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dq.MEPropagatorResult

Result of the Lindblad master equation integration to obtain the propagator.

Attributes

  • propagators (array of shape (..., nsave, n^2, n^2)) –

    Saved propagators with nsave = ntsave, or nsave = 1 if options.save_states is set to False.

  • final_propagator (array of shape (..., n^2, n^2)) –

    Saved final propagator.

  • extra (PyTree or None) –

    Extra data saved with save_extra() if specified in options (see dq.Options).

  • infos (PyTree or None) –

    Solver-dependent information on the resolution.

  • tsave (array of shape (ntsave,)) –

    Times for which results were saved.

  • solver (Solver) –

    Solver used.

  • gradient (Gradient) –

    Gradient used.

  • options (Options) –

    Options used.

Result of running multiple simulations concurrently

The resulting propagators are batched according to the leading dimensions of the Hamiltonian H and jump operators jump_ops. The behaviour depends on the value of the cartesian_batching option

The results leading dimensions are 

... = ...H, ...L0, ...L1, (...)
For example if:

  • H has shape (2, 3, n, n),
  • jump_ops = [L0, L1] has shape [(4, 5, n, n), (6, n, n)],

then propagators has shape (2, 3, 4, 5, 6, ntsave, n, n).

The results leading dimensions are 

... = ...H = ...L0 = ...L1 = (...)  # (once broadcasted)
For example if:

  • H has shape (2, 3, n, n),
  • jump_ops = [L0, L1] has shape [(3, n, n), (2, 1, n, n)],

then propagators has shape (2, 3, ntsave, n, n).

See the Batching simulations tutorial for more details.