MagnusSolver#

class MagnusSolver(operators, rotating_frame, dt, carrier_freqs, chebyshev_orders, expansion_order=None, expansion_labels=None, integration_method=None, include_imag=None, **kwargs)[source]#

Bases: _PerturbativeSolver

Solver for linear matrix differential equations based on the Magnus expansion.

This class implements the Magnus expansion-based solver presented in [[1]], which is a Magnus expansion variant of the Dysolve algorithm originally introduced in [[2]]. Its setup and behaviour are the same as as the DysonSolver class, with the sole exception being that it uses a truncated Magnus expansion and matrix exponentiation to solve over a single time step. See the Time-dependent perturbation theory and multi-variable series expansions review for a description of the Magnus expansion, and the documentation for DysonSolver for more detailed behaviour of this class.

Initialize.

Parameters:

  • operators (List[Operator]) – List of constant operators specifying the operators with signal coefficients.

  • rotating_frame (Union[Array, Operator, RotatingFrame, None]) – Rotating frame to setup the solver in. Must be Hermitian or anti-Hermitian.

  • dt (float) – Fixed step size to compile to.

  • carrier_freqs (Array) – Carrier frequencies of the signals in the generator decomposition.

  • chebyshev_orders (List[int]) – Approximation degrees for each signal over the interval [0, dt].

  • expansion_order (Optional[int]) – Order of perturbation terms to compute up to. Specifying this argument results in computation of all terms up to the given order. Can be used in conjunction with expansion_terms.

  • expansion_labels (Optional[List[Multiset]]) – Specific perturbation terms to compute. If both expansion_order and expansion_terms are specified, then all terms up to expansion_order are computed, along with the additional terms specified in expansion_terms. Labels are specified either as Multiset or as valid arguments to the Multiset constructor. This function further requires that Multisets consist only of non-negative integers.

  • integration_method (Optional[str]) – ODE solver method to use when computing perturbation terms.

  • include_imag (Optional[List[bool]]) – List of bools determining whether to keep imaginary components in the signal approximation. Defaults to True for all signals.

  • kwargs – Additional arguments to pass to the solver when computing perturbation terms.

Methods

solve(t0, n_steps, y0, signals)#

Solve given an initial time, number of steps, signals, and initial state.

Note that this method can be used to solve a list of simulations at once, by specifying one or more of the arguments t0, n_steps, y0, or signals as a list of valid inputs. For this mode of operation, all of these arguments must be either lists of the same length, or a single valid input, which will be used repeatedly.

Parameters:

  • t0 (Union[float, List[float]]) – Initial time.

  • n_steps (Union[int, List[int]]) – Number of time steps to solve for.

  • y0 (Union[Array, List[Array]]) – Initial state at time t0.

  • signals (Union[List[Signal], List[List[Signal]]]) – List of signals.

Returns:

Results object, or list of results objects.

Return type:

OdeResult

Raises:

QiskitError – If improperly formatted arguments.

Attributes

model#

Model object storing expansion details.