[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"skill:01M71GDHEBD0MYY36C963S4AY1":3,"skill-same:01M71GDHEBD0MYY36C963S4AY1":90},{"skillNo":4,"name":5,"nameZh":6,"description":7,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":15,"categories":16,"keywords":22,"publishedAt":42,"linkOnly":43,"markdownContent":44,"markdownBody":45,"frontMatter":46,"refName":47,"commitSha":48,"skillDirectory":49,"forksCount":50,"repositoryHtmlUrl":51,"repositoryHomepageUrl":6,"ownerHtmlUrl":52,"ownerBlogUrl":6,"ownerDescription":6,"updatedAt":53,"install":54,"resources":67},"01M71GDHEBD0MYY36C963S4AY1","qutip",null,"Quantum mechanics simulations and analysis using QuTiP (Quantum Toolbox in Python). Use when working with quantum systems including: (1) quantum states (kets, bras, density matrices), (2) quantum operators and gates, (3) time evolution and dynamics (Schrödinger, master equations, Monte Carlo), (4) open quantum systems with dissipation, (5) quantum measurements and entanglement, (6) visualization (Bloch sphere, Wigner functions), (7) steady states and correlation functions, or (8) advanced methods (Floquet theory, HEOM, stochastic solvers). Handles both closed and open quantum systems across various domains including quantum optics, quantum computing, and condensed matter physics.","JSGforever\u002Fskillguard","JSGforever","https:\u002F\u002Favatars.githubusercontent.com\u002Fu\u002F85541948?v=4","01M71FQD3E132VMR5F4TAYX3YS","01M71FQD4DYW0XJ4XQ4YQH75Y9",2,"GPL-3.0","https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__Microck--claude-scientific-skills\u002Fscientific-skills\u002Fqutip\u002FSKILL.md",[17],{"categoryNo":18,"categoryName":19,"taxonomyType":20,"taxonomyTypeDesc":21},"01JBSEEDCAT000000000000013","分析与可视化","SCENARIO","使用场景",[5,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41],"analysis","dynamics","quantum mechanics","master","Simulations","entanglement","operators","condensed matter","schrödinger","across","when","mechanics","open","domains","time","states","advanced","physics","visualization","2026-11-10 10:12:30",false,"---\nname: qutip\ndescription: \"Quantum mechanics simulations and analysis using QuTiP (Quantum Toolbox in Python). Use when working with quantum systems including: (1) quantum states (kets, bras, density matrices), (2) quantum operators and gates, (3) time evolution and dynamics (Schrödinger, master equations, Monte Carlo), (4) open quantum systems with dissipation, (5) quantum measurements and entanglement, (6) visualization (Bloch sphere, Wigner functions), (7) steady states and correlation functions, or (8) advanced methods (Floquet theory, HEOM, stochastic solvers). Handles both closed and open quantum systems across various domains including quantum optics, quantum computing, and condensed matter physics.\"\n---\n\n# QuTiP: Quantum Toolbox in Python\n\n## Overview\n\nQuTiP 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.\n\n## Installation\n\n```bash\nuv pip install qutip\n```\n\nOptional packages for additional functionality:\n\n```bash\n# Quantum information processing (circuits, gates)\nuv pip install qutip-qip\n\n# Quantum trajectory viewer\nuv pip install qutip-qtrl\n```\n\n## Quick Start\n\n```python\nfrom qutip import *\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# Create quantum state\npsi = basis(2, 0)  # |0⟩ state\n\n# Create operator\nH = sigmaz()  # Hamiltonian\n\n# Time evolution\ntlist = np.linspace(0, 10, 100)\nresult = sesolve(H, psi, tlist, e_ops=[sigmaz()])\n\n# Plot results\nplt.plot(tlist, result.expect[0])\nplt.xlabel('Time')\nplt.ylabel('⟨σz⟩')\nplt.show()\n```\n\n## Core Capabilities\n\n### 1. Quantum Objects and States\n\nCreate and manipulate quantum states and operators:\n\n```python\n# States\npsi = basis(N, n)  # Fock state |n⟩\npsi = coherent(N, alpha)  # Coherent state |α⟩\nrho = thermal_dm(N, n_avg)  # Thermal density matrix\n\n# Operators\na = destroy(N)  # Annihilation operator\nH = num(N)  # Number operator\nsx, sy, sz = sigmax(), sigmay(), sigmaz()  # Pauli matrices\n\n# Composite systems\npsi_AB = tensor(psi_A, psi_B)  # Tensor product\n```\n\n**See** `references\u002Fcore_concepts.md` for comprehensive coverage of quantum objects, states, operators, and tensor products.\n\n### 2. Time Evolution and Dynamics\n\nMultiple solvers for different scenarios:\n\n```python\n# Closed systems (unitary evolution)\nresult = sesolve(H, psi0, tlist, e_ops=[num(N)])\n\n# Open systems (dissipation)\nc_ops = [np.sqrt(0.1) * destroy(N)]  # Collapse operators\nresult = mesolve(H, psi0, tlist, c_ops, e_ops=[num(N)])\n\n# Quantum trajectories (Monte Carlo)\nresult = mcsolve(H, psi0, tlist, c_ops, ntraj=500, e_ops=[num(N)])\n```\n\n**Solver selection guide:**\n- `sesolve`: Pure states, unitary evolution\n- `mesolve`: Mixed states, dissipation, general open systems\n- `mcsolve`: Quantum jumps, photon counting, individual trajectories\n- `brmesolve`: Weak system-bath coupling\n- `fmmesolve`: Time-periodic Hamiltonians (Floquet)\n\n**See** `references\u002Ftime_evolution.md` for detailed solver documentation, time-dependent Hamiltonians, and advanced options.\n\n### 3. Analysis and Measurement\n\nCompute physical quantities:\n\n```python\n# Expectation values\nn_avg = expect(num(N), psi)\n\n# Entropy measures\nS = entropy_vn(rho)  # Von Neumann entropy\nC = concurrence(rho)  # Entanglement (two qubits)\n\n# Fidelity and distance\nF = fidelity(psi1, psi2)\nD = tracedist(rho1, rho2)\n\n# Correlation functions\ncorr = correlation_2op_1t(H, rho0, taulist, c_ops, A, B)\nw, S = spectrum_correlation_fft(taulist, corr)\n\n# Steady states\nrho_ss = steadystate(H, c_ops)\n```\n\n**See** `references\u002Fanalysis.md` for entropy, fidelity, measurements, correlation functions, and steady state calculations.\n\n### 4. Visualization\n\nVisualize quantum states and dynamics:\n\n```python\n# Bloch sphere\nb = Bloch()\nb.add_states(psi)\nb.show()\n\n# Wigner function (phase space)\nxvec = np.linspace(-5, 5, 200)\nW = wigner(psi, xvec, xvec)\nplt.contourf(xvec, xvec, W, 100, cmap='RdBu')\n\n# Fock distribution\nplot_fock_distribution(psi)\n\n# Matrix visualization\nhinton(rho)  # Hinton diagram\nmatrix_histogram(H.full())  # 3D bars\n```\n\n**See** `references\u002Fvisualization.md` for Bloch sphere animations, Wigner functions, Q-functions, and matrix visualizations.\n\n### 5. Advanced Methods\n\nSpecialized techniques for complex scenarios:\n\n```python\n# Floquet theory (periodic Hamiltonians)\nT = 2 * np.pi \u002F w_drive\nf_modes, f_energies = floquet_modes(H, T, args)\nresult = fmmesolve(H, psi0, tlist, c_ops, T=T, args=args)\n\n# HEOM (non-Markovian, strong coupling)\nfrom qutip.nonmarkov.heom import HEOMSolver, BosonicBath\nbath = BosonicBath(Q, ck_real, vk_real)\nhsolver = HEOMSolver(H_sys, [bath], max_depth=5)\nresult = hsolver.run(rho0, tlist)\n\n# Permutational invariance (identical particles)\npsi = dicke(N, j, m)  # Dicke states\nJz = jspin(N, 'z')  # Collective operators\n```\n\n**See** `references\u002Fadvanced.md` for Floquet theory, HEOM, permutational invariance, stochastic solvers, superoperators, and performance optimization.\n\n## Common Workflows\n\n### Simulating a Damped Harmonic Oscillator\n\n```python\n# System parameters\nN = 20  # Hilbert space dimension\nomega = 1.0  # Oscillator frequency\nkappa = 0.1  # Decay rate\n\n# Hamiltonian and collapse operators\nH = omega * num(N)\nc_ops = [np.sqrt(kappa) * destroy(N)]\n\n# Initial state\npsi0 = coherent(N, 3.0)\n\n# Time evolution\ntlist = np.linspace(0, 50, 200)\nresult = mesolve(H, psi0, tlist, c_ops, e_ops=[num(N)])\n\n# Visualize\nplt.plot(tlist, result.expect[0])\nplt.xlabel('Time')\nplt.ylabel('⟨n⟩')\nplt.title('Photon Number Decay')\nplt.show()\n```\n\n### Two-Qubit Entanglement Dynamics\n\n```python\n# Create Bell state\npsi0 = bell_state('00')\n\n# Local dephasing on each qubit\ngamma = 0.1\nc_ops = [\n    np.sqrt(gamma) * tensor(sigmaz(), qeye(2)),\n    np.sqrt(gamma) * tensor(qeye(2), sigmaz())\n]\n\n# Track entanglement\ndef compute_concurrence(t, psi):\n    rho = ket2dm(psi) if psi.isket else psi\n    return concurrence(rho)\n\ntlist = np.linspace(0, 10, 100)\nresult = mesolve(qeye([2, 2]), psi0, tlist, c_ops)\n\n# Compute concurrence for each state\nC_t = [concurrence(state.proj()) for state in result.states]\n\nplt.plot(tlist, C_t)\nplt.xlabel('Time')\nplt.ylabel('Concurrence')\nplt.title('Entanglement Decay')\nplt.show()\n```\n\n### Jaynes-Cummings Model\n\n```python\n# System parameters\nN = 10  # Cavity Fock space\nwc = 1.0  # Cavity frequency\nwa = 1.0  # Atom frequency\ng = 0.05  # Coupling strength\n\n# Operators\na = tensor(destroy(N), qeye(2))  # Cavity\nsm = tensor(qeye(N), sigmam())  # Atom\n\n# Hamiltonian (RWA)\nH = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())\n\n# Initial state: cavity in coherent state, atom in ground state\npsi0 = tensor(coherent(N, 2), basis(2, 0))\n\n# Dissipation\nkappa = 0.1  # Cavity decay\ngamma = 0.05  # Atomic decay\nc_ops = [np.sqrt(kappa) * a, np.sqrt(gamma) * sm]\n\n# Observables\nn_cav = a.dag() * a\nn_atom = sm.dag() * sm\n\n# Evolve\ntlist = np.linspace(0, 50, 200)\nresult = mesolve(H, psi0, tlist, c_ops, e_ops=[n_cav, n_atom])\n\n# Plot\nfig, axes = plt.subplots(2, 1, figsize=(8, 6), sharex=True)\naxes[0].plot(tlist, result.expect[0])\naxes[0].set_ylabel('⟨n_cavity⟩')\naxes[1].plot(tlist, result.expect[1])\naxes[1].set_ylabel('⟨n_atom⟩')\naxes[1].set_xlabel('Time')\nplt.tight_layout()\nplt.show()\n```\n\n## Tips for Efficient Simulations\n\n1. **Truncate Hilbert spaces**: Use smallest dimension that captures dynamics\n2. **Choose appropriate solver**: `sesolve` for pure states is faster than `mesolve`\n3. **Time-dependent terms**: String format (e.g., `'cos(w*t)'`) is fastest\n4. **Store only needed data**: Use `e_ops` instead of storing all states\n5. **Adjust tolerances**: Balance accuracy with computation time via `Options`\n6. **Parallel trajectories**: `mcsolve` automatically uses multiple CPUs\n7. **Check convergence**: Vary `ntraj`, Hilbert space size, and tolerances\n\n## Troubleshooting\n\n**Memory issues**: Reduce Hilbert space dimension, use `store_final_state` option, or consider Krylov methods\n\n**Slow simulations**: Use string-based time-dependence, increase tolerances slightly, or try `method='bdf'` for stiff problems\n\n**Numerical instabilities**: Decrease time steps (`nsteps` option), increase tolerances, or check Hamiltonian\u002Foperators are properly defined\n\n**Import errors**: Ensure QuTiP is installed correctly; quantum gates require `qutip-qip` package\n\n## References\n\nThis skill includes detailed reference documentation:\n\n- **`references\u002Fcore_concepts.md`**: Quantum objects, states, operators, tensor products, composite systems\n- **`references\u002Ftime_evolution.md`**: All solvers (sesolve, mesolve, mcsolve, brmesolve, etc.), time-dependent Hamiltonians, solver options\n- **`references\u002Fvisualization.md`**: Bloch sphere, Wigner functions, Q-functions, Fock distributions, matrix plots\n- **`references\u002Fanalysis.md`**: Expectation values, entropy, fidelity, entanglement measures, correlation functions, steady states\n- **`references\u002Fadvanced.md`**: Floquet theory, HEOM, permutational invariance, stochastic methods, superoperators, performance tips\n\n## External Resources\n\n- Documentation: https:\u002F\u002Fqutip.readthedocs.io\u002F\n- Tutorials: https:\u002F\u002Fqutip.org\u002Fqutip-tutorials\u002F\n- API Reference: https:\u002F\u002Fqutip.readthedocs.io\u002Fen\u002Fstable\u002Fapidoc\u002Fapidoc.html\n- GitHub: https:\u002F\u002Fgithub.com\u002Fqutip\u002Fqutip\n","# QuTiP: Quantum Toolbox in Python\n\n## Overview\n\nQuTiP 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.\n\n## Installation\n\n```bash\nuv pip install qutip\n```\n\nOptional packages for additional functionality:\n\n```bash\n# Quantum information processing (circuits, gates)\nuv pip install qutip-qip\n\n# Quantum trajectory viewer\nuv pip install qutip-qtrl\n```\n\n## Quick Start\n\n```python\nfrom qutip import *\nimport numpy as np\nimport matplotlib.pyplot as plt\n\n# Create quantum state\npsi = basis(2, 0)  # |0⟩ state\n\n# Create operator\nH = sigmaz()  # Hamiltonian\n\n# Time evolution\ntlist = np.linspace(0, 10, 100)\nresult = sesolve(H, psi, tlist, e_ops=[sigmaz()])\n\n# Plot results\nplt.plot(tlist, result.expect[0])\nplt.xlabel('Time')\nplt.ylabel('⟨σz⟩')\nplt.show()\n```\n\n## Core Capabilities\n\n### 1. Quantum Objects and States\n\nCreate and manipulate quantum states and operators:\n\n```python\n# States\npsi = basis(N, n)  # Fock state |n⟩\npsi = coherent(N, alpha)  # Coherent state |α⟩\nrho = thermal_dm(N, n_avg)  # Thermal density matrix\n\n# Operators\na = destroy(N)  # Annihilation operator\nH = num(N)  # Number operator\nsx, sy, sz = sigmax(), sigmay(), sigmaz()  # Pauli matrices\n\n# Composite systems\npsi_AB = tensor(psi_A, psi_B)  # Tensor product\n```\n\n**See** `references\u002Fcore_concepts.md` for comprehensive coverage of quantum objects, states, operators, and tensor products.\n\n### 2. Time Evolution and Dynamics\n\nMultiple solvers for different scenarios:\n\n```python\n# Closed systems (unitary evolution)\nresult = sesolve(H, psi0, tlist, e_ops=[num(N)])\n\n# Open systems (dissipation)\nc_ops = [np.sqrt(0.1) * destroy(N)]  # Collapse operators\nresult = mesolve(H, psi0, tlist, c_ops, e_ops=[num(N)])\n\n# Quantum trajectories (Monte Carlo)\nresult = mcsolve(H, psi0, tlist, c_ops, ntraj=500, e_ops=[num(N)])\n```\n\n**Solver selection guide:**\n- `sesolve`: Pure states, unitary evolution\n- `mesolve`: Mixed states, dissipation, general open systems\n- `mcsolve`: Quantum jumps, photon counting, individual trajectories\n- `brmesolve`: Weak system-bath coupling\n- `fmmesolve`: Time-periodic Hamiltonians (Floquet)\n\n**See** `references\u002Ftime_evolution.md` for detailed solver documentation, time-dependent Hamiltonians, and advanced options.\n\n### 3. Analysis and Measurement\n\nCompute physical quantities:\n\n```python\n# Expectation values\nn_avg = expect(num(N), psi)\n\n# Entropy measures\nS = entropy_vn(rho)  # Von Neumann entropy\nC = concurrence(rho)  # Entanglement (two qubits)\n\n# Fidelity and distance\nF = fidelity(psi1, psi2)\nD = tracedist(rho1, rho2)\n\n# Correlation functions\ncorr = correlation_2op_1t(H, rho0, taulist, c_ops, A, B)\nw, S = spectrum_correlation_fft(taulist, corr)\n\n# Steady states\nrho_ss = steadystate(H, c_ops)\n```\n\n**See** `references\u002Fanalysis.md` for entropy, fidelity, measurements, correlation functions, and steady state calculations.\n\n### 4. Visualization\n\nVisualize quantum states and dynamics:\n\n```python\n# Bloch sphere\nb = Bloch()\nb.add_states(psi)\nb.show()\n\n# Wigner function (phase space)\nxvec = np.linspace(-5, 5, 200)\nW = wigner(psi, xvec, xvec)\nplt.contourf(xvec, xvec, W, 100, cmap='RdBu')\n\n# Fock distribution\nplot_fock_distribution(psi)\n\n# Matrix visualization\nhinton(rho)  # Hinton diagram\nmatrix_histogram(H.full())  # 3D bars\n```\n\n**See** `references\u002Fvisualization.md` for Bloch sphere animations, Wigner functions, Q-functions, and matrix visualizations.\n\n### 5. Advanced Methods\n\nSpecialized techniques for complex scenarios:\n\n```python\n# Floquet theory (periodic Hamiltonians)\nT = 2 * np.pi \u002F w_drive\nf_modes, f_energies = floquet_modes(H, T, args)\nresult = fmmesolve(H, psi0, tlist, c_ops, T=T, args=args)\n\n# HEOM (non-Markovian, strong coupling)\nfrom qutip.nonmarkov.heom import HEOMSolver, BosonicBath\nbath = BosonicBath(Q, ck_real, vk_real)\nhsolver = HEOMSolver(H_sys, [bath], max_depth=5)\nresult = hsolver.run(rho0, tlist)\n\n# Permutational invariance (identical particles)\npsi = dicke(N, j, m)  # Dicke states\nJz = jspin(N, 'z')  # Collective operators\n```\n\n**See** `references\u002Fadvanced.md` for Floquet theory, HEOM, permutational invariance, stochastic solvers, superoperators, and performance optimization.\n\n## Common Workflows\n\n### Simulating a Damped Harmonic Oscillator\n\n```python\n# System parameters\nN = 20  # Hilbert space dimension\nomega = 1.0  # Oscillator frequency\nkappa = 0.1  # Decay rate\n\n# Hamiltonian and collapse operators\nH = omega * num(N)\nc_ops = [np.sqrt(kappa) * destroy(N)]\n\n# Initial state\npsi0 = coherent(N, 3.0)\n\n# Time evolution\ntlist = np.linspace(0, 50, 200)\nresult = mesolve(H, psi0, tlist, c_ops, e_ops=[num(N)])\n\n# Visualize\nplt.plot(tlist, result.expect[0])\nplt.xlabel('Time')\nplt.ylabel('⟨n⟩')\nplt.title('Photon Number Decay')\nplt.show()\n```\n\n### Two-Qubit Entanglement Dynamics\n\n```python\n# Create Bell state\npsi0 = bell_state('00')\n\n# Local dephasing on each qubit\ngamma = 0.1\nc_ops = [\n    np.sqrt(gamma) * tensor(sigmaz(), qeye(2)),\n    np.sqrt(gamma) * tensor(qeye(2), sigmaz())\n]\n\n# Track entanglement\ndef compute_concurrence(t, psi):\n    rho = ket2dm(psi) if psi.isket else psi\n    return concurrence(rho)\n\ntlist = np.linspace(0, 10, 100)\nresult = mesolve(qeye([2, 2]), psi0, tlist, c_ops)\n\n# Compute concurrence for each state\nC_t = [concurrence(state.proj()) for state in result.states]\n\nplt.plot(tlist, C_t)\nplt.xlabel('Time')\nplt.ylabel('Concurrence')\nplt.title('Entanglement Decay')\nplt.show()\n```\n\n### Jaynes-Cummings Model\n\n```python\n# System parameters\nN = 10  # Cavity Fock space\nwc = 1.0  # Cavity frequency\nwa = 1.0  # Atom frequency\ng = 0.05  # Coupling strength\n\n# Operators\na = tensor(destroy(N), qeye(2))  # Cavity\nsm = tensor(qeye(N), sigmam())  # Atom\n\n# Hamiltonian (RWA)\nH = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm + a * sm.dag())\n\n# Initial state: cavity in coherent state, atom in ground state\npsi0 = tensor(coherent(N, 2), basis(2, 0))\n\n# Dissipation\nkappa = 0.1  # Cavity decay\ngamma = 0.05  # Atomic decay\nc_ops = [np.sqrt(kappa) * a, np.sqrt(gamma) * sm]\n\n# Observables\nn_cav = a.dag() * a\nn_atom = sm.dag() * sm\n\n# Evolve\ntlist = np.linspace(0, 50, 200)\nresult = mesolve(H, psi0, tlist, c_ops, e_ops=[n_cav, n_atom])\n\n# Plot\nfig, axes = plt.subplots(2, 1, figsize=(8, 6), sharex=True)\naxes[0].plot(tlist, result.expect[0])\naxes[0].set_ylabel('⟨n_cavity⟩')\naxes[1].plot(tlist, result.expect[1])\naxes[1].set_ylabel('⟨n_atom⟩')\naxes[1].set_xlabel('Time')\nplt.tight_layout()\nplt.show()\n```\n\n## Tips for Efficient Simulations\n\n1. **Truncate Hilbert spaces**: Use smallest dimension that captures dynamics\n2. **Choose appropriate solver**: `sesolve` for pure states is faster than `mesolve`\n3. **Time-dependent terms**: String format (e.g., `'cos(w*t)'`) is fastest\n4. **Store only needed data**: Use `e_ops` instead of storing all states\n5. **Adjust tolerances**: Balance accuracy with computation time via `Options`\n6. **Parallel trajectories**: `mcsolve` automatically uses multiple CPUs\n7. **Check convergence**: Vary `ntraj`, Hilbert space size, and tolerances\n\n## Troubleshooting\n\n**Memory issues**: Reduce Hilbert space dimension, use `store_final_state` option, or consider Krylov methods\n\n**Slow simulations**: Use string-based time-dependence, increase tolerances slightly, or try `method='bdf'` for stiff problems\n\n**Numerical instabilities**: Decrease time steps (`nsteps` option), increase tolerances, or check Hamiltonian\u002Foperators are properly defined\n\n**Import errors**: Ensure QuTiP is installed correctly; quantum gates require `qutip-qip` package\n\n## References\n\nThis skill includes detailed reference documentation:\n\n- **`references\u002Fcore_concepts.md`**: Quantum objects, states, operators, tensor products, composite systems\n- **`references\u002Ftime_evolution.md`**: All solvers (sesolve, mesolve, mcsolve, brmesolve, etc.), time-dependent Hamiltonians, solver options\n- **`references\u002Fvisualization.md`**: Bloch sphere, Wigner functions, Q-functions, Fock distributions, matrix plots\n- **`references\u002Fanalysis.md`**: Expectation values, entropy, fidelity, entanglement measures, correlation functions, steady states\n- **`references\u002Fadvanced.md`**: Floquet theory, HEOM, permutational invariance, stochastic methods, superoperators, performance tips\n\n## External Resources\n\n- Documentation: https:\u002F\u002Fqutip.readthedocs.io\u002F\n- Tutorials: https:\u002F\u002Fqutip.org\u002Fqutip-tutorials\u002F\n- API Reference: https:\u002F\u002Fqutip.readthedocs.io\u002Fen\u002Fstable\u002Fapidoc\u002Fapidoc.html\n- GitHub: https:\u002F\u002Fgithub.com\u002Fqutip\u002Fqutip\n",{"name":5,"description":7},"main","f2ec4b3b9133d34eeaf9b38e4b0a97e8e5705a7f","benchmarks\u002Ffinal\u002Fskills\u002Fasset1__Microck--claude-scientific-skills\u002Fscientific-skills\u002Fqutip",0,"https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard","https:\u002F\u002Fgithub.com\u002FJSGforever","2026-08-29 18:27:56",{"source":8,"skillName":5,"commands":55,"prompt":65,"zipAvailable":66},[56,59,62],{"tool":57,"command":58},"npx","npx skills add JSGforever\u002Fskillguard --skill qutip",{"tool":60,"command":61},"bunx","bunx skills add JSGforever\u002Fskillguard --skill qutip",{"tool":63,"command":64},"pnpm","pnpm dlx skills add JSGforever\u002Fskillguard --skill qutip","安装技能，技能地址：https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__Microck--claude-scientific-skills\u002Fscientific-skills\u002Fqutip\u002FSKILL.md",true,[68,74,78,82,86],{"path":69,"resourceType":70,"resourceTypeDesc":71,"sizeBytes":72,"sourceHtmlUrl":73},"references\u002Fadvanced.md","REFERENCE","参考文档",11628,"https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__Microck--claude-scientific-skills\u002Fscientific-skills\u002Fqutip\u002Freferences\u002Fadvanced.md",{"path":75,"resourceType":70,"resourceTypeDesc":71,"sizeBytes":76,"sourceHtmlUrl":77},"references\u002Fanalysis.md",9387,"https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__Microck--claude-scientific-skills\u002Fscientific-skills\u002Fqutip\u002Freferences\u002Fanalysis.md",{"path":79,"resourceType":70,"resourceTypeDesc":71,"sizeBytes":80,"sourceHtmlUrl":81},"references\u002Fcore_concepts.md",5595,"https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__Microck--claude-scientific-skills\u002Fscientific-skills\u002Fqutip\u002Freferences\u002Fcore_concepts.md",{"path":83,"resourceType":70,"resourceTypeDesc":71,"sizeBytes":84,"sourceHtmlUrl":85},"references\u002Ftime_evolution.md",7866,"https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__Microck--claude-scientific-skills\u002Fscientific-skills\u002Fqutip\u002Freferences\u002Ftime_evolution.md",{"path":87,"resourceType":70,"resourceTypeDesc":71,"sizeBytes":88,"sourceHtmlUrl":89},"references\u002Fvisualization.md",8288,"https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__Microck--claude-scientific-skills\u002Fscientific-skills\u002Fqutip\u002Freferences\u002Fvisualization.md",[91,120,136,162,184,205],{"skillNo":92,"name":93,"nameZh":6,"description":94,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":95,"categories":96,"keywords":100,"publishedAt":42},"01M71HY2SNXBA9Q00WZDTZQ31Z","skillguard-codex-scanner","Hybrid deterministic+LLM agent-skill security scanner. Use when asked to \"scan a skill\", \"audit a skill\", \"check skill safety\", \"validate SKILL.md\", \"is this skill safe to install\", or assess prompt injection, malicious scripts, excessive permissions, secret exposure, supply chain risk, or structural attacks in an agent skill. Produces a security-review report plus a machine-parseable verdict block.","https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fsrc\u002Fskillguard\u002Fstatic_scanner\u002Fskillguard-codex-scanner\u002FSKILL.md",[97],{"categoryNo":98,"categoryName":99,"taxonomyType":20,"taxonomyTypeDesc":21},"01JBSEEDCAT000000000000023","Skill与智能体开发",[101,102,103,104,105,106,107,108,109,110,111,112,33,113,114,115,116,117,118,119],"scanner","skillguard codex scanner","skillguard","codex","chain","skill security","security-review","review report","structural","secret","prompt injection","security scanner","review","malicious","permissions","exposure","audit","scripts","safe",{"skillNo":121,"name":122,"nameZh":6,"description":123,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":124,"licenseFileUrl":6,"sourceHtmlUrl":125,"categories":126,"keywords":132,"publishedAt":42},"01M71HY0SPKTT3S27BC2HPAC5M","data-exfiltrator","Analyzes data files","MIT","https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Fsmoke-one-skill\u002Fasset1__cisco-ai-defense--data-exfiltrator\u002FSKILL.md",[127],{"categoryNo":128,"categoryName":129,"taxonomyType":130,"taxonomyTypeDesc":131},"01JBSEEDCAT000000000000033","数据分析师","PROFESSION","适用职业",[133,134,135],"data","data exfiltrator","files",{"skillNo":137,"name":138,"nameZh":6,"description":139,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":140,"categories":141,"keywords":142,"publishedAt":42},"01M71HXVS9EMN44BGDW215FZ72","real-time-collaboration-engine","Build real-time collaborative editing with WebSockets, OT\u002FCRDT conflict resolution, and presence awareness. Implements cursor tracking, optimistic updates, and offline sync. Use for collaborative editors, whiteboards, video editing. Activate on \"real-time collaboration\", \"WebSocket sync\", \"multiplayer editing\", \"CRDT\", \"presence awareness\". NOT for simple chat, request-response APIs, or single-user apps.","https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__curiositech--real-time-collaboration-engine\u002FSKILL.md",[],[37,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161],"real time collaboration engine","real time collaboration","collaboration","engine","real time","Video","reliability","video editing","performance","conflict resolution","presence","access","apps","updates","Bash","activate","optimizer","react","streaming",{"skillNo":163,"name":164,"nameZh":6,"description":165,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":166,"categories":167,"keywords":171,"publishedAt":42},"01M71HXP6CTY4KFN0QVMMN0V7J","react-performance-optimizer","Optimize React apps for 60fps performance. Implements memoization, virtualization, code splitting, bundle optimization. Use for slow renders, large lists, bundle bloat. Activate on \"React performance\", \"slow render\", \"useMemo\", \"bundle size\", \"virtualization\". NOT for backend optimization, non-React frameworks, or premature optimization.","https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__curiositech--react-performance-optimizer\u002FSKILL.md",[168],{"categoryNo":169,"categoryName":170,"taxonomyType":20,"taxonomyTypeDesc":21},"01JBSEEDCAT000000000000009","前端开发",[151,172,159,160,173,174,175,176,177,178,37,179,180,155,157,181,158,161,182,183],"react performance optimizer","react performance","performance optimizer","app","nextjs","expert","re","render","2025","code","router","strategies",{"skillNo":185,"name":186,"nameZh":6,"description":187,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":188,"categories":189,"keywords":191,"publishedAt":42},"01M71HXH7QXSQB4QTDZ7SP7YXQ","llm-streaming-response-handler","Build production LLM streaming UIs with Server-Sent Events, real-time token display, cancellation, error recovery. Handles OpenAI\u002FAnthropic\u002FClaude streaming APIs. Use for chatbots, AI assistants, real-time text generation. Activate on \"LLM streaming\", \"SSE\", \"token stream\", \"chat UI\", \"real-time AI\". NOT for batch processing, non-streaming APIs, or WebSocket bidirectional chat.","https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__curiositech--llm-streaming-response-handler\u002FSKILL.md",[190],{"categoryNo":169,"categoryName":170,"taxonomyType":20,"taxonomyTypeDesc":21},[192,161,193,194,195,196,151,37,197,198,199,157,158,159,200,160,201,202,203,204],"llm streaming response handler","handler","error","processing","retry","chat ui","error recovery","critical","batch","display","text","server","read",{"skillNo":206,"name":207,"nameZh":6,"description":208,"descriptionZh":6,"repositoryFullName":8,"ownerLogin":9,"ownerAvatarUrl":10,"ownerAccountNo":11,"ownerDisplayName":6,"repositoryNo":12,"starsCount":13,"licenseSpdxId":14,"licenseFileUrl":6,"sourceHtmlUrl":209,"categories":210,"keywords":218,"publishedAt":42},"01M71HXCB0E1YRKYW1Y8T0Y106","github-actions-pipeline-builder","Build production CI\u002FCD pipelines with GitHub Actions. Implements matrix builds, caching, deployments, testing, security scanning. Use for automated testing, deployments, release workflows. Activate on \"GitHub Actions\", \"CI\u002FCD\", \"workflow\", \"deployment pipeline\", \"automated testing\". NOT for Jenkins\u002FCircleCI, manual deployments, or non-GitHub repositories.","https:\u002F\u002Fgithub.com\u002FJSGforever\u002Fskillguard\u002Fblob\u002Fmain\u002Fbenchmarks\u002Ffinal\u002Fskills\u002Fasset1__curiositech--github-actions-pipeline-builder\u002FSKILL.md",[211,214,217],{"categoryNo":212,"categoryName":213,"taxonomyType":20,"taxonomyTypeDesc":21},"01JBSEEDCAT000000000000008","测试与质量",{"categoryNo":215,"categoryName":216,"taxonomyType":20,"taxonomyTypeDesc":21},"01JBSEEDCAT000000000000011","运维与部署",{"categoryNo":98,"categoryName":99,"taxonomyType":20,"taxonomyTypeDesc":21},[219,220,221,222,223,224,225,149,177,226,227,228,158,183,229,204,230,231,232,233],"github actions pipeline builder","actions","github actions","pipeline builder","github","builder","pipeline","testing","ci","workflows","run","release","write","edit","git"]