Source code for qutip.control.propcomp

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

"""
Propagator Computer
Classes used to calculate the propagators,
and also the propagator gradient when exact gradient methods are used

Note the methods in the _Diag class was inspired by:
DYNAMO - Dynamic Framework for Quantum Optimal Control
See Machnes et.al., arXiv.1011.4874
"""

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

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)

[docs]class PropagatorComputer(object): """ Base for all Propagator Computer classes that are used to calculate the propagators, and also the propagator gradient when exact gradient methods are used Note: they must be instantiated with a Dynamics object, that is the container for the data that the functions operate on This base class cannot be used directly. See subclass descriptions and choose the appropriate one for the application Attributes ---------- log_level : integer level of messaging output from the logger. Options are attributes of qutip_utils.logging, 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 grad_exact : boolean indicates whether the computer class instance is capable of computing propagator gradients. It is used to determine whether to create the Dynamics prop_grad array """ def __init__(self, dynamics, params=None): self.parent = dynamics self.params = params self.reset()
[docs] def reset(self): """ reset any configuration data """ self.id_text = 'PROP_COMP_BASE' self.log_level = self.parent.log_level self._grad_exact = False
[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) def grad_exact(self): return self._grad_exact def compute_propagator(self, k): _func_deprecation("'compute_propagator' has been replaced " "by '_compute_propagator'") return self._compute_propagator(k) def _compute_propagator(self, k): """ calculate the progator between X(k) and X(k+1) Uses matrix expm of the dyn_gen at that point (in time) Assumes that the dyn_gen have been been calculated, i.e. drift and ctrls combined Return the propagator """ dyn = self.parent dgt = dyn._get_phased_dyn_gen(k)*dyn.tau[k] if dyn.oper_dtype == Qobj: prop = dgt.expm() else: prop = la.expm(dgt) return prop def compute_diff_prop(self, k, j, epsilon): _func_deprecation("'compute_diff_prop' has been replaced " "by '_compute_diff_prop'") return self._compute_diff_prop( k, j, epsilon) def _compute_diff_prop(self, k, j, epsilon): """ Calculate the propagator from the current point to a trial point a distance 'epsilon' (change in amplitude) in the direction the given control j in timeslot k Returns the propagator """ raise errors.UsageError("Not implemented in the baseclass." " Choose a subclass") def compute_prop_grad(self, k, j, compute_prop=True): _func_deprecation("'compute_prop_grad' has been replaced " "by '_compute_prop_grad'") return self._compute_prop_grad(self, k, j, compute_prop=compute_prop) def _compute_prop_grad(self, k, j, compute_prop=True): """ Calculate the gradient of propagator wrt the control amplitude in the timeslot. """ raise errors.UsageError("Not implemented in the baseclass." " Choose a subclass")
[docs]class PropCompApproxGrad(PropagatorComputer): """ This subclass can be used when the propagator is calculated simply by expm of the dynamics generator, i.e. when gradients will be calculated using approximate methods. """
[docs] def reset(self): """ reset any configuration data """ PropagatorComputer.reset(self) self.id_text = 'APPROX' self.grad_exact = False self.apply_params()
def _compute_diff_prop(self, k, j, epsilon): """ Calculate the propagator from the current point to a trial point a distance 'epsilon' (change in amplitude) in the direction the given control j in timeslot k Returns the propagator """ dyn = self.parent dgt_eps = (dyn._get_phased_dyn_gen(k) + epsilon*dyn._get_phased_ctrl_dyn_gen(k, j))*dyn.tau[k] if dyn.oper_dtype == Qobj: prop_eps = dgt_eps.expm() else: prop_eps = la.expm(dgt_eps) return prop_eps
[docs]class PropCompDiag(PropagatorComputer): """ Coumputes the propagator exponentiation using diagonalisation of of the dynamics generator """
[docs] def reset(self): """ reset any configuration data """ PropagatorComputer.reset(self) self.id_text = 'DIAG' self.grad_exact = True self.apply_params()
def _compute_propagator(self, k): """ Calculates the exponentiation of the dynamics generator (H) As part of the calc the the eigen decomposition is required, which is reused in the propagator gradient calculation """ dyn = self.parent dyn._ensure_decomp_curr(k) if dyn.oper_dtype == Qobj: prop = (dyn._dyn_gen_eigenvectors[k]*dyn._prop_eigen[k]* dyn._get_dyn_gen_eigenvectors_adj(k)) else: prop = dyn._dyn_gen_eigenvectors[k].dot( dyn._prop_eigen[k]).dot( dyn._get_dyn_gen_eigenvectors_adj(k)) return prop def _compute_prop_grad(self, k, j, compute_prop=True): """ Calculate the gradient of propagator wrt the control amplitude in the timeslot. Returns: [prop], prop_grad """ dyn = self.parent dyn._ensure_decomp_curr(k) if compute_prop: prop = self._compute_propagator(k) if dyn.oper_dtype == Qobj: # put control dyn_gen in combined dg diagonal basis cdg = (dyn._get_dyn_gen_eigenvectors_adj(k)* dyn._get_phased_ctrl_dyn_gen(k, j)* dyn._dyn_gen_eigenvectors[k]) # multiply (elementwise) by timeslice and factor matrix cdg = Qobj(np.multiply(cdg.full()*dyn.tau[k], dyn._dyn_gen_factormatrix[k]), dims=dyn.dyn_dims) # Return to canonical basis prop_grad = (dyn._dyn_gen_eigenvectors[k]*cdg* dyn._get_dyn_gen_eigenvectors_adj(k)) else: # put control dyn_gen in combined dg diagonal basis cdg = dyn._get_dyn_gen_eigenvectors_adj(k).dot( dyn._get_phased_ctrl_dyn_gen(k, j)).dot( dyn._dyn_gen_eigenvectors[k]) # multiply (elementwise) by timeslice and factor matrix cdg = np.multiply(cdg*dyn.tau[k], dyn._dyn_gen_factormatrix[k]) # Return to canonical basis prop_grad = dyn._dyn_gen_eigenvectors[k].dot(cdg).dot( dyn._get_dyn_gen_eigenvectors_adj(k)) if compute_prop: return prop, prop_grad else: return prop_grad
class PropCompAugMat(PropagatorComputer): """ Augmented Matrix (deprecated - see _Frechet) It should work for all systems, e.g. open, symplectic There will be other PropagatorComputer subclasses that are more efficient The _Frechet class should provide exactly the same functionality more efficiently. Note the propagator gradient calculation using the augmented matrix 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 """ def reset(self): PropagatorComputer.reset(self) self.id_text = 'AUG_MAT' self.grad_exact = True self.apply_params() def _get_aug_mat(self, k, j): """ Generate the matrix [[A, E], [0, A]] where A is the overall dynamics generator E is the control dynamics generator for a given timeslot and control returns this augmented matrix """ dyn = self.parent dg = dyn._get_phased_dyn_gen(k) if dyn.oper_dtype == Qobj: A = dg.data*dyn.tau[k] E = dyn._get_phased_ctrl_dyn_gen(k, j).data*dyn.tau[k] Z = sp.csr_matrix(dg.data.shape) aug = Qobj(sp.vstack([sp.hstack([A, E]), sp.hstack([Z, A])])) else: A = dg*dyn.tau[k] E = dyn._get_phased_ctrl_dyn_gen(k, j)*dyn.tau[k] Z = np.zeros(dg.shape) aug = np.vstack([np.hstack([A, E]), np.hstack([Z, A])]) return aug def _compute_prop_grad(self, k, j, compute_prop=True): """ Calculate the gradient of propagator wrt the control amplitude in the timeslot using the exponentiation of the the augmented matrix. The propagtor is calculated for 'free' in this method and hence it is returned if compute_prop==True Returns: [prop], prop_grad """ dyn = self.parent dg = dyn._get_phased_dyn_gen(k) aug = self._get_aug_mat(k, j) if dyn.oper_dtype == Qobj: aug_exp = aug.expm() prop_grad = Qobj(aug_exp.data[:dg.shape[0], dg.shape[1]:], dims=dyn.dyn_dims) if compute_prop: prop = Qobj(aug_exp.data[:dg.shape[0], :dg.shape[1]], dims=dyn.dyn_dims) else: aug_exp = la.expm(aug) prop_grad = aug_exp[:dg.shape[0], dg.shape[1]:] if compute_prop: prop = aug_exp[:dg.shape[0], :dg.shape[1]] if compute_prop: return prop, prop_grad else: return prop_grad
[docs]class PropCompFrechet(PropagatorComputer): """ Frechet method for calculating the propagator: exponentiating the combined dynamics generator and the propagator gradient. It should work for all systems, e.g. unitary, open, symplectic. There are other :obj:`PropagatorComputer` subclasses that may be more efficient. """
[docs] def reset(self): PropagatorComputer.reset(self) self.id_text = 'FRECHET' self.grad_exact = True self.apply_params()
def _compute_prop_grad(self, k, j, compute_prop=True): """ Calculate the gradient of propagator wrt the control amplitude in the timeslot using the expm_frechet method The propagtor is calculated (almost) for 'free' in this method and hence it is returned if compute_prop==True Returns: [prop], prop_grad """ dyn = self.parent if dyn.oper_dtype == Qobj: A = dyn._get_phased_dyn_gen(k).full()*dyn.tau[k] E = dyn._get_phased_ctrl_dyn_gen(k, j).full()*dyn.tau[k] if compute_prop: prop_dense, prop_grad_dense = la.expm_frechet(A, E) prop = Qobj(prop_dense, dims=dyn.dyn_dims) prop_grad = Qobj(prop_grad_dense, dims=dyn.dyn_dims) else: prop_grad_dense = la.expm_frechet(A, E, compute_expm=False) prop_grad = Qobj(prop_grad_dense, dims=dyn.dyn_dims) else: A = dyn._get_phased_dyn_gen(k)*dyn.tau[k] E = dyn._get_phased_ctrl_dyn_gen(k, j)*dyn.tau[k] if compute_prop: prop, prop_grad = la.expm_frechet(A, E) else: prop_grad = la.expm_frechet(A, E, compute_expm=False) if compute_prop: return prop, prop_grad else: return prop_grad