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.

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.

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.

`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.