The krotov
package is designed around QuTiP, a very powerful "Quantum Toolbox" in Python. This means that all operators and states are expressed as qutip.Qobj
quantum objects. The .optimize_pulses
interface for Krotov's optimization method is closely linked to the interface of QuTiP's central ~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 H = [H0, [H1, eps]]
where H0
and H1
are ~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 ~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 krotov
package is .optimize_pulses
. It takes as input a list of objectives, each of which is an instance of .Objective
. Each objective has an ~.Objective.initial_state
, which is a qutip.Qobj
representing a Hilbert space state or density matrix, a ~.Objective.target
(usually the target state that the ~.Objective.initial_state
should evolve into when the objective is fulfilled), and a Hamiltonian ~.Objective.H
in the nested-list format described above. For dissipative dynamics, ~.Objective.H
should be a Liouvillian, which can be obtained from the Hamiltonian and a set of Lindblad operators via krotov.objectives.liouvillian
. The Liouvillian again is in nested list format to express time-dependencies. Alternatively, each objective could also directly include a list ~.Objective.c_ops
of collapse (Lindblad) operators , where each collapse operator is a ~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 ~qutip.mcsolve.mcsolve
. Otherwise, the use of ~.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 .optimize_pulses
. See HowtoUseArgs
.
In order to simulate the dynamics of the guess control, you can use .Objective.mesolve
, which delegates to qutip.mesolve.mesolve
. There is also a related method .Objective.propagate
that uses a different sampling of the control values, see 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 .Result
object, with a list of the optimized controls in ~.Result.optimized_controls
. The ~.Result.optimized_objectives
property contains a copy of the objectives with the ~.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 .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 ~.Result.optimized_controls
will always be an array of control values.