API
Krotov.KrotovResult — TypeResult object returned by optimize_krotov.
Attributes
The attributes of a KrotovResult object include
iter: The number of the current iterationJ_T: The value of the final-time functional in the current iterationJ_T_prev: The value of the final-time functional in the previous iterationtlist: The time grid on which the control are discretized.guess_controls: A vector of the original control fields (each field discretized to the points oftlist)optimized_controls: A vector of the optimized control fields. Calculated only at the end of the optimization, not after each iteration.tau_vals: For any trajectory that defines atarget_state, the complex overlap of that target state with the propagated state. For any trajectory for which thetarget_stateisnothing, the value is zero.records: A vector of tuples with values returned by acallbackroutine passed tooptimizeconverged: A boolean flag on whether the optimization is converged. This may be set totrueby acheck_convergencefunction.message: A message string to explain the reason for convergence. This may be set by acheck_convergencefunction.
All of the above attributes may be referenced in a check_convergence function passed to optimize(problem; method=Krotov)
Krotov.KrotovWrk — TypeKrotov workspace.
The workspace is for internal use. However, it is also accessible in a callback function. The callback may use or modify some of the following attributes:
trajectories: a copy of the trajectories defining the control problemadjoint_trajectories: Thetrajectorieswith the adjoint generatorkwargs: The keyword arguments from theControlProblemor the call tooptimize.controls: A tuple of the original controls (probably functions)ga_a_int: The current value of $∫gₐ(t)dt$ for each controlupdate_shapes: The update shapes $S(t)$ for each pulse, discretized on the intervals of the time grid.lambda_vals: The current value of λₐ for each controlresult: The current result objectfw_storage: The storage of states for the forward propagationfw_propagators: The propagators used for the forward propagationbw_propagators: The propagators used for the backward propagationuse_threads: Flag indicating whether the propagations are performed in parallel.
Krotov.optimize_krotov — MethodQuantumControlBase.optimize — Methodusing Krotov
-result = optimize(problem; method=Krotov, kwargs...)optimizes the given control problem using Krotov's method, returning a KrotovResult.
Keyword arguments that control the optimization are taken from the keyword arguments used in the instantiation of problem; any of these can be overridden with explicit keyword arguments to optimize.
Required problem keyword arguments
J_T: A functionJ_T(Ψ, trajectories)that evaluates the final time functional from a listΨof forward-propagated states andproblem.trajectories. The functionJ_Tmay also take a keyword argumenttau. If it does, a vector containing the complex overlaps of the target states (target_stateproperty of each trajectory inproblem.trajectories) with the propagated states will be passed toJ_T.
Recommended problem keyword arguments
lambda_a=1.0: The inverse Krotov step width λₐ for every pulse.update_shape=(t->1.0): A functionS(t)for the "update shape" that scales the update for every pulse.
If different controls require different lambda_a or update_shape, a dict pulse_options must be given instead of a global lambda_a and update_shape; see below.
Optional problem keyword arguments
The following keyword arguments are supported (with default values):
pulse_options: A dictionary that maps every control (as obtained byget_controlsfrom theproblem.trajectories) to the following dict::lambda_a: The value for inverse Krotov step width λₐ.:update_shape: A functionS(t)for the "update shape" that scales the Krotov pulse update.
This overrides the global
lambda_aandupdate_shapearguments.chi: A functionchi(Ψ, trajectories)that receives a listΨof the forward propagated states and returns a vector of states $|χₖ⟩ = -∂J_T/∂⟨Ψₖ|$. If not given, it will be automatically determined fromJ_Tviamake_chiwith the default parameters. Similarly toJ_T, ifchiaccepts a keyword argumenttau, it will be passed a vector of complex overlaps.sigma=nothing: A function that calculates the second-order contribution. If not given, the first-order Krotov method is used.iter_start=0: The initial iteration number.iter_stop=5000: The maximum iteration number.prop_method: The propagation method to use for each trajectory; see below.print_iters=true: Whether to print information after each iteration.store_iter_info=Set(): Which fields fromprint_itersto store inresult.records. A subset ofSet(["iter.", "J_T", "∫gₐ(t)dt", "J", "ΔJ_T", "ΔJ", "secs"]).callback: A function (or tuple of functions) that receives the Krotov workspace, the iteration number, the list of updated pulses, and the list of guess pulses as positional arguments. The function may return a tuple of values which are stored in theKrotovResultobjectresult.records. The function can also mutate any of its arguments, in particular the updated pulses. This may be used, e.g., to apply a spectral filter to the updated pulses or to perform similar manipulations. Note thatprint_iters=true(default) adds an automatic callback to print information after each iteration. Withstore_iter_info, that callback automatically stores a subset of the printed information.check_convergence: A function to check whether convergence has been reached. Receives aKrotovResultobjectresult, and should setresult.convergedtotrueandresult.messageto an appropriate string in case of convergence. Multiple convergence checks can be performed by chaining functions with∘. The convergence check is performed after anycallback.verbose=false: Iftrue, print information during initialization.rethrow_exceptions: By default, any exception ends the optimization but still returns aKrotovResultthat captures the message associated with the exception. This is to avoid losing results from a long-running optimization when an exception occurs in a later iteration. Ifrethrow_exceptions=true, instead of capturing the exception, it will be thrown normally.
Trajectory propagation
Krotov's method involves the forward and backward propagation for every Trajectory in the problem. The keyword arguments for each propagation (see propagate) are determined from any properties of each Trajectory that have a prop_ prefix, cf. init_prop_trajectory.
In situations where different parameters are required for the forward and backward propagation, instead of the prop_ prefix, the fw_prop_ and bw_prop_ prefixes can be used, respectively. These override any setting with the prop_ prefix. This applies both to the properties of each Trajectory and the problem keyword arguments.
Note that the propagation method for each propagation must be specified. In most cases, it is sufficient (and recommended) to pass a global prop_method problem keyword argument.