Source code for qutip.control.fidcomp

# -*- coding: utf-8 -*-
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# @author: Alexander Pitchford
# @email1: agp1@aber.ac.uk
# @email2: alex.pitchford@gmail.com
# @organization: Aberystwyth University
# @supervisor: Daniel Burgarth

"""
Fidelity Computer

These classes calculate the fidelity error - function to be minimised
and fidelity error gradient, which is used to direct the optimisation

They may calculate the fidelity as an intermediary step, as in some case
e.g. unitary dynamics, this is more efficient

The idea is that different methods for computing the fidelity can be tried
and compared using simple configuration switches.

Note the methods in these classes were inspired by:
DYNAMO - Dynamic Framework for Quantum Optimal Control
See Machnes et.al., arXiv.1011.4874
The unitary dynamics fidelity is taken directly frm DYNAMO
The other fidelity measures are extensions, and the sources are given
in the class descriptions.
"""

import os
import warnings
import numpy as np
import scipy.sparse as sp
# import scipy.linalg as la
import timeit
# QuTiP
from qutip import Qobj
# QuTiP logging
import qutip.logging_utils as logging
logger = logging.get_logger()
# QuTiP control modules
import qutip.control.errors as errors

warnings.simplefilter('always', DeprecationWarning) #turn off filter
def _attrib_deprecation(message, stacklevel=3):
    """
    Issue deprecation warning
    Using stacklevel=3 will ensure message refers the function
    calling with the deprecated parameter,
    """
    warnings.warn(message, DeprecationWarning, stacklevel=stacklevel)

def _func_deprecation(message, stacklevel=3):
    """
    Issue deprecation warning
    Using stacklevel=3 will ensure message refers the function
    calling with the deprecated parameter,
    """
    warnings.warn(message, DeprecationWarning, stacklevel=stacklevel)

def _trace(A):
    """wrapper for calculating the trace"""
    # input is an operator (Qobj, array, sparse etc), so
    if isinstance(A, Qobj):
        return A.tr()
    elif isinstance(A, np.ndarray):
        return np.trace(A)
    else:
        #Assume A some sparse matrix
        return np.sum(A.diagonal())


[docs]class FidelityComputer(object): """ Base class for all Fidelity Computers. This cannot be used directly. See subclass descriptions and choose one appropriate for the application Note: this must be instantiated with a Dynamics object, that is the container for the data that the methods operate on Attributes ---------- log_level : integer level of messaging output from the logger. Options are attributes of qutip.logging_utils, in decreasing levels of messaging, are: DEBUG_INTENSE, DEBUG_VERBOSE, DEBUG, INFO, WARN, ERROR, CRITICAL Anything WARN or above is effectively 'quiet' execution, assuming everything runs as expected. The default NOTSET implies that the level will be taken from the QuTiP settings file, which by default is WARN dimensional_norm : float Normalisation constant fid_norm_func : function Used to normalise the fidelity See SU and PSU options for the unitary dynamics grad_norm_func : function Used to normalise the fidelity gradient See SU and PSU options for the unitary dynamics uses_onwd_evo : boolean flag to specify whether the onwd_evo evolution operator (see Dynamics) is used by the FidelityComputer uses_onto_evo : boolean flag to specify whether the onto_evo evolution operator (see Dynamics) is used by the FidelityComputer fid_err : float Last computed value of the fidelity error fidelity : float Last computed value of the normalised fidelity fidelity_current : boolean flag to specify whether the fidelity / fid_err are based on the current amplitude values. Set False when amplitudes change fid_err_grad: array[num_tslot, num_ctrls] of float Last computed values for the fidelity error gradients wrt the control in the timeslot grad_norm : float Last computed value for the norm of the fidelity error gradients (sqrt of the sum of the squares) fid_err_grad_current : boolean flag to specify whether the fidelity / fid_err are based on the current amplitude values. Set False when amplitudes change """ def __init__(self, dynamics, params=None): self.parent = dynamics self.params = params self.reset()
[docs] def reset(self): """ reset any configuration data and clear any temporarily held status data """ self.log_level = self.parent.log_level self.id_text = 'FID_COMP_BASE' self.dimensional_norm = 1.0 self.fid_norm_func = None self.grad_norm_func = None self.uses_onwd_evo = False self.uses_onto_evo = False self.apply_params() self.clear()
[docs] def clear(self): """ clear any temporarily held status data """ self.fid_err = None self.fidelity = None self.fid_err_grad = None self.grad_norm = np.inf self.fidelity_current = False self.fid_err_grad_current = False self.grad_norm = 0.0
[docs] def apply_params(self, params=None): """ Set object attributes based on the dictionary (if any) passed in the instantiation, or passed as a parameter This is called during the instantiation automatically. The key value pairs are the attribute name and value Note: attributes are created if they do not exist already, and are overwritten if they do. """ if not params: params = self.params if isinstance(params, dict): self.params = params for key in params: setattr(self, key, params[key])
@property def log_level(self): return logger.level @log_level.setter def log_level(self, lvl): """ Set the log_level attribute and set the level of the logger that is call logger.setLevel(lvl) """ logger.setLevel(lvl)
[docs] def init_comp(self): """ initialises the computer based on the configuration of the Dynamics """ # optionally implemented in subclass pass
[docs] def get_fid_err(self): """ returns the absolute distance from the maximum achievable fidelity """ # must be implemented by subclass raise errors.UsageError( "No method defined for getting fidelity error." " Suspect base class was used where sub class should have been")
[docs] def get_fid_err_gradient(self): """ Returns the normalised gradient of the fidelity error in a (nTimeslots x n_ctrls) array wrt the timeslot control amplitude """ # must be implemented by subclass raise errors.UsageError("No method defined for getting fidelity" " error gradient. Suspect base class was" " used where sub class should have been")
[docs] def flag_system_changed(self): """ Flag fidelity and gradients as needing recalculation """ self.fidelity_current = False # Flag gradient as needing recalculating self.fid_err_grad_current = False
@property def uses_evo_t2end(self): _attrib_deprecation( "'uses_evo_t2end' has been replaced by 'uses_onwd_evo'") return self.uses_onwd_evo @uses_evo_t2end.setter def uses_evo_t2end(self, value): _attrib_deprecation( "'uses_evo_t2end' has been replaced by 'uses_onwd_evo'") self.uses_onwd_evo = value @property def uses_evo_t2targ(self): _attrib_deprecation( "'uses_evo_t2targ' has been replaced by 'uses_onto_evo'") return self.uses_onto_evo @uses_evo_t2targ.setter def uses_evo_t2targ(self, value): _attrib_deprecation( "'uses_evo_t2targ' has been replaced by 'uses_onto_evo'") self.uses_onto_evo = value
[docs]class FidCompUnitary(FidelityComputer): """ Computes fidelity error and gradient assuming unitary dynamics, e.g. closed qubit systems Note fidelity and gradient calculations were taken from DYNAMO (see file header) Attributes ---------- phase_option : string determines how global phase is treated in fidelity calculations: PSU - global phase ignored SU - global phase included fidelity_prenorm : complex Last computed value of the fidelity before it is normalised It is stored to use in the gradient normalisation calculation fidelity_prenorm_current : boolean flag to specify whether fidelity_prenorm are based on the current amplitude values. Set False when amplitudes change """
[docs] def reset(self): FidelityComputer.reset(self) self.id_text = 'UNIT' self.uses_onto_evo = True self._init_phase_option('PSU') self.apply_params()
[docs] def clear(self): FidelityComputer.clear(self) self.fidelity_prenorm = None self.fidelity_prenorm_current = False
[docs] def set_phase_option(self, phase_option=None): """ Deprecated - use phase_option Phase options are SU - global phase important PSU - global phase is not important """ _func_deprecation("'set_phase_option' is deprecated. " "Use phase_option property") self._init_phase_option(phase_option)
@property def phase_option(self): return self._phase_option @phase_option.setter def phase_option(self, value): """ # Phase options are # SU - global phase important # PSU - global phase is not important """ self._init_phase_option(value) def _init_phase_option(self, value): self._phase_option = value if value == 'PSU': self.fid_norm_func = self.normalize_PSU self.grad_norm_func = self.normalize_gradient_PSU elif value == 'SU': self.fid_norm_func = self.normalize_SU self.grad_norm_func = self.normalize_gradient_SU elif value is None: raise errors.UsageError("phase_option cannot be set to None" " for this FidelityComputer.") else: raise errors.UsageError( "No option for phase_option '{}'".format(value))
[docs] def init_comp(self): """ Check configuration and initialise the normalisation """ if self.fid_norm_func is None or self.grad_norm_func is None: raise errors.UsageError("The phase_option must be be set" "for this fidelity computer") self.init_normalization()
[docs] def flag_system_changed(self): """ Flag fidelity and gradients as needing recalculation """ FidelityComputer.flag_system_changed(self) # Flag the fidelity (prenormalisation) value as needing calculation self.fidelity_prenorm_current = False
[docs] def init_normalization(self): """ Calc norm of <Ufinal | Ufinal> to scale subsequent norms When considering unitary time evolution operators, this basically results in calculating the trace of the identity matrix and is hence equal to the size of the target matrix There may be situations where this is not the case, and hence it is not assumed to be so. The normalisation function called should be set to either the PSU - global phase ignored SU - global phase respected """ dyn = self.parent self.dimensional_norm = 1.0 self.dimensional_norm = \ self.fid_norm_func(dyn.target.dag()*dyn.target)
[docs] def normalize_SU(self, A): """ """ try: if A.shape[0] == A.shape[1]: # input is an operator (Qobj, array, sparse etc), so norm = _trace(A) else: raise TypeError("Cannot compute trace (not square)") except: # assume input is already scalar and hence assumed # to be the prenormalised scalar value, e.g. fidelity norm = A return np.real(norm) / self.dimensional_norm
[docs] def normalize_gradient_SU(self, grad): """ Normalise the gradient matrix passed as grad This SU version respects global phase """ grad_normalized = np.real(grad) / self.dimensional_norm return grad_normalized
[docs] def normalize_PSU(self, A): """ """ try: if A.shape[0] == A.shape[1]: # input is an operator (Qobj, array, sparse etc), so norm = _trace(A) else: raise TypeError("Cannot compute trace (not square)") except: # assume input is already scalar and hence assumed # to be the prenormalised scalar value, e.g. fidelity norm = A return np.abs(norm) / self.dimensional_norm
[docs] def normalize_gradient_PSU(self, grad): """ Normalise the gradient matrix passed as grad This PSU version is independent of global phase """ fid_pn = self.get_fidelity_prenorm() grad_normalized = np.real(grad * np.exp(-1j * np.angle(fid_pn)) / self.dimensional_norm) return grad_normalized
[docs] def get_fid_err(self): """ Gets the absolute error in the fidelity """ return np.abs(1 - self.get_fidelity())
[docs] def get_fidelity(self): """ Gets the appropriately normalised fidelity value The normalisation is determined by the fid_norm_func pointer which should be set in the config """ if not self.fidelity_current: self.fidelity = \ self.fid_norm_func(self.get_fidelity_prenorm()) self.fidelity_current = True if self.log_level <= logging.DEBUG: logger.debug("Fidelity (normalised): {}".format(self.fidelity)) return self.fidelity
[docs] def get_fidelity_prenorm(self): """ Gets the current fidelity value prior to normalisation Note the gradient function uses this value The value is cached, because it is used in the gradient calculation """ if not self.fidelity_prenorm_current: dyn = self.parent k = dyn.tslot_computer._get_timeslot_for_fidelity_calc() dyn.compute_evolution() if dyn.oper_dtype == Qobj: f = (dyn._onto_evo[k]*dyn._fwd_evo[k]).tr() else: f = _trace(dyn._onto_evo[k].dot(dyn._fwd_evo[k])) self.fidelity_prenorm = f self.fidelity_prenorm_current = True if dyn.stats is not None: dyn.stats.num_fidelity_computes += 1 if self.log_level <= logging.DEBUG: logger.debug("Fidelity (pre normalisation): {}".format( self.fidelity_prenorm)) return self.fidelity_prenorm
[docs] def get_fid_err_gradient(self): """ Returns the normalised gradient of the fidelity error in a (nTimeslots x n_ctrls) array The gradients are cached in case they are requested mutliple times between control updates (although this is not typically found to happen) """ if not self.fid_err_grad_current: dyn = self.parent grad_prenorm = self.compute_fid_grad() if self.log_level <= logging.DEBUG_INTENSE: logger.log(logging.DEBUG_INTENSE, "pre-normalised fidelity " "gradients:\n{}".format(grad_prenorm)) # AJGP: Note this check should not be necessary if dynamics are # unitary. However, if they are not then this gradient # can still be used, however the interpretation is dubious if self.get_fidelity() >= 1: self.fid_err_grad = self.grad_norm_func(grad_prenorm) else: self.fid_err_grad = -self.grad_norm_func(grad_prenorm) self.fid_err_grad_current = True if dyn.stats is not None: dyn.stats.num_grad_computes += 1 self.grad_norm = np.sqrt(np.sum(self.fid_err_grad**2)) if self.log_level <= logging.DEBUG_INTENSE: logger.log(logging.DEBUG_INTENSE, "Normalised fidelity error " "gradients:\n{}".format(self.fid_err_grad)) if self.log_level <= logging.DEBUG: logger.debug("Gradient (sum sq norm): " "{} ".format(self.grad_norm)) return self.fid_err_grad
[docs] def compute_fid_grad(self): """ Calculates exact gradient of function wrt to each timeslot control amplitudes. Note these gradients are not normalised These are returned as a (nTimeslots x n_ctrls) array """ dyn = self.parent n_ctrls = dyn.num_ctrls n_ts = dyn.num_tslots # create n_ts x n_ctrls zero array for grad start point grad = np.zeros([n_ts, n_ctrls], dtype=complex) dyn.tslot_computer.flag_all_calc_now() dyn.compute_evolution() # loop through all ctrl timeslots calculating gradients time_st = timeit.default_timer() for j in range(n_ctrls): for k in range(n_ts): fwd_evo = dyn._fwd_evo[k] onto_evo = dyn._onto_evo[k+1] if dyn.oper_dtype == Qobj: g = (onto_evo*dyn._get_prop_grad(k, j)*fwd_evo).tr() else: g = _trace(onto_evo.dot( dyn._get_prop_grad(k, j)).dot(fwd_evo)) grad[k, j] = g if dyn.stats is not None: dyn.stats.wall_time_gradient_compute += \ timeit.default_timer() - time_st return grad
[docs]class FidCompTraceDiff(FidelityComputer): """ Computes fidelity error and gradient for general system dynamics by calculating the the fidelity error as the trace of the overlap of the difference between the target and evolution resulting from the pulses with the transpose of the same. This should provide a distance measure for dynamics described by matrices Note the gradient calculation is taken from: 'Robust quantum gates for open systems via optimal control: Markovian versus non-Markovian dynamics' Frederik F Floether, Pierre de Fouquieres, and Sophie G Schirmer Attributes ---------- scale_factor : float The fidelity error calculated is of some arbitary scale. This factor can be used to scale the fidelity error such that it may represent some physical measure If None is given then it is caculated as 1/2N, where N is the dimension of the drift, when the Dynamics are initialised. """
[docs] def reset(self): FidelityComputer.reset(self) self.id_text = 'TRACEDIFF' self.scale_factor = None self.uses_onwd_evo = True if not self.parent.prop_computer.grad_exact: raise errors.UsageError( "This FidelityComputer can only be" " used with an exact gradient PropagatorComputer.") self.apply_params()
[docs] def init_comp(self): """ initialises the computer based on the configuration of the Dynamics Calculates the scale_factor is not already set """ if self.scale_factor is None: self.scale_factor = 1.0 / (2.0*self.parent.get_drift_dim()) if self.log_level <= logging.DEBUG: logger.debug("Scale factor calculated as {}".format( self.scale_factor))
[docs] def get_fid_err(self): """ Gets the absolute error in the fidelity """ if not self.fidelity_current: dyn = self.parent dyn.compute_evolution() n_ts = dyn.num_tslots evo_final = dyn._fwd_evo[n_ts] evo_f_diff = dyn._target - evo_final if self.log_level <= logging.DEBUG_VERBOSE: logger.log(logging.DEBUG_VERBOSE, "Calculating TraceDiff " "fidelity...\n Target:\n{}\n Evo final:\n{}\n" "Evo final diff:\n{}".format(dyn._target, evo_final, evo_f_diff)) # Calculate the fidelity error using the trace difference norm # Note that the value should have not imagnary part, so using # np.real, just avoids the complex casting warning if dyn.oper_dtype == Qobj: self.fid_err = self.scale_factor*np.real( (evo_f_diff.dag()*evo_f_diff).tr()) else: self.fid_err = self.scale_factor*np.real(_trace( evo_f_diff.conj().T.dot(evo_f_diff))) if np.isnan(self.fid_err): self.fid_err = np.Inf if dyn.stats is not None: dyn.stats.num_fidelity_computes += 1 self.fidelity_current = True if self.log_level <= logging.DEBUG: logger.debug("Fidelity error: {}".format(self.fid_err)) return self.fid_err
[docs] def get_fid_err_gradient(self): """ Returns the normalised gradient of the fidelity error in a (nTimeslots x n_ctrls) array The gradients are cached in case they are requested mutliple times between control updates (although this is not typically found to happen) """ if not self.fid_err_grad_current: dyn = self.parent self.fid_err_grad = self.compute_fid_err_grad() self.fid_err_grad_current = True if dyn.stats is not None: dyn.stats.num_grad_computes += 1 self.grad_norm = np.sqrt(np.sum(self.fid_err_grad**2)) if self.log_level <= logging.DEBUG_INTENSE: logger.log(logging.DEBUG_INTENSE, "fidelity error gradients:\n" "{}".format(self.fid_err_grad)) if self.log_level <= logging.DEBUG: logger.debug("Gradient norm: " "{} ".format(self.grad_norm)) return self.fid_err_grad
[docs] def compute_fid_err_grad(self): """ Calculate exact gradient of the fidelity error function wrt to each timeslot control amplitudes. Uses the trace difference norm fidelity These are returned as a (nTimeslots x n_ctrls) array """ dyn = self.parent n_ctrls = dyn.num_ctrls n_ts = dyn.num_tslots # create n_ts x n_ctrls zero array for grad start point grad = np.zeros([n_ts, n_ctrls]) dyn.tslot_computer.flag_all_calc_now() dyn.compute_evolution() # loop through all ctrl timeslots calculating gradients time_st = timeit.default_timer() evo_final = dyn._fwd_evo[n_ts] evo_f_diff = dyn._target - evo_final for j in range(n_ctrls): for k in range(n_ts): fwd_evo = dyn._fwd_evo[k] if dyn.oper_dtype == Qobj: evo_grad = dyn._get_prop_grad(k, j)*fwd_evo if k+1 < n_ts: evo_grad = dyn._onwd_evo[k+1]*evo_grad # Note that the value should have not imagnary part, so # using np.real, just avoids the complex casting warning g = -2*self.scale_factor*np.real( (evo_f_diff.dag()*evo_grad).tr()) else: evo_grad = dyn._get_prop_grad(k, j).dot(fwd_evo) if k+1 < n_ts: evo_grad = dyn._onwd_evo[k+1].dot(evo_grad) g = -2*self.scale_factor*np.real(_trace( evo_f_diff.conj().T.dot(evo_grad))) if np.isnan(g): g = np.Inf grad[k, j] = g if dyn.stats is not None: dyn.stats.wall_time_gradient_compute += \ timeit.default_timer() - time_st return grad
[docs]class FidCompTraceDiffApprox(FidCompTraceDiff): """ As FidCompTraceDiff, except uses the finite difference method to compute approximate gradients Attributes ---------- epsilon : float control amplitude offset to use when approximating the gradient wrt a timeslot control amplitude """
[docs] def reset(self): FidelityComputer.reset(self) self.id_text = 'TDAPPROX' self.uses_onwd_evo = True self.scale_factor = None self.epsilon = 0.001 self.apply_params()
[docs] def compute_fid_err_grad(self): """ Calculates gradient of function wrt to each timeslot control amplitudes. Note these gradients are not normalised They are calulated These are returned as a (nTimeslots x n_ctrls) array """ dyn = self.parent prop_comp = dyn.prop_computer n_ctrls = dyn.num_ctrls n_ts = dyn.num_tslots if self.log_level >= logging.DEBUG: logger.debug("Computing fidelity error gradient") # create n_ts x n_ctrls zero array for grad start point grad = np.zeros([n_ts, n_ctrls]) dyn.tslot_computer.flag_all_calc_now() dyn.compute_evolution() curr_fid_err = self.get_fid_err() # loop through all ctrl timeslots calculating gradients time_st = timeit.default_timer() for j in range(n_ctrls): for k in range(n_ts): fwd_evo = dyn._fwd_evo[k] prop_eps = prop_comp._compute_diff_prop(k, j, self.epsilon) if dyn.oper_dtype == Qobj: evo_final_eps = fwd_evo*prop_eps if k+1 < n_ts: evo_final_eps = evo_final_eps*dyn._onwd_evo[k+1] evo_f_diff_eps = dyn._target - evo_final_eps # Note that the value should have not imagnary part, so # using np.real, just avoids the complex casting warning fid_err_eps = self.scale_factor*np.real( (evo_f_diff_eps.dag()*evo_f_diff_eps).tr()) else: evo_final_eps = fwd_evo.dot(prop_eps) if k+1 < n_ts: evo_final_eps = evo_final_eps.dot(dyn._onwd_evo[k+1]) evo_f_diff_eps = dyn._target - evo_final_eps fid_err_eps = self.scale_factor*np.real(_trace( evo_f_diff_eps.conj().T.dot(evo_f_diff_eps))) g = (fid_err_eps - curr_fid_err)/self.epsilon if np.isnan(g): g = np.Inf grad[k, j] = g if dyn.stats is not None: dyn.stats.wall_time_gradient_compute += \ timeit.default_timer() - time_st return grad