Python API

The Dynamiqs Python API features two main types of functions: solvers of differential equations describing quantum systems, and various utility functions to ease the creation and manipulation of quantum states and operators.

Quantum solvers

sesolve	Solve the Schrödinger equation.
mesolve	Solve the Lindblad master equation.
smesolve	Solve the diffusive stochastic master equation (SME).
sepropagator	Compute the propagator of the Schrödinger equation.
mepropagator	Compute the propagator of the Lindblad master equation.
floquet	Compute Floquet modes and quasienergies of a periodic closed system.

Core

Time-dependent arrays

TimeArray	Base class for time-dependent arrays.
constant	Instantiate a constant time-array.
pwc	Instantiate a piecewise constant (PWC) time-array.
modulated	Instantiate a modulated time-array.
timecallable	Instantiate a callable time-array.

Solvers (dq.solver)

Tsit5	Tsitouras method of order 5 (adaptive step size ODE solver).
Dopri5	Dormand-Prince method of order 5 (adaptive step size ODE solver).
Dopri8	Dormand-Prince method of order 8 (adaptive step size ODE solver).
Kvaerno3	Kvaerno's method of order 3 (adaptive step size and implicit ODE solver).
Kvaerno5	Kvaerno's method of order 5 (adaptive step size and implicit ODE solver).
Euler	Euler method (fixed step size ODE solver).
Rouchon1	First-order Rouchon method (fixed step size ODE solver).
Rouchon2	Second-order Rouchon method (fixed step size ODE solver).
Expm	Explicit matrix exponentiation to compute propagators.

Gradients (dq.gradient)

Autograd	Standard automatic differentiation of JAX.
CheckpointAutograd	Checkpointed automatic differentiation.

Options

Options

Generic options for the quantum solvers.

Results

SESolveResult	Result of the Schrödinger equation integration.
MESolveResult	Result of the Lindblad master equation integration.
SEPropagatorResult	Result of the Schrödinger equation integration to obtain the propagator.
MEPropagatorResult	Result of the Lindblad master equation integration to obtain the propagator.
FloquetResult	Result of the Floquet integration.

Utilities

Operators

eye	Returns the identity operator.
zero	Returns the null operator.
destroy	Returns a bosonic annihilation operator, or a tuple of annihilation operators for a multi-mode system.
create	Returns a bosonic creation operator, or a tuple of creation operators for a multi-mode system.
number	Returns the number operator of a bosonic mode, or a tuple of number operators for a multi-mode system.
parity	Returns the parity operator of a bosonic mode.
displace	Returns the displacement operator of complex amplitude \(\alpha\).
squeeze	Returns the squeezing operator of complex squeezing amplitude \(z\).
quadrature	Returns the quadrature operator of phase angle \(\phi\).
position	Returns the position operator \(x = (a^\dag + a) / 2\).
momentum	Returns the momentum operator \(p = i (a^\dag - a) / 2\).
sigmax	Returns the Pauli \(\sigma_x\) operator.
sigmay	Returns the Pauli \(\sigma_y\) operator.
sigmaz	Returns the Pauli \(\sigma_z\) operator.
sigmap	Returns the Pauli raising operator \(\sigma_+\).
sigmam	Returns the Pauli lowering operator \(\sigma_-\).
hadamard	Returns the Hadamard transform on \(n\) qubits.
rx	Returns the \(R_x(\theta)\) rotation gate.
ry	Returns the \(R_y(\theta)\) rotation gate.
rz	Returns the \(R_z(\theta)\) rotation gate.
sgate	Returns the \(\text{S}\) gate.
tgate	Returns the \(\text{T}\) gate.
cnot	Returns the \(\text{CNOT}\) gate.
toffoli	Returns the \(\text{Toffoli}\) gate.

States

fock	Returns the ket of a Fock state or a tensor product of Fock states.
fock_dm	Returns the density matrix of a Fock state or a tensor product of Fock states.
basis	Alias of dq.fock().
basis_dm	Alias of dq.fock_dm().
coherent	Returns the ket of a coherent state or a tensor product of coherent states.
coherent_dm	Returns the density matrix of a coherent state or a tensor product of coherent states.
ground	Returns the eigenvector with eigenvalue -1 of the Pauli \(\sigma_z\) operator.
excited	Returns the eigenvector with eigenvalue +1 of the Pauli \(\sigma_z\) operator.

Quantum utilities

dag	Returns the adjoint (complex conjugate transpose) of a matrix.
powm	Returns the \(n\)-th matrix power of an array.
expm	Returns the matrix exponential of an array.
cosm	Returns the cosine of an array.
sinm	Returns the sine of an array.
trace	Returns the trace of an array along its last two dimensions.
tracemm	Return the trace of a matrix multiplication using a fast implementation.
ptrace	Returns the partial trace of a ket, bra or density matrix.
tensor	Returns the tensor product of multiple kets, bras, density matrices or operators.
expect	Returns the expectation value of an operator or list of operators on a ket, bra or density matrix.
norm	Returns the norm of a ket, bra or density matrix.
unit	Normalize a ket, bra or density matrix to unit norm.
dissipator	Applies the Lindblad dissipation superoperator to a density matrix.
lindbladian	Applies the Lindbladian superoperator to a density matrix.
isket	Returns True if the array is in the format of a ket.
isbra	Returns True if the array is in the format of a bra.
isdm	Returns True if the array is in the format of a density matrix.
isop	Returns True if the array is in the format of an operator.
isherm	Returns True if the array is Hermitian.
toket	Returns the ket representation of a pure quantum state.
tobra	Returns the bra representation of a pure quantum state.
todm	Returns the density matrix representation of a quantum state.
proj	Returns the projection operator onto a pure quantum state.
braket	Returns the inner product \(\braket{\psi|\varphi}\) between two kets.
overlap	Returns the overlap between two quantum states.
fidelity	Returns the fidelity of two states, kets or density matrices.
entropy_vn	Returns the Von Neumann entropy of a ket or density matrix.
bloch_coordinates	Returns the spherical coordinates \((r, \theta, \phi)\) of a ket or density matrix on the Bloch sphere.
wigner	Compute the Wigner distribution of a ket or density matrix.

JAX-related utilities

to_qutip	Convert an array-like object into a QuTiP quantum object (or a list of QuTiP quantum objects if it has more than two dimensions).
set_device	Configure the default device.
set_precision	Configure the default floating point precision.
set_matmul_precision	Configure the default precision for matrix multiplications on GPUs and TPUs.

Vectorization

operator_to_vector	Returns the vectorized version of an operator.
vector_to_operator	Returns the operator version of a vectorized operator.
spre	Returns the superoperator formed from pre-multiplication by an operator.
spost	Returns the superoperator formed from post-multiplication by an operator.
sprepost	Returns the superoperator formed from pre- and post-multiplication by operators.
sdissipator	Returns the Lindblad dissipation superoperator (in matrix form).
slindbladian	Returns the Lindbladian superoperator (in matrix form).

Quantum optimal control

snap_gate	Returns a SNAP gate.
cd_gate	Returns a conditional displacement gate.

Random arrays (dq.random)

real	Returns an array of uniformly distributed random real numbers.
complex	Returns an array of uniformly distributed random complex numbers.
herm	Returns a random complex Hermitian matrix.
psd	Returns a random complex positive semi-definite matrix.
dm	Returns a random density matrix (hermitian, positive semi-definite, and unit trace).
ket	Returns a random ket with unit norm.

Plotting (dq.plot)

wigner	Plot the Wigner function of a state.
wigner_mosaic	Plot the Wigner function of multiple states in a mosaic arrangement.
wigner_gif	Plot a GIF of the Wigner function of multiple states.
pwc_pulse	Plot a piecewise constant pulse.
fock	Plot the photon number population of a state.
fock_evolution	Plot the photon number population of state as a function of time.
hinton	Plot a Hinton diagram.
gifit	Transform a plot function into a new function that returns an animated GIF.
grid	Returns a figure and an iterator of subplots organised in a grid.
mplstyle	Set custom Matplotlib style.