From cced4740118d8f996a36ec5830bc0c2dc681c9af Mon Sep 17 00:00:00 2001 From: Hugh Date: Wed, 22 Apr 2026 13:22:58 +0800 Subject: [PATCH] add lih vqe example --- .../vqe_lih/data_lih/LiH_data_0.1.pkl | Bin 0 -> 2892 bytes .../vqe_lih/data_lih/LiH_data_0.2.pkl | Bin 0 -> 2892 bytes .../vqe_lih/data_lih/LiH_data_0.3.pkl | Bin 0 -> 2892 bytes .../vqe_lih/data_lih/LiH_data_0.4.pkl | Bin 0 -> 2892 bytes .../vqe_lih/data_lih/LiH_data_0.5.pkl | Bin 0 -> 2892 bytes .../vqe_lih/data_lih/LiH_data_0.6.pkl | Bin 0 -> 2892 bytes .../vqe_lih/data_lih/LiH_data_0.7.pkl | Bin 0 -> 2892 bytes .../vqe_lih/data_lih/LiH_data_0.8.pkl | Bin 0 -> 2892 bytes .../vqe_lih/data_lih/LiH_data_0.9.pkl | Bin 0 -> 2892 bytes .../vqe_lih/tutorial_LiH_molecule_vqe.ipynb | 862 ++++++++++++++++++ .../vqe_lih/tutorial_LiH_molecule_vqe.py | 580 ++++++++++++ 11 files changed, 1442 insertions(+) create mode 100644 docs/source/demos/difficult/vqe_lih/data_lih/LiH_data_0.1.pkl create mode 100644 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b/docs/source/demos/difficult/vqe_lih/tutorial_LiH_molecule_vqe.ipynb new file mode 100644 index 00000000..a9ad7f58 --- /dev/null +++ b/docs/source/demos/difficult/vqe_lih/tutorial_LiH_molecule_vqe.ipynb @@ -0,0 +1,862 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# LiH 基态能量求解教程\n", + "\n", + "## 背景与动机\n", + "对于大分子基态能量问题的求解，传统量子模拟方法需要消耗大量量子比特资源，文献《Doubling the size of quantum simulators by entanglement forging》提出了一种思路：先对基态做 Schmidt 分解，从而把需要处理的有效维度降低一半。比如对 10 比特的水分子，Schmidt 分解可将其等效为两个 5 比特子系统，这样后续计算只需在 5 比特线路上完成。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 方法概述\n", + "这个案例将使用一个三比特光量子电路去求解，原本需要六比特表示的 LiH 分子基态能量。\n", + "采用的一元编码会把光学模式（qumode）映射到等效的qubit计算空间。下面按步骤展开：\n", + "\n", + "### 1) Schmidt 分解与参数化表示\n", + "1. 选定三个 Schmidt 基矢进行 Schmidt 分解（取 $n=3$）。此时，六比特基态 $\\psi_6$ 可写成：\n", + "\n", + "$$\\psi_6 = \\sum_n \\lambda_n{U\\psi_3^n\\otimes V \\psi_3^n}$$\n", + "\n", + "这里 $U$ 与 $V$ 表示两个不同的量子电路 Ansatz。为了降低参数量，也可以先取 $U=V$。\n", + "\n", + "### 2) 哈密顿量分解与期望值重构\n", + "2. 把 LiH 的哈密顿量写成 Pauli 基矢的线性组合：$H=\\sum_k w_k O_k$，其中 $w_k$ 是分解系数。则哈密顿量期望值满足：\n", + "$$ = \\sum_k w_k $$\n", + "\n", + "在这里，每个 Pauli 基矢对应一个 6 比特算符（例如 `IIIZZZ`）。\n", + "接着把它切分成两个 3 比特算符 $O_a$ 与 $O_b$，使得 $O_k=O_a\\otimes O_b$。\n", + "然后分别用 $U\\psi_3^n$ 与 $V\\psi_3^n$ 计算对应子系统上的算符期望值。\n", + "\n", + "$$ = = \\sum_{nm} \\lambda_n \\lambda_m <\\psi_3^n|U^+O_a U|\\psi_3^n><\\psi_3^n|V^+O_b V|\\psi_3^n> = \\vec{\\lambda}^T M \\vec{\\lambda}$$\n", + "\n", + "其中\n", + "$\\vec{\\lambda}=(\\lambda_1, \\lambda_2, \\lambda_3)， ||\\vec{\\lambda}||=1$， $M=\\begin{pmatrix}\n", + "M_{00} & M_{01} & M_{02}\\\\\n", + "M_{10} & M_{11} & M_{12} \\\\\n", + "M_{20} & M_{21} & M_{22}\n", + "\\end{pmatrix}$， 其中$M_{ij}=<\\psi_3^i|U^+O_a U|\\psi_3^j><\\psi_3^i|V^+O_b V|\\psi_3^j>$。由于哈密顿量是厄米算符，可以得到 $M$ 的厄米性：$M^\\dagger = M$（其中 $\\dagger$ 表示转置并取共轭）。\n", + "\n", + "### 3) 最小特征值与基态能量\n", + "3. 把所有算符的期望值按分解系数求和，可得到\n", + "$M_{sum}=\\sum_k w_k M_k$。\n", + "于是哈密顿量的期望值可以写成二次型：$\\langle H\\rangle = \\vec{\\lambda}^T M_{sum} \\vec{\\lambda}$。\n", + "在约束 $||\\vec{\\lambda}||=1$ 下，这个二次型的最小值等于矩阵 $M_{sum}$ 的最小特征值；对应的 $\\vec{\\lambda}$ 就是该特征值的特征向量。因此，最小特征值也对应于哈密顿量的基态能量。" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 构建期望值计算线路\n", + "首先搭建一个 `Clements` 光量子电路。它采用一元编码将光学模式等效成可计算的量子比特，使得在前向计算中可以得到任意 Pauli 基矢算符的期望值。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import pickle\n", + "from functools import reduce\n", + "from itertools import product\n", + "\n", + "import deepquantum as dq\n", + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import torch\n", + "import torch.nn.functional as nnf\n", + "from torch import nn\n", + "\n", + "\n", + "class QumodeExpectValue(nn.Module):\n", + " # 使用Clements线路计算算符的平均值\n", + " def __init__(self, nmode, init_state=None, if_sup=False, u_sup=None, loss=None):\n", + " super().__init__()\n", + " if init_state is None:\n", + " init_state = [1] + [0] * (nmode - 1)\n", + " # 一元编码\n", + " cir = dq.Clements(nmode=nmode, init_state=init_state, cutoff=2)\n", + " if loss is not None:\n", + " for k in range(nmode):\n", + " cir.loss_db(k, loss)\n", + " cir.set_fock_basis()\n", + " nqubit = int(torch.log2(torch.tensor(nmode)))\n", + " basis_list = torch.tensor(list(product(range(2), repeat=nqubit)))\n", + " # 考虑初始态是不是叠加态\n", + " u_start = torch.eye(cir.nmode) if not if_sup else u_sup\n", + " u_start = u_start.to(dtype=torch.complex64)\n", + " self.cir = cir\n", + " self.nmode = nmode\n", + " self.init_state = init_state\n", + " self.basis_list = basis_list\n", + " self.u_start = u_start\n", + " self.if_sup = if_sup\n", + " self.ndata = cir.ndata\n", + " self.loss = loss\n", + "\n", + " def forward(self, data=None, op=None, u_measure=None, idx_z=None, shots=None):\n", + " \"\"\"Obtain expectation value for given operator using single-rail encoding\"\"\"\n", + " cir = self.cir\n", + " basis_list = self.basis_list\n", + " state = self.init_state\n", + " u_start = self.u_start\n", + "\n", + " if u_measure is None:\n", + " u_measure, idx_z = self.get_u_measure(op)\n", + " if not isinstance(idx_z, torch.Tensor):\n", + " idx_z = torch.tensor(idx_z).unsqueeze(0)\n", + " if u_measure.ndim == 2:\n", + " u_measure = u_measure.unsqueeze(0)\n", + "\n", + " if self.loss is not None:\n", + " # 带loss情况下计算维度加倍\n", + " u_measure_loss = torch.eye(2 * self.nmode).repeat(u_measure.shape[0], 1, 1)\n", + " u_start_loss = torch.eye(2 * self.nmode)\n", + " u_measure_loss = u_measure_loss.to(dtype=torch.complex64)\n", + " u_start_loss = u_start_loss.to(dtype=torch.complex64)\n", + " u_measure_loss[:, : self.nmode, : self.nmode] = u_measure\n", + " u_start_loss[: self.nmode, : self.nmode] = u_start\n", + " u_total = u_measure_loss @ cir(data=data) @ u_start_loss\n", + " else:\n", + " u_total = u_measure @ cir(data=data) @ u_start\n", + " if u_total.ndim == 2:\n", + " u_total = u_total.unsqueeze(0)\n", + " idx = torch.nonzero(state)[0][0]\n", + " # 根据取行列规则，一元编码只需要取酉矩阵的一行(列)即可\n", + " state = u_total[:, :, idx]\n", + " if shots is None:\n", + " probs = (abs(state) ** 2)[:, : self.nmode]\n", + " else:\n", + " probs = sample(abs(state) ** 2, shots)\n", + " probs = probs[:, : self.nmode]\n", + " norm = torch.sum(probs, dim=1)\n", + " # 概率归一化\n", + " probs = probs / (norm + 1e-10).unsqueeze(-1)\n", + " # False 时对应的列变成0，然后求和\n", + " masked_basis = basis_list.unsqueeze(0) * idx_z.unsqueeze(1)\n", + " parity_sum = masked_basis.sum(dim=-1)\n", + " temp_coeff = torch.tensor(-1) ** parity_sum\n", + " return (probs.squeeze() * temp_coeff).sum(-1)\n", + "\n", + " @staticmethod\n", + " def get_u_measure(op):\n", + " idx_z = []\n", + " u_list = []\n", + " x_rotate_gate = torch.tensor([[0.7071 + 0.0j, 0.7071 + 0.0j], [0.7071 + 0.0j, -0.7071 - 0.0j]])\n", + " y_rotate_gate = torch.tensor([[0.7071 + 0.0000j, 0.0000 - 0.7071j], [0.7071 + 0.0000j, 0.0000 + 0.7071j]])\n", + " iden2 = torch.eye(2, dtype=x_rotate_gate.dtype)\n", + " # 处理每个qubit的Pauli算符，旋转到Z基进行测量\n", + " for k in range(len(op)):\n", + " op_k = op[k]\n", + " if op_k == 'I':\n", + " u_list.append(iden2)\n", + " idx_z.append(False)\n", + " elif op_k == 'Z':\n", + " idx_z.append(True)\n", + " u_list.append(iden2)\n", + " elif op_k == 'X':\n", + " # X算符：通过H门旋转到Z基 (H X H† = Z)\n", + " idx_z.append(True)\n", + " u_list.append(x_rotate_gate)\n", + " elif op_k == 'Y':\n", + " # Y算符：通过S†H旋转到Z基 ((S†H) Y (H†S) = Z)\n", + " idx_z.append(True)\n", + " u_list.append(y_rotate_gate)\n", + " u_measure = reduce(torch.kron, u_list)\n", + " return u_measure, idx_z\n", + "\n", + "\n", + "# 提前计算各个算符的测量变换基矢\n", + "def get_measure_u(pauli_list_full):\n", + " u_measure_list_q3 = []\n", + " idx_z_list_q3 = []\n", + "\n", + " pauli_coef = []\n", + " len_ = len(pauli_list_full)\n", + " for i in range(len_):\n", + " pauli_coef.append(pauli_list_full[i][-1])\n", + " temp_op1 = pauli_list_full[i][:3]\n", + " temp_op2 = pauli_list_full[i][3:6]\n", + " temp_u_q3 = []\n", + " temp_idx_q3 = []\n", + "\n", + " for op in [temp_op1, temp_op2]:\n", + " temp_q3 = QumodeExpectValue.get_u_measure(op)\n", + " temp_u_q3.append(temp_q3[0])\n", + " temp_idx_q3.append(temp_q3[1])\n", + "\n", + " u_measure_list_q3.append(torch.stack(temp_u_q3))\n", + " idx_z_list_q3.append(torch.tensor(temp_idx_q3))\n", + "\n", + " u_measure_list_q3_ts = torch.stack(u_measure_list_q3)\n", + " idx_z_list_q3_ts = torch.stack(idx_z_list_q3)\n", + " return u_measure_list_q3_ts, idx_z_list_q3_ts, pauli_coef\n", + "\n", + "\n", + "# 保持梯度的采样方法\n", + "def sample(probs, shots):\n", + " eps = 1e-20\n", + " logits = torch.log(probs + eps)\n", + " logits_expanded = logits.unsqueeze(1).expand(-1, shots, -1)\n", + " samples = nnf.gumbel_softmax(logits_expanded, tau=0.01, hard=True)\n", + " sampled_probs = samples.mean(dim=1)\n", + " return sampled_probs" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "tensor([-0.0533], grad_fn=)\n" + ] + } + ], + "source": [ + "# 测试算符平均值计算\n", + "torch.manual_seed(12)\n", + "data = nn.Parameter(torch.rand(64))\n", + "init_state = torch.tensor([1] + [0] * 7)\n", + "qv_test = QumodeExpectValue(nmode=8, init_state=init_state, loss=None)\n", + "re = qv_test(data, op='YYY', shots=None)\n", + "print(re)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 加载哈密顿量分解数据\n", + "载入哈密顿量在 Pauli 基底上的分解数据。该例中总共分解出 62 个基矢；每个基矢对应一个 6 比特的 Pauli 算符字符串（例如 `IIIZZZ` 这类张量积算符）。" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "62 ['I', 'I', 'I', 'I', 'I', 'I', np.complex128(-0.558829025352944+0j)]\n" + ] + } + ], + "source": [ + "## load 数据\n", + "radius = 0.1\n", + "\n", + "with open(f'data_lih/LiH_data_{radius}.pkl', 'rb') as f:\n", + " dic = pickle.load(f)\n", + "constant = dic['constant']\n", + "pauli_list_full = dic['pauli_list']\n", + "energy_full = dic['fci_energy']\n", + "\n", + "print(len(pauli_list_full), pauli_list_full[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 预计算测量变换\n", + "接下来计算哈密顿量的平均值。\n", + "为了提高计算效率，我们把“测量步骤”提前做成可复用的量：对每个算符预先计算其测量变换（把相应的 Pauli 算符旋转到 Z 基）以及 Z 算符在测量中的位置。\n", + "因此得到的测量变换矩阵张量形状为 `(62, 2, 8, 8)`：`62` 表示泡利基矢组合的数量，`2` 表示两个三比特子系统，每个子系统对应的矩阵维度为 $8\\times 8$。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "(torch.Size([62, 2, 8, 8]), torch.Size([62, 2, 3]))" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "u_measure_list_q3_ts, idx_z_list_q3_ts, pauli_coef = get_measure_u(pauli_list_full)\n", + "print(u_measure_list_q3_ts.shape, idx_z_list_q3_ts.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 非对角项期望值与叠加态制备\n", + "接下来计算每个 Pauli 算符的平均值。\n", + "因为不同算符的计算结构高度相似，我们使用 batch 处理并行加速求期望。\n", + "\n", + "### 选取 Schmidt 基矢\n", + "接下来我们从 Schmidt 分解中选取 3 个基矢：$\\ket{110}$、$\\ket{101}$ 和 $\\ket{011}$。\n", + "\n", + "### 非对角元的重构公式\n", + "- 为了计算非对角元 $<\\psi_i|O|\\psi_j>$（$i\\neq j$），我们需要制备下面两种叠加态：\n", + " $$\\psi_{R} = \\frac{\\sqrt{2}}{2}(\\psi_i + \\psi_j),\\quad \\psi_{I} = \\frac{\\sqrt{2}}{2}(\\psi_i + i * \\psi_j)$$\n", + "$<\\psi_i|O|\\psi_j>$ 可以表示为下面的平均值的线性组合，\n", + "$$<\\psi_i|O|\\psi_j> = (O_{RR}-0.5*(O_{ii} + O_{jj})) + i *(0.5*(O_{ii} + O_{jj}) - O_{II}) $$\n", + "$$O_{RR} = <\\psi_R|O|\\psi_R>，O_{II} = <\\psi_I|O|\\psi_I>，O_{ii} = <\\psi_i|O|\\psi_i>，O_{jj} = <\\psi_j|O|\\psi_j>$$\n", + "\n", + "### 叠加态制备门序列\n", + "对于叠加态 $\\psi_{R}$ 和 $\\psi_{I}$ 的制备：在光量子电路中，我们通常先制备一个 Fock 初态，然后再作用“叠加态变换矩阵”，即可得到相应的叠加态。\n", + "在实现中，这个叠加态变换往往可以与后续 Ansatz 的酉变换合并，从而减少电路深度。\n", + "下面给出 6 个叠加态所对应的构造顺序。涉及的基本门 $H$、$S$、$SWAP$、$CNOT$ 的矩阵形式如下。\n", + "$$\n", + "H = \\frac{\\sqrt{2}}{2}\\begin{pmatrix}\n", + "1 & 1\\\\\n", + "1 & -1\n", + "\\end{pmatrix},\n", + "S = \\frac{\\sqrt{2}}{2}\\begin{pmatrix}\n", + "1 & 1\\\\\n", + "1 & i\n", + "\\end{pmatrix},\n", + "SWAP=\\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & 0 & 1 & 0 \\\\\n", + "0 & 1 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 1\n", + "\\end{pmatrix},\n", + "CNOT=\\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & 1 & 0 & 0 \\\\\n", + "0 & 0 & 0 & 1 \\\\\n", + "0 & 0 & 1 & 0\n", + "\\end{pmatrix}\n", + "$$\n", + "\n", + "- ($\\ket{110}$, $\\ket{101}$):\n", + "\n", + "线路初态：$\\ket{110}$\n", + "\n", + "$\\psi_{R} = \\frac{\\sqrt{2}}{2}(\\ket{110} + \\ket{101}),\\psi_{I} = \\frac{\\sqrt{2}}{2}(\\ket{110} + i * \\ket{101})$\n", + "\n", + "$H(2) \\ket{110} --> \\frac{\\sqrt{2}}{2}(\\ket{110} + \\ket{111})$,\n", + "\n", + "$SWAP (1,2) --> \\frac{\\sqrt{2}}{2}(\\ket{101} + \\ket{111})$,\n", + "\n", + "$CNOT (1,2) --> \\frac{\\sqrt{2}}{2}(\\ket{101} + \\ket{110})$,\n", + "\n", + "$S(2) --> \\frac{\\sqrt{2}}{2}(\\ket{110} + i * \\ket{101})$\n", + "\n", + "- ($\\ket{110}$, $\\ket{011}$):\n", + "\n", + "线路初态：$\\ket{110}$\n", + "\n", + "$\\psi_{R} = \\frac{\\sqrt{2}}{2}(\\ket{110} + \\ket{011}),\\psi_{I} = \\frac{\\sqrt{2}}{2}(\\ket{110} + i * \\ket{011})$\n", + "\n", + "$H(2) \\ket{110} --> \\frac{\\sqrt{2}}{2}(\\ket{110} + \\ket{111})$,\n", + "\n", + "$SWAP (1,2) --> \\frac{\\sqrt{2}}{2}(\\ket{101} + \\ket{111})$,\n", + "\n", + "$CNOT (1,2) --> \\frac{\\sqrt{2}}{2}(\\ket{101} + \\ket{110})$,\n", + "\n", + "$SWAP (0,1)--> \\frac{\\sqrt{2}}{2}(\\ket{110} + \\ket{011})$,\n", + "\n", + "$S (2) --> \\frac{\\sqrt{2}}{2}(\\ket{110} + i * \\ket{011})$\n", + "\n", + "- ($\\ket{101}$, $\\ket{011}$):\n", + "\n", + "线路初态：$\\ket{101}$\n", + "\n", + "$\\psi_{R} = \\frac{\\sqrt{2}}{2}(\\ket{101} + \\ket{011}),\\psi_{I} = \\frac{\\sqrt{2}}{2}(\\ket{101} + i * \\ket{011})$\n", + "\n", + "$H(1) \\ket{101} --> \\frac{\\sqrt{2}}{2}(\\ket{101} + \\ket{111})$,\n", + "\n", + "$SWAP (0,1) --> \\frac{\\sqrt{2}}{2}(\\ket{011} + \\ket{111})$,\n", + "\n", + "$CNOT (0,1) --> \\frac{\\sqrt{2}}{2}(\\ket{011} + \\ket{101})$,\n", + "\n", + "$S (1) --> \\frac{\\sqrt{2}}{2}(\\ket{101} + i * \\ket{011})$\n", + "\n", + "下面开始计算叠加态制备酉矩阵。" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "## 构建三比特系统的三个初始量子态110， 101， 011，以及他们的叠加态\n", + "u_state = torch.tensor([0.0, 1.0])\n", + "d_state = torch.tensor([1.0, 0.0])\n", + "state1 = reduce(torch.kron, [u_state, u_state, d_state])\n", + "state2 = reduce(torch.kron, [u_state, d_state, u_state])\n", + "state3 = reduce(torch.kron, [d_state, u_state, u_state])\n", + "state = torch.stack([state1, state2, state3])\n", + "\n", + "## 构建子系统的初始量子态\n", + "# 在八模线路中分别一元编码映射qubit\n", + "state_sub3 = torch.stack([state1.to(int), state2.to(int), state3.to(int)])\n", + "\n", + "# 求解制备叠加态酉矩阵\n", + "# 110 --> sqrt(2)/2*(110+101)\n", + "# 110 --> sqrt(2)/2*(110+011)\n", + "# 101 --> sqrt(2)/2*(101+011)\n", + "state_sup = [state1.to(int), state1.to(int), state2.to(int)]\n", + "\n", + "h_mat = torch.tensor([[1, 1], [1, -1]]) * np.sqrt(2) / 2 + 0j\n", + "x_mat = torch.tensor([[0.0, 1.0], [1.0, 0.0]]) + 0j\n", + "s_mat = torch.tensor([[1.0, 0.0], [0.0, 1j]]) + 0j\n", + "cnot_mat = torch.tensor([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]) + 0j\n", + "swap_mat = torch.tensor([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]) + 0j\n", + "iden2 = torch.eye(2)\n", + "\n", + "temp1_real = torch.kron(iden2, cnot_mat) @ torch.kron(iden2, swap_mat) @ reduce(torch.kron, [iden2, iden2, h_mat])\n", + "temp1_imag = reduce(torch.kron, [iden2, iden2, s_mat]) @ temp1_real\n", + "\n", + "temp2_real = torch.kron(swap_mat, iden2) @ temp1_real\n", + "temp2_imag = reduce(torch.kron, [iden2, iden2, s_mat]) @ temp2_real\n", + "\n", + "temp3_real = torch.kron(cnot_mat, iden2) @ torch.kron(swap_mat, iden2) @ reduce(torch.kron, [iden2, h_mat, iden2])\n", + "temp3_imag = reduce(torch.kron, [iden2, s_mat, iden2]) @ temp3_real\n", + "\n", + "u_list_sup = [temp1_real, temp2_real, temp3_real, temp1_imag, temp2_imag, temp3_imag]\n", + "u_state_sup = state_sup + state_sup" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 初始化与形状检查\n", + "下面开始做一个初始化测试。\n", + "我们分别搭建 3 条线路计算对角项 $M_{ii}$，并搭建 6 条线路计算非对角项 $M_{ij}$。\n", + "`loss` 用来调节光损耗强度，单位为 dB。" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "torch.Size([3, 124])\n", + "torch.Size([6, 124])\n" + ] + } + ], + "source": [ + "## 初始化测试\n", + "torch.manual_seed(12)\n", + "d1 = 64\n", + "nmode_q3 = 8\n", + "data = torch.rand(d1, requires_grad=True)\n", + "loss = None # dB\n", + "# diag\n", + "output_q3_diag = []\n", + "models_q3_diag = [QumodeExpectValue(nmode=nmode_q3, init_state=state_sub3[k], loss=loss) for k in range(3)] # schimdt 3\n", + "for i in range(len(models_q3_diag)):\n", + " output_q3_diag_i = models_q3_diag[i](\n", + " data=data[:d1], u_measure=u_measure_list_q3_ts.reshape(-1, 8, 8), idx_z=idx_z_list_q3_ts.reshape(-1, 3)\n", + " )\n", + " output_q3_diag.append(output_q3_diag_i)\n", + "output_q3_diag = torch.stack(output_q3_diag)\n", + "print(output_q3_diag.shape)\n", + "\n", + "# off diag\n", + "output_q3_off_diag = []\n", + "models_q3_off_diag = [\n", + " QumodeExpectValue(nmode=nmode_q3, init_state=u_state_sup[k], loss=loss, if_sup=True, u_sup=u_list_sup[k])\n", + " for k in range(6)\n", + "] # 包括实部也包括虚部计算 schimdt 3\n", + "\n", + "for i in range(len(models_q3_off_diag)):\n", + " output_q3_off_diag_i = models_q3_off_diag[i](\n", + " data=data[:d1], u_measure=u_measure_list_q3_ts.reshape(-1, 8, 8), idx_z=idx_z_list_q3_ts.reshape(-1, 3)\n", + " )\n", + " output_q3_off_diag.append(output_q3_off_diag_i)\n", + "output_q3_off_diag = torch.stack(output_q3_off_diag)\n", + "print(output_q3_off_diag.shape)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "下面定义一个用于估计基态能量的函数。\n", + "它通过调用前面构建的线路来计算哈密顿量中各 Pauli 基矢的贡献，并把结果按 Schmidt 系数与哈密顿量分解系数加权求和，最终返回一个基态能量标量。函数返回基态能量的估计值。参数说明如下，\n", + "- `models_q3_diag`：用于计算对角项 $M_{ii}$ 的 3 条线路；\n", + "- `models_q3_off_diag`：用于计算非对角项 $M_{ij}$ 的 6 条线路；\n", + "- `n_subs`：子系统个数，这里为 2；\n", + "- `u_measure_list_q3_ts`：各 Pauli 基矢对应的测量变换矩阵；\n", + "- `idx_z_list_q3_ts`：Z 算符在测量设置中的位置；\n", + "- `pauli_coef`：哈密顿量分解中各基矢的叠加权重；\n", + "- `data`：线路编码的数据（变分参数）；\n", + "- `shots`：采样次数（用于带采样的期望值估计）。" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "## 定义用于估计基态能量的函数\n", + "d1 = 64\n", + "\n", + "\n", + "def compute_eigen_energy_measure_photonic_lih(\n", + " models_q3_diag, models_q3_off_diag, n_subs, u_measure_list_q3_ts, idx_z_list_q3_ts, pauli_coef, data, shots\n", + "):\n", + " output_q3_diag = []\n", + " for i in range(len(models_q3_diag)):\n", + " # print(u_measure_list_q3_ts.shape)\n", + " output_q3_diag_i = models_q3_diag[i](\n", + " data=data[:d1],\n", + " u_measure=u_measure_list_q3_ts.reshape(-1, 8, 8),\n", + " idx_z=idx_z_list_q3_ts.reshape(-1, 3),\n", + " shots=shots,\n", + " )\n", + " output_q3_diag.append(output_q3_diag_i)\n", + " output_q3_diag = torch.stack(output_q3_diag)\n", + " shape1 = output_q3_diag.shape # (batch, n_subs * n_ops)\n", + " temp1_diag = output_q3_diag.reshape(shape1[0], -1, n_subs)\n", + "\n", + " temp2_diag = torch.prod(temp1_diag, dim=2)\n", + " diag = (temp2_diag * pauli_coef).sum(dim=1)\n", + " temp1_sub3 = torch.stack(\n", + " [\n", + " output_q3_diag[0] + output_q3_diag[1],\n", + " output_q3_diag[0] + output_q3_diag[2],\n", + " output_q3_diag[1] + output_q3_diag[2],\n", + " ]\n", + " )\n", + "\n", + " # off diag\n", + " output_q3_off_diag = []\n", + " for i in range(len(models_q3_off_diag)):\n", + " output_q3_off_diag_i = models_q3_off_diag[i](\n", + " data=data[:d1],\n", + " u_measure=u_measure_list_q3_ts.reshape(-1, 8, 8),\n", + " idx_z=idx_z_list_q3_ts.reshape(-1, 3),\n", + " shots=shots,\n", + " )\n", + " output_q3_off_diag.append(output_q3_off_diag_i)\n", + " output_q3_off_diag = torch.stack(output_q3_off_diag)\n", + "\n", + " shape2 = output_q3_off_diag.shape\n", + " real_ndim = shape2[0] // 2\n", + " temp1_off_diag = (output_q3_off_diag[:real_ndim] - 0.5 * temp1_sub3) + 1j * (\n", + " 0.5 * temp1_sub3 - output_q3_off_diag[real_ndim:]\n", + " )\n", + " temp2_off_diag = torch.prod(temp1_off_diag.reshape(shape2[0] // 2, -1, n_subs), dim=2)\n", + " off_diag = (temp2_off_diag * pauli_coef).sum(dim=1)\n", + "\n", + " h_mat_ob2 = torch.diag_embed(diag)\n", + " rows = [0, 0, 1]\n", + " cols = [1, 2, 2]\n", + " h_mat_ob2[rows, cols] = off_diag\n", + " h_mat_ob2[cols, rows] = off_diag.conj()\n", + " # print(diag, off_diag)\n", + " h_mat_ob2 = h_mat_ob2 + torch.eye(3, device=data.device) * 1e-9\n", + " eigen_value, _ = torch.linalg.eigh(h_mat_ob2)\n", + " return eigen_value[0], h_mat_ob2" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## 变分优化实验（无损耗）\n", + "下面我们使用“基态能量计算函数”来做梯度变分，从而得到不同核间距下 LiH 的基态能量。\n", + "在本节中先不考虑光损耗（`loss` 设为 `None`），便于验证方法本身的正确性。" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "d1 = 64\n", + "nmode_q3 = 8\n", + "data = torch.rand(d1, requires_grad=True)\n", + "loss_db = None # dB\n", + "# diag\n", + "output_q3_diag = []\n", + "models_q3_diag = [QumodeExpectValue(nmode=nmode_q3, init_state=state_sub3[k], loss=loss_db) for k in range(3)]\n", + "# off diag\n", + "output_q3_off_diag = []\n", + "models_q3_off_diag = [\n", + " QumodeExpectValue(nmode=nmode_q3, init_state=u_state_sup[k], loss=loss_db, if_sup=True, u_sup=u_list_sup[k])\n", + " for k in range(6)\n", + "] # 包括实部也包括虚部计算" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.9 149 tensor(-7.7973, dtype=torch.float64, grad_fn=)\r" + ] + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "## 梯度下降法\n", + "n_subs = 2\n", + "shots_list = [50, 100, 500]\n", + "shots = None\n", + "all_loss = []\n", + "\n", + "radius_list = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]\n", + "# radius_list = [0.1]\n", + "for radius in radius_list:\n", + " # radius = 0.2\n", + " with open(f'data_lih/LiH_data_{radius}.pkl', 'rb') as f:\n", + " dic = pickle.load(f)\n", + " constant = dic['constant']\n", + " pauli_list_full = dic['pauli_list']\n", + " energy_full = dic['fci_energy']\n", + " u_measure_list_q3_ts, idx_z_list_q3_ts, pauli_coef = get_measure_u(pauli_list_full)\n", + "\n", + " loss_all = []\n", + " pauli_coef_ts = torch.tensor(pauli_coef)\n", + " data = nn.Parameter(torch.rand(64) * 2 * torch.pi)\n", + " lambdas = nn.Parameter(torch.rand(1, 3, dtype=torch.complex128))\n", + " optimizer = torch.optim.Adam([data, lambdas], lr=2e-2)\n", + " # print(u_measure_list_q3_ts.shape)\n", + " for epoch in range(150):\n", + " optimizer.zero_grad()\n", + " test = compute_eigen_energy_measure_photonic_lih(\n", + " models_q3_diag,\n", + " models_q3_off_diag,\n", + " n_subs,\n", + " u_measure_list_q3_ts,\n", + " idx_z_list_q3_ts,\n", + " pauli_coef_ts,\n", + " data,\n", + " shots,\n", + " )\n", + " loss = test[0] + constant\n", + " loss.backward() # backpropagetion\n", + " optimizer.step() # update parameters\n", + " loss_all.append(loss.detach())\n", + " print(radius, epoch, loss, end='\\r')\n", + "\n", + " all_loss.append(loss_all)\n", + "\n", + " plt.figure(figsize=(8, 6), dpi=400)\n", + " plt.plot(range(len(loss_all)), loss_all, label=f'8 modes, R={radius}, loss={loss_db}, shots={shots}')\n", + " plt.hlines(energy_full, 0, 150, ls='--', color='red')\n", + " plt.legend()\n", + " plt.xlabel('epoch')\n", + " plt.ylabel('eigen energy of LiH (Hartree)')" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "3.630842648889124 2.6820088502228137\n", + "-3.20818574477686 -4.128724200288428\n", + "-5.044894665036592 -5.9581181204277875\n", + "-5.7823104238036 -6.711312207915317\n", + "-6.143032703268023 -7.122643610296507\n", + "-6.346696128267634 -7.393552184436494\n", + "-6.476678952629687 -7.579731757667254\n", + "-6.5685402691750285 -7.708995288126277\n", + "-6.638589093321304 -7.798451241458049\n" + ] + }, + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'eigen energy of LiH (Hartree)')" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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dGazFixeHX/7yl1njJ510klMIwxCVS52Jn6Ni+G6g3xU9//zzycHOTz/9dNHmBmmXxjpzzjnn5Hy/8rnPfW5A24lnFoth/U0Zre/P6B+BWCBVep5yoW/b9qHKtY22trYhbxcoLerMRvFLmPiFS64PVDGIku/UFYA6M9Q6/Jvf/CYJmZx88snJzg5g4P8fpfFzU3xes2bN6vXeJAbUYkcRYPiktcbEwFk8ld7b3/72pNtRf8UQ22mnnZZ8fjriiCOybs9kMuGSSy5JLoHyrDP92f7VV18dPv3pT2/2y+v9998/6Sobg/l93XfffZs8JSiQ3jozWN/73vdy7vuNn7uAoUl7nVm5cmVSK3bffffkTIKPPfbYgNZ/6aWXwrXXXhv222+/5HuoV155pWhzhbRKY5256KKLcp4FLH4v/fOf/7zf24n7YfqejSNXaJbSJRALpEq+HYKF+OObaxu5jnwB0k2d6RRPCRo7reU6rd+FF14YPvKRjwz77wbSotzqTDztVQyA9FziqXxiN6S777472ZERv9TN5Re/+EU47LDDwsKFC4d93lDK0lpn4mmFY1e0ni6//PKw5ZZbDsvjA+muMUMVA/rxvcurXvWqrNseeuih8JOf/GRE5gWlKG11ZnPbP+OMM8L555/f7+1ts802Yc6cOUkgv68vf/nLg5ojlJu01ZnBuv7667PGZsyYEU444YQRmQ+kSZrrzKOPPhpe85rXJKcx7zuX2OF+5syZSdg1dqD+/e9/H2677bYwe/bs8O53vztMmjQpa3sx5LbPPvskn5uA8q4z06ZNCx/96Edzhn/j56YvfelLec/AEcVwfTxzRn8aKMSzcVC6ht4HGWAUydehoxDtzHNtYyAdQYB0UGdCeO6558LRRx+dHKHb17nnnhuuvPLKEfndQFqoMyE0NDQkSzy18FFHHZWcjvh3v/td+Nd//dfwxBNPZAX046mKYwiutrZ2xH5vUErSWGeeeeaZcOmll/YaO/LII8N73vOeoj82kP4aUygTJ04MV111VVKf+vrpT3+afHkDlF+d2dTnmBhq/cIXvjDgbcY6E8+qMXfu3F7j8XNV7NiWK2wCpLfODMb999+fs6NjDLIVorMclLu01pm4fyZ+f9S3o2sM5n3mM59JmqmMGzcu57px329slPA///M/yenPe3a3XLJkSTj22GPDH//4x7DXXnsV/XlAGqS1zsR9wPfee2+45557eo3HmvGpT30q2e9y+umnh0MPPTRMnz496XYfG7Dceeed4ZZbbknqTE+ve93rsposRGPHji36c6F4dIgFUmX8+PE5x9esWTPkbefaxoQJE4a8XaC0lHudiR8Y3vjGN4bnn38+67azzjorfOc738nZgQTov3KvM5v6Qnf+/Pnh8MMPz7rtkUceSY78Bcq3zrzvfe8L69at67UDNnYX8b4Ehl8aa0wh/cu//EvOQGw8jXm+0xkC6a4zmwqnxgMEd9ttt0FtN4ZKcp32M3ZiA8qrzgxG7OyYy3nnnTfsc4E0SmOdiZ9nzjnnnKwwbDz45/bbb09CbPnCsN3i7fF+8f59DxqKZyx817veNSynZYc0SGOdieKBOTfeeGN47Wtfm/P2eEbBr3/968n31m94wxvCcccdlzRN+MEPfpAVho37lOP9cnHWsdImEAukypQpU3KOx6Peh2L9+vU5W6vnezwgvcq5zrz88stJGDYe4dvXW9/61vD9738/VFZ6ewlDVc51ZnNi19h4Cq14VG9fsTt1zzAcUD51Jh6Qc9ddd/Ua++QnPxn22GOPoj4uUB41phhOOumkrLH45W7sfA+UX52ZOnXqJkP0g5Vv3dj1ESivOjNQcf9KDJr0dcQRRww6pA+kv87EujFv3rys8RhMi11jB+KYY44JV1xxRdb4Qw89lITagPKsMz3Dqn/4wx/CKaecMuhtxI7V11xzTc5wb01NzSY/pzH6SSwAqbLVVlvlDXENRb718z0ekF7lWmcWL16chGH7nqo8estb3hJ+9KMfJae8AYauXOvMQE41/J//+Z9Z48uXL086qwHlVWdeeumlcMkll/Qa23PPPZNALDAy0lRjiuWAAw7IOd63kxJQHnUmfsaJB//lkq/rUX9sscUWYbvttsu5jwcorzozUDfddFNYvXp11visWbNGZD6QRmmsM9/85jezxuLByrED42C73ec62DnX4wDlUWd6ip+hbr755mTZd999+73e3nvvnXSh/upXv5o0elq1alXWfXbddVdnHitxUgtAqmy99dbJqTH7HpGS69TeA5Fv/Z122mlI2wVKTznWmSVLliRh2McffzzrtuOPPz7ZQRqPlAMKoxzrzECdccYZ4cILL8w6rXA8IvjUU08dsXlBqUhTnYlB+L5dDeIpPOfPnz/gYG0uTz/9dM4uavvtt1/yGgLprjHFku+0e0JqUL51Zueddw4LFizIGWoditil6YUXXug1tmzZsiFtE8pBGuvMQFx33XU5T4Mc98cAhZG2OhMDZQ888EDW+Dve8Y7k9OaDEdc788wzw+c+97msLrHxDBuTJ08e9HyhHKStzuQTu8SefPLJ4U9/+lP49a9/He65556wcOHCsHTp0uQAn3HjxiVzO+SQQ8Jpp50Wjj322F5h17///e9Z23z1q189zM+CQhOIBVIl/uHaZZddwmOPPdZrPFdHw4F48sknc47HI0OA8lJudSZ+WIinsnn00UdznrLm5z//uTAIFFi51ZnBfqm74447JkG1Qu7IgXKRpjqTyWSyxj72sY8VbPv/7//9v2Tp69lnn03qEJDuGjPcWlpaRnoKUBLSWGf22muvnIHYsWPHDmm7uTrPrl27dkjbhHKQxjrTX3Ffy+9///us8RhKG2pNAtJbZ/7617+Gjo6OrPHDDz98SNs94ogjcu4Levjhh8NRRx01pG1D2qWtzmzuuR588MHJcumllw5o3UceeSRr7PWvf30BZ8dIqByRRwUootipp6/4pngo/vKXv2SNbbvttmHq1KlD2i5QmsqlzsTTj8ej5HJ9IfOGN7wh3HrrraG+vn5E5gZpVy51ZiimTZuWNRY7AwD9o84AxaTGbFq+TrCx8xpQnnXmwAMPzDme65TlA5Hr9J9D7ToL5SJtdWYg3WFzHXg4a9asEZkPpFma6kw802Au06dPH9J2860fm7kA5VVnilW7Fi1alPN7cEqbQCyQOvGoj77iUS+5dv7117x58/r1OEB5KIc6E089HMOw8ajevv7lX/4l3HbbbWHMmDEjMjcoB+VQZ4aqsbExa6y2tnZE5gKlSJ0B1JiRE0/xmcv2228/7HOBUpW29zKHHXbYgAL0/ZVr/VL8ohpGQtrqTH+0t7eHOXPmZI2/6lWvGlXzhLRIU51pa2vLOV5TUzOk7eZbP1c3WiDddaYYfvrTn2aNxa66r3nNa0ZkPhSOQCyQOvEU3rk+xN95552D3mmY6yiXXI8DlIe015nYfeS4444L8+fPz/kFzS9/+Uunx4IiS3udGarYqSTXUbtD7TgA5USdAdSYkfOLX/wiayyefWPPPfcckflAKUrbe5n4BfKkSZOyxh988MFBb/P555/PGYjdcccdB71NKCdpqzP98etf/zrn/pbzzjtvROYDaZemOpPvgJt8nWP7K9/6uc4eBqS7zhTD97///ayxs88+e0TmQmEJxAKps9deeyVHbfR14403Dmp7P/7xj7NOD1NRURFOOumkQc8RKG1prjNr1qwJxx9/fPjzn/+cdduhhx4a5s6dG8aNGzfs84Jyk+Y6UwjxS+Hly5dnje+9994jMh8oRWmpM+eee27yuENdnn322Zzbv/7663PeX5AEyqPGFMO9996bLH0dccQRut1DGdeZqqqqcOqpp2aN33HHHYPeZr51nf4TyrPO9Md1112Xszvju971rhGZD6RdmurMlltuOaCzY/RXru+qIoFYKL86U2j33XdfsvRUV1cX3v/+94/YnCgcgVgglc4555yssZtvvjm88MILA9pO/GP+rW99K2v8qKOOCttuu+2Q5giUtjTWmXj68RNPPDHvqS5uv/32MH78+GGdE5SzNNaZQpk9e3bO8ficgP5TZ4BiUmOyxVMSfuADH+j36wWUV53J1YFxwYIF4Q9/+MOgtnfVVVdljW2xxRZhv/32G9T2oBylrc5sytKlS3N2sX/LW94ieAZFlJY6E8920dDQkDX+85//fEjb/dnPfpY1NmHCBGfXgDKsM4XU1tYWLrjggqzxWbNmha222mpE5kRhCcQCqfSv//qvWV01Wltbw3/8x38MaDuxG9Df//73rPELL7yw39uInYPiUTE9F92EoPSlrc40NTUlOzdzfcnyute9LjldVtzJAAyftNWZQrnnnntydizZfffdw4EHHjgic4JSpc4Aakz/xC9x4wGEQxG728fPXI8++mjWbTvssEN4xzve4R8klPl7mdgp+qCDDsoa//CHP5x8YTsQ//u//5vzVKYxdFtZ6atBKNc6syk33HBDaGlpyRkMAYonLXUmPodcXeh/97vfhbvvvjsMRmzS8sc//jFr/I1vfGOorq4e1DahHKWlzhRKDPZ+6EMfSg4+7Gny5Mnhs5/97LDOheLxqRdIpa233jrnEfXf+973wk033dSvbTzxxBPhIx/5SNb4q1/96pynrwLKS5rqTHNzc/J4uXZKHHDAAckp9iZOnDhs8wHSV2dmzpyZBFmH6s4770yCJH1PyRN98pOfHPL2odykqc4Ao0+aakz8QmS77bYLn/rUp8IjjzwyoHXj+5Zbbrkl7LvvvuH3v/99zvt84xvfSE5HDJRvnen2hS98IWvswQcfDB/84Adzfg7KJQZHYoi2r7Fjx4aPfexjBZknlIs01pl8ch18vM0224Q3velNIzIfKBdpqjP5DvI7++yzB9yJ8tlnn032KQ/kcYD015lua9euHdR6MQgcO8NeffXVWbfF7rdTp04twOwYDQRigdT6/Oc/n5wCqq93vetd4f/+7/82uW48ev7oo49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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "full_e = []\n", + "vqe_e = []\n", + "\n", + "radius_list = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9]\n", + "for i in range(9):\n", + " # radius = 0.2\n", + " radius = radius_list[i]\n", + " with open(f'data_lih/LiH_data_{radius}.pkl', 'rb') as f:\n", + " dic = pickle.load(f)\n", + " constant = dic['constant']\n", + " pauli_list_full = dic['pauli_list']\n", + " energy_full = dic['fci_energy']\n", + " print(constant, energy_full)\n", + " full_e.append(energy_full)\n", + " vqe_e.append(all_loss[i][-1])\n", + "\n", + "torch.save(torch.tensor(vqe_e), f'data_lih/opt_results_{loss_db}db_{shots}shots_3schimdt.pt')\n", + "plt.figure(figsize=(8, 6), dpi=400)\n", + "plt.plot(radius_list, full_e, label='fci')\n", + "plt.scatter(radius_list, vqe_e, marker='x', label=f'vqe_e, {loss_db}db_{shots}shots', color='red')\n", + "\n", + "# plt.hlines(energy_full, 0, 100, ls='--', color='red')\n", + "plt.legend()\n", + "plt.xlabel('R')\n", + "plt.ylabel('eigen energy of LiH (Hartree)')" + ] + } + ], + "metadata": { + "execution": { + "allow_errors": true, + "timeout": 400 + }, + "jupytext": { + "formats": "ipynb,py:percent" + }, + "kernelspec": { + "display_name": "dq202602", + "language": "python", + "name": "dq202602" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.10.19" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/docs/source/demos/difficult/vqe_lih/tutorial_LiH_molecule_vqe.py b/docs/source/demos/difficult/vqe_lih/tutorial_LiH_molecule_vqe.py new file mode 100644 index 00000000..0d3848e8 --- /dev/null +++ b/docs/source/demos/difficult/vqe_lih/tutorial_LiH_molecule_vqe.py @@ -0,0 +1,580 @@ +# --- +# jupyter: +# jupytext: +# formats: ipynb,py:percent +# text_representation: +# extension: .py +# format_name: percent +# format_version: '1.3' +# jupytext_version: 1.19.1 +# kernelspec: +# display_name: dq202602 +# language: python +# name: dq202602 +# --- + +# %% [markdown] +# # LiH 基态能量求解教程 +# +# ## 背景与动机 +# 对于大分子基态能量问题的求解，传统量子模拟方法需要消耗大量量子比特资源，文献《Doubling the size of quantum simulators by entanglement forging》提出了一种思路：先对基态做 Schmidt 分解，从而把需要处理的有效维度降低一半。比如对 10 比特的水分子，Schmidt 分解可将其等效为两个 5 比特子系统，这样后续计算只需在 5 比特线路上完成。 + +# %% [markdown] +# ## 方法概述 +# 这个案例将使用一个三比特光量子电路去求解，原本需要六比特表示的 LiH 分子基态能量。 +# 采用的一元编码会把光学模式（qumode）映射到等效的qubit计算空间。下面按步骤展开： +# +# ### 1) Schmidt 分解与参数化表示 +# 1. 选定三个 Schmidt 基矢进行 Schmidt 分解（取 $n=3$）。此时，六比特基态 $\psi_6$ 可写成： +# +# $$\psi_6 = \sum_n \lambda_n{U\psi_3^n\otimes V \psi_3^n}$$ +# +# 这里 $U$ 与 $V$ 表示两个不同的量子电路 Ansatz。为了降低参数量，也可以先取 $U=V$。 +# +# ### 2) 哈密顿量分解与期望值重构 +# 2. 把 LiH 的哈密顿量写成 Pauli 基矢的线性组合：$H=\sum_k w_k O_k$，其中 $w_k$ 是分解系数。则哈密顿量期望值满足： +# $$ = \sum_k w_k $$ +# +# 在这里，每个 Pauli 基矢对应一个 6 比特算符（例如 `IIIZZZ`）。 +# 接着把它切分成两个 3 比特算符 $O_a$ 与 $O_b$，使得 $O_k=O_a\otimes O_b$。 +# 然后分别用 $U\psi_3^n$ 与 $V\psi_3^n$ 计算对应子系统上的算符期望值。 +# +# $$ = = \sum_{nm} \lambda_n \lambda_m <\psi_3^n|U^+O_a U|\psi_3^n><\psi_3^n|V^+O_b V|\psi_3^n> = \vec{\lambda}^T M \vec{\lambda}$$ +# +# 其中 +# $\vec{\lambda}=(\lambda_1, \lambda_2, \lambda_3)， ||\vec{\lambda}||=1$， $M=\begin{pmatrix} +# M_{00} & M_{01} & M_{02}\\ +# M_{10} & M_{11} & M_{12} \\ +# M_{20} & M_{21} & M_{22} +# \end{pmatrix}$， 其中$M_{ij}=<\psi_3^i|U^+O_a U|\psi_3^j><\psi_3^i|V^+O_b V|\psi_3^j>$。由于哈密顿量是厄米算符，可以得到 $M$ 的厄米性：$M^\dagger = M$（其中 $\dagger$ 表示转置并取共轭）。 +# +# ### 3) 最小特征值与基态能量 +# 3. 把所有算符的期望值按分解系数求和，可得到 +# $M_{sum}=\sum_k w_k M_k$。 +# 于是哈密顿量的期望值可以写成二次型：$\langle H\rangle = \vec{\lambda}^T M_{sum} \vec{\lambda}$。 +# 在约束 $||\vec{\lambda}||=1$ 下，这个二次型的最小值等于矩阵 $M_{sum}$ 的最小特征值；对应的 $\vec{\lambda}$ 就是该特征值的特征向量。因此，最小特征值也对应于哈密顿量的基态能量。 + +# %% [markdown] +# ## 构建期望值计算线路 +# 首先搭建一个 `Clements` 光量子电路。它采用一元编码将光学模式等效成可计算的量子比特，使得在前向计算中可以得到任意 Pauli 基矢算符的期望值。 + +# %% +import pickle +from functools import reduce +from itertools import product + +import deepquantum as dq +import matplotlib.pyplot as plt +import numpy as np +import torch +import torch.nn.functional as nnf +from torch import nn + + +class QumodeExpectValue(nn.Module): + # 使用Clements线路计算算符的平均值 + def __init__(self, nmode, init_state=None, if_sup=False, u_sup=None, loss=None): + super().__init__() + if init_state is None: + init_state = [1] + [0] * (nmode - 1) + # 一元编码 + cir = dq.Clements(nmode=nmode, init_state=init_state, cutoff=2) + if loss is not None: + for k in range(nmode): + cir.loss_db(k, loss) + cir.set_fock_basis() + nqubit = int(torch.log2(torch.tensor(nmode))) + basis_list = torch.tensor(list(product(range(2), repeat=nqubit))) + # 考虑初始态是不是叠加态 + u_start = torch.eye(cir.nmode) if not if_sup else u_sup + u_start = u_start.to(dtype=torch.complex64) + self.cir = cir + self.nmode = nmode + self.init_state = init_state + self.basis_list = basis_list + self.u_start = u_start + self.if_sup = if_sup + self.ndata = cir.ndata + self.loss = loss + + def forward(self, data=None, op=None, u_measure=None, idx_z=None, shots=None): + """Obtain expectation value for given operator using single-rail encoding""" + cir = self.cir + basis_list = self.basis_list + state = self.init_state + u_start = self.u_start + + if u_measure is None: + u_measure, idx_z = self.get_u_measure(op) + if not isinstance(idx_z, torch.Tensor): + idx_z = torch.tensor(idx_z).unsqueeze(0) + if u_measure.ndim == 2: + u_measure = u_measure.unsqueeze(0) + + if self.loss is not None: + # 带loss情况下计算维度加倍 + u_measure_loss = torch.eye(2 * self.nmode).repeat(u_measure.shape[0], 1, 1) + u_start_loss = torch.eye(2 * self.nmode) + u_measure_loss = u_measure_loss.to(dtype=torch.complex64) + u_start_loss = u_start_loss.to(dtype=torch.complex64) + u_measure_loss[:, : self.nmode, : self.nmode] = u_measure + u_start_loss[: self.nmode, : self.nmode] = u_start + u_total = u_measure_loss @ cir(data=data) @ u_start_loss + else: + u_total = u_measure @ cir(data=data) @ u_start + if u_total.ndim == 2: + u_total = u_total.unsqueeze(0) + idx = torch.nonzero(state)[0][0] + # 根据取行列规则，一元编码只需要取酉矩阵的一行(列)即可 + state = u_total[:, :, idx] + if shots is None: + probs = (abs(state) ** 2)[:, : self.nmode] + else: + probs = sample(abs(state) ** 2, shots) + probs = probs[:, : self.nmode] + norm = torch.sum(probs, dim=1) + # 概率归一化 + probs = probs / (norm + 1e-10).unsqueeze(-1) + # False 时对应的列变成0，然后求和 + masked_basis = basis_list.unsqueeze(0) * idx_z.unsqueeze(1) + parity_sum = masked_basis.sum(dim=-1) + temp_coeff = torch.tensor(-1) ** parity_sum + return (probs.squeeze() * temp_coeff).sum(-1) + + @staticmethod + def get_u_measure(op): + idx_z = [] + u_list = [] + x_rotate_gate = torch.tensor([[0.7071 + 0.0j, 0.7071 + 0.0j], [0.7071 + 0.0j, -0.7071 - 0.0j]]) + y_rotate_gate = torch.tensor([[0.7071 + 0.0000j, 0.0000 - 0.7071j], [0.7071 + 0.0000j, 0.0000 + 0.7071j]]) + iden2 = torch.eye(2, dtype=x_rotate_gate.dtype) + # 处理每个qubit的Pauli算符，旋转到Z基进行测量 + for k in range(len(op)): + op_k = op[k] + if op_k == 'I': + u_list.append(iden2) + idx_z.append(False) + elif op_k == 'Z': + idx_z.append(True) + u_list.append(iden2) + elif op_k == 'X': + # X算符：通过H门旋转到Z基 (H X H† = Z) + idx_z.append(True) + u_list.append(x_rotate_gate) + elif op_k == 'Y': + # Y算符：通过S†H旋转到Z基 ((S†H) Y (H†S) = Z) + idx_z.append(True) + u_list.append(y_rotate_gate) + u_measure = reduce(torch.kron, u_list) + return u_measure, idx_z + + +# 提前计算各个算符的测量变换基矢 +def get_measure_u(pauli_list_full): + u_measure_list_q3 = [] + idx_z_list_q3 = [] + + pauli_coef = [] + len_ = len(pauli_list_full) + for i in range(len_): + pauli_coef.append(pauli_list_full[i][-1]) + temp_op1 = pauli_list_full[i][:3] + temp_op2 = pauli_list_full[i][3:6] + temp_u_q3 = [] + temp_idx_q3 = [] + + for op in [temp_op1, temp_op2]: + temp_q3 = QumodeExpectValue.get_u_measure(op) + temp_u_q3.append(temp_q3[0]) + temp_idx_q3.append(temp_q3[1]) + + u_measure_list_q3.append(torch.stack(temp_u_q3)) + idx_z_list_q3.append(torch.tensor(temp_idx_q3)) + + u_measure_list_q3_ts = torch.stack(u_measure_list_q3) + idx_z_list_q3_ts = torch.stack(idx_z_list_q3) + return u_measure_list_q3_ts, idx_z_list_q3_ts, pauli_coef + + +# 保持梯度的采样方法 +def sample(probs, shots): + eps = 1e-20 + logits = torch.log(probs + eps) + logits_expanded = logits.unsqueeze(1).expand(-1, shots, -1) + samples = nnf.gumbel_softmax(logits_expanded, tau=0.01, hard=True) + sampled_probs = samples.mean(dim=1) + return sampled_probs + + +# %% +# 测试算符平均值计算 +torch.manual_seed(12) +data = nn.Parameter(torch.rand(64)) +init_state = torch.tensor([1] + [0] * 7) +qv_test = QumodeExpectValue(nmode=8, init_state=init_state, loss=None) +re = qv_test(data, op='YYY', shots=None) +print(re) + +# %% [markdown] +# ## 加载哈密顿量分解数据 +# 载入哈密顿量在 Pauli 基底上的分解数据。该例中总共分解出 62 个基矢；每个基矢对应一个 6 比特的 Pauli 算符字符串（例如 `IIIZZZ` 这类张量积算符）。 + +# %% +## load 数据 +radius = 0.1 + +with open(f'data_lih/LiH_data_{radius}.pkl', 'rb') as f: + dic = pickle.load(f) +constant = dic['constant'] +pauli_list_full = dic['pauli_list'] +energy_full = dic['fci_energy'] + +print(len(pauli_list_full), pauli_list_full[0]) + +# %% [markdown] +# ## 预计算测量变换 +# 接下来计算哈密顿量的平均值。 +# 为了提高计算效率，我们把“测量步骤”提前做成可复用的量：对每个算符预先计算其测量变换（把相应的 Pauli 算符旋转到 Z 基）以及 Z 算符在测量中的位置。 +# 因此得到的测量变换矩阵张量形状为 `(62, 2, 8, 8)`：`62` 表示泡利基矢组合的数量，`2` 表示两个三比特子系统，每个子系统对应的矩阵维度为 $8\times 8$。 + +# %% +u_measure_list_q3_ts, idx_z_list_q3_ts, pauli_coef = get_measure_u(pauli_list_full) +print(u_measure_list_q3_ts.shape, idx_z_list_q3_ts.shape) + +# %% [markdown] +# ## 非对角项期望值与叠加态制备 +# 接下来计算每个 Pauli 算符的平均值。 +# 因为不同算符的计算结构高度相似，我们使用 batch 处理并行加速求期望。 +# +# ### 选取 Schmidt 基矢 +# 接下来我们从 Schmidt 分解中选取 3 个基矢：$\ket{110}$、$\ket{101}$ 和 $\ket{011}$。 +# +# ### 非对角元的重构公式 +# - 为了计算非对角元 $<\psi_i|O|\psi_j>$（$i\neq j$），我们需要制备下面两种叠加态： +# $$\psi_{R} = \frac{\sqrt{2}}{2}(\psi_i + \psi_j),\quad \psi_{I} = \frac{\sqrt{2}}{2}(\psi_i + i * \psi_j)$$ +# $<\psi_i|O|\psi_j>$ 可以表示为下面的平均值的线性组合， +# $$<\psi_i|O|\psi_j> = (O_{RR}-0.5*(O_{ii} + O_{jj})) + i *(0.5*(O_{ii} + O_{jj}) - O_{II}) $$ +# $$O_{RR} = <\psi_R|O|\psi_R>，O_{II} = <\psi_I|O|\psi_I>，O_{ii} = <\psi_i|O|\psi_i>，O_{jj} = <\psi_j|O|\psi_j>$$ +# +# ### 叠加态制备门序列 +# 对于叠加态 $\psi_{R}$ 和 $\psi_{I}$ 的制备：在光量子电路中，我们通常先制备一个 Fock 初态，然后再作用“叠加态变换矩阵”，即可得到相应的叠加态。 +# 在实现中，这个叠加态变换往往可以与后续 Ansatz 的酉变换合并，从而减少电路深度。 +# 下面给出 6 个叠加态所对应的构造顺序。涉及的基本门 $H$、$S$、$SWAP$、$CNOT$ 的矩阵形式如下。 +# $$ +# H = \frac{\sqrt{2}}{2}\begin{pmatrix} +# 1 & 1\\ +# 1 & -1 +# \end{pmatrix}, +# S = \frac{\sqrt{2}}{2}\begin{pmatrix} +# 1 & 1\\ +# 1 & i +# \end{pmatrix}, +# SWAP=\begin{pmatrix} +# 1 & 0 & 0 & 0\\ +# 0 & 0 & 1 & 0 \\ +# 0 & 1 & 0 & 0 \\ +# 0 & 0 & 0 & 1 +# \end{pmatrix}, +# CNOT=\begin{pmatrix} +# 1 & 0 & 0 & 0\\ +# 0 & 1 & 0 & 0 \\ +# 0 & 0 & 0 & 1 \\ +# 0 & 0 & 1 & 0 +# \end{pmatrix} +# $$ +# +# - ($\ket{110}$, $\ket{101}$): +# +# 线路初态：$\ket{110}$ +# +# $\psi_{R} = \frac{\sqrt{2}}{2}(\ket{110} + \ket{101}),\psi_{I} = \frac{\sqrt{2}}{2}(\ket{110} + i * \ket{101})$ +# +# $H(2) \ket{110} --> \frac{\sqrt{2}}{2}(\ket{110} + \ket{111})$, +# +# $SWAP (1,2) --> \frac{\sqrt{2}}{2}(\ket{101} + \ket{111})$, +# +# $CNOT (1,2) --> \frac{\sqrt{2}}{2}(\ket{101} + \ket{110})$, +# +# $S(2) --> \frac{\sqrt{2}}{2}(\ket{110} + i * \ket{101})$ +# +# - ($\ket{110}$, $\ket{011}$): +# +# 线路初态：$\ket{110}$ +# +# $\psi_{R} = \frac{\sqrt{2}}{2}(\ket{110} + \ket{011}),\psi_{I} = \frac{\sqrt{2}}{2}(\ket{110} + i * \ket{011})$ +# +# $H(2) \ket{110} --> \frac{\sqrt{2}}{2}(\ket{110} + \ket{111})$, +# +# $SWAP (1,2) --> \frac{\sqrt{2}}{2}(\ket{101} + \ket{111})$, +# +# $CNOT (1,2) --> \frac{\sqrt{2}}{2}(\ket{101} + \ket{110})$, +# +# $SWAP (0,1)--> \frac{\sqrt{2}}{2}(\ket{110} + \ket{011})$, +# +# $S (2) --> \frac{\sqrt{2}}{2}(\ket{110} + i * \ket{011})$ +# +# - ($\ket{101}$, $\ket{011}$): +# +# 线路初态：$\ket{101}$ +# +# $\psi_{R} = \frac{\sqrt{2}}{2}(\ket{101} + \ket{011}),\psi_{I} = \frac{\sqrt{2}}{2}(\ket{101} + i * \ket{011})$ +# +# $H(1) \ket{101} --> \frac{\sqrt{2}}{2}(\ket{101} + \ket{111})$, +# +# $SWAP (0,1) --> \frac{\sqrt{2}}{2}(\ket{011} + \ket{111})$, +# +# $CNOT (0,1) --> \frac{\sqrt{2}}{2}(\ket{011} + \ket{101})$, +# +# $S (1) --> \frac{\sqrt{2}}{2}(\ket{101} + i * \ket{011})$ +# +# 下面开始计算叠加态制备酉矩阵。 + +# %% +## 构建三比特系统的三个初始量子态110， 101， 011，以及他们的叠加态 +u_state = torch.tensor([0.0, 1.0]) +d_state = torch.tensor([1.0, 0.0]) +state1 = reduce(torch.kron, [u_state, u_state, d_state]) +state2 = reduce(torch.kron, [u_state, d_state, u_state]) +state3 = reduce(torch.kron, [d_state, u_state, u_state]) +state = torch.stack([state1, state2, state3]) + +## 构建子系统的初始量子态 +# 在八模线路中分别一元编码映射qubit +state_sub3 = torch.stack([state1.to(int), state2.to(int), state3.to(int)]) + +# 求解制备叠加态酉矩阵 +# 110 --> sqrt(2)/2*(110+101) +# 110 --> sqrt(2)/2*(110+011) +# 101 --> sqrt(2)/2*(101+011) +state_sup = [state1.to(int), state1.to(int), state2.to(int)] + +h_mat = torch.tensor([[1, 1], [1, -1]]) * np.sqrt(2) / 2 + 0j +x_mat = torch.tensor([[0.0, 1.0], [1.0, 0.0]]) + 0j +s_mat = torch.tensor([[1.0, 0.0], [0.0, 1j]]) + 0j +cnot_mat = torch.tensor([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1, 0]]) + 0j +swap_mat = torch.tensor([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, 1]]) + 0j +iden2 = torch.eye(2) + +temp1_real = torch.kron(iden2, cnot_mat) @ torch.kron(iden2, swap_mat) @ reduce(torch.kron, [iden2, iden2, h_mat]) +temp1_imag = reduce(torch.kron, [iden2, iden2, s_mat]) @ temp1_real + +temp2_real = torch.kron(swap_mat, iden2) @ temp1_real +temp2_imag = reduce(torch.kron, [iden2, iden2, s_mat]) @ temp2_real + +temp3_real = torch.kron(cnot_mat, iden2) @ torch.kron(swap_mat, iden2) @ reduce(torch.kron, [iden2, h_mat, iden2]) +temp3_imag = reduce(torch.kron, [iden2, s_mat, iden2]) @ temp3_real + +u_list_sup = [temp1_real, temp2_real, temp3_real, temp1_imag, temp2_imag, temp3_imag] +u_state_sup = state_sup + state_sup + +# %% [markdown] +# ## 初始化与形状检查 +# 下面开始做一个初始化测试。 +# 我们分别搭建 3 条线路计算对角项 $M_{ii}$，并搭建 6 条线路计算非对角项 $M_{ij}$。 +# `loss` 用来调节光损耗强度，单位为 dB。 + +# %% +## 初始化测试 +torch.manual_seed(12) +d1 = 64 +nmode_q3 = 8 +data = torch.rand(d1, requires_grad=True) +loss = None # dB +# diag +output_q3_diag = [] +models_q3_diag = [QumodeExpectValue(nmode=nmode_q3, init_state=state_sub3[k], loss=loss) for k in range(3)] # schimdt 3 +for i in range(len(models_q3_diag)): + output_q3_diag_i = models_q3_diag[i]( + data=data[:d1], u_measure=u_measure_list_q3_ts.reshape(-1, 8, 8), idx_z=idx_z_list_q3_ts.reshape(-1, 3) + ) + output_q3_diag.append(output_q3_diag_i) +output_q3_diag = torch.stack(output_q3_diag) +print(output_q3_diag.shape) + +# off diag +output_q3_off_diag = [] +models_q3_off_diag = [ + QumodeExpectValue(nmode=nmode_q3, init_state=u_state_sup[k], loss=loss, if_sup=True, u_sup=u_list_sup[k]) + for k in range(6) +] # 包括实部也包括虚部计算 schimdt 3 + +for i in range(len(models_q3_off_diag)): + output_q3_off_diag_i = models_q3_off_diag[i]( + data=data[:d1], u_measure=u_measure_list_q3_ts.reshape(-1, 8, 8), idx_z=idx_z_list_q3_ts.reshape(-1, 3) + ) + output_q3_off_diag.append(output_q3_off_diag_i) +output_q3_off_diag = torch.stack(output_q3_off_diag) +print(output_q3_off_diag.shape) + +# %% [markdown] +# 下面定义一个用于估计基态能量的函数。 +# 它通过调用前面构建的线路来计算哈密顿量中各 Pauli 基矢的贡献，并把结果按 Schmidt 系数与哈密顿量分解系数加权求和，最终返回一个基态能量标量。函数返回基态能量的估计值。参数说明如下， +# - `models_q3_diag`：用于计算对角项 $M_{ii}$ 的 3 条线路； +# - `models_q3_off_diag`：用于计算非对角项 $M_{ij}$ 的 6 条线路； +# - `n_subs`：子系统个数，这里为 2； +# - `u_measure_list_q3_ts`：各 Pauli 基矢对应的测量变换矩阵； +# - `idx_z_list_q3_ts`：Z 算符在测量设置中的位置； +# - `pauli_coef`：哈密顿量分解中各基矢的叠加权重； +# - `data`：线路编码的数据（变分参数）； +# - `shots`：采样次数（用于带采样的期望值估计）。 + +# %% +## 定义用于估计基态能量的函数 +d1 = 64 + + +def compute_eigen_energy_measure_photonic_lih( + models_q3_diag, models_q3_off_diag, n_subs, u_measure_list_q3_ts, idx_z_list_q3_ts, pauli_coef, data, shots +): + output_q3_diag = [] + for i in range(len(models_q3_diag)): + # print(u_measure_list_q3_ts.shape) + output_q3_diag_i = models_q3_diag[i]( + data=data[:d1], + u_measure=u_measure_list_q3_ts.reshape(-1, 8, 8), + idx_z=idx_z_list_q3_ts.reshape(-1, 3), + shots=shots, + ) + output_q3_diag.append(output_q3_diag_i) + output_q3_diag = torch.stack(output_q3_diag) + shape1 = output_q3_diag.shape # (batch, n_subs * n_ops) + temp1_diag = output_q3_diag.reshape(shape1[0], -1, n_subs) + + temp2_diag = torch.prod(temp1_diag, dim=2) + diag = (temp2_diag * pauli_coef).sum(dim=1) + temp1_sub3 = torch.stack( + [ + output_q3_diag[0] + output_q3_diag[1], + output_q3_diag[0] + output_q3_diag[2], + output_q3_diag[1] + output_q3_diag[2], + ] + ) + + # off diag + output_q3_off_diag = [] + for i in range(len(models_q3_off_diag)): + output_q3_off_diag_i = models_q3_off_diag[i]( + data=data[:d1], + u_measure=u_measure_list_q3_ts.reshape(-1, 8, 8), + idx_z=idx_z_list_q3_ts.reshape(-1, 3), + shots=shots, + ) + output_q3_off_diag.append(output_q3_off_diag_i) + output_q3_off_diag = torch.stack(output_q3_off_diag) + + shape2 = output_q3_off_diag.shape + real_ndim = shape2[0] // 2 + temp1_off_diag = (output_q3_off_diag[:real_ndim] - 0.5 * temp1_sub3) + 1j * ( + 0.5 * temp1_sub3 - output_q3_off_diag[real_ndim:] + ) + temp2_off_diag = torch.prod(temp1_off_diag.reshape(shape2[0] // 2, -1, n_subs), dim=2) + off_diag = (temp2_off_diag * pauli_coef).sum(dim=1) + + h_mat_ob2 = torch.diag_embed(diag) + rows = [0, 0, 1] + cols = [1, 2, 2] + h_mat_ob2[rows, cols] = off_diag + h_mat_ob2[cols, rows] = off_diag.conj() + # print(diag, off_diag) + h_mat_ob2 = h_mat_ob2 + torch.eye(3, device=data.device) * 1e-9 + eigen_value, _ = torch.linalg.eigh(h_mat_ob2) + return eigen_value[0], h_mat_ob2 + + +# %% [markdown] +# ## 变分优化实验（无损耗） +# 下面我们使用“基态能量计算函数”来做梯度变分，从而得到不同核间距下 LiH 的基态能量。 +# 在本节中先不考虑光损耗（`loss` 设为 `None`），便于验证方法本身的正确性。 + +# %% +d1 = 64 +nmode_q3 = 8 +data = torch.rand(d1, requires_grad=True) +loss_db = None # dB +# diag +output_q3_diag = [] +models_q3_diag = [QumodeExpectValue(nmode=nmode_q3, init_state=state_sub3[k], loss=loss_db) for k in range(3)] +# off diag +output_q3_off_diag = [] +models_q3_off_diag = [ + QumodeExpectValue(nmode=nmode_q3, init_state=u_state_sup[k], loss=loss_db, if_sup=True, u_sup=u_list_sup[k]) + for k in range(6) +] # 包括实部也包括虚部计算 + +# %% +## 梯度下降法 +n_subs = 2 +shots_list = [50, 100, 500] +shots = None +all_loss = [] + +radius_list = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] +# radius_list = [0.1] +for radius in radius_list: + # radius = 0.2 + with open(f'data_lih/LiH_data_{radius}.pkl', 'rb') as f: + dic = pickle.load(f) + constant = dic['constant'] + pauli_list_full = dic['pauli_list'] + energy_full = dic['fci_energy'] + u_measure_list_q3_ts, idx_z_list_q3_ts, pauli_coef = get_measure_u(pauli_list_full) + + loss_all = [] + pauli_coef_ts = torch.tensor(pauli_coef) + data = nn.Parameter(torch.rand(64) * 2 * torch.pi) + lambdas = nn.Parameter(torch.rand(1, 3, dtype=torch.complex128)) + optimizer = torch.optim.Adam([data, lambdas], lr=2e-2) + # print(u_measure_list_q3_ts.shape) + for epoch in range(150): + optimizer.zero_grad() + test = compute_eigen_energy_measure_photonic_lih( + models_q3_diag, + models_q3_off_diag, + n_subs, + u_measure_list_q3_ts, + idx_z_list_q3_ts, + pauli_coef_ts, + data, + shots, + ) + loss = test[0] + constant + loss.backward() # backpropagetion + optimizer.step() # update parameters + loss_all.append(loss.detach()) + print(radius, epoch, loss, end='\r') + + all_loss.append(loss_all) + + plt.figure(figsize=(8, 6), dpi=400) + plt.plot(range(len(loss_all)), loss_all, label=f'8 modes, R={radius}, loss={loss_db}, shots={shots}') + plt.hlines(energy_full, 0, 150, ls='--', color='red') + plt.legend() + plt.xlabel('epoch') + plt.ylabel('eigen energy of LiH (Hartree)') + +# %% +full_e = [] +vqe_e = [] + +radius_list = [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9] +for i in range(9): + # radius = 0.2 + radius = radius_list[i] + with open(f'data_lih/LiH_data_{radius}.pkl', 'rb') as f: + dic = pickle.load(f) + constant = dic['constant'] + pauli_list_full = dic['pauli_list'] + energy_full = dic['fci_energy'] + print(constant, energy_full) + full_e.append(energy_full) + vqe_e.append(all_loss[i][-1]) + +torch.save(torch.tensor(vqe_e), f'data_lih/opt_results_{loss_db}db_{shots}shots_3schimdt.pt') +plt.figure(figsize=(8, 6), dpi=400) +plt.plot(radius_list, full_e, label='fci') +plt.scatter(radius_list, vqe_e, marker='x', label=f'vqe_e, {loss_db}db_{shots}shots', color='red') + +# plt.hlines(energy_full, 0, 100, ls='--', color='red') +plt.legend() +plt.xlabel('R') +plt.ylabel('eigen energy of LiH (Hartree)')