introduction_cn.ipynb

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   "source": [
    "## 1. VSQL 模型简介\n",
    "\n",
    "变分影子量子学习（variational shadow quantum learning, VSQL）是一个在监督学习框架下的量子–经典混合算法。它使用了参数化量子电路（parameterized quantum circuit, PQC）和经典影子（classical shadow），和通常使用的变分量子算法（variational quantum alogorithm, VQA）不同的是，VSQL 只从子空间获取局部特征，而不是从整个希尔伯特空间获取特征。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8429d648",
   "metadata": {},
   "source": [
    "## 2. 模型原理简介\n",
    "\n",
    "VSQL 的流程图如下：\n",
    "\n",
    "![pipeline](https://ai-studio-static-online.cdn.bcebos.com/36c5194bc48a4af88560172fdd7ec15b8fd3225c27b644acad1981046a48d1ec \"VSQL 流程图\")\n",
    "<div style=\"text-align:center\">VSQL 流程图</div>\n",
    "\n",
    "其训练步骤为：\n",
    "\n",
    "1. 将经典数据 $\\mathbf{x}^i$ 编码到量子态 $\\left|\\mathbf{x}^i\\right>$。\n",
    "2. 准备一个参数化局部量子电路 $U(\\mathbf{\\theta})$ 并且初始化它的参数 $\\mathbf{\\theta}$。\n",
    "3. 在前几个量子比特上作用 $U(\\mathbf{\\theta})$，然后通过测量局部可观测量（比如说泡利 $X\\otimes X\\cdots \\otimes X$ 算符）来获取一个局部影子特征。\n",
    "4. 每次将 $U(\\mathbf{\\theta})$ 向下移动一个量子比特，重复步骤3直到 $U(\\mathbf{\\theta})$ 作用到最后一个量子比特上。\n",
    "5. 将步骤3–4中得到的所有局部影子特征传入经典 FCNN 并通过激活函数得到预测的标签 $\\tilde{\\mathbf{y}}^i$。对于多分类问题来说，我们使用归一化指数函数 (softmax) 作为激活函数。\n",
    "6. 重复步骤3–5直到数据集内所有的数据点都经过了处理。然后计算损失函数 $\\mathcal{L}(\\mathbf{\\theta}, \\mathbf{W}, \\mathbf{b})$。\n",
    "7. 通过梯度下降等优化方法调整参数 $\\mathbf{\\theta}$、$\\mathbf{W}$ 和 $\\mathbf{b}$ 的值，从而最小化损失函数。这样我们就得到了优化后的模型 $\\mathcal{F}$。\n",
    "\n",
    "由于 VSQL 只获取局部影子特征，所以它可以比较容易地在有拓扑连接限制的量子设备上实现。除此之外，因为我们用同一个 $U(\\mathbf{\\theta})$ 来获取整个电路上的局部影子特征，所以需要训练的参数数量相对于通常使用的变分量子分类器来说大大减少。\n",
    "\n",
    "### 2.1 局部影子电路介绍\n",
    "\n",
    "在讲电路的细节之前，我们需要说明几个参数：\n",
    "- $n$：编码后量子态的量子比特数目。\n",
    "- $n_{qsc}$：量子影子电路的宽度。我们每次只在连续 $n_{qsc}$ 个量子比特上作用 $U(\\mathbf{\\theta})$。\n",
    "- $D$：电路的深度，表示 $U(\\mathbf{\\theta})$ 门中某一层电路重复的次数。\n",
    "\n",
    "这里我们给出 $n=4$、$n_{qsc}=2$ 时的一个例子：\n",
    "\n",
    "我们首先在前两个量子比特上作用 $U(\\mathbf{\\theta})$，并且获取第一个影子特征 $O_1$。\n",
    "\n",
    "![qubit0](https://ai-studio-static-online.cdn.bcebos.com/a544360d2b864cd2882c6965bf30e1a0f5fbf089173043cd95a5821b1cdbd799 \"获取第一个影子特征\")\n",
    "<div style=\"text-align:center\">获取第一个影子特征</div>\n",
    "\n",
    "然后我们准备一样的输入态 $\\left|\\mathbf{x}^i\\right>$，在中间两个量子比特上作用 $U(\\mathbf{\\theta})$，得到第二个影子特征 $O_2$。\n",
    "\n",
    "![qubit1](https://ai-studio-static-online.cdn.bcebos.com/9cdb70da3e5f47c2bd089f020975a987e1348d71d724418d890591f298786d4c \"获取第二个影子特征\")\n",
    "<div style=\"text-align:center\">获取第二个影子特征</div>\n",
    "\n",
    "最后，我们再准备一个一样的输入态，在最后两个量子比特上作用 $U(\\mathbf{\\theta})$，得到影子特征 $O_3$。这样我们就处理完了这个数据点！\n",
    "\n",
    "![qubit2](https://ai-studio-static-online.cdn.bcebos.com/6a404995be1141bc9fd6ca36b5e394e00fbe302621c4413bbf86554de6bfc964 \"获取第三个影子特征\")\n",
    "<div style=\"text-align:center\">获取第三个影子特征</div>\n",
    "\n",
    "通常来说，处理一个数据点需要重复以上步骤 $n - n_{qsc} + 1$ 次。有一点需要指出的是，在上面这个例子中我们只使用了一个影子电路，在获取这三个影子特征时我们使用同样的参数 $\\mathbf{\\theta}$。你可以选择增加影子电路的数量来解决更复杂的问题，这里需要注意的是不同影子电路中的参数 $\\mathbf{\\theta}$ 不同。  \n",
    " \n",
    "在后面的 MNIST 二分类任务中，我们将使用2–局部影子电路，即 $n_{qsc}=2$。下图展示了这个影子电路的结构。\n",
    "\n",
    "![2-local](https://ai-studio-static-online.cdn.bcebos.com/0c1035262cb64f61bd3cc87dbf53253aa6a7ecc170634c4db8dd71d576a9409c \"local数为2时的影子电路结构\")\n",
    "<div style=\"text-align:center\">local数为2时的影子电路结构</div>\n",
    "\n",
    "为了增强量子电路的表达能力，我们将重复 $D$ 次虚线框中的结构。$U(\\mathbf{\\theta})$ 的设计并不是唯一的，这里展示的仅仅是一个例子，也可以设计别的电路结构。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f0070ae",
   "metadata": {},
   "source": [
    "## 3. 模型效果\n",
    "\n",
    "VSQL 在 MNIST 数据集上的二分类效果如下：\n",
    "\n",
    "![binary-classification](https://ai-studio-static-online.cdn.bcebos.com/03c38b174d0e47ae9dbeea6dfda1333d6d3aa74209594324b78c9159b72e7e8a \"二分类效果图\")\n",
    "<div style=\"text-align:center\">二分类效果图</div>\n",
    "\n",
    "VSQL 在 MNIST 数据集上的十分类效果如下：\n",
    "\n",
    "![10-classification](https://ai-studio-static-online.cdn.bcebos.com/54a0273672ad4ec5ba6b7d73b3b225f8d97380c43ceb495a82d16a258117182b \"十分类效果图\")\n",
    "<div style=\"text-align:center\">十分类效果图</div>\n",
    "\n",
    "由表可见，相比于其它的量子神经网络，VSQL 可以使用很少的参数实现更高的分类准确率。而与经典神经网络相比，在十分类任务上，VSQL 也可以使用较少的参数达到相近的效果。当数据量较小时，VSQL 比经典神经网络的效果会更好。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "17661d06",
   "metadata": {},
   "source": [
    "## 4. 模型如何使用\n",
    "\n",
    "按照如下代码来配置环境："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "eb7a2be4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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      "Requirement already satisfied: googleapis-common-protos<2.0dev,>=1.56.2 in /Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages (from google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq-google>=0.15.0->openfermion->paddle-quantum) (1.57.0)\n",
      "Requirement already satisfied: grpcio<2.0dev,>=1.33.2 in /Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages (from google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq-google>=0.15.0->openfermion->paddle-quantum) (1.50.0)\n",
      "Requirement already satisfied: grpcio-status<2.0dev,>=1.33.2 in /Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages (from google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq-google>=0.15.0->openfermion->paddle-quantum) (1.48.2)\n",
      "Requirement already satisfied: pytz>=2017.3 in /Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages (from pandas->cirq-core>=0.15.0->openfermion->paddle-quantum) (2022.6)\n",
      "Requirement already satisfied: pyasn1-modules>=0.2.1 in /Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages (from google-auth<3.0dev,>=1.25.0->google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq-google>=0.15.0->openfermion->paddle-quantum) (0.2.8)\n",
      "Requirement already satisfied: cachetools<6.0,>=2.0.0 in /Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages (from google-auth<3.0dev,>=1.25.0->google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq-google>=0.15.0->openfermion->paddle-quantum) (5.2.0)\n",
      "Requirement already satisfied: rsa<5,>=3.1.4 in /Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages (from google-auth<3.0dev,>=1.25.0->google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq-google>=0.15.0->openfermion->paddle-quantum) (4.9)\n",
      "Requirement already satisfied: pyasn1<0.5.0,>=0.4.6 in /Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages (from pyasn1-modules>=0.2.1->google-auth<3.0dev,>=1.25.0->google-api-core[grpc]<2.0.0dev,>=1.14.0->cirq-google>=0.15.0->openfermion->paddle-quantum) (0.4.8)\n",
      "Installing collected packages: typing-extensions, scipy, protobuf, qcompute\n",
      "  Attempting uninstall: typing-extensions\n",
      "    Found existing installation: typing_extensions 4.3.0\n",
      "    Uninstalling typing_extensions-4.3.0:\n",
      "      Successfully uninstalled typing_extensions-4.3.0\n",
      "  Attempting uninstall: scipy\n",
      "    Found existing installation: scipy 1.7.1\n",
      "    Uninstalling scipy-1.7.1:\n",
      "      Successfully uninstalled scipy-1.7.1\n",
      "  Attempting uninstall: protobuf\n",
      "    Found existing installation: protobuf 4.21.1\n",
      "    Uninstalling protobuf-4.21.1:\n",
      "      Successfully uninstalled protobuf-4.21.1\n",
      "  Attempting uninstall: qcompute\n",
      "    Found existing installation: qcompute 3.0.0\n",
      "    Uninstalling qcompute-3.0.0:\n",
      "      Successfully uninstalled qcompute-3.0.0\n",
      "Successfully installed protobuf-3.19.6 qcompute-2.0.4 scipy-1.1.0 typing-extensions-3.10.0.0\n",
      "Note: you may need to restart the kernel to use updated packages.\n",
      "--2022-11-24 13:44:45--  https://release-data.cdn.bcebos.com/PaddleQuantum/vsql.pdparams\n",
      "Resolving release-data.cdn.bcebos.com (release-data.cdn.bcebos.com)... 222.35.73.1\n",
      "Connecting to release-data.cdn.bcebos.com (release-data.cdn.bcebos.com)|222.35.73.1|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 857 [application/octet-stream]\n",
      "Saving to: ‘vsql.pdparams.1’\n",
      "\n",
      "vsql.pdparams.1     100%[===================>]     857  --.-KB/s    in 0s      \n",
      "\n",
      "2022-11-24 13:44:46 (204 MB/s) - ‘vsql.pdparams.1’ saved [857/857]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "# 安装量桨\n",
    "%pip install paddle-quantum\n",
    "# 下载预训练模型\n",
    "!wget https://release-data.cdn.bcebos.com/PaddleQuantum/vsql.pdparams"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8a3ebf3",
   "metadata": {},
   "source": [
    "接下来，可以加载模型并进行测试："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "53a5f59a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages/scipy/linalg/__init__.py:212: DeprecationWarning: The module numpy.dual is deprecated.  Instead of using dual, use the functions directly from numpy or scipy.\n",
      "  from numpy.dual import register_func\n",
      "/Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages/scipy/sparse/sputils.py:16: DeprecationWarning: `np.typeDict` is a deprecated alias for `np.sctypeDict`.\n",
      "  supported_dtypes = [np.typeDict[x] for x in supported_dtypes]\n",
      "/Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages/scipy/special/orthogonal.py:81: DeprecationWarning: `np.int` is a deprecated alias for the builtin `int`. To silence this warning, use `int` by itself. Doing this will not modify any behavior and is safe. When replacing `np.int`, you may wish to use e.g. `np.int64` or `np.int32` to specify the precision. If you wish to review your current use, check the release note link for additional information.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  from numpy import (exp, inf, pi, sqrt, floor, sin, cos, around, int,\n",
      "/Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages/scipy/io/matlab/mio5.py:98: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  from .mio5_utils import VarReader5\n"
     ]
    }
   ],
   "source": [
    "# 导入所需要的包\n",
    "import os\n",
    "import warnings\n",
    "\n",
    "warnings.filterwarnings('ignore')\n",
    "os.environ['PROTOCOL_BUFFERS_PYTHON_IMPLEMENTATION'] = 'python'\n",
    "\n",
    "import numpy as np\n",
    "import paddle\n",
    "import paddle_quantum as pq\n",
    "import matplotlib.pyplot as plt\n",
    "from paddle_quantum.qml.vsql import VSQL\n",
    "\n",
    "# 设置模型参数\n",
    "num_qubits = 10\n",
    "num_shadow = 2\n",
    "classes = [0, 1]\n",
    "num_classes = len(classes)\n",
    "depth = 1\n",
    "\n",
    "# 加载已训练的模型\n",
    "model = VSQL(\n",
    "    num_qubits=num_qubits,\n",
    "    num_shadow=num_shadow,\n",
    "    num_classes=num_classes,\n",
    "    depth=depth,\n",
    ")\n",
    "state_dict = paddle.load('./vsql.pdparams')\n",
    "model.set_state_dict(state_dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "8f54b4de",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2022-11-24 13:45:04--  https://ai-studio-static-online.cdn.bcebos.com/088dc9dbabf349c88d029dfd2e07827aa6e41ba958c5434bbd96bc167fc65347\n",
      "Resolving ai-studio-static-online.cdn.bcebos.com (ai-studio-static-online.cdn.bcebos.com)... 222.35.73.1\n",
      "Connecting to ai-studio-static-online.cdn.bcebos.com (ai-studio-static-online.cdn.bcebos.com)|222.35.73.1|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 290 [image/png]\n",
      "Saving to: ‘data-0.png’\n",
      "\n",
      "data-0.png          100%[===================>]     290  --.-KB/s    in 0s      \n",
      "\n",
      "2022-11-24 13:45:05 (277 MB/s) - ‘data-0.png’ saved [290/290]\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fe752d095d0>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 加载手写数字0\n",
    "!wget https://ai-studio-static-online.cdn.bcebos.com/088dc9dbabf349c88d029dfd2e07827aa6e41ba958c5434bbd96bc167fc65347 -O data-0.png\n",
    "image0 = plt.imread('data-0.png')\n",
    "plt.imshow(image0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "40ebcb55",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2022-11-24 13:45:06--  https://ai-studio-static-online.cdn.bcebos.com/c755f723af3d4a1c8f113f8ac3bd365406decd1be70944b7b7b9d41413e8bc7a\n",
      "Resolving ai-studio-static-online.cdn.bcebos.com (ai-studio-static-online.cdn.bcebos.com)... 222.35.73.1\n",
      "Connecting to ai-studio-static-online.cdn.bcebos.com (ai-studio-static-online.cdn.bcebos.com)|222.35.73.1|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 173 [image/png]\n",
      "Saving to: ‘data-1.png’\n",
      "\n",
      "data-1.png          100%[===================>]     173  --.-KB/s    in 0s      \n",
      "\n",
      "2022-11-24 13:45:06 (165 MB/s) - ‘data-1.png’ saved [173/173]\n",
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fe77301dd10>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 加载手写数字1\n",
    "!wget https://ai-studio-static-online.cdn.bcebos.com/c755f723af3d4a1c8f113f8ac3bd365406decd1be70944b7b7b9d41413e8bc7a -O data-1.png\n",
    "image1 = plt.imread('data-1.png')\n",
    "plt.imshow(image1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c4830c1a",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages/paddle/tensor/creation.py:125: DeprecationWarning: `np.object` is a deprecated alias for the builtin `object`. To silence this warning, use `object` by itself. Doing this will not modify any behavior and is safe. \n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  if data.dtype == np.object:\n",
      "/Users/wangzihe/opt/anaconda3/envs/py37/lib/python3.7/site-packages/paddle/fluid/framework.py:1104: DeprecationWarning: `np.bool` is a deprecated alias for the builtin `bool`. To silence this warning, use `bool` by itself. Doing this will not modify any behavior and is safe. If you specifically wanted the numpy scalar type, use `np.bool_` here.\n",
      "Deprecated in NumPy 1.20; for more details and guidance: https://numpy.org/devdocs/release/1.20.0-notes.html#deprecations\n",
      "  elif dtype == np.bool:\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "对于手写数字 0，模型有 89.22% 的信心认为它是 0，有10.78%的信心认为它是 1。\n",
      "对于手写数字 1，模型有 18.29% 的信心认为它是 0，有81.71%的信心认为它是 1。\n"
     ]
    }
   ],
   "source": [
    "# 将图片编码为量子态\n",
    "test_data = [np.array(image0).flatten(), np.array(image1).flatten()]\n",
    "test_data = [np.pad(datum, pad_width=(0, 2 ** num_qubits - datum.size)) for datum in test_data]\n",
    "test_data = [paddle.to_tensor(datum / np.linalg.norm(datum), dtype=pq.get_dtype()) for datum in test_data]\n",
    "# 使用模型进行预测并得到对应的概率值\n",
    "test_output = model(test_data)\n",
    "test_prob = paddle.nn.functional.softmax(test_output)\n",
    "print(f\"对于手写数字 0，模型有 {test_prob[0][0].item():3.2%} 的信心认为它是 0，有{test_prob[0][1].item():3.2%}的信心认为它是 1。\")\n",
    "print(f\"对于手写数字 1，模型有 {test_prob[1][0].item():3.2%} 的信心认为它是 0，有{test_prob[1][1].item():3.2%}的信心认为它是 1。\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f6f3b91",
   "metadata": {},
   "source": [
    "## 5. 注意事项\n",
    "\n",
    "我们提供的模型为二分类模型，仅可以用来分辨手写数字0和1。对于其它分类任务，需要重新进行训练。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4857182b",
   "metadata": {},
   "source": [
    "## 6. 相关论文以及引用信息\n",
    "\n",
    "```\n",
    "@inproceedings{li2021vsql,\n",
    "  title={VSQL: Variational shadow quantum learning for classification},\n",
    "  author={Li, Guangxi and Song, Zhixin and Wang, Xin},\n",
    "  booktitle={Proceedings of the AAAI Conference on Artificial Intelligence},\n",
    "  volume={35},\n",
    "  number={9},\n",
    "  pages={8357--8365},\n",
    "  year={2021}\n",
    "}\n",
    "```"
   ]
  }
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