{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 量子模拟器\n", "\n", "[![下载Notebook](https://mindspore-website.obs.cn-north-4.myhuaweicloud.com/website-images/r2.0.0-alpha/resource/_static/logo_notebook.png)](https://mindspore-website.obs.cn-north-4.myhuaweicloud.com/notebook/r2.0.0-alpha/mindquantum/zh_cn/mindspore_quantum_simulator.ipynb) \n", "[![下载样例代码](https://mindspore-website.obs.cn-north-4.myhuaweicloud.com/website-images/r2.0.0-alpha/resource/_static/logo_download_code.png)](https://mindspore-website.obs.cn-north-4.myhuaweicloud.com/notebook/r2.0.0-alpha/mindquantum/zh_cn/mindspore_quantum_simulator.py) \n", "[![查看源文件](https://mindspore-website.obs.cn-north-4.myhuaweicloud.com/website-images/r2.0.0-alpha/resource/_static/logo_source.png)](https://gitee.com/mindspore/docs/blob/r2.0.0-alpha/docs/mindquantum/docs/source_zh_cn/quantum_simulator.ipynb) \n", "[![在ModelArts平台运行](https://mindspore-website.obs.cn-north-4.myhuaweicloud.com/website-images/r2.0.0-alpha/resource/_static/logo_modelarts.png)](https://authoring-modelarts-cnnorth4.huaweicloud.com/console/lab?share-url-b64=aHR0cHM6Ly9taW5kc3BvcmUtd2Vic2l0ZS5vYnMuY24tbm9ydGgtNC5teWh1YXdlaWNsb3VkLmNvbS9ub3RlYm9vay9yMi4wLjAtYWxwaGEvbWluZHF1YW50dW0vemhfY24vbWluZHNwb3JlX3F1YW50dW1fc2ltdWxhdG9yLmlweW5i&imageid=b711ac95-db2b-45b7-ab9b-98de275dd57e)\n", "\n", "## 概述\n", "\n", "搭建出量子线路后,我们需要指定一个后端来运行量子线路,在MindQuantum中,我们可以利用量子模拟器`Simulator`来对量子线路进行模拟运行。在本教程中我们声明一个两比特的`mqvector`模拟器,并以此来简介模拟器的关键功能。\n", "\n", "## 环境准备\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "导入本教程所依赖的模块。" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np # 导入numpy库并简写为np\n", "from mindquantum.simulator import Simulator # 从mindquantum.simulator中导入Simulator类\n", "from mindquantum.core.gates import X, H, RY # 导入量子门H, X, RY" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "说明:\n", "\n", "(1)numpy是一个功能强大的Python库,主要用于对多维数组执行计算,支持大量的维度数组与矩阵运算,此外也针对数组运算提供大量的数学函数库;\n", "\n", "(2)mindquantum是量子-经典混合计算框架,支持多种量子神经网络的训练和推理;\n", "\n", "(3)搭建的量子线路中所需执行的量子门需要从mindquantum.core模块中导入;" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "mqvector simulator with 2 qubits (little endian).\n", "Current quantum state:\n", "1¦00⟩" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sim = Simulator('mqvector', 2) #声明一个两比特的mqvector模拟器\n", "sim #展示模拟器状态" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "在MindQuantum中,我们可以在`mindquantum.simulator`模块导入模拟器。`Simulator`类可以接受三个参数:\n", "\n", "- `backend`:所用到的模拟器名称,目前`mindquantum`支持`mqvector`、`mqvector_gpu`和`projectq`作为后端进行模拟。\n", "- `n_qubits`:模拟器所用到的比特数,也就是这里的2。\n", "- `seed`:模拟器在运行随机性相关算法时的随机种子,默认为一个随机数,可以不用提供。\n", "\n", "通过模拟器的输出结果我们可以发现,这是一个`mqvector`的2比特模拟器,并且是little endian的。这里little endian的意思是,整个模拟器中,我们都是将比特序号小的比特放在量子态矢量的右边。接下来,输出还说明了模拟器当前所处的量子态是多少,且在模拟器初始化后,当前的量子态默认处于零态。注意,量子模拟器始终会维护一个内部的量子态,当我们作用量子门或者量子线路到模拟器上时,这个量子态会随即发生改变,而当我们只是想获取关于这个量子态的一些信息时,这个量子态则不会改变。这里就涉及到对量子模拟器的两类操作:\n", "\n", "- 会改变量子态的操作,通常以`apply`开头,主要有如下几个\n", " - `apply_gate`: 作用一个量子门到模拟器上\n", " - `apply_circuit`: 作用一个量子线路到模拟器上\n", " - `apply_hamiltonian`: 将一个哈密顿量作用到模拟器上,注意,此后模拟器的量子态将不再是一个真的量子态\n", " - `set_qs`: 直接设置模拟器的当前量子态\n", " - `reset`: 重置模拟器的状态为|0⟩态\n", "- 不会改变量子态的操作,通常以`get`开头,主要有如下几个\n", " - `get_qs`: 获取模拟器的当前量子态\n", " - `get_expectation`: 计算模拟器当前量子态关于某个观察量的期望值\n", " - `get_expectation_with_grad`: 跟上一个接口类似,只不过这个方法还会计算期望值关于参数化量子线路的梯度\n", " - `sampling`: 在当前量子态下,对给定的量子线路进行采样\n", "\n", "下面我们简单学习模拟器的基本操作。\n", "\n", "## 作用量子门和量子线路" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "mqvector simulator with 2 qubits (little endian).\n", "Current quantum state:\n", "√2/2¦00⟩\n", "√2/2¦01⟩" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sim = Simulator('mqvector', 2) #声明一个2比特的mqvector模拟器\n", "sim.apply_gate(H.on(0)) #作用一个Hadamard门到0号比特上\n", "sim #输出量子模拟器的信息" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "上面我们在量子模拟器的初态上作用了一个Hadamard门,并输出了演化过后的量子态。接下来我们生成一个参数化量子线路,并将其作用到当前的量子态上。" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": "\n\n\nq0:\n \n\nq1:\n \n\n\n\n\n\nH\n \n\n\n\n\nRY\n \n\na\n \n\n", "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from mindquantum.core.circuit import Circuit # 导入Circuit模块,用于搭建量子线路\n", "\n", "circ = Circuit() #声明一个空的量子线路\n", "circ += H.on(1) #向其中添加一个hadamard门,并作用到1号比特上\n", "circ += RY('a').on(0) #向其中添加一个参数化的RY门,并作用到0号比特上\n", "circ.svg() #绘制SVG格式的量子线路图片" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "mqvector simulator with 2 qubits (little endian).\n", "Current quantum state:\n", "0.11851349145283657¦00⟩\n", "0.6971044056263442¦01⟩\n", "0.11851349145283657¦10⟩\n", "0.6971044056263442¦11⟩" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sim.apply_circuit(circ, pr={'a': 1.234}) #作用一个量子线路,当线路是一个参数化量子线路时,我们还需要提供参数值。\n", "sim" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "在上面的代码中,我们先生成了一个参数化量子线路`circ`,随后我们将其作用到量子模拟器上,并通过传入字典的方式,将参数`a`设置为`1.234`。最后输出量子模拟器演化出来的量子态。" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 设置并获取模拟器状态\n", "\n", "我们使用`get_qs(ket=False)`查看当前模拟器的状态,\n", "参数ket是一个bool类型的数,它决定了当前模拟器的状态是否以ket的形式返回,ket=False时是以numpy.ndarray形式,ket=True时是以ket形式。默认ket=False。" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.11851349+0.j 0.69710441+0.j 0.11851349+0.j 0.69710441+0.j]\n" ] } ], "source": [ "print(sim.get_qs()) #查看模拟器状态,以numpy.ndarray形式返回结果" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.11851349145283657¦00⟩\n", "0.6971044056263442¦01⟩\n", "0.11851349145283657¦10⟩\n", "0.6971044056263442¦11⟩\n" ] } ], "source": [ "print(sim.get_qs(True)) #查看模拟器状态,以ket形式返回结果" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "在实际写代码过程中,我们常常需要将模拟器指定一个初始态开始演化,这个操作可以使用`set_qs()`实现。\n", "\n", "例如,我们希望模拟器状态为\n", "\n", "$$\n", "\\frac{\\sqrt{3}}{3}|00⟩+\\frac{\\sqrt{6}}{3}|11⟩\n", "$$\n", "\n", "第一步:我们计算出目标状态的向量形式:\n", "\n", "$$\n", "\\frac{\\sqrt{3}}{3}|00⟩+\\frac{\\sqrt{6}}{3}|11⟩ =\\frac{\\sqrt{3}}{3}\\times\n", "\\left(\n", "\\begin{array}{l}\n", "1\\\\\n", "0\n", "\\end{array}\n", "\\right)\n", "\\otimes\n", "\\left(\n", "\\begin{array}{l}\n", "1\\\\\n", "0\n", "\\end{array}\n", "\\right)+\n", "\\frac{\\sqrt{6}}{3}\\times\n", "\\left(\n", "\\begin{array}{l}\n", "0\\\\\n", "1\n", "\\end{array}\n", "\\right)\\otimes\n", "\\left(\n", "\\begin{array}{l}\n", "0\\\\\n", "1\n", "\\end{array}\n", "\\right)= \\frac{\\sqrt{3}}{3}\\times\n", "\\left(\n", "\\begin{array}{l}\n", "1\\\\\n", "0\\\\\n", "0\\\\\n", "0\n", "\\end{array}\n", "\\right)+\n", "\\frac{\\sqrt{6}}{3}\\times\n", "\\left(\n", "\\begin{array}{l}\n", "0\\\\\n", "0\\\\\n", "0\\\\\n", "1\n", "\\end{array}\n", "\\right)=\n", "\\left(\n", "\\begin{array}{l}\n", "\\frac{\\sqrt{3}}{3}\\\\\n", "0\\\\\n", "0\\\\\n", "\\frac{\\sqrt{6}}{3}\n", "\\end{array}\n", "\\right)\n", "$$\n", "\n", "第二步:我们将这个向量使用`set_qs()`赋值给模拟器,让其作为模拟器的状态:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.5773502691896258¦00⟩\n", "0.816496580927726¦11⟩\n" ] } ], "source": [ "sim.set_qs(np.array([3**0.5, 0, 0, 6**0.5])) #设置模拟器状态,无需归一化\n", "print(sim.get_qs(True)) #查看模拟器状态" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "通过`get_qs()`查看模拟器状态可以发现,当前模拟器状态即为我们希望设置的$\\frac{\\sqrt{3}}{3}|00⟩+\\frac{\\sqrt{6}}{3}|11⟩$。\n", "\n", "在实际编程过程中,我们常常需要多次模拟电路,通过多开模拟器的方式会导致内存占用非常大,我们可以通过现有模拟器复位的方式来复用模拟器,从而减少内存消耗。\n", "\n", "我们使用`reset()`来复位模拟器:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.+0.j 0.+0.j 0.+0.j 0.+0.j]\n" ] } ], "source": [ "sim.reset() #复位模拟器\n", "print(sim.get_qs()) #查看模拟器状态" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "可以发现,当前模拟器被复位成了初始的$1|00⟩$态,相当于一个全新的模拟器。\n", "\n", "因此,我们可以根据自身所需的量子初态,设置对应的量子模拟器,并运行自定义的量子线路。赶紧动手运行你构造出的的第一个量子线路吧!\n", "\n", "## 量子线路采样\n", "\n", "线路采样是指对量子线路执行多次模拟测量,统计测量出各种结果出现的频次。**采样不会改变量子线路中的状态**。\n", "\n", "`sampling(circuit, pr=None, shots=1, seed=None)`是`MindQuantum`中提供的对模拟器进行线路采样方法,它接受四个参数:\n", "\n", "- `circuit (Circuit)`:希望进行采样的量子线路,注意,该线路中必须包含至少一个测量操作(即采样点)。\n", "- `pr (Union[None, dict, ParameterResolver])`:parameter resolver,当 `circuit`是含参线路时,需要给出参数的值。\n", "- `shots (int)`:采样的次数,默认为1。\n", "- `seed`:采样时的随机种子,默认为一个随机数,可以不用提供。" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": "\n\n\nq0:\n \n\nq1:\n \n\n\n\n\n\nH\n \n\n\n\n\n\n\n\n\n\n\n\n\n\n\n", "text/plain": [ "" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 不含参线路采样:\n", "from mindquantum.core.gates import Measure # 引入测量门\n", "\n", "circ = Circuit() # 初始化量子线路\n", "circ += H.on(0) # H门作用在第0位量子比特\n", "circ += X.on(1, 0) # X门作用在第1位量子比特且受第0位量子比特控制\n", "circ += Measure('q0').on(0) # 在0号量子比特作用一个测量,并将该测量命名为'q0'\n", "circ += Measure('q1').on(1) # 在1号量子比特作用一个测量,并将该测量命名为'q1'\n", "circ.svg() # 绘制SVG格式的量子线路图片" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/html": [ "
shots: 1000\n",
              "Keys: q1 q0│0.00   0.128       0.256       0.384       0.512        0.64\n",
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              "\n",
              "{'00': 488, '11': 512}\n",
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\n" ], "text/plain": [ "shots: 1000\n", "Keys: q1 q0│0.00 0.128 0.256 0.384 0.512 0.64\n", "───────────┼───────────┴───────────┴───────────┴───────────┴───────────┴\n", " 00│▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒▒\n", " │\n", " 11│▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓▓\n", " │\n", "{'00': 488, '11': 512}" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sim.reset()\n", "result = sim.sampling(circ, shots=1000) # 对上面定义的线路采样1000次\n", "result" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "MindQuantum还提供了采样结果绘制SVG图的功能:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": "\n\n\nShots:\n 1000\n \n\nKeys: q0 q1\n \n\n\n\n0.0\n \n\n\n\n0.102\n \n\n\n\n0.205\n \n\n\n\n0.307\n \n\n\n\n0.41\n \n\n\n\n0.512\n \n\n\n00\n \n\n\n\n488\n \n\n11\n \n\n\n\n512\n \n\n\n\n\n\n\nprobability\n \n", "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "result.svg() # 打印出测量结果的SVG格式" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我们可以看到,采样1000中,'00'出现了488次,'11'出现了512次。我们搭建的线路实际上制备出了一个贝尔态$\\frac{\\sqrt{2}}{2}|00⟩+\\frac{\\sqrt{2}}{2}|11⟩$。直观上,我们可以看到对该状态进行测量得到'00'的概率为$\\frac{1}{2}$,得到'11'的概率为$\\frac{1}{2}$,采样结果符合概率,细微的误差是由模拟器噪声导致。" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": "\n\n\nq0:\n \n\nq1:\n \n\n\n\n\n\nH\n \n\n\n\n\n\n\n\n\n\nRY\n \n\ntheta\n \n\n\n\n\n\n\n\n\n\n", "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# 含参线路采样:\n", "para_circ = Circuit() # 初始化量子线路\n", "para_circ += H.on(0) # H门作用在第0位量子比特\n", "para_circ += X.on(1, 0) # X门作用在第1位量子比特且受第0位量子比特控制\n", "para_circ += RY('theta').on(1) # RY(theta)门作用在第2位量子比特\n", "para_circ += Measure('0').on(0) # 在0号量子比特作用一个测量,并将该测量命名为'q0'\n", "para_circ += Measure('q1').on(1) # 在1号量子比特作用一个测量,并将该测量命名为'q1'\n", "para_circ.svg() # 绘制SVG格式的量子线路图片" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/svg+xml": "\n\n\nShots:\n 1000\n \n\nKeys: 0 q1\n \n\n\n\n0.0\n \n\n\n\n0.103\n \n\n\n\n0.205\n \n\n\n\n0.308\n \n\n\n\n0.41\n \n\n\n\n0.513\n \n\n\n00\n \n\n\n\n513\n \n\n11\n \n\n\n\n487\n \n\n\n\n\n\n\nprobability\n \n", "text/plain": [ "" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "sim.reset()\n", "result = sim.sampling(para_circ, {'theta': 0},\n", " shots=1000) # 将上面定义的线路参数'theta'赋值为0采样1000次\n", "result.svg()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "我们可以看到,采样结果中'00'出现了513次,'11'出现了487次。事实上把RY门参数赋值为0,它即为我们熟悉的I门,相当于不对线路做任何操作,因此该采样线路与上面不含参线路本质是同一个,可以观察到二次采样结果几乎相同,符合预期结果。\n", "\n", "想进一步学习如何对量子线路做测量操作,想了解采样结果分布的理论解释,请点击:[量子测量教程](https://www.mindspore.cn/mindquantum/docs/zh-CN/r0.8/quantum_measurement.html)。\n", "\n", "若想查询更多关于MindQuantum的API,请点击:[https://mindspore.cn/mindquantum/](https://mindspore.cn/mindquantum/)。" ] } ], "metadata": { "kernelspec": { "display_name": "MindSpore", "language": "python", "name": "mindspore" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.8" } }, "nbformat": 4, "nbformat_minor": 4 }