solvers

Solvers

mesolve(H, rho0, tlist, c_ops=None, solver_options=None)

Quantum Master Equation solver.

Parameters:

Name	Type	Description	Default
H	Union[Qarray, Callable[[float], Qarray]]	time dependent Hamiltonian function or time-independent Qarray.	required
rho0	Qarray	initial state, must be a density matrix. For statevector evolution, please use sesolve.	required
tlist	Array	time list	required
c_ops	Optional[Qarray]	qarray list of collapse operators	None
solver_options	Optional[SolverOptions]	SolverOptions with solver options	None

Returns:

Type	Description
Qarray	list of states

Source code in jaxquantum/core/solvers.py

def mesolve(
    H: Union[Qarray, Callable[[float], Qarray]],
    rho0: Qarray,
    tlist: Array,
    c_ops: Optional[Qarray] = None,
    solver_options: Optional[SolverOptions] = None,
) -> Qarray:
    """Quantum Master Equation solver.

    Args:
        H: time dependent Hamiltonian function or time-independent Qarray.
        rho0: initial state, must be a density matrix. For statevector evolution, please use sesolve.
        tlist: time list
        c_ops: qarray list of collapse operators
        solver_options: SolverOptions with solver options

    Returns:
        list of states
    """

    c_ops = c_ops if c_ops is not None else Qarray.from_list([])

    # if isinstance(H, Qarray):

    if len(c_ops) == 0 and rho0.qtype != Qtypes.oper:
        logging.warning(
            "Consider using `jqt.sesolve()` instead, as `c_ops` is an empty list and the initial state is not a density matrix."
        )

    ρ0 = rho0.to_dm()
    dims = ρ0.dims
    ρ0 = ρ0.data

    c_ops = c_ops.data

    if isinstance(H, Qarray):
        Ht_data = lambda t: H.data
    else:
        Ht_data = lambda t: H(t).data if H is not None else None

    ys = _mesolve_data(Ht_data, ρ0, tlist, c_ops, solver_options=solver_options)

    return jnp2jqt(ys, dims=dims)

sesolve(H, rho0, tlist, solver_options=None)

Schrödinger Equation solver.

Parameters:

Name	Type	Description	Default
H	Union[Qarray, Callable[[float], Qarray]]	time dependent Hamiltonian function or time-independent Qarray.	required
rho0	Qarray	initial state, must be a density matrix. For statevector evolution, please use sesolve.	required
tlist	Array	time list	required
solver_options	Optional[SolverOptions]	SolverOptions with solver options	None

Returns:

Type	Description
Qarray	list of states

Source code in jaxquantum/core/solvers.py

def sesolve(
    H: Union[Qarray, Callable[[float], Qarray]],
    rho0: Qarray,
    tlist: Array,
    solver_options: Optional[SolverOptions] = None,
) -> Qarray:
    """Schrödinger Equation solver.

    Args:
        H: time dependent Hamiltonian function or time-independent Qarray.
        rho0: initial state, must be a density matrix. For statevector evolution, please use sesolve.
        tlist: time list
        solver_options: SolverOptions with solver options

    Returns:
        list of states
    """

    ψ = rho0

    if ψ.qtype == Qtypes.oper:
        raise ValueError(
            "Please use `jqt.mesolve` for initial state inputs in density matrix form."
        )

    ψ = ψ.to_ket()
    dims = ψ.dims
    ψ = ψ.data

    if isinstance(H, Qarray):
        Ht_data = lambda t: H.data
    else:
        Ht_data = lambda t: H(t).data if H is not None else None

    ys = _sesolve_data(Ht_data, ψ, tlist, solver_options=solver_options)

    return jnp2jqt(ys, dims=dims)

solve(f, ρ0, tlist, args, solver_options=None)

Gets teh desired solver from diffrax.

Parameters:

Name	Type	Description	Default
solver_options	Optional[SolverOptions]	dictionary with solver options	None

Returns:

Type	Description
	solution

Source code in jaxquantum/core/solvers.py

def solve(f, ρ0, tlist, args, solver_options: Optional[SolverOptions] = None):
    """Gets teh desired solver from diffrax.

    Args:
        solver_options: dictionary with solver options

    Returns:
        solution
    """

    # f and ts
    term = ODETerm(f)
    saveat = SaveAt(ts=tlist)

    # solver
    solver_options = solver_options or SolverOptions.create()

    solver_name = solver_options.solver
    solver = getattr(diffrax, solver_name)()
    stepsize_controller = PIDController(rtol=1e-6, atol=1e-6)

    # solve!
    with warnings.catch_warnings():
        warnings.simplefilter(
            "ignore", UserWarning
        )  # NOTE: suppresses complex dtype warning in diffrax
        sol = diffeqsolve(
            term,
            solver,
            t0=tlist[0],
            t1=tlist[-1],
            dt0=tlist[1] - tlist[0],
            y0=ρ0,
            saveat=saveat,
            stepsize_controller=stepsize_controller,
            args=args,
            max_steps=solver_options.max_steps,
            progress_meter=CustomProgressMeter()
            if solver_options.progress_meter
            else NoProgressMeter(),
        )

    return sol