Qutip

QuTiP 5

Scope

Use QuTiP for finite-dimensional quantum mechanics, quantum optics, Lindblad

dynamics, trajectories, weak-coupling Bloch-Redfield models, and specialized

Floquet, HEOM, and permutational-invariance methods. It is not a hardware

execution SDK. Circuit and control functionality moved to separate QuTiP family

packages.

This skill targets QuTiP 5.3.0, released 2026-05-22. QuTiP 5.3 requires

Python 3.11 or newer. Its required distributions are NumPy (>=1.23.2), SciPy

(>=1.9.2, excluding 1.16.0 and 1.17.0), and packaging.

Reproducible uv snapshot

Create a dedicated environment and pin every direct distribution:

uv venv --python 3.11
uv pip install "qutip==5.3.0"

For plots:

uv pip install "qutip[graphics]==5.3.0"

Optional QuTiP family packages are independently versioned:

uv pip install "qutip-qip==0.4.2"
uv pip install "qutip-qtrl==0.2.0"
uv pip install "qutip-jax==0.1.1"

• qutip-qip 0.4.2 (2026-06-23) is the production/stable circuit, gate, and

noisy-device simulation package. Import from qutip_qip, not qutip.qip.

• qutip-qtrl 0.2.0 (2026-06-23) provides GRAPE and CRAB **quantum optimal

control**. It is not a trajectory viewer. Import from qutip_qtrl, not

qutip.control; PyPI still classifies it pre-alpha.

• qutip-jax 0.1.1 (2025-05-29) is the official JAX data backend for GPU and

automatic-differentiation experiments. It is explicitly pre-alpha.

• qutip-cupy is an official QuTiP-organization repository, but it has no PyPI

release and its own README says it is not officially released. Do not put an

unreleased Git install into a reproducible workflow.

Use a project lockfile or a hash-generating uv pip compile workflow when

transitive dependency identity must also be frozen.

Non-negotiable model contract

Before solving, record:

• Units and convention. QuTiP equations normally set \(\hbar=1\).

Hamiltonian entries are angular frequencies and rates have reciprocal-time

units. Convert cyclic frequency with \(2\pi f\); never mix Hz and rad/s.

• Subsystem order. tensor(A, B, C) fixes subsystem indices 0, 1, 2.

Preserve that order in every state, operator, collapse channel, and partial

trace. obj.ptrace([0, 2]) keeps those subsystems; it does not trace them.

• State validity. Check ket norm or density-matrix Hermiticity, unit trace,

and eigenvalues above a stated negative tolerance. Tiny negative values may

be numerical; material negativity invalidates a claimed state.

• Generator meaning. A Lindblad channel with rate gamma is represented

by sqrt(gamma) * A, not gamma * A. Define what each rate measures. For

example, sqrt(gamma_phi / 2) * sigmaz() gives coherence decay

exp(-gamma_phi * t).

• Approximations. State rotating-wave, Born-Markov, secular, weak-coupling,

bath-equilibrium, truncation, symmetry, and initial-factorization assumptions

wherever used.

• Numerics. Justify Hilbert truncation, output grid, integration method,

tolerances, trajectory count, and random seeds. Report result.stats.

• Convergence. Sweep every artificial cutoff: Fock dimension, time/frequency

window and spacing, ODE tolerances, trajectories, Floquet harmonics, HEOM

depth and bath exponents, or PIQS representation as applicable.

Qobj, dimensions, and tensor order

Prefer explicit imports and inspect both shape and structured dimensions:

from qutip import basis, qeye, sigmaz, tensor

psi = tensor(basis(2, 0), basis(3, 1))
z_on_first = tensor(sigmaz(), qeye(3))

assert psi.shape == (6, 1)
assert psi.dims == [[2, 3], [1]]
assert z_on_first.dims == [[2, 3], [2, 3]]
rho_first = psi.proj().ptrace(0)  # keep subsystem 0

Matrix shape alone is insufficient: two objects can both be 6-by-6 but encode

different tensor factorizations. Read references/core_concepts.md before

building composite, superoperator, or channel models.

Choose the solver by physics

| Model | Current API | Required justification |

|---|---|---|

| Closed, pure, unitary | sesolve | Hermitian Hamiltonian; no dissipation |

| Lindblad/open or mixed | mesolve | Markovian completely positive model and channel rates |

| Quantum jumps | mcsolve | Unravelling, trajectory convergence, seeds |

| Microscopic weak bath | brmesolve | Born-Markov/weak coupling, spectra, secular choice |

| Diffusive measurement | ssesolve, smesolve | monitored versus unmonitored channels |

| Periodic drive | FloquetBasis, fsesolve, fmmesolve | verified period and Floquet convergence |

| Structured non-Markovian bath | qutip.solver.heom | bath expansion and hierarchy convergence |

| Symmetric spin ensemble | qutip.piqs | permutation symmetry and basis choice |

Do not select a more specialized solver merely because it exists.

Deterministic open-system example

QuTiP 5.3 uses ordinary option dictionaries. Solver controls, e_ops, and

args are keyword-only; the old mutable options object is gone.

import numpy as np
from qutip import basis, mesolve, sigmam, sigmaz

omega = 2.0
gamma = 0.15
tlist = np.linspace(0.0, 20.0, 401)
excited = basis(2, 0)

result = mesolve(
    0.5 * omega * sigmaz(),
    excited,
    tlist,
    c_ops=[np.sqrt(gamma) * sigmam()],
    e_ops={"sigma_z": sigmaz(), "excited": excited.proj()},
    options={
        "method": "adams",
        "atol": 1e-10,
        "rtol": 1e-8,
        "store_final_state": True,
        "progress_bar": "",
    },
)

population = np.asarray(result.e_data["excited"])
assert np.max(np.abs(population - np.exp(-gamma * tlist))) < 2e-6
assert isinstance(result.stats, dict)

If the problem is stiff, compare bdf or lsoda; do not change an integrator

without rerunning tolerance and invariant checks. QuTiP 5.3 also supports

options={"matrix_form": True} in mesolve; benchmark and validate it before

using it as a default.

Time-dependent systems

Prefer trusted Pythonic callables or numeric coefficient arrays. Do not create

coefficient source strings from user input.

import numpy as np
from qutip import QobjEvo, sigmax, sigmaz

def envelope(t, amplitude, center, width):
    return amplitude * np.exp(-0.5 * ((t - center) / width) ** 2)

H = QobjEvo(
    [0.5 * sigmaz(), [sigmax(), envelope]],
    args={"amplitude": 0.2, "center": 5.0, "width": 1.0},
)
instantaneous_H = H(5.0)
H.arguments(amplitude=0.1)

The older f(t, args) coefficient signature is deprecated in 5.3 and is

scheduled for removal in 5.5. See references/time_evolution.md.

Trajectories and stochastic solvers

import numpy as np
from qutip import basis, mcsolve, sigmam, sigmaz

tlist = np.linspace(0.0, 10.0, 201)
result = mcsolve(
    0.5 * sigmaz(),
    basis(2, 0),
    tlist,
    [np.sqrt(0.2) * sigmam()],
    e_ops=[basis(2, 0).proj()],
    ntraj=400,
    seeds=20260723,
    options={"keep_runs_results": False, "progress_bar": ""},
)

Report ntraj, result.seeds, uncertainty or repeated-seed sensitivity, and

whether individual runs were retained. Reuse seeds=previous_result.seeds only

when paired trajectories are intentional. ssesolve and smesolve use the

boolean heterodyne argument, not legacy integer noise codes.

Steady states, spectra, and phase space

import numpy as np
from qutip import QFunc, liouvillian, operator_to_vector, qfunc, steadystate

rho_ss = steadystate(H, c_ops, method="direct")
residual = (liouvillian(H, c_ops) * operator_to_vector(rho_ss)).norm()
assert residual < 1e-9

xvec = np.linspace(-5.0, 5.0, 151)
Q_once = qfunc(rho_ss, xvec, xvec)
q_many = QFunc(xvec, xvec)
Q_again = q_many(rho_ss)
assert Q_once.shape == (len(xvec), len(xvec))

For wigner, qfunc, and QFunc, array element [j, k] corresponds to

yvec[j], xvec[k]. In QuTiP 5.3, QFunc is initialized with fixed

coordinates and called with a state; it has no .eval method. This skill never

uses Python dynamic-code execution. Prefer plot_wigner, Result.plot_expect,

or explicit Matplotlib axes as documented in references/visualization.md.

Direct spectrum is a stationary steady-state spectrum. An FFT of a finite

correlation requires explicit checks for tail decay, timestep aliasing,

frequency resolution, window sensitivity, and transform convention. See

references/analysis.md.

Advanced boundaries

• Import HEOM from qutip.solver.heom; the legacy QuTiP 4 nonmarkov HEOM

namespace is stale.

• Use FloquetBasis for modes and quasi-energies. Verify

H(t + T) == H(t) numerically and sweep basis/truncation choices.

• Access PIQS with from qutip import piqs. Dicke.pisolve is only the

optimized diagonal-state/diagonal-Hamiltonian route; general Dicke-basis

dynamics use the Liouvillian with mesolve.

• brmesolve can violate positivity, especially without secularization. Check

density-matrix eigenvalues over time.

• QIP and optimal control are extension-package concerns. Never present local

simulation as quantum-hardware execution.

See references/advanced.md for HEOM, Floquet, PIQS, stochastic, and extension

boundaries.

Safe local CLIs

All bundled tools are local-only, emit strict JSON, reject non-finite JSON and

unknown keys, and never load pickle files or executable model code. Simulation

imports are lazy, so every --help works without QuTiP installed.

| Script | Purpose |

|---|---|

| scripts/qobj_model_validator.py | Validate bounded Qobj model JSON, dimensions, states, rates, and role compatibility |

| scripts/two_level_simulation.py | Run a bounded two-level Lindblad or jump simulation |

| scripts/solver_config_planner.py | Select a current solver and option/checklist plan |

| scripts/convergence_sweep.py | Sweep tolerances/grid size or trajectory count on a synthetic model |

| scripts/result_audit.py | Audit JSON output without deserializing Python objects |

| scripts/steady_state_spectrum_planner.py | Plan bounded steady-state and direct/FFT spectral checks |

Example:

python skills/qutip/scripts/two_level_simulation.py --help
python skills/qutip/scripts/two_level_simulation.py \
  --decay-rate 0.2 --t-final 10 --time-points 201 \
  --output two-level.json
python skills/qutip/scripts/result_audit.py two-level.json

Completion checklist

• Record units, \(\hbar\), tensor order, initial state, channels, and model

assumptions.

• Validate Hermiticity, norm/trace, positivity, dimensions, and generator units.
• Pin QuTiP and direct extensions; record platform, Python, NumPy, and SciPy.
• Inspect result options and stats; do not assume states were stored.
• Perform cutoff, grid, tolerance/integrator, and stochastic convergence sweeps.
• Save portable numeric/configuration summaries as JSON or text. Do not load

untrusted QuTiP object/result files because object serialization can execute

code.

References

• references/core_concepts.md — Qobj, dimensions, tensor products, states,

channels, and unit conventions

• references/time_evolution.md — current solver signatures, options, results,

QobjEvo, trajectories, and numerical controls

• references/analysis.md — physical-state audits, steady states,

correlations, spectra, and convergence

• references/visualization.md — Wigner, Q functions, QFunc, Bloch, result,

and matrix plots

• references/advanced.md — Bloch-Redfield, stochastic, Floquet, HEOM, PIQS,

and QuTiP family package boundaries

Dated official sources

Verified 2026-07-23:

• QuTiP 5.3.0 PyPI metadata
• QuTiP 5.3.0 release
• QuTiP 5.3 changelog
• QuTiP 5.3 API
• QuTiP version-5 tutorials
• qutip-qip PyPI
• qutip-qtrl PyPI
• qutip-jax PyPI
• official unreleased qutip-cupy repository