krotov.conversions module¶

Routines for structural conversions.

Conversion between between data structures used by QuTiP’s mesolve() and data structures used internally in an optimization with Krotov’s method. This includes the time discretization of control fields, and in particular converting between a discretization defined on the points of the time grid (“controls”) and piecewise-constant “pulses” defined on the intervals of the time grid.

Summary¶

Functions:

 control_onto_interval Convert control on time grid to control on time grid intervals discretize Discretize the given control onto the tlist time grid extract_controls Extract a list of (unique) controls from the objectives extract_controls_mapping Extract a map of where controls are used in objectives plug_in_pulse_values Plug pulse values into H pulse_onto_tlist Convert pulse from time-grid intervals to time-grid points pulse_options_dict_to_list Convert pulse_options into a list

Reference¶

krotov.conversions.discretize(control, tlist, args=(None, ), kwargs=None)[source]

Discretize the given control onto the tlist time grid

If control is a callable, return array of values for control evaluated at all points in tlist. If control is already discretized, check that the discretization matches tlist

Parameters
• control (callable or numpy.ndarray) – control to be discretized. If callable, must take time value t as its first argument.

• tlist (numpy.ndarray) – time grid to discretize one

• args (tuple or list) – If control is a callable, further positional arguments to pass to control. The default passes a single value None, to match the requirements for a callable control function in QuTiP.

• kwargs (None or dict) – If control is callable, further keyword arguments to pass to control. If None, no keyword arguments will be passed.

Returns

Discretized array of real control values, same length

as tlist

Return type

numpy.ndarray

Raises
• TypeError – If control is not a function that takes two arguments (t, None), or a numpy array

• ValueError – If control is numpy array of incorrect size.

krotov.conversions.extract_controls(objectives)[source]

Extract a list of (unique) controls from the objectives

Controls are unique if they are not the same object, cf. Python’s is keyword.

Parameters

objectives (list) – List of Objective instances

Returns

list of controls in objectives

See extract_controls_mapping() for an example.

krotov.conversions.extract_controls_mapping(objectives, controls)[source]

Extract a map of where controls are used in objectives

The result is a nested list where the first index relates to the objectives, the second index relates to the Hamiltonian (0) or the c_ops (1…), and the third index relates to the controls.

Example

>>> import qutip
>>> import krotov
>>> X, Y, Z = qutip.Qobj(), qutip.Qobj(), qutip.Qobj() # dummy Hams
>>> u1, u2 = np.array([]), np.array([])                # dummy controls
>>> psi0, psi_tgt = qutip.Qobj(), qutip.Qobj()         # dummy states

>>> H1 = [X, [Y, u1], [Z, u1]]  # ham for first objective
>>> H2 = [X, [Y, u2]]           # ham for second objective
>>> c_ops = [[[X, u1]], [[Y, u2]]]
>>> objectives = [
...     krotov.Objective(
...         initial_state=psi0,
...         target=psi_tgt,
...         H=H1,
...         c_ops=c_ops
...     ),
...     krotov.Objective(
...         initial_state=psi0,
...         target=psi_tgt,
...         H=H2,
...         c_ops=c_ops
...     )
... ]
>>> controls = extract_controls(objectives)
>>> assert controls == [u1, u2]

>>> controls_mapping = extract_controls_mapping(objectives, controls)
>>> controls_mapping
[[[[1, 2], []], [[0], []], [[], [0]]], [[[], [1]], [[0], []], [[], [0]]]]


The structure should be read as follows:

• For the first objective (0), in the Hamiltonian (0), where is the first pulse (0) used? (answer: in H1[1] and H1[2])

>>> controls_mapping[0][0][0]
[1, 2]

• For the second objective (1), in the second c_ops (2), where is the second pulse (1) used? (answer: in c_ops[1][0])

>>> controls_mapping[1][2][1]
[0]

• For the second objective (1), in the Hamiltonian (0), where is the first pulse (0) used? (answer: nowhere)

>>> controls_mapping[1][0][0]
[]

krotov.conversions.pulse_options_dict_to_list(pulse_options, controls)[source]

Convert pulse_options into a list

Given a dict pulse_options that contains an options-dict for every control in controls (cf. optimize_pulses()), return a list of the options-dicts in the same order as controls.

Raises

ValueError – if pulse_options to not contain all of the controls

krotov.conversions.plug_in_pulse_values(H, pulses, mapping, time_index, conjugate=False)[source]

Plug pulse values into H

Parameters
• H (list) – nested list for a QuTiP-time-dependent operator

• pulses (list) – list of pulses in array format

• mapping (list) – nested list: for each pulse, a list of indices in H where pulse value should be inserted

• time_index (int) – Index of the value of each pulse that should be plugged in

• conjugate (bool) – If True, use conjugate complex pulse values

Returns

a list with the same structure as H that contains the same Qobj operators as H, but where every time dependency is replaced by the value of the appropriate pulse at time_index.

Return type

list

Example

>>> X, Y, Z = 'X', 'Y', 'Z' # dummy Hams, these would normally be Qobjs
>>> u1, u2 = np.array([0, 10, 0]), np.array([0, 20, 0])
>>> H = [X, [X, u1], [Y, u1], [Z, u2]]
>>> pulses = [u1, u2]
>>> mapping = [[1, 2], [3]]  # u1 is in H[1] and H[2], u2 is in H[3]
>>> plug_in_pulse_values(H, pulses, mapping, time_index=1)
['X', ['X', 10], ['Y', 10], ['Z', 20]]


Note

It is of no consequence whether H contains the pulses, as long as it has the right structure:

>>> H = [X, [X, None], [Y, None], [Z, None]]
>>> plug_in_pulse_values(H, pulses, mapping, time_index=1)
['X', ['X', 10], ['Y', 10], ['Z', 20]]

krotov.conversions.control_onto_interval(control)[source]

Convert control on time grid to control on time grid intervals

Parameters

control (numpy.ndarray) – values of controls on time grid

Returns

pulse defined on the intervals of the time grid

Return type

numpy.ndarray

The value for the first and last interval will be identical to the values at control[0] and control[-1] to ensure proper boundary conditions. All other intervals are calculated such that the original values in control are the average of the interval-values before and after that point in time.

The pulse_onto_tlist() function calculates the inverse to this transformation.

Note

For a callable control, call discretize() first.

krotov.conversions.pulse_onto_tlist(pulse)[source]

Convert pulse from time-grid intervals to time-grid points

Parameters

pulse (numpy.ndarray) – values defined on the interval of a time grid

Returns

values of the control defined directly on the time grid points. The size of the returned array is one greater than the size of pulse.

Return type

numpy.ndarray

Inverse of control_onto_interval().

The first and last value are also the first and last value of the returned control field. For all other points, the value is the average of the value of the input values before and after the point.