {ground_state_energy:.4f} Ha')\n",
" print(f'Training took {time.time() - start_time:.2f}s')\n",
" \n",
" plt.plot(list(range(ITR)), summary_loss, color='r', label='loss')\n",
" plt.hlines(y=ground_state_energy, xmin=0, xmax=ITR, linestyle=':', label='ground truth')\n",
" plt.legend()\n",
" plt.title(f'Loss for {type(model).__name__} on a {N}-qubit Hamiltonian')\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "c8770b19",
"metadata": {},
"source": [
"现在，我们实例化并训练分布式模型。"
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "78b46dcc",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"iter: 20, loss: -0.9244 Ha\n",
"iter: 40, loss: -0.9906 Ha\n",
"iter: 60, loss: -0.9968 Ha\n",
"iter: 80, loss: -0.9977 Ha\n",
"iter: 100, loss: -0.9978 Ha\n",
"Ground truth is -0.9978 Ha\n",
"Training took 13.01s\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"# 注意，由于我们构造的哈密顿量在两子系统间相互作用较小，我们只需设置 S = 4.\n",
"#（更多解释请见总结部分）\n",
"vqe = DistributedVQE(N, D, S=4)\n",
"train(vqe)"
]
},
{
"cell_type": "markdown",
"id": "9eb85055",
"metadata": {},
"source": [
"在上图中，我们用虚线画出了真实的基态能量。可以看到，loss 曲线收敛至虚线，表明我们的分布式 VQE 成功找到了该哈密顿量的基态能量。然而，要妥当地评估我们的模型，我们还需将它与标准 VQE 做比较。因此，下面我们构建标准 VQE 模型："
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "2fff9166",
"metadata": {},
"outputs": [],
"source": [
"class StandardVQE(paddle.nn.Layer):\n",
" def __init__(self, N, D):\n",
" super().__init__()\n",
" paddle.seed(SEED)\n",
" self.N, self.D = N, D\n",
" self.theta = self.create_parameter(shape=[D, N, 3], dtype=\"float64\",\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n",
" \n",
" def forward(self):\n",
" vec = output_states(self.theta, 1, self.N, self.D)\n",
" loss = vec.conj().t() @ H_mtr @ vec\n",
" return loss.cast('float64').flatten()"
]
},
{
"cell_type": "markdown",
"id": "8bc5dcfd",
"metadata": {},
"source": [
"实例化并训练标准 VQE。"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "a35f3eb4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"iter: 20, loss: -0.8365 Ha\n",
"iter: 40, loss: -0.9852 Ha\n",
"iter: 60, loss: -0.9958 Ha\n",
"iter: 80, loss: -0.9975 Ha\n",
"iter: 100, loss: -0.9978 Ha\n",
"Ground truth is -0.9978 Ha\n",
"Training took 721.76s\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"svqe = StandardVQE(N, D)\n",
"train(svqe) # 训练标准 VQE"
]
},
{
"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 快了五十多倍！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。"
]
},
{
"cell_type": "markdown",
"id": "94cda668",
"metadata": {
"tags": []
},
"source": [
"## 总结\n",
"\n",
"在此教程中，我们构造了一个分布式 VQE 并展示了其部分优势：\n",
"- NISQ 设备的计算范围得以拓展。通过分布式策略，我们可以运行超过硬件量子比特数的量子算法。\n",
"- 计算效率得到提升。对于量子过程的经典模拟而言，分布式算法降低了酉矩阵的维度，因此降低了模拟这些矩阵所需的时间、空间消耗。\n",
"\n",
"同时，需要注意的是，用户定义的常数 $S$ 在训练准确度和效率上扮演了重要角色：\n",
"- 对于子系统间相互作用弱的哈密顿量而言，其基态在子系统间纠缠较弱 [7]。因此，其施密特秩较低，可以被一个较小的 $S$ 精确且高效地模拟。事实上，我们所给的演示及大多数物理、化学中有意义的哈密顿量都具有此性质。\n",
"- 相反的，对于子系统间相互作用强的哈密顿量而言，其基态在子系统间纠缠较强，因此需要一个较大的 $S$ 来模拟。但是，无论如何，$S$ 的上界是 $2^{N/2}$，因此矩阵 $M$ 的维度上界是 $2^{N/2}\\times2^{N/2}$，这仍然比初始哈密顿量的维度（$2^{N}\\times 2^{N}$）小。因此，该算法的效率总是优于纯经典模拟。"
]
},
{
"cell_type": "markdown",
"id": "922679aa",
"metadata": {
"jp-MarkdownHeadingCollapsed": true,
"tags": []
},
"source": [
"_______\n",
"\n",
"# 参考文献\n",
"\n",
"[1] Fujii, Keisuke, et al. \"Deep Variational Quantum Eigensolver: a divide-and-conquer method for solving a larger problem with smaller size quantum computers.\" [arXiv preprint arXiv:2007.10917 (2020)](https://arxiv.org/abs/2007.10917).\n",
"\n",
"[2] Zhang, Yu, et al. \"Variational Quantum Eigensolver with Reduced Circuit Complexity.\" [arXiv preprint arXiv:2106.07619 (2021)](https://arxiv.org/abs/2106.07619).\n",
"\n",
"[3] Peng, Tianyi et al. \"Simulating Large Quantum Circuits On A Small Quantum Computer\". [Physical Review Letters 125.15, (2020): 150504](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.150504).\n",
"\n",
"[4] Eddins, Andrew, et al. \"Doubling the size of quantum simulators by entanglement forging.\" [arXiv preprint arXiv:2104.10220 (2021)](https://arxiv.org/abs/2104.10220).\n",
"\n",
"[5] Nielsen, Michael A., and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010.\n",
"\n",
"[6] Moll, Nikolaj, et al. \"Quantum optimization using variational algorithms on near-term quantum devices.\" [Quantum Science and Technology 3.3 (2018): 030503](https://iopscience.iop.org/article/10.1088/2058-9565/aab822).\n",
"\n",
"[7] Khatri, Sumeet, and Mark M. Wilde. \"Principles of quantum communication theory: A modern approach.\" [arXiv preprint arXiv:2011.04672 (2020)](https://arxiv.org/abs/2011.04672)."
]
}
],
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tutorial/quantum_simulation/DistributedVQE_EN.ipynb 0 → 100644
浏览文件 @ 016af983
{
"cells": [
{
"cell_type": "markdown",
"id": "responsible-handle",
"metadata": {},
"source": [
"# Distributed Variational Quantum Eigensolver Based on Schmidt Decomposition\n",
"*Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved.*"
]
},
{
"cell_type": "markdown",
"id": "superb-sunrise",
"metadata": {
"tags": []
},
"source": [
"## Overview\n",
"\n",
"Retrieving ground state information of a Hamiltonian in amongst the essential questions in physics and chemistry. Currently, it is widely believed that quantum computers are advantageous in solving this kind of problem. As one of the promising algorithms to demonstrate quantum supremacy in the near term, [Variational Quantum Eigensolver (VQE)](https://qml.baidu.com/tutorials/quantum-simulation/variational-quantum-eigensolver.html)\n",
"enables the study of quantum chemistry on Noisy Intermediate-Scale Quantum (NISQ) devices. However, various technical limitations still exist on current NISQ hardware, forbidding the deployment of large-scale quantum algorithms. For example, limited by the number of available qubits, researchers have not been able to simulate realistic large molecules with high precision. To overcome this barrier, researchers have proposed a wide range of distributed strategies [1-3]. In this tutorial, we take the distributed VQE based on Schmidt decomposition, proposed in [4], as an example to demonstrate how to implement distributed quantum algorithms using Paddle Quantum."
]
},
{
"cell_type": "markdown",
"id": "illegal-zealand",
"metadata": {},
"source": [
"## Schmidt Decomposition\n",
"We start with the following trivial decomposition for any pure state $|\\psi\\rangle$ of a composite system $AB$:\n",
"\n",
"$$\n",
"|\\psi\\rangle=\\sum_{ij}a_{ij}|i\\rangle\\otimes|j\\rangle,\n",
"\\tag{1}\n",
"$$\n",
"\n",
"where $|i\\rangle$ and $|j\\rangle$ are computational bases of subsystems $A$ and $B$ respectively, and $a_{ij}$ are elements of some complex matrix $a$. Then, we apply [singular value decomposition (SVD)](https://en.wikipedia.org/wiki/Singular_value_decomposition)\n",
"on $a$, i.e., $a = udv$ with $u,v$ being unitary and $d$ diagonal. Hence, $a_{ij}=\\sum_ku_{ik}d_{kk}v_{kj}$. \n",
"\n",
"By defining\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"|k_A\\rangle\\equiv & \\sum_iu_{ik}|i\\rangle=u|k\\rangle,\\\\\n",
"|k_B\\rangle\\equiv & \\sum_jv_{kj}|j\\rangle=v^T|k\\rangle,\\\\\n",
"\\lambda_k\\equiv & d_{kk},\n",
"\\end{aligned}\n",
"\\tag{2}\n",
"$$\n",
"\n",
"we may rewrite Eq. (1) as\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
" |\\psi\\rangle &= \\sum_{ijk}u_{ik}d_{kk}v_{kj}|i\\rangle\\otimes|j\\rangle \\\\\n",
" &= \\sum_{k}\\lambda_{k}\\Big(\\sum_iu_{ik}|i\\rangle\\Big)\\otimes\\Big(\\sum_jv_{kj}|j\\rangle\\Big) \\\\\n",
" &=\\sum_{k}\\lambda_k(u|k\\rangle\\otimes v^T|k\\rangle)\\\\\n",
" &=\\sum_{k}\\lambda_k|k_A\\rangle\\otimes|k_B\\rangle.\n",
"\\end{aligned}\n",
"\\tag{3}\n",
"$$\n",
"\n",
"The decomposition of $|\\psi\\rangle$ into the form of $\\sum_k\\lambda_k|k_A\\rangle\\otimes|k_B\\rangle$ is known as its ***Schmidt decomposition*** [5], with $\\{\\lambda_k\\}_k$ called the *Schmidt coefficients* and the number of non-zero $\\lambda_k$'s its *Schmidt rank*. In fact, the property of SVD also guarantees that $\\lambda_k\\in\\mathbb{R}^+$ and $\\sum_k\\lambda_k^2=1$. "
]
},
{
"cell_type": "markdown",
"id": "looking-detail",
"metadata": {
"tags": []
},
"source": [
"## Distributed VQE Based on Schmidt Decomposition\n",
"\n",
"As a variation of the standard VQE [6], the distributed VQE also seeks to solve the ground state and its energy of an $N$-qubit Hamiltonian $\\hat{H}=\\sum_tc_t\\hat{H}_t^{(A)}\\otimes\\hat{H}_t^{(B)}$， where $\\hat{H}_t^{(A)},\\hat{H}_t^{(B)}$ are Hamiltonian terms on subsystems $A,B$ respectively (we have assumed that $A$, $B$ both have $N/2$ qubits).\n",
"\n",
"To start with, we write the trial wave function as\n",
"\n",
"$$\n",
"|\\psi\\rangle\\equiv\\sum_{k=1}^S\\lambda_k\\Big(U(\\boldsymbol{\\theta})|k\\rangle\\Big)\\otimes\\Big(V(\\boldsymbol{\\phi})|k\\rangle\\Big),\n",
"\\tag{4}\n",
"$$\n",
"\n",
"for some $\\boldsymbol{\\lambda}\\equiv(\\lambda_1, \\lambda_2,...,\\lambda_S)^T$ and $1\\leq S\\leq 2^{N/2}$ a user-defined constant. According to Schmidt decomposition, the target ground state also has the form of Eq. (4) and hence can be approximated with high precision by choosing appropriate parameters $\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}$ and $\\boldsymbol{\\phi}$.\n",
"\n",
"Now, for all $i,j=1,...,S$, we evaluate the following terms on an $N/2$-qubit quantum computer:\n",
"\n",
"$$\n",
"\\begin{aligned}\n",
"E_{ijt}^A(\\boldsymbol{\\theta}) &\\equiv \\langle i|U^\\dagger(\\boldsymbol{\\theta}) \\hat{H}_t^{(A)} U(\\boldsymbol{\\theta})|j\\rangle,\\\\\n",
"E_{ijt}^B(\\boldsymbol{\\phi}) &\\equiv \\langle i|V^\\dagger(\\boldsymbol{\\phi}) \\hat{H}_t^{(B)} V(\\boldsymbol{\\phi}))|j\\rangle.\n",
"\\end{aligned}\n",
"\\tag{5}\n",
"$$\n",
"\n",
"Then, on a classical computer, we construct an $S\\times S$ dimensional matrix $M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$ according to\n",
"\n",
"$$\n",
"[M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})]_{ij}\\equiv\\sum_tc_tE_{ijt}^A(\\boldsymbol{\\theta})E_{ijt}^B(\\boldsymbol{\\phi}).\n",
"\\tag{6}\n",
"$$\n",
"\n",
"In this way, the target ground state energy can be written as \n",
"$$\n",
"\\begin{aligned}\n",
"E_{tar} &= \\min_{\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}, \\boldsymbol{\\phi}} \\langle{\\psi}|\\hat{H}|\\psi\\rangle \\\\\n",
" &= \\min_{\\boldsymbol{\\lambda}, \\boldsymbol{\\theta}, \\boldsymbol{\\phi}}\\Big(\\sum_{i,j=1}^S\\lambda_i\\lambda_j[M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})]_{ij}\\Big)\\\\\n",
" &= \\min_{\\boldsymbol{\\theta}, \\boldsymbol{\\phi}} E(\\boldsymbol{\\theta},\\boldsymbol{\\phi}),\n",
"\\end{aligned}\n",
"\\tag{7}\n",
"$$\n",
"\n",
"where $E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})\\equiv\\min_{\\boldsymbol{\\lambda}} \\boldsymbol{\\lambda}^T M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})\\boldsymbol{\\lambda}$. By linear algebra, we see that $E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$ is exactly the minimal eigenvalue of $M(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$, which can be solved using classical algorithms.\n",
"\n",
"Finally, we repeat the whole process and minimize $E(\\boldsymbol{\\theta},\\boldsymbol{\\phi})$ to approximate $E_{tar}$ using gradient-based optimization methods."
]
},
{
"cell_type": "markdown",
"id": "enabling-bulletin",
"metadata": {
"tags": []
},
"source": [
"## Paddle Quantum implementation\n",
"\n",
"First of all, we import necessary packages. Please make sure that you have *PaddlePaddle* >= 2.2.0 and *Paddle Quantum* >= 2.1.3, as we will use some of their latest features."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "sized-girlfriend",
"metadata": {},
"outputs": [],
"source": [
"import time\n",
"import numpy as np\n",
"from matplotlib import pyplot as plt\n",
"\n",
"import paddle\n",
"from paddle_quantum.circuit import UAnsatz\n",
"from paddle_quantum.utils import pauli_str_to_matrix, schmidt_decompose"
]
},
{
"cell_type": "markdown",
"id": "central-internet",
"metadata": {},
"source": [
"Define some global constants:"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "diverse-village",
"metadata": {},
"outputs": [],
"source": [
"N = 10 # Number of qubits\n",
"SEED = 16 # Fix a random seed\n",
"ITR = 100 # Set the number of learning iterations\n",
"LR = 0.1 # Set the learning rate\n",
"D = 3 # Set the depth for QNN"
]
},
{
"cell_type": "markdown",
"id": "strange-challenge",
"metadata": {},
"source": [
"The following function classically calculates the ground state information (the energy and the Schmidt rank of the ground state) of a Hamiltonian $H$, which we will use as the ground truth to benchmark our quantum models."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "musical-ultimate",
"metadata": {},
"outputs": [],
"source": [
"def get_ground_state_info(H):\n",
"\n",
" # Calculate the eigenvalues and eigenvectors of H\n",
" vals, vecs = paddle.linalg.eigh(H)\n",
" # Retrieve the ground state\n",
" ground_state = vecs[:, 0].numpy()\n",
" # Retrieve the ground state energy\n",
" ground_state_energy = vals.tolist()[0]\n",
" print(f'The ground state energy is {ground_state_energy:.5f} Ha.')\n",
" # Run Schmidt decomposition on the ground state.\n",
" l, _, _ = schmidt_decompose(ground_state)\n",
" print(f'Schmidt rank of the ground state is {l.size}.')\n",
"\n",
" return ground_state_energy"
]
},
{
"cell_type": "markdown",
"id": "lesbian-employment",
"metadata": {},
"source": [
"Now, we generate a Hamiltonian and calculate its ground state information."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "indie-detroit",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The ground state energy is -0.99783 Ha.\n",
"Schmidt rank of the ground state is 3.\n"
]
}
],
"source": [
"# Fix a random seed\n",
"np.random.seed(SEED)\n",
"\n",
"# Hard code a random a Hamiltonian\n",
"coefs = [-0.8886258, 0.453882]\n",
"pauli_str = ['x0,z1,z2,z4,x5,y6,y7,x8,x9', 'y0,x1,x2,x3,y4,x5,z6,z7,y8,x9']\n",
"pauli_str_A = ['x0,z1,z2,z4', 'y0,x1,x2,x3,y4'] # pauli substring for system A\n",
"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",
"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",
"H_B = [pauli_str_to_matrix([[1., pstr]], n=N-N//2) for pstr in pauli_str_B]\n",
"H_B = paddle.to_tensor(np.stack(H_B))\n",
"\n",
"# calculate the ground state information\n",
"ground_state_energy = get_ground_state_info(H_mtr)"
]
},
{
"cell_type": "markdown",
"id": "dietary-hotel",
"metadata": {},
"source": [
"Now that we have prepared a Hamiltonian, we may build a distributed VQE to solve it."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "international-wesley",
"metadata": {},
"outputs": [],
"source": [
"# Construct parameterized circuit\n",
"def U_theta(param, N, D):\n",
" \n",
" cir = UAnsatz(N) # Initialize an N-qubit-width circuit\n",
" cir.complex_entangled_layer(param, D) # Add quantum gates\n",
" return cir.U # Retrieve the unitary matrix for the parameterized circuit\n",
"\n",
"# Apply a parameterized circuit on the conputational bases\n",
"# and return a tensor of shape [2**N, num_states]\n",
"def output_states(theta, num_states, N, D):\n",
" # Create num_states-many computational bases\n",
" basis = paddle.eye(2**N, num_states)\n",
" \n",
" # Acquire a parameterized circuit\n",
" U = U_theta(theta, N, D)\n",
" \n",
" # Apply the parameterized circuit on these bases\n",
" vec = U @ basis \n",
" \n",
" return vec"
]
},
{
"cell_type": "markdown",
"id": "disturbed-strap",
"metadata": {},
"source": [
"The code below is core to this tutorial. Please compare them with the formulae given in the beginning section and make sure that they are well understood."
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "normal-leader",
"metadata": {},
"outputs": [],
"source": [
"# Construct the distributed model\n",
"class DistributedVQE(paddle.nn.Layer):\n",
" def __init__(self, N, D, S):\n",
" super().__init__()\n",
" paddle.seed(SEED)\n",
"\n",
" # Define constant S\n",
" self.S = S\n",
" self.N, self.D = N, D\n",
" # Initialize the parameter lists theta, phi, filled by a uniform distribution in [0, 2*pi]\n",
" self.theta = self.create_parameter(shape=[D, N//2, 3], dtype=\"float64\",\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n",
" self.phi = self.create_parameter(shape=[D, N - N//2, 3], dtype=\"float64\",\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n",
" \n",
" # The core logic of distributed VQE\n",
" def forward(self):\n",
" # Obtain U|k> and V|k> for subsystems A and B respectively \n",
" vec_A = output_states(self.theta, self.S, self.N//2, self.D)\n",
" vec_B = output_states(self.phi, self.S, self.N - self.N//2, self.D)\n",
" \n",
" # Calculate tensor E_A, E_B, which have elements E_{ijt}^A and E_{ijt}^B, as per defined in above\n",
" E_A = vec_A.conj().t() @ H_A @ vec_A\n",
" E_B = vec_B.conj().t() @ H_B @ vec_B\n",
" M = (coefs.reshape([-1, 1, 1]) * E_A * E_B).sum(0)\n",
"\n",
" # Find the minimal eigenvalue of M\n",
" eigval = paddle.linalg.eigvalsh(M)\n",
" loss = eigval[0]\n",
" \n",
" return loss"
]
},
{
"cell_type": "markdown",
"id": "independent-undergraduate",
"metadata": {},
"source": [
"Define training function."
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "liberal-mountain",
"metadata": {},
"outputs": [],
"source": [
"def train(model):\n",
" start_time = time.time() # To calculate the running time of this function\n",
" \n",
" # We will use Adam, a gradient-based optimizer to optimize theta and phi\n",
" opt = paddle.optimizer.Adam(learning_rate=LR, parameters=model.parameters())\n",
" summary_loss = [] # Save loss history\n",
"\n",
" # Optimization iteration\n",
" for itr in range(ITR):\n",
"\n",
" # Forward propagation to calculates the loss function\n",
" loss = model()\n",
"\n",
" # Backward propagation to optimize the loss function\n",
" loss.backward()\n",
" opt.minimize(loss)\n",
" opt.clear_grad()\n",
"\n",
" # Update optimization result\n",
" summary_loss.append(loss.numpy())\n",
"\n",
" # Print itermediary result\n",
" if (itr+1) % 20 == 0:\n",
" print(f\"iter: {itr+1}, loss: {loss.tolist()[0]: .4f} Ha\")\n",
"\n",
" print(f'Ground truth is {ground_state_energy:.4f} Ha')\n",
" print(f'Training took {time.time() - start_time:.2f}s')\n",
" \n",
" plt.plot(list(range(ITR)), summary_loss, color='r', label='loss')\n",
" plt.hlines(y=ground_state_energy, xmin=0, xmax=ITR, linestyle=':', label='ground truth')\n",
" plt.legend()\n",
" plt.title(f'Loss for {type(model).__name__} on a {N}-qubit Hamiltonian')\n",
" plt.show()"
]
},
{
"cell_type": "markdown",
"id": "civic-distance",
"metadata": {},
"source": [
"Now, we are ready to instantiate the model and train it!"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "compressed-reviewer",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"iter: 20, loss: -0.9244 Ha\n",
"iter: 40, loss: -0.9906 Ha\n",
"iter: 60, loss: -0.9968 Ha\n",
"iter: 80, loss: -0.9977 Ha\n",
"iter: 100, loss: -0.9978 Ha\n",
"Ground truth is -0.9978 Ha\n",
"Training took 13.01s\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Note that we manually set S = 4 as the Hamiltonian we just created interacts weakly across the subsystems.\n",
"# (See the Conclusion section for further description)\n",
"vqe = DistributedVQE(N, D, S=4)\n",
"train(vqe)"
]
},
{
"cell_type": "markdown",
"id": "convenient-receiver",
"metadata": {},
"source": [
"We have plotted the actual ground state energy as a dotted line in the figure above. We see that the loss curve converges to the dotted line, meaning that our distributed VQE successfully found the ground state energy of the Hamiltonian. However, to properly evaluate our model, we need to compare it with the standard VQE, which we build below:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "intensive-pickup",
"metadata": {},
"outputs": [],
"source": [
"class StandardVQE(paddle.nn.Layer):\n",
" def __init__(self, N, D):\n",
" super().__init__()\n",
" paddle.seed(SEED)\n",
" self.N, self.D = N, D\n",
" self.theta = self.create_parameter(shape=[D, N, 3], dtype=\"float64\",\n",
" default_initializer=paddle.nn.initializer.Uniform(low=0.0, high=2*np.pi))\n",
" \n",
" def forward(self):\n",
" vec = output_states(self.theta, 1, self.N, self.D)\n",
" loss = vec.conj().t() @ H_mtr @ vec\n",
" return loss.cast('float64').flatten()"
]
},
{
"cell_type": "markdown",
"id": "dress-vulnerability",
"metadata": {},
"source": [
"Instantiate and train the StandardVQE."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "a35f3eb4",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"iter: 20, loss: -0.8365 Ha\n",
"iter: 40, loss: -0.9852 Ha\n",
"iter: 60, loss: -0.9958 Ha\n",
"iter: 80, loss: -0.9975 Ha\n",
"iter: 100, loss: -0.9978 Ha\n",
"Ground truth is -0.9978 Ha\n",
"Training took 721.76s\n"
]
},
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"svqe = StandardVQE(N, D)\n",
"train(svqe) # Train the standard VQE "
]
},
{
"cell_type": "markdown",
"id": "centered-sheffield",
"metadata": {},
"source": [
"Interestingly, by comparing the running time of the two models, we find that the distributed model runs 50 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."
]
},
{
"cell_type": "markdown",
"id": "blocked-determination",
"metadata": {
"tags": []
},
"source": [
"## Conclusion\n",
"\n",
"In this tutorial, we built a distributed VQE and demonstrated some of its advantages:\n",
"- The capability of NISQ devices is expanded. Distributed strategies enable the deployment of quantum algorithms which require qubits that exceed the capability of current hardware.\n",
"- The computation efficiency is improved. For classical simulation of quantum processes, distributed algorithms reduce the dimension of unitary matrices, hence reducing the space and time cost for simulating them.\n",
"\n",
"In the meantime, one must note that $S$, as a user-defined constant, plays a key role in the training accuracy and efficiency:\n",
"- For Hamiltonians which encode weak inter-subsystem interactions, their ground states are weakly entangled across the subsystems [7]. Hence, the Schmidt ranks are small and can be accurately and efficiently simulated by a small $S$. In fact, our example and most physically and chemically interesting Hamiltonians fall into this category.\n",
"- In contrast, for Hamiltonians which encode strong inter-subsystem interactions, their ground states are strongly entangled. Hence, a large $S$ may be required. But anyway, $S$ is upper-bounded by $2^{N/2}$ and thus the dimension of $M$ is upper-bounded by $2^{N/2}\\times2^{N/2}$, which is still much smaller than the dimension of the initial Hamiltonian ($2^{N}\\times 2^{N}$). Consequently, the efficiency of this algorithm is always better than the purely classical simulation."
]
},
{
"cell_type": "markdown",
"id": "suspended-monroe",
"metadata": {
"jp-MarkdownHeadingCollapsed": true,
"tags": []
},
"source": [
"_______\n",
"\n",
"# References\n",
"\n",
"[1] Fujii, Keisuke, et al. \"Deep Variational Quantum Eigensolver: a divide-and-conquer method for solving a larger problem with smaller size quantum computers.\" [arXiv preprint arXiv:2007.10917 (2020)](https://arxiv.org/abs/2007.10917).\n",
"\n",
"[2] Zhang, Yu, et al. \"Variational Quantum Eigensolver with Reduced Circuit Complexity.\" [arXiv preprint arXiv:2106.07619(2021)](https://arxiv.org/abs/2106.07619).\n",
"\n",
"[3] Peng, Tianyi et al. \"Simulating Large Quantum Circuits On A Small Quantum Computer\". [Physical Review Letters 125.15, (2020): 150504](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.125.150504).\n",
"\n",
"[4] Eddins, Andrew, et al. \"Doubling the size of quantum simulators by entanglement forging.\" [arXiv preprint arXiv:2104.10220 (2021)](https://arxiv.org/abs/2104.10220).\n",
"\n",
"[5] Nielsen, Michael A., and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2010.\n",
"\n",
"[6] Moll, Nikolaj, et al. \"Quantum optimization using variational algorithms on near-term quantum devices.\" [Quantum Science and Technology 3.3 (2018): 030503](https://iopscience.iop.org/article/10.1088/2058-9565/aab822).\n",
"\n",
"[7] Khatri, Sumeet, and Mark M. Wilde. \"Principles of quantum communication theory: A modern approach.\" [arXiv preprint arXiv:2011.04672 (2020)](https://arxiv.org/abs/2011.04672)."
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"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": "3.7.10"
}
},
"nbformat": 4,
"nbformat_minor": 5
}
tutorial/quantum_simulation/GibbsState_CN.ipynb
浏览文件 @ 016af983
...@@ -430,7 +430,7 @@ ...@@ -430,7 +430,7 @@
"\n", "\n",
"[3] Somma, R. D., Boixo, S., Barnum, H. & Knill, E. Quantum Simulations of Classical Annealing Processes. [Phys. Rev. Lett. 101, 130504 (2008).](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.130504)\n", "[3] Somma, R. D., Boixo, S., Barnum, H. & Knill, E. Quantum Simulations of Classical Annealing Processes. [Phys. Rev. Lett. 101, 130504 (2008).](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.130504)\n",
"\n", "\n",
"[4] Wang, Y., Li, G. & Wang, X. Variational quantum Gibbs state preparation with a truncated Taylor series. [arXiv:2005.08797 (2020).](https://arxiv.org/pdf/2005.08797.pdf)" "[4] Wang, Y., Li, G. & Wang, X. Variational quantum Gibbs state preparation with a truncated Taylor series. [Phys. Rev. A 16, 054035 (2021).](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.16.054035)"
] ]
} }
], ],
...@@ -450,7 +450,7 @@ ...@@ -450,7 +450,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.3" "version": "3.7.10"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/quantum_simulation/GibbsState_EN.ipynb
浏览文件 @ 016af983
...@@ -411,7 +411,7 @@ ...@@ -411,7 +411,7 @@
"\n", "\n",
"[3] Somma, R. D., Boixo, S., Barnum, H. & Knill, E. Quantum Simulations of Classical Annealing Processes. [Phys. Rev. Lett. 101, 130504 (2008).](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.130504)\n", "[3] Somma, R. D., Boixo, S., Barnum, H. & Knill, E. Quantum Simulations of Classical Annealing Processes. [Phys. Rev. Lett. 101, 130504 (2008).](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.101.130504)\n",
"\n", "\n",
"[4] Wang, Y., Li, G. & Wang, X. Variational quantum Gibbs state preparation with a truncated Taylor series. [arXiv:2005.08797 (2020).](https://arxiv.org/pdf/2005.08797.pdf)" "[4] Wang, Y., Li, G. & Wang, X. Variational quantum Gibbs state preparation with a truncated Taylor series. [Phys. Rev. A 16, 054035 (2021).](https://journals.aps.org/prapplied/abstract/10.1103/PhysRevApplied.16.054035)"
] ]
} }
], ],
...@@ -431,7 +431,7 @@ ...@@ -431,7 +431,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.3" "version": "3.7.10"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/quantum_simulation/SSVQE_CN.ipynb
浏览文件 @ 016af983
...@@ -2,8 +2,9 @@ ...@@ -2,8 +2,9 @@
"cells": [ "cells": [
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {},
"source": [ "source": [
"# 子空间搜索-量子变分本征求解器\n", "# 子空间搜索-变分量子本征求解器\n",
"\n", "\n",
"<em> Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. </em>\n", "<em> Copyright (c) 2021 Institute for Quantum Computing, Baidu Inc. All Rights Reserved. </em>\n",
"\n", "\n",
...@@ -12,12 +13,18 @@ ...@@ -12,12 +13,18 @@
"- 在本案例中，我们将展示如何通过 Paddle Quantum 训练量子神经网络来求解量子系统的整个能量谱。\n", "- 在本案例中，我们将展示如何通过 Paddle Quantum 训练量子神经网络来求解量子系统的整个能量谱。\n",
"\n", "\n",
"- 首先，让我们通过下面几行代码引入必要的 library 和 package。" "- 首先，让我们通过下面几行代码引入必要的 library 和 package。"
], ]
"metadata": {}
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 1, "execution_count": 1,
"metadata": {
"ExecuteTime": {
"end_time": "2021-04-30T09:12:57.571029Z",
"start_time": "2021-04-30T09:12:54.960356Z"
}
},
"outputs": [],
"source": [ "source": [
"import numpy\n", "import numpy\n",
"from numpy import pi as PI\n", "from numpy import pi as PI\n",
...@@ -25,17 +32,11 @@ ...@@ -25,17 +32,11 @@
"from paddle import matmul\n", "from paddle import matmul\n",
"from paddle_quantum.circuit import UAnsatz\n", "from paddle_quantum.circuit import UAnsatz\n",
"from paddle_quantum.utils import random_pauli_str_generator, pauli_str_to_matrix, dagger" "from paddle_quantum.utils import random_pauli_str_generator, pauli_str_to_matrix, dagger"
], ]
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2021-04-30T09:12:57.571029Z",
"start_time": "2021-04-30T09:12:54.960356Z"
}
}
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {},
"source": [ "source": [
"## 背景\n", "## 背景\n",
"\n", "\n",
...@@ -47,67 +48,73 @@ ...@@ -47,67 +48,73 @@
"\n", "\n",
"- 对于具体需要分析的分子，我们需要其几何构型（geometry）、电荷（charge）以及自旋多重度（spin multiplicity）等多项信息来建模获取描述系统的 Hamilton 量。具体的，通过我们内置的量子化学工具包可以利用 fermionic-to-qubit 映射的技术来输出目标分子的量子比特 Hamilton 量表示。\n", "- 对于具体需要分析的分子，我们需要其几何构型（geometry）、电荷（charge）以及自旋多重度（spin multiplicity）等多项信息来建模获取描述系统的 Hamilton 量。具体的，通过我们内置的量子化学工具包可以利用 fermionic-to-qubit 映射的技术来输出目标分子的量子比特 Hamilton 量表示。\n",
"- 作为简单的入门案例，我们在这里提供一个简单的随机双量子比特 Hamilton 量作为例子。" "- 作为简单的入门案例，我们在这里提供一个简单的随机双量子比特 Hamilton 量作为例子。"
], ]
"metadata": {}
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 3,
"source": [
"N = 2 # 量子比特数/量子神经网络的宽度\n",
"SEED = 14 # 固定随机种子"
],
"outputs": [],
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:12:57.580461Z", "end_time": "2021-04-30T09:12:57.580461Z",
"start_time": "2021-04-30T09:12:57.574080Z" "start_time": "2021-04-30T09:12:57.574080Z"
} }
} },
"outputs": [],
"source": [
"N = 2 # 量子比特数/量子神经网络的宽度\n",
"SEED = 14 # 固定随机种子"
]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 8, "execution_count": 8,
"source": [ "metadata": {
"# 生成用泡利字符串表示的随机哈密顿量\n", "ExecuteTime": {
"numpy.random.seed(SEED)\n", "end_time": "2021-04-30T09:12:57.604652Z",
"hamiltonian = random_pauli_str_generator(N, terms=10)\n", "start_time": "2021-04-30T09:12:57.592553Z"
"print(\"Random Hamiltonian in Pauli string format = \\n\", hamiltonian)\n", }
"\n", },
"# 生成 Hamilton 量的矩阵信息\n",
"H = pauli_str_to_matrix(hamiltonian, N)"
],
"outputs": [ "outputs": [
{ {
"output_type": "stream",
"name": "stdout", "name": "stdout",
"output_type": "stream",
"text": [ "text": [
"Random Hamiltonian in Pauli string format = \n", "Random Hamiltonian in Pauli string format = \n",
" [[0.9152074787317819, 'x1,y0'], [-0.2717604556798945, 'z0'], [0.3628495008719168, 'x0'], [-0.5050129214094752, 'x1'], [-0.6971554357833791, 'y0,x1'], [0.8651151857574237, 'x0,y1'], [0.7409989105435002, 'y0'], [-0.39981603921243236, 'y0'], [0.06862640764702, 'z0'], [-0.7647553733438246, 'y1']]\n" " [[0.9152074787317819, 'x1,y0'], [-0.2717604556798945, 'z0'], [0.3628495008719168, 'x0'], [-0.5050129214094752, 'x1'], [-0.6971554357833791, 'y0,x1'], [0.8651151857574237, 'x0,y1'], [0.7409989105435002, 'y0'], [-0.39981603921243236, 'y0'], [0.06862640764702, 'z0'], [-0.7647553733438246, 'y1']]\n"
] ]
} }
], ],
"metadata": { "source": [
"ExecuteTime": { "# 生成用泡利字符串表示的随机哈密顿量\n",
"end_time": "2021-04-30T09:12:57.604652Z", "numpy.random.seed(SEED)\n",
"start_time": "2021-04-30T09:12:57.592553Z" "hamiltonian = random_pauli_str_generator(N, terms=10)\n",
} "print(\"Random Hamiltonian in Pauli string format = \\n\", hamiltonian)\n",
} "\n",
"# 生成 Hamilton 量的矩阵信息\n",
"H = pauli_str_to_matrix(hamiltonian, N)"
]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {},
"source": [ "source": [
"## 搭建量子神经网络\n", "## 搭建量子神经网络\n",
"\n", "\n",
"- 在实现 SSVQE 的过程中，我们首先需要设计量子神经网络（quantum neural network, QNN），也即参数化量子电路。在本教程中，我们提供一个预设的适用于双量子比特的通用量子电路模板。理论上，该模板具有足够强大的表达能力可以表示任意的双量子比特逻辑运算 [5]。具体的实现方式是需要 3 个 $CNOT$ 门加上任意 15 个单比特旋转门 $\\in \\{R_y, R_z\\}$。\n", "- 在实现 SSVQE 的过程中，我们首先需要设计量子神经网络（quantum neural network, QNN），也即参数化量子电路。在本教程中，我们提供一个预设的适用于双量子比特的通用量子电路模板。理论上，该模板具有足够强大的表达能力可以表示任意的双量子比特逻辑运算 [5]。具体的实现方式是需要 3 个 $CNOT$ 门加上任意 15 个单比特旋转门 $\\in \\{R_y, R_z\\}$。\n",
"\n", "\n",
"- 初始化其中的变量参数，${\\bf{\\theta}}$ 代表我们量子神经网络中的参数组成的向量，一共有 15 个参数。" "- 初始化其中的变量参数，${\\bf{\\theta}}$ 代表我们量子神经网络中的参数组成的向量，一共有 15 个参数。"
], ]
"metadata": {}
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 9, "execution_count": 9,
"metadata": {
"ExecuteTime": {
"end_time": "2021-04-30T09:12:57.673600Z",
"start_time": "2021-04-30T09:12:57.664882Z"
}
},
"outputs": [],
"source": [ "source": [
"THETA_SIZE = 15 # 量子神经网络中参数的数量\n", "THETA_SIZE = 15 # 量子神经网络中参数的数量\n",
"\n", "\n",
...@@ -123,17 +130,11 @@ ...@@ -123,17 +130,11 @@
"\n", "\n",
" # 返回量子神经网络的电路\n", " # 返回量子神经网络的电路\n",
" return cir" " return cir"
], ]
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2021-04-30T09:12:57.673600Z",
"start_time": "2021-04-30T09:12:57.664882Z"
}
}
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {},
"source": [ "source": [
"## 配置训练模型——损失函数\n", "## 配置训练模型——损失函数\n",
"\n", "\n",
...@@ -148,12 +149,18 @@ ...@@ -148,12 +149,18 @@
"$$\n", "$$\n",
"\\mathcal{L}(\\boldsymbol{\\theta}) = \\sum_{k=1}^{2^n}w_k*\\left\\langle {\\psi_k \\left( {\\bf{\\theta }} \\right)} \\right|H\\left| {\\psi_k \\left( {\\bf{\\theta }} \\right)} \\right\\rangle. \\tag{1}\n", "\\mathcal{L}(\\boldsymbol{\\theta}) = \\sum_{k=1}^{2^n}w_k*\\left\\langle {\\psi_k \\left( {\\bf{\\theta }} \\right)} \\right|H\\left| {\\psi_k \\left( {\\bf{\\theta }} \\right)} \\right\\rangle. \\tag{1}\n",
"$$" "$$"
], ]
"metadata": {}
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 10, "execution_count": 10,
"metadata": {
"ExecuteTime": {
"end_time": "2021-04-30T09:12:58.591349Z",
"start_time": "2021-04-30T09:12:58.577120Z"
}
},
"outputs": [],
"source": [ "source": [
"class Net(paddle.nn.Layer):\n", "class Net(paddle.nn.Layer):\n",
" def __init__(self, shape, dtype='float64'):\n", " def __init__(self, shape, dtype='float64'):\n",
...@@ -186,51 +193,74 @@ ...@@ -186,51 +193,74 @@
" loss += weight * loss_components[i]\n", " loss += weight * loss_components[i]\n",
" \n", " \n",
" return loss, loss_components, cir" " return loss, loss_components, cir"
], ]
"outputs": [],
"metadata": {
"ExecuteTime": {
"end_time": "2021-04-30T09:12:58.591349Z",
"start_time": "2021-04-30T09:12:58.577120Z"
}
}
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {},
"source": [ "source": [
"## 配置训练模型——模型参数\n", "## 配置训练模型——模型参数\n",
"在进行量子神经网络的训练之前，我们还需要进行一些训练的超参数设置，主要是学习速率（learning rate, LR）、迭代次数（iteration, ITR。这里我们设定学习速率为 0.3，迭代次数为 50 次。读者不妨自行调整来直观感受下超参数调整对训练效果的影响。" "在进行量子神经网络的训练之前，我们还需要进行一些训练的超参数设置，主要是学习速率（learning rate, LR）、迭代次数（iteration, ITR。这里我们设定学习速率为 0.3，迭代次数为 50 次。读者不妨自行调整来直观感受下超参数调整对训练效果的影响。"
], ]
"metadata": {}
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 11, "execution_count": 11,
"source": [
"ITR = 100 # 设置训练的总迭代次数\n",
"LR = 0.3 # 设置学习速率"
],
"outputs": [],
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:12:59.351881Z", "end_time": "2021-04-30T09:12:59.351881Z",
"start_time": "2021-04-30T09:12:59.343240Z" "start_time": "2021-04-30T09:12:59.343240Z"
} }
} },
"outputs": [],
"source": [
"ITR = 100 # 设置训练的总迭代次数\n",
"LR = 0.3 # 设置学习速率"
]
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {},
"source": [ "source": [
"## 进行训练\n", "## 进行训练\n",
"- 当训练模型的各项参数都设置完成后，我们将数据转化为 PaddlePaddle 动态图中的张量，进而进行量子神经网络的训练。\n", "- 当训练模型的各项参数都设置完成后，我们将数据转化为 PaddlePaddle 动态图中的张量，进而进行量子神经网络的训练。\n",
"- 过程中我们用的是 Adam Optimizer，也可以调用 PaddlePaddle 中提供的其他优化器。\n", "- 过程中我们用的是 Adam Optimizer，也可以调用 PaddlePaddle 中提供的其他优化器。\n",
"- 我们可以将训练过程中的每一轮 loss 打印出来。" "- 我们可以将训练过程中的每一轮 loss 打印出来。"
], ]
"metadata": {}
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 13, "execution_count": 13,
"metadata": {
"ExecuteTime": {
"end_time": "2021-04-30T09:13:07.503094Z",
"start_time": "2021-04-30T09:13:04.968574Z"
}
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"iter: 10 loss: -4.5668\n",
"iter: 20 loss: -5.3998\n",
"iter: 30 loss: -5.6210\n",
"iter: 40 loss: -5.8872\n",
"iter: 50 loss: -5.9246\n",
"iter: 60 loss: -5.9471\n",
"iter: 70 loss: -5.9739\n",
"iter: 80 loss: -5.9833\n",
"iter: 90 loss: -5.9846\n",
"iter: 100 loss: -5.9848\n",
"\n",
"训练后的电路：\n",
"--U----x----Rz(-1.18)----*-----------------x----U--\n",
" | | | \n",
"--U----*----Ry(-0.03)----x----Ry(2.362)----*----U--\n",
" \n"
]
}
],
"source": [ "source": [
"paddle.seed(SEED)\n", "paddle.seed(SEED)\n",
" \n", " \n",
...@@ -261,40 +291,11 @@ ...@@ -261,40 +291,11 @@
" if itr == ITR:\n", " if itr == ITR:\n",
" print(\"\\n训练后的电路：\")\n", " print(\"\\n训练后的电路：\")\n",
" print(cir)" " print(cir)"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"iter: 10 loss: -4.5668\n",
"iter: 20 loss: -5.3998\n",
"iter: 30 loss: -5.6210\n",
"iter: 40 loss: -5.8872\n",
"iter: 50 loss: -5.9246\n",
"iter: 60 loss: -5.9471\n",
"iter: 70 loss: -5.9739\n",
"iter: 80 loss: -5.9833\n",
"iter: 90 loss: -5.9846\n",
"iter: 100 loss: -5.9848\n",
"\n",
"训练后的电路：\n",
"--U----x----Rz(-1.18)----*-----------------x----U--\n",
" | | | \n",
"--U----*----Ry(-0.03)----x----Ry(2.362)----*----U--\n",
" \n"
] ]
}
],
"metadata": {
"ExecuteTime": {
"end_time": "2021-04-30T09:13:07.503094Z",
"start_time": "2021-04-30T09:13:04.968574Z"
}
}
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {},
"source": [ "source": [
"## 测试效果\n", "## 测试效果\n",
"\n", "\n",
...@@ -302,12 +303,28 @@ ...@@ -302,12 +303,28 @@
"- 理论值由 NumPy 中的工具来求解哈密顿量的各个本征值；\n", "- 理论值由 NumPy 中的工具来求解哈密顿量的各个本征值；\n",
"- 我们将训练 QNN 得到的各个能级的能量和理想情况下的理论值进行比对。\n", "- 我们将训练 QNN 得到的各个能级的能量和理想情况下的理论值进行比对。\n",
"- 可以看到，SSVQE 训练输出的值与理想值高度接近。" "- 可以看到，SSVQE 训练输出的值与理想值高度接近。"
], ]
"metadata": {}
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 15, "execution_count": 15,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The estimated ground state energy is: [-2.18762366]\n",
"The theoretical ground state energy is: -2.18790201165885\n",
"The estimated 1st excited state energy is: [-0.13721024]\n",
"The theoretical 1st excited state energy is: -0.13704127143749587\n",
"The estimated 2nd excited state energy is: [0.85251457]\n",
"The theoretical 2nd excited state energy is: 0.8523274042087416\n",
"The estimated 3rd excited state energy is: [1.47231932]\n",
"The theoretical 3rd excited state energy is: 1.4726158788876045\n"
]
}
],
"source": [ "source": [
"def output_ordinalvalue(num):\n", "def output_ordinalvalue(num):\n",
" r\"\"\"\n", " r\"\"\"\n",
...@@ -339,27 +356,11 @@ ...@@ -339,27 +356,11 @@
" print('The theoretical {} excited state energy is: {}'.format(\n", " print('The theoretical {} excited state energy is: {}'.format(\n",
" output_ordinalvalue(i), numpy.linalg.eigh(H)[0][i])\n", " output_ordinalvalue(i), numpy.linalg.eigh(H)[0][i])\n",
" )" " )"
],
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"The estimated ground state energy is: [-2.18762366]\n",
"The theoretical ground state energy is: -2.18790201165885\n",
"The estimated 1st excited state energy is: [-0.13721024]\n",
"The theoretical 1st excited state energy is: -0.13704127143749587\n",
"The estimated 2nd excited state energy is: [0.85251457]\n",
"The theoretical 2nd excited state energy is: 0.8523274042087416\n",
"The estimated 3rd excited state energy is: [1.47231932]\n",
"The theoretical 3rd excited state energy is: 1.4726158788876045\n"
] ]
}
],
"metadata": {}
}, },
{ {
"cell_type": "markdown", "cell_type": "markdown",
"metadata": {},
"source": [ "source": [
"_______\n", "_______\n",
"\n", "\n",
...@@ -374,14 +375,17 @@ ...@@ -374,14 +375,17 @@
"[4] Nakanishi, K. M., Mitarai, K. & Fujii, K. Subspace-search variational quantum eigensolver for excited states. [Phys. Rev. Res. 1, 033062 (2019).](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.1.033062)\n", "[4] Nakanishi, K. M., Mitarai, K. & Fujii, K. Subspace-search variational quantum eigensolver for excited states. [Phys. Rev. Res. 1, 033062 (2019).](https://journals.aps.org/prresearch/pdf/10.1103/PhysRevResearch.1.033062)\n",
"\n", "\n",
"[5] Vatan, F. & Williams, C. Optimal quantum circuits for general two-qubit gates. [Phys. Rev. A 69, 032315 (2004).](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.69.032315)" "[5] Vatan, F. & Williams, C. Optimal quantum circuits for general two-qubit gates. [Phys. Rev. A 69, 032315 (2004).](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.69.032315)"
], ]
"metadata": {}
} }
], ],
"metadata": { "metadata": {
"interpreter": {
"hash": "1ba3360425d54dc61cc146cb8ddc529b6d51be6719655a3ca16cefddffc9595a"
},
"kernelspec": { "kernelspec": {
"name": "python3", "display_name": "Python 3",
"display_name": "Python 3.8.10 64-bit ('paddle_quantum_test': conda)" "language": "python",
"name": "python3"
}, },
"language_info": { "language_info": {
"codemirror_mode": { "codemirror_mode": {
...@@ -393,7 +397,7 @@ ...@@ -393,7 +397,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.10" "version": "3.7.10"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
...@@ -407,9 +411,6 @@ ...@@ -407,9 +411,6 @@
"toc_position": {}, "toc_position": {},
"toc_section_display": true, "toc_section_display": true,
"toc_window_display": false "toc_window_display": false
},
"interpreter": {
"hash": "1ba3360425d54dc61cc146cb8ddc529b6d51be6719655a3ca16cefddffc9595a"
} }
}, },
"nbformat": 4, "nbformat": 4,
......
tutorial/quantum_simulation/VQE_CN.ipynb
浏览文件 @ 016af983
...@@ -117,7 +117,7 @@ ...@@ -117,7 +117,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 1, "execution_count": 2,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:13:45.528201Z", "end_time": "2021-04-30T09:13:45.528201Z",
...@@ -152,7 +152,7 @@ ...@@ -152,7 +152,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 2, "execution_count": 3,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:13:45.545018Z", "end_time": "2021-04-30T09:13:45.545018Z",
...@@ -164,24 +164,24 @@ ...@@ -164,24 +164,24 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"FCI energy for H2_sto-3g_singlet (2 electrons) is -1.137283834485513.\n", "FCI energy for H2_sto-3g_singlet (2 electrons) is -1.1372838344855134.\n",
"\n", "\n",
"The generated h2 Hamiltonian is \n", "The generated h2 Hamiltonian is \n",
" -0.09706626861762556 I\n", " -0.0970662686176252 I\n",
"-0.04530261550868938 X0, X1, Y2, Y3\n", "-0.04530261550868938 X0, X1, Y2, Y3\n",
"0.04530261550868938 X0, Y1, Y2, X3\n", "0.04530261550868938 X0, Y1, Y2, X3\n",
"0.04530261550868938 Y0, X1, X2, Y3\n", "0.04530261550868938 Y0, X1, X2, Y3\n",
"-0.04530261550868938 Y0, Y1, X2, X3\n", "-0.04530261550868938 Y0, Y1, X2, X3\n",
"0.1714128263940239 Z0\n", "0.1714128263940238 Z0\n",
"0.16868898168693286 Z0, Z1\n", "0.16868898168693292 Z0, Z1\n",
"0.12062523481381837 Z0, Z2\n", "0.12062523481381847 Z0, Z2\n",
"0.16592785032250773 Z0, Z3\n", "0.1659278503225078 Z0, Z3\n",
"0.17141282639402394 Z1\n", "0.17141282639402383 Z1\n",
"0.16592785032250773 Z1, Z2\n", "0.1659278503225078 Z1, Z2\n",
"0.12062523481381837 Z1, Z3\n", "0.12062523481381847 Z1, Z3\n",
"-0.2234315367466399 Z2\n", "-0.22343153674664024 Z2\n",
"0.17441287610651626 Z2, Z3\n", "0.17441287610651632 Z2, Z3\n",
"-0.2234315367466399 Z3\n" "-0.2234315367466403 Z3\n"
] ]
} }
], ],
...@@ -203,7 +203,7 @@ ...@@ -203,7 +203,7 @@
"molecular_hamiltonian = qchem.spin_hamiltonian(molecule=molecule,\n", "molecular_hamiltonian = qchem.spin_hamiltonian(molecule=molecule,\n",
" filename=None, \n", " filename=None, \n",
" multiplicity=1, \n", " multiplicity=1, \n",
" mapping_method = 'jordan_wigner',)\n", " mapping_method='jordan_wigner',)\n",
"# 打印结果\n", "# 打印结果\n",
"print(\"\\nThe generated h2 Hamiltonian is \\n\", molecular_hamiltonian)" "print(\"\\nThe generated h2 Hamiltonian is \\n\", molecular_hamiltonian)"
] ]
...@@ -236,7 +236,7 @@ ...@@ -236,7 +236,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 3, "execution_count": 4,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -281,7 +281,7 @@ ...@@ -281,7 +281,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 4, "execution_count": 5,
"metadata": {}, "metadata": {},
"outputs": [], "outputs": [],
"source": [ "source": [
...@@ -318,7 +318,7 @@ ...@@ -318,7 +318,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 5, "execution_count": 6,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:14:03.744957Z", "end_time": "2021-04-30T09:14:03.744957Z",
...@@ -344,30 +344,30 @@ ...@@ -344,30 +344,30 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 6, "execution_count": 7,
"metadata": {}, "metadata": {},
"outputs": [ "outputs": [
{ {
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"iter: 20 loss: -1.0621\n", "iter: 20 loss: -1.0861\n",
"iter: 20 Ground state energy: -1.0621 Ha\n", "iter: 20 Ground state energy: -1.0861 Ha\n",
"iter: 40 loss: -1.1305\n", "iter: 40 loss: -1.1304\n",
"iter: 40 Ground state energy: -1.1305 Ha\n", "iter: 40 Ground state energy: -1.1304 Ha\n",
"iter: 60 loss: -1.1358\n", "iter: 60 loss: -1.1363\n",
"iter: 60 Ground state energy: -1.1358 Ha\n", "iter: 60 Ground state energy: -1.1363 Ha\n",
"iter: 80 loss: -1.1370\n", "iter: 80 loss: -1.1372\n",
"iter: 80 Ground state energy: -1.1370 Ha\n", "iter: 80 Ground state energy: -1.1372 Ha\n",
"\n", "\n",
"训练后的电路：\n", "训练后的电路：\n",
"--Ry(4.702)----*--------------x----Ry(4.759)----*--------------x----Ry(0.001)--\n", "--Ry(1.572)----*--------------x----Ry(1.568)----*--------------x----Ry(0.012)--\n",
" | | | | \n", " | | | | \n",
"--Ry(-1.56)----x----*---------|----Ry(4.698)----x----*---------|----Ry(1.607)--\n", "--Ry(4.724)----x----*---------|----Ry(4.722)----x----*---------|----Ry(1.619)--\n",
" | | | | \n", " | | | | \n",
"--Ry(3.170)---------x----*----|----Ry(1.789)---------x----*----|----Ry(4.817)--\n", "--Ry(-0.03)---------x----*----|----Ry(4.954)---------x----*----|----Ry(-0.41)--\n",
" | | | | \n", " | | | | \n",
"--Ry(6.365)--------------x----*----Ry(1.562)--------------x----*----Ry(3.178)--\n", "--Ry(4.288)--------------x----*----Ry(1.564)--------------x----*----Ry(3.137)--\n",
" \n" " \n"
] ]
} }
...@@ -418,12 +418,12 @@ ...@@ -418,12 +418,12 @@
"metadata": {}, "metadata": {},
"source": [ "source": [
"### 测试效果\n", "### 测试效果\n",
"我们现在已经完成了量子神经网络的训练，通过 VQE 得到的基态能量的估计值大致为 $E_0 \\approx -1.137$ Ha，这与通过全价构型相互作用（FCI）$E_0 = -1.13728$ Ha 计算得出的值是在化学精度 $\\varepsilon = 1.6 \\times 10^{-3}$ Ha 内相符合的。" "我们现在已经完成了量子神经网络的训练，通过 VQE 得到的基态能量的估计值大致为 $E_0 \\approx -1.137$ Ha，这与通过 `Psi4` 在 sto-3g 基底下使用 FCI (full configuration-interaction) 方法计算得到的基态能量值 $E_0 = -1.13728$ Ha 是在化学精度 $\\varepsilon = 1.6 \\times 10^{-3}$ Ha 内相符合的。"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 7, "execution_count": 8,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:14:21.341323Z", "end_time": "2021-04-30T09:14:21.341323Z",
...@@ -433,14 +433,12 @@ ...@@ -433,14 +433,12 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
"image/png": 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\n",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 640x480 with 1 Axes>"
] ]
}, },
"metadata": { "metadata": {},
"needs_background": "light"
},
"output_type": "display_data" "output_type": "display_data"
} }
], ],
...@@ -469,7 +467,7 @@ ...@@ -469,7 +467,7 @@
" r'\\right|H\\left| {\\psi \\left( {\\theta } \\right)} \\right\\rangle $',\n", " r'\\right|H\\left| {\\psi \\left( {\\theta } \\right)} \\right\\rangle $',\n",
" 'Ground-state energy',\n", " 'Ground-state energy',\n",
" ], loc='best')\n", " ], loc='best')\n",
"\n", "plt.text(-15.5, -1.145, f'{min_eig_H:.5f}', fontsize=10, color='b')\n",
"#plt.savefig(\"vqe.png\", bbox_inches='tight', dpi=300)\n", "#plt.savefig(\"vqe.png\", bbox_inches='tight', dpi=300)\n",
"plt.show()" "plt.show()"
] ]
...@@ -484,7 +482,7 @@ ...@@ -484,7 +482,7 @@
"\n", "\n",
"![vqe-fig-dist](figures/vqe-fig-distance.png)\n", "![vqe-fig-dist](figures/vqe-fig-distance.png)\n",
"\n", "\n",
"从上图可以看出，最小值确实发生在 $d = 74$ pm (1 pm = $1\\times 10^{-12}$m) 附近，这是与[实验测得数据](https://cccbdb.nist.gov/exp2x.asp?casno=1333740&charge=0)相符合的 $d_{exp} (H_2) = 74.14$ pm." "从上图可以看出，最小值确实发生在 $d = 74$ pm (1 pm = $1\\times 10^{-12}$ m) 附近，这是与[实验测得数据](https://cccbdb.nist.gov/exp2x.asp?casno=1333740&charge=0)相符合的 $d_{exp} (H_2) = 74.14$ pm."
] ]
}, },
{ {
...@@ -530,7 +528,7 @@ ...@@ -530,7 +528,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.10" "version": "3.8.0"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
tutorial/quantum_simulation/VQE_EN.ipynb
浏览文件 @ 016af983
...@@ -109,7 +109,7 @@ ...@@ -109,7 +109,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 1, "execution_count": 8,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:14:44.970178Z", "end_time": "2021-04-30T09:14:44.970178Z",
...@@ -144,7 +144,7 @@ ...@@ -144,7 +144,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 2, "execution_count": 9,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:14:44.982005Z", "end_time": "2021-04-30T09:14:44.982005Z",
...@@ -156,24 +156,24 @@ ...@@ -156,24 +156,24 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"FCI energy for H2_sto-3g_singlet (2 electrons) is -1.137283834485513.\n", "FCI energy for H2_sto-3g_singlet (2 electrons) is -1.1372838344855134.\n",
"\n", "\n",
"The generated h2 Hamiltonian is \n", "The generated h2 Hamiltonian is \n",
" -0.09706626861762556 I\n", " -0.0970662686176252 I\n",
"-0.04530261550868938 X0, X1, Y2, Y3\n", "-0.04530261550868938 X0, X1, Y2, Y3\n",
"0.04530261550868938 X0, Y1, Y2, X3\n", "0.04530261550868938 X0, Y1, Y2, X3\n",
"0.04530261550868938 Y0, X1, X2, Y3\n", "0.04530261550868938 Y0, X1, X2, Y3\n",
"-0.04530261550868938 Y0, Y1, X2, X3\n", "-0.04530261550868938 Y0, Y1, X2, X3\n",
"0.1714128263940239 Z0\n", "0.1714128263940238 Z0\n",
"0.16868898168693286 Z0, Z1\n", "0.16868898168693292 Z0, Z1\n",
"0.12062523481381837 Z0, Z2\n", "0.12062523481381847 Z0, Z2\n",
"0.16592785032250773 Z0, Z3\n", "0.1659278503225078 Z0, Z3\n",
"0.17141282639402394 Z1\n", "0.17141282639402383 Z1\n",
"0.16592785032250773 Z1, Z2\n", "0.1659278503225078 Z1, Z2\n",
"0.12062523481381837 Z1, Z3\n", "0.12062523481381847 Z1, Z3\n",
"-0.2234315367466399 Z2\n", "-0.22343153674664024 Z2\n",
"0.17441287610651626 Z2, Z3\n", "0.17441287610651632 Z2, Z3\n",
"-0.2234315367466399 Z3\n" "-0.2234315367466403 Z3\n"
] ]
} }
], ],
...@@ -195,7 +195,7 @@ ...@@ -195,7 +195,7 @@
"molecular_hamiltonian = qchem.spin_hamiltonian(molecule=molecule,\n", "molecular_hamiltonian = qchem.spin_hamiltonian(molecule=molecule,\n",
" filename=None, \n", " filename=None, \n",
" multiplicity=1, \n", " multiplicity=1, \n",
" mapping_method = 'jordan_wigner',)\n", " mapping_method='jordan_wigner',)\n",
"# Print results\n", "# Print results\n",
"print(\"\\nThe generated h2 Hamiltonian is \\n\", molecular_hamiltonian)" "print(\"\\nThe generated h2 Hamiltonian is \\n\", molecular_hamiltonian)"
] ]
...@@ -226,7 +226,7 @@ ...@@ -226,7 +226,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 11, "execution_count": 10,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:14:50.083041Z", "end_time": "2021-04-30T09:14:50.083041Z",
...@@ -277,7 +277,7 @@ ...@@ -277,7 +277,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 12, "execution_count": 11,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:14:50.183996Z", "end_time": "2021-04-30T09:14:50.183996Z",
...@@ -319,7 +319,7 @@ ...@@ -319,7 +319,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 13, "execution_count": 12,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:14:50.222465Z", "end_time": "2021-04-30T09:14:50.222465Z",
...@@ -345,7 +345,7 @@ ...@@ -345,7 +345,7 @@
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 14, "execution_count": 13,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:15:52.165788Z", "end_time": "2021-04-30T09:15:52.165788Z",
...@@ -357,23 +357,23 @@ ...@@ -357,23 +357,23 @@
"name": "stdout", "name": "stdout",
"output_type": "stream", "output_type": "stream",
"text": [ "text": [
"iter: 20 loss: -1.0510\n", "iter: 20 loss: -1.0487\n",
"iter: 20 Ground state energy: -1.0510 Ha\n", "iter: 20 Ground state energy: -1.0487 Ha\n",
"iter: 40 loss: -1.1298\n", "iter: 40 loss: -1.1070\n",
"iter: 40 Ground state energy: -1.1298 Ha\n", "iter: 40 Ground state energy: -1.1070 Ha\n",
"iter: 60 loss: -1.1361\n", "iter: 60 loss: -1.1152\n",
"iter: 60 Ground state energy: -1.1361 Ha\n", "iter: 60 Ground state energy: -1.1152 Ha\n",
"iter: 80 loss: -1.1371\n", "iter: 80 loss: -1.1165\n",
"iter: 80 Ground state energy: -1.1371 Ha\n", "iter: 80 Ground state energy: -1.1165 Ha\n",
"\n", "\n",
"Circuit after training:\n", "Circuit after training:\n",
"--Ry(4.710)----*--------------x----Ry(1.569)----*--------------x----Ry(-0.01)--\n", "--Ry(4.725)----*--------------x----Ry(-0.01)----*--------------x----Ry(-1.56)--\n",
" | | | | \n", " | | | | \n",
"--Ry(1.507)----x----*---------|----Ry(1.566)----x----*---------|----Ry(4.392)--\n", "--Ry(4.718)----x----*---------|----Ry(3.132)----x----*---------|----Ry(4.703)--\n",
" | | | | \n", " | | | | \n",
"--Ry(5.984)---------x----*----|----Ry(4.476)---------x----*----|----Ry(1.692)--\n", "--Ry(4.720)---------x----*----|----Ry(3.124)---------x----*----|----Ry(4.721)--\n",
" | | | | \n", " | | | | \n",
"--Ry(0.132)--------------x----*----Ry(7.773)--------------x----*----Ry(3.194)--\n", "--Ry(1.574)--------------x----*----Ry(6.291)--------------x----*----Ry(1.552)--\n",
" \n" " \n"
] ]
} }
...@@ -424,13 +424,12 @@ ...@@ -424,13 +424,12 @@
"metadata": {}, "metadata": {},
"source": [ "source": [
"### Benchmarking\n", "### Benchmarking\n",
"We have now completed the training of the quantum neural network, and the estimated value of the ground state energy obtained is $E_0 \\approx -1.137 $ Hartree, we compare it with the theoretical value $E_0 = -1.1371$ to benchmark our model. The estimation obtained with VQE agree with a full configuration-interaction (FCI) calculation within chemical accuracy $\\varepsilon = 1.6 \\times 10^{-3}$ Hartree.\n", "We have now completed the training of the quantum neural network, and the estimated value of the ground state energy obtained is $E_0 \\approx -1.137 $ Hartree. The estimation obtained with VQE is consistent with the value of the ground state energy $E_0 = -1.13728$ Hartree calculated by `Psi4` at sto-3g basis using the full configuration-interaction (FCI) method within the chemical accuracy $\\varepsilon = 1.6 \\times 10^{-3}$ Hartree.\n"
"\n"
] ]
}, },
{ {
"cell_type": "code", "cell_type": "code",
"execution_count": 15, "execution_count": 14,
"metadata": { "metadata": {
"ExecuteTime": { "ExecuteTime": {
"end_time": "2021-04-30T09:15:18.096944Z", "end_time": "2021-04-30T09:15:18.096944Z",
...@@ -440,14 +439,12 @@ ...@@ -440,14 +439,12 @@
"outputs": [ "outputs": [
{ {
"data": { "data": {
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\n", 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",
"text/plain": [ "text/plain": [
"<Figure size 432x288 with 1 Axes>" "<Figure size 640x480 with 1 Axes>"
] ]
}, },
"metadata": { "metadata": {},
"needs_background": "light"
},
"output_type": "display_data" "output_type": "display_data"
} }
], ],
...@@ -476,7 +473,7 @@ ...@@ -476,7 +473,7 @@
" r'\\right|H\\left| {\\psi \\left( {\\theta } \\right)} \\right\\rangle $',\n", " r'\\right|H\\left| {\\psi \\left( {\\theta } \\right)} \\right\\rangle $',\n",
" 'Ground-state energy',\n", " 'Ground-state energy',\n",
" ], loc='best')\n", " ], loc='best')\n",
"\n", "plt.text(-15.5, -1.145, f'{min_eig_H:.5f}', fontsize=10, color='b')\n",
"#plt.savefig(\"vqe.png\", bbox_inches='tight', dpi=300)\n", "#plt.savefig(\"vqe.png\", bbox_inches='tight', dpi=300)\n",
"plt.show()" "plt.show()"
] ]
...@@ -535,7 +532,7 @@ ...@@ -535,7 +532,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.10" "version": "3.8.0"
}, },
"toc": { "toc": {
"base_numbering": 1, "base_numbering": 1,
......
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