QuTiP量子工具箱：Python量子模拟与计算完整指南

qutip by davila7/claude-code-templates

182 周安装量

24,200 GitHub Stars

GitHub

安装命令

npx skills add https://github.com/davila7/claude-code-templates --skill qutip

Python Web框架科研工具量子计算

🇨🇳中文介绍

QuTiP: Python 中的量子工具箱

概述

QuTiP 提供了用于模拟和分析量子力学系统的全面工具。它能够处理封闭（幺正）和开放（耗散）量子系统，并配备了针对不同场景优化的多种求解器。

安装

uv pip install qutip

用于附加功能的可选包：

# 量子信息处理（电路、门）
uv pip install qutip-qip

# 量子轨迹查看器
uv pip install qutip-qtrl

快速入门

from qutip import *
import numpy as np
import matplotlib.pyplot as plt

# 创建量子态
psi = basis(2, 0)  # |0⟩ 态

# 创建算符
H = sigmaz()  # 哈密顿量

# 时间演化
tlist = np.linspace(0, 10, 100)
result = sesolve(H, psi, tlist, e_ops=[sigmaz()])

# 绘制结果
plt.plot(tlist, result.expect[0])
plt.xlabel('时间')
plt.ylabel('⟨σz⟩')
plt.show()

核心功能

1. 量子对象与态

创建和操作量子态及算符：

# 态
psi = basis(N, n)  # Fock 态 |n⟩
psi = coherent(N, alpha)  # 相干态 |α⟩
rho = thermal_dm(N, n_avg)  # 热密度矩阵

# 算符
a = destroy(N)  # 湮灭算符
H = num(N)  # 粒子数算符
sx, sy, sz = sigmax(), sigmay(), sigmaz()  # 泡利矩阵

# 复合系统
psi_AB = tensor(psi_A, psi_B)  # 张量积

广告位招租

在这里展示您的产品或服务

触达数万 AI 开发者，精准高效

联系我们

相关 Skills

FlyClaw：零登录航班聚合查询工具，Python实现多源航班信息与价格搜索

4,000,000 周安装

AI论文代码复现工具 - 自动化复现AI论文仓库，实现最小化可信运行

9,100 周安装

FastAPI官方技能：Python Web开发最佳实践与CLI工具使用指南

1,100 周安装

Python PDF 提取技能：使用 pdfplumber 库精确提取文本、表格和元数据

998 周安装

# 创建 Bell 态
psi0 = bell_state('00')

# 每个量子比特上的局域退相位
gamma = 0.1
c_ops = [
    np.sqrt(gamma) * tensor(sigmaz(), qeye(2)),
    np.sqrt(gamma) * tensor(qeye(2), sigmaz())
]

# 跟踪纠缠
def compute_concurrence(t, psi):
    rho = ket2dm(psi) if psi.isket else psi
    return concurrence(rho)

tlist = np.linspace(0, 10, 100)
result = mesolve(qeye([2, 2]), psi0, tlist, c_ops)

# 计算每个态的 concurrence
C_t = [concurrence(state.proj()) for state in result.states]

plt.plot(tlist, C_t)
plt.xlabel('时间')
plt.ylabel('Concurrence')
plt.title('纠缠衰减')
plt.show()

# 系统参数
N = 10  # 腔 Fock 空间
wc = 1.0  # 腔频率
wa = 1.0  # 原子频率
g = 0.05  # 耦合强度

# 算符
a = tensor(destroy(N), qeye(2))  # 腔
sm = tensor(qeye(N), sigmam())  # 原子

# 哈密顿量（RWA）
H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())

# 初始态：腔处于相干态，原子处于基态
psi0 = tensor(coherent(N, 2), basis(2, 0))

# 耗散
kappa = 0.1  # 腔衰减
gamma = 0.05  # 原子衰减
c_ops = [np.sqrt(kappa) * a, np.sqrt(gamma) * sm]

# 可观测量
n_cav = a.dag() * a
n_atom = sm.dag() * sm

# 演化
tlist = np.linspace(0, 50, 200)
result = mesolve(H, psi0, tlist, c_ops, e_ops=[n_cav, n_atom])

# 绘图
fig, axes = plt.subplots(2, 1, figsize=(8, 6), sharex=True)
axes[0].plot(tlist, result.expect[0])
axes[0].set_ylabel('⟨n_cavity⟩')
axes[1].plot(tlist, result.expect[1])
axes[1].set_ylabel('⟨n_atom⟩')
axes[1].set_xlabel('时间')
plt.tight_layout()
plt.show()

截断 Hilbert 空间：使用能捕捉动力学的最小维度
选择合适的求解器：对于纯态，sesolve 比 mesolve 更快
时间相关项：字符串格式（例如 'cos(w*t)'）是最快的
仅存储所需数据：使用 e_ops 而不是存储所有态
调整容差：通过 Options 在精度和计算时间之间取得平衡
并行轨迹：mcsolve 自动使用多个 CPU
检查收敛性：改变 ntraj、Hilbert 空间大小和容差

references/core_concepts.md：量子对象、态、算符、张量积、复合系统
references/time_evolution.md：所有求解器（sesolve、mesolve、mcsolve、brmesolve 等）、时间相关哈密顿量、求解器选项
references/visualization.md：Bloch 球、Wigner 函数、Q-函数、Fock 分布、矩阵图
references/analysis.md：期望值、熵、保真度、纠缠度量、关联函数、稳态
references/advanced.md：Floquet 理论、HEOM、置换不变性、随机方法、超算符、性能提示

🇺🇸English

QuTiP: Quantum Toolbox in Python

Overview

QuTiP provides comprehensive tools for simulating and analyzing quantum mechanical systems. It handles both closed (unitary) and open (dissipative) quantum systems with multiple solvers optimized for different scenarios.

Installation

uv pip install qutip

Optional packages for additional functionality:

# Quantum information processing (circuits, gates)
uv pip install qutip-qip

# Quantum trajectory viewer
uv pip install qutip-qtrl

Quick Start

from qutip import *
import numpy as np
import matplotlib.pyplot as plt

# Create quantum state
psi = basis(2, 0)  # |0⟩ state

# Create operator
H = sigmaz()  # Hamiltonian

# Time evolution
tlist = np.linspace(0, 10, 100)
result = sesolve(H, psi, tlist, e_ops=[sigmaz()])

# Plot results
plt.plot(tlist, result.expect[0])
plt.xlabel('Time')
plt.ylabel('⟨σz⟩')
plt.show()

Core Capabilities

1. Quantum Objects and States

Create and manipulate quantum states and operators:

# States
psi = basis(N, n)  # Fock state |n⟩
psi = coherent(N, alpha)  # Coherent state |α⟩
rho = thermal_dm(N, n_avg)  # Thermal density matrix

# Operators
a = destroy(N)  # Annihilation operator
H = num(N)  # Number operator
sx, sy, sz = sigmax(), sigmay(), sigmaz()  # Pauli matrices

# Composite systems
psi_AB = tensor(psi_A, psi_B)  # Tensor product

See references/core_concepts.md for comprehensive coverage of quantum objects, states, operators, and tensor products.

2. Time Evolution and Dynamics

Multiple solvers for different scenarios:

# Closed systems (unitary evolution)
result = sesolve(H, psi0, tlist, e_ops=[num(N)])

# Open systems (dissipation)
c_ops = [np.sqrt(0.1) * destroy(N)]  # Collapse operators
result = mesolve(H, psi0, tlist, c_ops, e_ops=[num(N)])

# Quantum trajectories (Monte Carlo)
result = mcsolve(H, psi0, tlist, c_ops, ntraj=500, e_ops=[num(N)])

Solver selection guide:

sesolve: Pure states, unitary evolution
mesolve: Mixed states, dissipation, general open systems
mcsolve: Quantum jumps, photon counting, individual trajectories
brmesolve: Weak system-bath coupling
fmmesolve: Time-periodic Hamiltonians (Floquet)

See references/time_evolution.md for detailed solver documentation, time-dependent Hamiltonians, and advanced options.

3. Analysis and Measurement

Compute physical quantities:

# Expectation values
n_avg = expect(num(N), psi)

# Entropy measures
S = entropy_vn(rho)  # Von Neumann entropy
C = concurrence(rho)  # Entanglement (two qubits)

# Fidelity and distance
F = fidelity(psi1, psi2)
D = tracedist(rho1, rho2)

# Correlation functions
corr = correlation_2op_1t(H, rho0, taulist, c_ops, A, B)
w, S = spectrum_correlation_fft(taulist, corr)

# Steady states
rho_ss = steadystate(H, c_ops)

See references/analysis.md for entropy, fidelity, measurements, correlation functions, and steady state calculations.

4. Visualization

Visualize quantum states and dynamics:

# Bloch sphere
b = Bloch()
b.add_states(psi)
b.show()

# Wigner function (phase space)
xvec = np.linspace(-5, 5, 200)
W = wigner(psi, xvec, xvec)
plt.contourf(xvec, xvec, W, 100, cmap='RdBu')

# Fock distribution
plot_fock_distribution(psi)

# Matrix visualization
hinton(rho)  # Hinton diagram
matrix_histogram(H.full())  # 3D bars

See references/visualization.md for Bloch sphere animations, Wigner functions, Q-functions, and matrix visualizations.

5. Advanced Methods

Specialized techniques for complex scenarios:

# Floquet theory (periodic Hamiltonians)
T = 2 * np.pi / w_drive
f_modes, f_energies = floquet_modes(H, T, args)
result = fmmesolve(H, psi0, tlist, c_ops, T=T, args=args)

# HEOM (non-Markovian, strong coupling)
from qutip.nonmarkov.heom import HEOMSolver, BosonicBath
bath = BosonicBath(Q, ck_real, vk_real)
hsolver = HEOMSolver(H_sys, [bath], max_depth=5)
result = hsolver.run(rho0, tlist)

# Permutational invariance (identical particles)
psi = dicke(N, j, m)  # Dicke states
Jz = jspin(N, 'z')  # Collective operators

See references/advanced.md for Floquet theory, HEOM, permutational invariance, stochastic solvers, superoperators, and performance optimization.

Common Workflows

Simulating a Damped Harmonic Oscillator

# System parameters
N = 20  # Hilbert space dimension
omega = 1.0  # Oscillator frequency
kappa = 0.1  # Decay rate

# Hamiltonian and collapse operators
H = omega * num(N)
c_ops = [np.sqrt(kappa) * destroy(N)]

# Initial state
psi0 = coherent(N, 3.0)

# Time evolution
tlist = np.linspace(0, 50, 200)
result = mesolve(H, psi0, tlist, c_ops, e_ops=[num(N)])

# Visualize
plt.plot(tlist, result.expect[0])
plt.xlabel('Time')
plt.ylabel('⟨n⟩')
plt.title('Photon Number Decay')
plt.show()

Two-Qubit Entanglement Dynamics

# Create Bell state
psi0 = bell_state('00')

# Local dephasing on each qubit
gamma = 0.1
c_ops = [
    np.sqrt(gamma) * tensor(sigmaz(), qeye(2)),
    np.sqrt(gamma) * tensor(qeye(2), sigmaz())
]

# Track entanglement
def compute_concurrence(t, psi):
    rho = ket2dm(psi) if psi.isket else psi
    return concurrence(rho)

tlist = np.linspace(0, 10, 100)
result = mesolve(qeye([2, 2]), psi0, tlist, c_ops)

# Compute concurrence for each state
C_t = [concurrence(state.proj()) for state in result.states]

plt.plot(tlist, C_t)
plt.xlabel('Time')
plt.ylabel('Concurrence')
plt.title('Entanglement Decay')
plt.show()

Jaynes-Cummings Model

# System parameters
N = 10  # Cavity Fock space
wc = 1.0  # Cavity frequency
wa = 1.0  # Atom frequency
g = 0.05  # Coupling strength

# Operators
a = tensor(destroy(N), qeye(2))  # Cavity
sm = tensor(qeye(N), sigmam())  # Atom

# Hamiltonian (RWA)
H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())

# Initial state: cavity in coherent state, atom in ground state
psi0 = tensor(coherent(N, 2), basis(2, 0))

# Dissipation
kappa = 0.1  # Cavity decay
gamma = 0.05  # Atomic decay
c_ops = [np.sqrt(kappa) * a, np.sqrt(gamma) * sm]

# Observables
n_cav = a.dag() * a
n_atom = sm.dag() * sm

# Evolve
tlist = np.linspace(0, 50, 200)
result = mesolve(H, psi0, tlist, c_ops, e_ops=[n_cav, n_atom])

# Plot
fig, axes = plt.subplots(2, 1, figsize=(8, 6), sharex=True)
axes[0].plot(tlist, result.expect[0])
axes[0].set_ylabel('⟨n_cavity⟩')
axes[1].plot(tlist, result.expect[1])
axes[1].set_ylabel('⟨n_atom⟩')
axes[1].set_xlabel('Time')
plt.tight_layout()
plt.show()

Tips for Efficient Simulations

Truncate Hilbert spaces : Use smallest dimension that captures dynamics
Choose appropriate solver : sesolve for pure states is faster than mesolve
Time-dependent terms : String format (e.g., 'cos(w*t)') is fastest
Store only needed data : Use e_ops instead of storing all states
Adjust tolerances : Balance accuracy with computation time via Options
Parallel trajectories : mcsolve automatically uses multiple CPUs
Check convergence : Vary ntraj, Hilbert space size, and tolerances

Troubleshooting

Memory issues : Reduce Hilbert space dimension, use store_final_state option, or consider Krylov methods

Slow simulations : Use string-based time-dependence, increase tolerances slightly, or try method='bdf' for stiff problems

Numerical instabilities : Decrease time steps (nsteps option), increase tolerances, or check Hamiltonian/operators are properly defined

Import errors : Ensure QuTiP is installed correctly; quantum gates require qutip-qip package

References

This skill includes detailed reference documentation:

references/core_concepts.md : Quantum objects, states, operators, tensor products, composite systems
references/time_evolution.md : All solvers (sesolve, mesolve, mcsolve, brmesolve, etc.), time-dependent Hamiltonians, solver options
references/visualization.md : Bloch sphere, Wigner functions, Q-functions, Fock distributions, matrix plots
references/analysis.md : Expectation values, entropy, fidelity, entanglement measures, correlation functions, steady states
references/advanced.md : Floquet theory, HEOM, permutational invariance, stochastic methods, superoperators, performance tips

External Resources

Documentation: https://qutip.readthedocs.io/
Tutorials: https://qutip.org/qutip-tutorials/
API Reference: https://qutip.readthedocs.io/en/stable/apidoc/apidoc.html
GitHub: https://github.com/qutip/qutip

Weekly Installs

122

Repository

davila7/claude-…emplates

GitHub Stars

22.6K

First Seen

Jan 21, 2026

Security Audits

Gen Agent Trust HubWarn SocketPass SnykPass

Installed on

claude-code106

opencode97

cursor92

gemini-cli90

antigravity87

codex79

QuTiP量子工具箱：Python量子模拟与计算完整指南

🇨🇳中文介绍

QuTiP: Python 中的量子工具箱

概述

安装

快速入门

核心功能

1. 量子对象与态

相关 Skills

2. 时间演化与动力学

3. 分析与测量

4. 可视化

5. 高级方法

常见工作流程

模拟阻尼谐振子

双量子比特纠缠动力学

Jaynes-Cummings 模型

高效模拟技巧

故障排除

参考资料

外部资源