The :mod:`krotov` package is designed around QuTiP, a very powerful "Quantum
Toolbox" in Python. This means that all operators and states are expressed as
:class:`qutip.Qobj` quantum objects. The :func:`.optimize_pulses` interface
for Krotov's optimization method is closely linked to the interface of QuTiP's
central :func:`~qutip.mesolve.mesolve` routine for simulating the system
dynamics of a closed or open quantum system. In particular, when setting up an
optimization, the (time-dependent) system Hamiltonian should be represented by
a nested list. This is, a Hamiltonian of the form \Op{H} = \Op{H}_0 +
\epsilon(t) \Op{H}_1 is represented as H = [H0, [H1, eps]] where H0
and H1 are :class:`~qutip.Qobj` operators, and eps is a function with
signature eps(t, args), or an array of control values with the length of the
time grid (tlist parameter in :func:`~qutip.mesolve.mesolve`). The operator
can depend on multiple controls, resulting in expressions of the form H =
[H0, [H1, eps1], [H2, eps2], ...].
The central routine provided by the :mod:`krotov` package is :func:`.optimize_pulses`. It takes as input a list of objectives, each of which is an instance of :class:`.Objective`. Each objective has an :attr:`~.Objective.initial_state`, which is a :class:`qutip.Qobj` representing a Hilbert space state or density matrix, a :attr:`~.Objective.target` (usually the target state that the :attr:`~.Objective.initial_state` should evolve into when the objective is fulfilled), and a Hamiltonian :attr:`~.Objective.H` in the nested-list format described above. For dissipative dynamics, :attr:`~.Objective.H` should be a Liouvillian, which can be obtained from the Hamiltonian and a set of Lindblad operators via :func:`krotov.objectives.liouvillian`. The Liouvillian again is in nested list format to express time-dependencies. Alternatively, each objective could also directly include a list :attr:`~.Objective.c_ops` of collapse (Lindblad) operators , where each collapse operator is a :class:`~qutip.Qobj` operator. However, this only makes sense if the time propagation routine takes the collapse operators into account explicitly, such as in the Monte-Carlo :func:`~qutip.mcsolve.mcsolve`. Otherwise, the use of :attr:`~.Objective.c_ops` is strongly discouraged.
If the control function (eps in the above example) relies on the dict
args for static parameters, those args can be specified via the
pulse_options argument in :func:`.optimize_pulses`. See :ref:`HowtoUseArgs`.
In order to simulate the dynamics of the guess control, you can use :meth:`.Objective.mesolve`, which delegates to :func:`qutip.mesolve.mesolve`. There is also a related method :meth:`.Objective.propagate` that uses a different sampling of the control values, see :mod:`krotov.propagators`.
The optimization routine will automatically extract all controls that it can find in the objectives, and iteratively calculate updates to all controls in order to meet all objectives simultaneously. The result of the optimization will be in the returned :class:`.Result` object, with a list of the optimized controls in :attr:`~.Result.optimized_controls`. The :obj:`~.Result.optimized_objectives` property contains a copy of the objectives with the :attr:`~.Result.optimized_controls` plugged into the Hamiltonian or Liouvillian and/or collapse operators. The dynamics under the optimized controls can then again be simulated through :meth:`.Objective.mesolve`.
While the guess controls that are in the objectives on input may be functions, or an array of control values on the time grid, the output :attr:`~.Result.optimized_controls` will always be an array of control values.