qiskit_dynamics.solvers.solve_ode#

solve_ode(rhs, t_span, y0, method='DOP853', t_eval=None, **kwargs)[source]#

General interface for solving Ordinary Differential Equations (ODEs).

ODEs are differential equations of the form

\[\dot{y}(t) = f(t, y(t)),\]

where \(f\) is a callable function and the state \(y(t)\) is an arbitrarily-shaped complex array.

The method argument exposes a variety of underlying ODE solvers. Optional arguments for any of the solver routines can be passed via kwargs. Available methods are:

  • scipy.integrate.solve_ivp - supports methods ['RK45', 'RK23', 'BDF', 'DOP853', 'Radau', 'LSODA'] or by passing a valid scipy OdeSolver instance.

  • 'RK4': A fixed-step 4th order Runge-Kutta solver. Requires additional kwarg max_dt, indicating the maximum step size to take. This solver will break integration periods into even sub-intervals no larger than max_dt, and step over each sub-interval using the standard 4th order Runge-Kutta integration rule.

  • 'jax_RK4': JAX backend implementation of 'RK4' method.

  • 'jax_odeint': Calls jax.experimental.ode.odeint variable step solver.

  • diffrax.diffeqsolve - a JAX solver function, called by passing method as a valid diffrax.AbstractSolver instance. Requires the diffrax library.

Results are returned as a OdeResult object.

Parameters:

  • rhs (Union[Callable, BaseGeneratorModel]) – RHS function \(f(t, y)\).

  • t_span (Union[ndarray, number, int, float, complex, Tracer, Array, Array, spmatrix, BCOO, list]) – Tuple or list of initial and final time.

  • y0 (Union[ndarray, number, int, float, complex, Tracer, Array, Array, spmatrix, BCOO, list]) – State at initial time.

  • method (Union[str, OdeSolver, TypeVar(AbstractSolver), None]) – Solving method to use.

  • t_eval (Union[ndarray, number, int, float, complex, Tracer, Array, Array, spmatrix, BCOO, list, None]) – Times at which to return the solution. Must lie within t_span. If unspecified, the solution will be returned at the points in t_span.

  • **kwargs – Additional arguments to pass to the solver.

Returns:

Results object.

Return type:

OdeResult

Raises:

QiskitError – If specified method does not exist.