QuTiP 5.3 Visualization

Research and API verification date: 2026-10-01. Examples target qutip==5.3.1 with its pinned graphics extra.

uv pip install "qutip[graphics]==5.3.1"

Plots are diagnostics and communication artifacts, not substitutes for normalization, positivity, convergence, or uncertainty checks.

Phase-space coordinates and axis order

For QuTiP's oscillator phase-space functions, the default scaling is

\[ a = \tfrac12 g(x + i y), \qquad g=\sqrt{2}, \]

which corresponds to \(\hbar=2/g^2=1\).

In QuTiP 5.3, returned arrays use:

array[j, k] <-> yvec[j], xvec[k]

This applies to wigner, qfunc, and class-based QFunc. Therefore, pass xvec horizontally and yvec vertically to Matplotlib:

image = ax.pcolormesh(xvec, yvec, values, shading="auto")

The 5.3 release notes explicitly clarified this order. Do not transpose by habit; test with unequal x/y lengths.

Wigner function

Current signature:

wigner(psi, xvec, yvec=None, method="clenshaw", g=sqrt(2),
       sparse=False, parfor=False, offset=0)

import numpy as np
import matplotlib.pyplot as plt
from qutip import coherent, wigner

N = 30
state = coherent(N, 1.5)
xvec = np.linspace(-5.0, 5.0, 201)
yvec = np.linspace(-4.0, 4.0, 161)
W = wigner(state, xvec, yvec, method="clenshaw")

fig, ax = plt.subplots()
limit = float(np.max(np.abs(W)))
mesh = ax.pcolormesh(
    xvec,
    yvec,
    W,
    shading="auto",
    cmap="RdBu_r",
    vmin=-limit,
    vmax=limit,
)
ax.set(xlabel="x", ylabel="y", title="Wigner function")
fig.colorbar(mesh, ax=ax)
fig.tight_layout()

Methods:

• clenshaw: robust default, especially at higher excitation;
• iterative: recurrence method;
• laguerre: can help for sparse high-dimensional states;
• fft: computes y coordinates internally and has a different return form.

The offset argument added in 5.3 supports Fock representations whose first represented number state is not zero.

Numerical checks:

• sweep Hilbert cutoff and phase-space extent;
• increase grid density;
• compare normalization using the documented coordinate scaling;
• treat tiny negative values near numerical tolerance separately from robust Wigner negativity;
• preserve an equal data aspect ratio when x and y share physical units.

Current convenience plotting:

from qutip import plot_wigner

fig, ax = plot_wigner(
    state,
    xvec=xvec,
    yvec=yvec,
    projection="2d",
    colorbar=True,
)

Use the returned figure and axis rather than relying on global plotting state.

Husimi Q function

One state

Current signature:

qfunc(state, xvec, yvec, g=sqrt(2), precompute_memory=1024, cutoff=170)

from qutip import qfunc

Q = qfunc(state, xvec, yvec)
assert Q.shape == (len(yvec), len(xvec))

fig, ax = plt.subplots()
mesh = ax.pcolormesh(xvec, yvec, Q, shading="auto", cmap="viridis")
fig.colorbar(mesh, ax=ax)

qfunc and QFunc gained cutoff=170 in 5.3.1 to stabilize large coherent amplitudes. This is an algorithmic threshold, not the Hilbert cutoff N; independently converge the physical state truncation.

The Q function is nonnegative in exact arithmetic, but plotting still needs truncation, extent, and grid checks.

Many states on the same grid

Current class usage is:

from qutip import QFunc

q_on_grid = QFunc(xvec, yvec, memory=256)
Q_first = q_on_grid(state_a)
Q_second = q_on_grid(state_b)

QFunc is constructed with fixed coordinates and then called with each state. QuTiP 5.3 exposes no .eval method on this class. This skill does not use Python dynamic-code execution.

The memory parameter bounds internal workspace in MB and can raise MemoryError for a large state. For a one-off large state, use qfunc with a carefully selected precompute_memory.

Bloch sphere

import matplotlib.pyplot as plt
from qutip import Bloch, basis

psi = (basis(2, 0) + 1j * basis(2, 1)).unit()
bloch = Bloch()
bloch.add_states(psi)
bloch.add_vectors([0.0, 0.0, 1.0], color="black")
bloch.make_sphere()
plt.show()

For dynamics, solve with saved states or the three Pauli expectations:

from qutip import sigmax, sigmay, sigmaz

result = mesolve(
    H,
    rho0,
    tlist,
    c_ops=c_ops,
    e_ops=[sigmax(), sigmay(), sigmaz()],
)
bloch = Bloch()
bloch.add_points([result.expect[0], result.expect[1], result.expect[2]])
bloch.make_sphere()

Audit each Bloch vector norm. A density matrix maps inside the unit sphere; a vector materially outside it indicates numerical or modeling error.

Use explicit colors and line styles and a colorblind-safe palette. QuTiP settings include:

import qutip

qutip.settings.colorblind_safe = True

Avoid mutating global settings in reusable library code unless the caller expects it.

Fock distributions

from qutip import plot_fock_distribution

fig, ax = plot_fock_distribution(state)
ax.set(title="Fock probabilities", xlabel="n", ylabel="Probability")
fig.tight_layout()

For comparisons, share axes and use the returned fig, ax:

fig, axes = plt.subplots(1, 2, figsize=(9, 3), sharey=True)
plot_fock_distribution(state_a, fig=fig, ax=axes[0])
plot_fock_distribution(state_b, fig=fig, ax=axes[1])

Report the probability in the highest represented levels. A visually small last bar may still be insufficient if a target observable weights high occupations strongly.

Matrix diagnostics

Hinton diagrams:

from qutip import hinton

fig, ax = hinton(rho, color_style="phase")

Three-dimensional matrix histograms:

from qutip import matrix_histogram

fig, ax = matrix_histogram(rho, bar_style="abs", color_style="phase")

QuTiP 5 uses x_basis, y_basis, bar_style, and color_style rather than old ad hoc label and bar-type recipes. Pass a Qobj where supported so dimension-aware labels can be retained.

For dense matrices beyond a modest size, a heatmap is usually more legible and less expensive than 3D bars. Never hide the imaginary part when it is relevant.

Solver result plots

QuTiP 5.3 adds result methods:

fig, axes = result.plot_expect(labels=["population", "coherence"])

For publication or reusable analysis, explicit plotting remains clearer:

fig, ax = plt.subplots()
ax.plot(result.times, result.e_data["population"], label="population")
ax.set(xlabel="time", ylabel="expectation value")
ax.legend()
fig.tight_layout()

Multi-trajectory means need uncertainty bands:

mean = np.asarray(result.average_expect[0])
standard_error = np.asarray(result.std_expect[0]) / np.sqrt(result.num_trajectories)
ax.plot(result.times, mean)
ax.fill_between(
    result.times,
    mean - 1.96 * standard_error,
    mean + 1.96 * standard_error,
    alpha=0.25,
)

Confirm that the trajectory estimator and sample count justify the chosen interval; the formula above is only a simple independent-sample approximation.

Correlation and spectrum plots

Plot complex correlations deliberately:

fig, axes = plt.subplots(2, 1, sharex=True)
axes[0].plot(taulist, np.real(correlation), label="real")
axes[1].plot(taulist, np.imag(correlation), label="imaginary")
axes[1].set_xlabel("delay")
for ax in axes:
    ax.legend()

For spectra:

• label angular frequency and units;
• show negative frequencies when physically meaningful;
• disclose windowing, smoothing, and zero-padding;
• avoid a logarithmic y-axis when values can be negative;
• include frequency resolution and convergence information in the caption.

Animations

Animations can conceal nonconvergence and are expensive to render. First produce static frames at physically meaningful times. If animation is needed:

• cap frame count and resolution;
• keep phase-space color limits fixed across frames;
• avoid recomputing solver dynamics inside the frame callback;
• save to a user-selected local path;
• record the time-to-frame mapping.

QuTiP 5 includes animation helpers in its visualization API, but their inputs still require stored states and memory planning.

Figure export

fig.savefig("phase_space.svg", bbox_inches="tight")
fig.savefig("phase_space.png", dpi=300, bbox_inches="tight")

Use an explicit local output path, avoid overwriting without user intent, and save the numeric data/configuration next to the figure. A raster image alone is not a reproducible result.

Sources (verified 2026-10-01)

• Visualization and animation API
• Wigner and Q-function API
• Bloch sphere guide
• QuTiP 5.3.1 release notes
• Official QuTiP version-5 tutorials