quantum_chemistry

# PennyLane 量子化学 ## 目录 1. [分子哈密顿量](#molecular-hamiltonians) 2. [变分量子本征求解器 (VQE)](#variational-quantum-eigensolver-vqe) 3. [分子结构](#molecular-structure) 4. [基组与映射](#basis-sets-and-mapping) 5. [激发态](#excited-states) 6. [量子化学工作流](#quantum-chemistry-workflows) ## 分子哈密顿量 ### 构建分子哈密顿量 python import pennylane as qml from pennylane import qchem import numpy as np # 定义分子 symbols = ['H', 'H'] coordinates = np.array([0.0, 0.0, 0.0, 0.0, 0.0, 0.74]) # 埃 # 生成哈密顿量 hamiltonian, n_qubits = qchem.molecular_hamiltonian( symbols, coordinates, charge=0, mult=1, # 自旋多重度 basis='sto-3g', method='dhf' # Dirac-Hartree-Fock ) print(f"哈密顿量: {hamiltonian}") print(f"所需量子比特数: {n_qubits}") ### Jordan-Wigner 变换 python # 哈密顿量通过 Jordan-Wigner 自动转换为量子比特形式 # 手动转换： from pennylane import fermi # 费米子算符 a_0 = fermi.FermiC(0) # 产生算符 a_1 = fermi.FermiA(1) # 湮灭算符 # 转换为量子比特 qubit_op = qml.qchem.jordan_wigner(a_0 * a_1) ### Bravyi-Kitaev 变换 python # 替代映射（对某些系统更高效） from pennylane.qchem import bravyi_kitaev # 使用 Bravyi-Kitaev 构建哈密顿量 hamiltonian, n_qubits = qchem.molecular_hamiltonian( symbols, coordinates, mapping='bravyi_kitaev' ) ### 自定义哈密顿量 python # 从系数和算符构建哈密顿量 coeffs = [0.2, -0.8, 0.5] obs = [ qml.PauliZ(0), qml.PauliZ(0) @ qml.PauliZ(1), qml.PauliX(0) @ qml.PauliX(1) ] H = qml.Hamiltonian(coeffs, obs) # 或者使用简化语法 H = 0.2 * qml.PauliZ(0) - 0.8 * qml.PauliZ(0) @ qml.PauliZ(1) + 0.5 * qml.PauliX(0) @ qml.PauliX(1) ## 变分量子本征求解器 (VQE) ### VQE 基本实现 python from pennylane import numpy as np # 定义设备 dev = qml.device('default.qubit', wires=n_qubits) # Hartree-Fock 态准备 hf_state = qchem.hf_state(electrons=2, orbitals=n_qubits) def ansatz(params, wires): """变分 ansatz.""" qml.BasisState(hf_state, wires=wires) for i in range(len(wires)): qml.RY(params[i], wires=i) for i in range(len(wires)-1): qml.CNOT(wires=[i, i+1]) @qml.qnode(dev)