# -*- coding: utf-8 -*-
# This file is part of QuTiP: Quantum Toolbox in Python.
#
# Copyright (c) 2014 and later, Alexander J G Pitchford
# All rights reserved.
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions are
# met:
#
# 1. Redistributions of source code must retain the above copyright notice,
# this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the QuTiP: Quantum Toolbox in Python nor the names
# of its contributors may be used to endorse or promote products derived
# from this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
# PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
# HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
# SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
# LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
# DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
# THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
# (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
# OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
###############################################################################
# @author: Alexander Pitchford
# @email1: agp1@aber.ac.uk
# @email2: alex.pitchford@gmail.com
# @organization: Aberystwyth University
# @supervisor: Daniel Burgarth
"""
Classes that define the dynamics of the (quantum) system and target evolution
to be optimised.
The contols are also defined here, i.e. the dynamics generators (Hamiltonians,
Limbladians etc). The dynamics for the time slices are calculated here, along
with the evolution as determined by the control amplitudes.
See the subclass descriptions and choose the appropriate class for the
application. The choice depends on the type of matrix used to define
the dynamics.
These class implement functions for getting the dynamics generators for
the combined (drift + ctrls) dynamics with the approriate operator applied
Note the methods in these classes were 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 import Qobj
from qutip.sparse import sp_eigs, _dense_eigs
import qutip.settings as settings
# QuTiP logging
import qutip.logging_utils as logging
logger = logging.get_logger()
# QuTiP control modules
import qutip.control.errors as errors
import qutip.control.tslotcomp as tslotcomp
import qutip.control.fidcomp as fidcomp
import qutip.control.propcomp as propcomp
import qutip.control.symplectic as sympl
import qutip.control.dump as qtrldump
DEF_NUM_TSLOTS = 10
DEF_EVO_TIME = 1.0
def _is_string(var):
try:
if isinstance(var, basestring):
return True
except NameError:
try:
if isinstance(var, str):
return True
except:
return False
except:
return False
return False
def _check_ctrls_container(ctrls):
"""
Check through the controls container.
Convert to an array if its a list of lists
return the processed container
raise type error if the container structure is invalid
"""
if isinstance(ctrls, (list, tuple)):
# Check to see if list of lists
try:
if isinstance(ctrls[0], (list, tuple)):
ctrls = np.array(ctrls, dtype=object)
except:
pass
if isinstance(ctrls, np.ndarray):
if len(ctrls.shape) != 2:
raise TypeError("Incorrect shape for ctrl dyn gen array")
for k in range(ctrls.shape[0]):
for j in range(ctrls.shape[1]):
if not isinstance(ctrls[k, j], Qobj):
raise TypeError("All control dyn gen must be Qobj")
elif isinstance(ctrls, (list, tuple)):
for ctrl in ctrls:
if not isinstance(ctrl, Qobj):
raise TypeError("All control dyn gen must be Qobj")
else:
raise TypeError("Controls list or array not set correctly")
return ctrls
def _check_drift_dyn_gen(drift):
if not isinstance(drift, Qobj):
if not isinstance(drift, (list, tuple)):
raise TypeError("drift should be a Qobj or a list of Qobj")
else:
for d in drift:
if not isinstance(d, Qobj):
raise TypeError(
"drift should be a Qobj or a list of Qobj")
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)
[docs]class Dynamics(object):
"""
This is a base class only. See subclass descriptions and choose an
appropriate one for the application.
Note that initialize_controls must be called before most of the methods
can be used. init_timeslots can be called sometimes earlier in order
to access timeslot related attributes
This acts as a container for the operators that are used to calculate
time evolution of the system under study. That is the dynamics generators
(Hamiltonians, Lindbladians etc), the propagators from one timeslot to
the next, and the evolution operators. Due to the large number of matrix
additions and multiplications, for small systems at least, the optimisation
performance is much better using ndarrays to represent these operators.
However
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
params: Dictionary
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.
stats : Stats
Attributes of which give performance stats for the optimisation
set to None to reduce overhead of calculating stats.
Note it is (usually) shared with the Optimizer object
tslot_computer : TimeslotComputer (subclass instance)
Used to manage when the timeslot dynamics
generators, propagators, gradients etc are updated
prop_computer : PropagatorComputer (subclass instance)
Used to compute the propagators and their gradients
fid_computer : FidelityComputer (subclass instance)
Used to computer the fidelity error and the fidelity error
gradient.
memory_optimization : int
Level of memory optimisation. Setting to 0 (default) means that
execution speed is prioritized over memory.
Setting to 1 means that some memory prioritisation steps will be
taken, for instance using Qobj (and hence sparse arrays) as the
the internal operator data type, and not caching some operators
Potentially further memory saving maybe made with
memory_optimization > 1.
The options are processed in _set_memory_optimizations, see
this for more information. Individual memory saving options can be
switched by settting them directly (see below)
oper_dtype : type
Data type for internal dynamics generators, propagators and time
evolution operators. This can be ndarray or Qobj, or (in theory) any
other representaion that supports typical matrix methods (e.g. dot)
ndarray performs best for smaller quantum systems.
Qobj may perform better for larger systems, and will also
perform better when (custom) fidelity measures use Qobj methods
such as partial trace.
See _choose_oper_dtype for how this is chosen when not specified
cache_phased_dyn_gen : bool
If True then the dynamics generators will be saved with and
without the propagation prefactor (if there is one)
Defaults to True when memory_optimization=0, otherwise False
cache_prop_grad : bool
If the True then the propagator gradients (for exact gradients) will
be computed when the propagator are computed and cache until
the are used by the fidelity computer. If False then the
fidelity computer will calculate them as needed.
Defaults to True when memory_optimization=0, otherwise False
cache_dyn_gen_eigenvectors_adj: bool
If True then DynamicsUnitary will cached the adjoint of
the Hamiltion eignvector matrix
Defaults to True when memory_optimization=0, otherwise False
sparse_eigen_decomp: bool
If True then DynamicsUnitary will use the sparse eigenvalue
decomposition.
Defaults to True when memory_optimization<=1, otherwise False
num_tslots : integer
Number of timeslots (aka timeslices)
num_ctrls : integer
Number of controls.
Note this is calculated as the length of ctrl_dyn_gen when first used.
And is recalculated during initialise_controls only.
evo_time : float
Total time for the evolution
tau : array[num_tslots] of float
Duration of each timeslot
Note that if this is set before initialize_controls is called
then num_tslots and evo_time are calculated from tau, otherwise
tau is generated from num_tslots and evo_time, that is
equal size time slices
time : array[num_tslots+1] of float
Cumulative time for the evolution, that is the time at the start
of each time slice
drift_dyn_gen : Qobj or list of Qobj
Drift or system dynamics generator (Hamiltonian)
Matrix defining the underlying dynamics of the system
Can also be a list of Qobj (length num_tslots) for time varying
drift dynamics
ctrl_dyn_gen : List of Qobj
Control dynamics generator (Hamiltonians)
List of matrices defining the control dynamics
initial : Qobj
Starting state / gate
The matrix giving the initial state / gate, i.e. at time 0
Typically the identity for gate evolution
target : Qobj
Target state / gate:
The matrix giving the desired state / gate for the evolution
ctrl_amps : array[num_tslots, num_ctrls] of float
Control amplitudes
The amplitude (scale factor) for each control in each timeslot
initial_ctrl_scaling : float
Scale factor applied to be applied the control amplitudes
when they are initialised
This is used by the PulseGens rather than in any fucntions in
this class
initial_ctrl_offset : float
Linear offset applied to be applied the control amplitudes
when they are initialised
This is used by the PulseGens rather than in any fucntions in
this class
dyn_gen : List of Qobj
Dynamics generators
the combined drift and control dynamics generators
for each timeslot
prop : list of Qobj
Propagators - used to calculate time evolution from one
timeslot to the next
prop_grad : array[num_tslots, num_ctrls] of Qobj
Propagator gradient (exact gradients only)
Array of Qobj that give the gradient
with respect to the control amplitudes in a timeslot
Note this attribute is only created when the selected
PropagatorComputer is an exact gradient type.
fwd_evo : List of Qobj
Forward evolution (or propagation)
the time evolution operator from the initial state / gate to the
specified timeslot as generated by the dyn_gen
onwd_evo : List of Qobj
Onward evolution (or propagation)
the time evolution operator from the specified timeslot to
end of the evolution time as generated by the dyn_gen
onto_evo : List of Qobj
'Backward' List of Qobj propagation
the overlap of the onward propagation with the inverse of the
target.
Note this is only used (so far) by the unitary dynamics fidelity
evo_current : Boolean
Used to flag that the dynamics used to calculate the evolution
operators is current. It is set to False when the amplitudes
change
fact_mat_round_prec : float
Rounding precision used when calculating the factor matrix
to determine if two eigenvalues are equivalent
Only used when the PropagatorComputer uses diagonalisation
def_amps_fname : string
Default name for the output used when save_amps is called
unitarity_check_level : int
If > 0 then unitarity of the system evolution is checked at at
evolution recomputation.
level 1 checks all propagators
level 2 checks eigen basis as well
Default is 0
unitarity_tol :
Tolerance used in checking if operator is unitary
Default is 1e-10
dump : :class:`dump.DynamicsDump`
Store of historical calculation data.
Set to None (Default) for no storing of historical data
Use dumping property to set level of data dumping
dumping : string
level of data dumping: NONE, SUMMARY, FULL or CUSTOM
See property docstring for details
dump_to_file : bool
If set True then data will be dumped to file during the calculations
dumping will be set to SUMMARY during init_evo if dump_to_file is True
and dumping not set.
Default is False
dump_dir : string
Basically a link to dump.dump_dir. Exists so that it can be set through
dyn_params.
If dump is None then will return None or will set dumping to SUMMARY
when setting a path
"""
def __init__(self, optimconfig, params=None):
self.config = optimconfig
self.params = params
self.reset()
def reset(self):
# Link to optimiser object if self is linked to one
self.parent = None
# Main functional attributes
self.time = None
self.initial = None
self.target = None
self.ctrl_amps = None
self.initial_ctrl_scaling = 1.0
self.initial_ctrl_offset = 0.0
self.drift_dyn_gen = None
self.ctrl_dyn_gen = None
self._tau = None
self._evo_time = None
self._num_ctrls = None
self._num_tslots = None
# attributes used for processing evolution
self.memory_optimization = 0
self.oper_dtype = None
self.cache_phased_dyn_gen = None
self.cache_prop_grad = None
self.cache_dyn_gen_eigenvectors_adj = None
self.sparse_eigen_decomp = None
self.dyn_dims = None
self.dyn_shape = None
self.sys_dims = None
self.sys_shape = None
self.time_depend_drift = False
self.time_depend_ctrl_dyn_gen = False
# These internal attributes will be of the internal operator data type
# used to compute the evolution
# Note this maybe ndarray, Qobj or some other depending on oper_dtype
self._drift_dyn_gen = None
self._ctrl_dyn_gen = None
self._phased_ctrl_dyn_gen = None
self._dyn_gen_phase = None
self._phase_application = None
self._initial = None
self._target = None
self._onto_evo_target = None
self._dyn_gen = None
self._phased_dyn_gen = None
self._prop = None
self._prop_grad = None
self._fwd_evo = None
self._onwd_evo = None
self._onto_evo = None
# The _qobj attribs are Qobj representations of the equivalent
# internal attribute. They are only set when the extenal accessors
# are used
self._onto_evo_target_qobj = None
self._dyn_gen_qobj = None
self._prop_qobj = None
self._prop_grad_qobj = None
self._fwd_evo_qobj = None
self._onwd_evo_qobj = None
self._onto_evo_qobj = None
# Atrributes used in diagonalisation
# again in internal operator data type (see above)
self._decomp_curr = None
self._prop_eigen = None
self._dyn_gen_eigenvectors = None
self._dyn_gen_eigenvectors_adj = None
self._dyn_gen_factormatrix = None
self.fact_mat_round_prec = 1e-10
# Debug and information attribs
self.stats = None
self.id_text = 'DYN_BASE'
self.def_amps_fname = "ctrl_amps.txt"
self.log_level = self.config.log_level
# Internal flags
self._dyn_gen_mapped = False
self._evo_initialized = False
self._timeslots_initialized = False
self._ctrls_initialized = False
self._ctrl_dyn_gen_checked = False
self._drift_dyn_gen_checked = False
# Unitary checking
self.unitarity_check_level = 0
self.unitarity_tol = 1e-10
# Data dumping
self.dump = None
self.dump_to_file = False
self.apply_params()
# Create the computing objects
self._create_computers()
self.clear()
[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)
@property
def dumping(self):
"""
The level of data dumping that will occur during the time evolution
calculation.
- NONE : No processing data dumped (Default)
- SUMMARY : A summary of each time evolution will be recorded
- FULL : All operators used or created in the calculation dumped
- CUSTOM : Some customised level of dumping
When first set to CUSTOM this is equivalent to SUMMARY. It is then up
to the user to specify which operators are dumped
WARNING: FULL could consume a lot of memory!
"""
if self.dump is None:
lvl = 'NONE'
else:
lvl = self.dump.level
return lvl
@dumping.setter
def dumping(self, value):
if value is None:
self.dump = None
else:
if not _is_string(value):
raise TypeError("Value must be string value")
lvl = value.upper()
if lvl == 'NONE':
self.dump = None
else:
if not isinstance(self.dump, qtrldump.DynamicsDump):
self.dump = qtrldump.DynamicsDump(self, level=lvl)
else:
self.dump.level = lvl
@property
def dump_dir(self):
if self.dump:
return self.dump.dump_dir
else:
return None
@dump_dir.setter
def dump_dir(self, value):
if not self.dump:
self.dumping = 'SUMMARY'
self.dump.dump_dir = value
def _create_computers(self):
"""
Create the default timeslot, fidelity and propagator computers
"""
# The time slot computer. By default it is set to UpdateAll
# can be set to DynUpdate in the configuration
# (see class file for details)
if self.config.tslot_type == 'DYNAMIC':
self.tslot_computer = tslotcomp.TSlotCompDynUpdate(self)
else:
self.tslot_computer = tslotcomp.TSlotCompUpdateAll(self)
self.prop_computer = propcomp.PropCompFrechet(self)
self.fid_computer = fidcomp.FidCompTraceDiff(self)
def clear(self):
self.ctrl_amps = None
self.evo_current = False
if self.fid_computer is not None:
self.fid_computer.clear()
@property
def num_tslots(self):
if not self._timeslots_initialized:
self.init_timeslots()
return self._num_tslots
@num_tslots.setter
def num_tslots(self, value):
self._num_tslots = value
if self._timeslots_initialized:
self._tau = None
self.init_timeslots()
@property
def evo_time(self):
if not self._timeslots_initialized:
self.init_timeslots()
return self._evo_time
@evo_time.setter
def evo_time(self, value):
self._evo_time = value
if self._timeslots_initialized:
self._tau = None
self.init_timeslots()
@property
def tau(self):
if not self._timeslots_initialized:
self.init_timeslots()
return self._tau
@tau.setter
def tau(self, value):
self._tau = value
self.init_timeslots()
[docs] def init_timeslots(self):
"""
Generate the timeslot duration array 'tau' based on the evo_time
and num_tslots attributes, unless the tau attribute is already set
in which case this step in ignored
Generate the cumulative time array 'time' based on the tau values
"""
# set the time intervals to be equal timeslices of the total if
# the have not been set already (as part of user config)
if self._num_tslots is None:
self._num_tslots = DEF_NUM_TSLOTS
if self._evo_time is None:
self._evo_time = DEF_EVO_TIME
if self._tau is None:
self._tau = np.ones(self._num_tslots, dtype='f') * \
self._evo_time/self._num_tslots
else:
self._num_tslots = len(self._tau)
self._evo_time = np.sum(self._tau)
self.time = np.zeros(self._num_tslots+1, dtype=float)
# set the cumulative time by summing the time intervals
for t in range(self._num_tslots):
self.time[t+1] = self.time[t] + self._tau[t]
self._timeslots_initialized = True
def _set_memory_optimizations(self):
"""
Set various memory optimisation attributes based on the
memory_optimization attribute
If they have been set already, e.g. in apply_params
then they will not be overridden here
"""
logger.info("Setting memory optimisations for level {}".format(
self.memory_optimization))
if self.oper_dtype is None:
self._choose_oper_dtype()
logger.info("Internal operator data type choosen to be {}".format(
self.oper_dtype))
else:
logger.info("Using operator data type {}".format(
self.oper_dtype))
if self.cache_phased_dyn_gen is None:
if self.memory_optimization > 0:
self.cache_phased_dyn_gen = False
else:
self.cache_phased_dyn_gen = True
logger.info("phased dynamics generator caching {}".format(
self.cache_phased_dyn_gen))
if self.cache_prop_grad is None:
if self.memory_optimization > 0:
self.cache_prop_grad = False
else:
self.cache_prop_grad = True
logger.info("propagator gradient caching {}".format(
self.cache_prop_grad))
if self.cache_dyn_gen_eigenvectors_adj is None:
if self.memory_optimization > 0:
self.cache_dyn_gen_eigenvectors_adj = False
else:
self.cache_dyn_gen_eigenvectors_adj = True
logger.info("eigenvector adjoint caching {}".format(
self.cache_dyn_gen_eigenvectors_adj))
if self.sparse_eigen_decomp is None:
if self.memory_optimization > 1:
self.sparse_eigen_decomp = True
else:
self.sparse_eigen_decomp = False
logger.info("use sparse eigen decomp {}".format(
self.sparse_eigen_decomp))
def _choose_oper_dtype(self):
"""
Attempt select most efficient internal operator data type
"""
if self.memory_optimization > 0:
self.oper_dtype = Qobj
else:
# Method taken from Qobj.expm()
# if method is not explicitly given, try to make a good choice
# between sparse and dense solvers by considering the size of the
# system and the number of non-zero elements.
if self.time_depend_drift:
dg = self.drift_dyn_gen[0]
else:
dg = self.drift_dyn_gen
if self.time_depend_ctrl_dyn_gen:
ctrls = self.ctrl_dyn_gen[0, :]
else:
ctrls = self.ctrl_dyn_gen
for c in ctrls:
dg = dg + c
N = dg.data.shape[0]
n = dg.data.nnz
if N ** 2 < 100 * n:
# large number of nonzero elements, revert to dense solver
self.oper_dtype = np.ndarray
elif N > 400:
# large system, and quite sparse -> qutips sparse method
self.oper_dtype = Qobj
else:
# small system, but quite sparse -> qutips sparse/dense method
self.oper_dtype = np.ndarray
return self.oper_dtype
def _init_evo(self):
"""
Create the container lists / arrays for the:
dynamics generations, propagators, and evolutions etc
Set the time slices and cumulative time
"""
# check evolution operators
if not self._drift_dyn_gen_checked:
_check_drift_dyn_gen(self.drift_dyn_gen)
if not self._ctrl_dyn_gen_checked:
self.ctrl_dyn_gen = _check_ctrls_container(self.ctrl_dyn_gen)
if not isinstance(self.initial, Qobj):
raise TypeError("initial must be a Qobj")
if not isinstance(self.target, Qobj):
raise TypeError("target must be a Qobj")
self.refresh_drift_attribs()
self.sys_dims = self.initial.dims
self.sys_shape = self.initial.shape
# Set the phase application method
self._init_phase()
self._set_memory_optimizations()
n_ts = self.num_tslots
n_ctrls = self.num_ctrls
if self.oper_dtype == Qobj:
self._initial = self.initial
self._target = self.target
self._drift_dyn_gen = self.drift_dyn_gen
self._ctrl_dyn_gen = self.ctrl_dyn_gen
elif self.oper_dtype == np.ndarray:
self._initial = self.initial.full()
self._target = self.target.full()
if self.time_depend_drift:
self._drift_dyn_gen = [d.full() for d in self.drift_dyn_gen]
else:
self._drift_dyn_gen = self.drift_dyn_gen.full()
if self.time_depend_ctrl_dyn_gen:
self._ctrl_dyn_gen = np.empty([n_ts, n_ctrls], dtype=object)
for k in range(n_ts):
for j in range(n_ctrls):
self._ctrl_dyn_gen[k, j] = \
self.ctrl_dyn_gen[k, j].full()
else:
self._ctrl_dyn_gen = [ctrl.full()
for ctrl in self.ctrl_dyn_gen]
elif self.oper_dtype == sp.csr_matrix:
self._initial = self.initial.data
self._target = self.target.data
if self.time_depend_drift:
self._drift_dyn_gen = [d.data for d in self.drift_dyn_gen]
else:
self._drift_dyn_gen = self.drift_dyn_gen.data
if self.time_depend_ctrl_dyn_gen:
self._ctrl_dyn_gen = np.empty([n_ts, n_ctrls], dtype=object)
for k in range(n_ts):
for j in range(n_ctrls):
self._ctrl_dyn_gen[k, j] = \
self.ctrl_dyn_gen[k, j].data
else:
self._ctrl_dyn_gen = [ctrl.data for ctrl in self.ctrl_dyn_gen]
else:
logger.warn("Unknown option '{}' for oper_dtype. "
"Assuming that internal drift, ctrls, initial and target "
"have been set correctly".format(self.oper_dtype))
if self.cache_phased_dyn_gen:
if self.time_depend_ctrl_dyn_gen:
self._phased_ctrl_dyn_gen = np.empty([n_ts, n_ctrls],
dtype=object)
for k in range(n_ts):
for j in range(n_ctrls):
self._phased_ctrl_dyn_gen[k, j] = self._apply_phase(
self._ctrl_dyn_gen[k, j])
else:
self._phased_ctrl_dyn_gen = [self._apply_phase(ctrl)
for ctrl in self._ctrl_dyn_gen]
self._dyn_gen = [object for x in range(self.num_tslots)]
if self.cache_phased_dyn_gen:
self._phased_dyn_gen = [object for x in range(self.num_tslots)]
self._prop = [object for x in range(self.num_tslots)]
if self.prop_computer.grad_exact and self.cache_prop_grad:
self._prop_grad = np.empty([self.num_tslots, self.num_ctrls],
dtype=object)
# Time evolution operator (forward propagation)
self._fwd_evo = [object for x in range(self.num_tslots+1)]
self._fwd_evo[0] = self._initial
if self.fid_computer.uses_onwd_evo:
# Time evolution operator (onward propagation)
self._onwd_evo = [object for x in range(self.num_tslots)]
if self.fid_computer.uses_onto_evo:
# Onward propagation overlap with inverse target
self._onto_evo = [object for x in range(self.num_tslots+1)]
self._onto_evo[self.num_tslots] = self._get_onto_evo_target()
if isinstance(self.prop_computer, propcomp.PropCompDiag):
self._create_decomp_lists()
if (self.log_level <= logging.DEBUG
and isinstance(self, DynamicsUnitary)):
self.unitarity_check_level = 1
if self.dump_to_file:
if self.dump is None:
self.dumping = 'SUMMARY'
self.dump.write_to_file = True
self.dump.create_dump_dir()
logger.info("Dynamics dump will be written to:\n{}".format(
self.dump.dump_dir))
self._evo_initialized = True
@property
def dyn_gen_phase(self):
"""
Some op that is applied to the dyn_gen before expontiating to
get the propagator.
See `phase_application` for how this is applied
"""
# Note that if this returns None then _apply_phase will never be
# called
return self._dyn_gen_phase
@dyn_gen_phase.setter
def dyn_gen_phase(self, value):
self._dyn_gen_phase = value
@property
def phase_application(self):
"""
phase_application : scalar(string), default='preop'
Determines how the phase is applied to the dynamics generators
- 'preop' : P = expm(phase*dyn_gen)
- 'postop' : P = expm(dyn_gen*phase)
- 'custom' : Customised phase application
The 'custom' option assumes that the _apply_phase method has been
set to a custom function
"""
return self._phase_application
@phase_application.setter
def phase_application(self, value):
self._set_phase_application(value)
def _set_phase_application(self, value):
self._config_phase_application(value)
self._phase_application = value
def _config_phase_application(self, ph_app=None):
"""
Set the appropriate function for the phase application
"""
err_msg = ("Invalid value '{}' for phase application. Must be either "
"'preop', 'postop' or 'custom'".format(ph_app))
if ph_app is None:
ph_app = self._phase_application
try:
ph_app = ph_app.lower()
except:
raise ValueError(err_msg)
if ph_app == 'preop':
self._apply_phase = self._apply_phase_preop
elif ph_app == 'postop':
self._apply_phase = self._apply_phase_postop
elif ph_app == 'custom':
# Do nothing, assume _apply_phase set elsewhere
pass
else:
raise ValueError(err_msg)
def _init_phase(self):
if self.dyn_gen_phase is not None:
self._config_phase_application()
else:
self.cache_phased_dyn_gen = False
def _apply_phase(self, dg):
"""
This default method does nothing.
It will be set to another method automatically if `phase_application`
is 'preop' or 'postop'. It should be overridden repointed if
`phase_application` is 'custom'
It will never be called if `dyn_gen_phase` is None
"""
return dg
def _apply_phase_preop(self, dg):
"""
Apply phasing operator to dynamics generator.
This called during the propagator calculation.
In this case it will be applied as phase*dg
"""
if hasattr(self.dyn_gen_phase, 'dot'):
phased_dg = self._dyn_gen_phase.dot(dg)
else:
phased_dg = self._dyn_gen_phase*dg
return phased_dg
def _apply_phase_postop(self, dg):
"""
Apply phasing operator to dynamics generator.
This called during the propagator calculation.
In this case it will be applied as dg*phase
"""
if hasattr(self.dyn_gen_phase, 'dot'):
phased_dg = dg.dot(self._dyn_gen_phase)
else:
phased_dg = dg*self._dyn_gen_phase
return phased_dg
def _create_decomp_lists(self):
"""
Create lists that will hold the eigen decomposition
used in calculating propagators and gradients
Note: used with PropCompDiag propagator calcs
"""
n_ts = self.num_tslots
self._decomp_curr = [False for x in range(n_ts)]
self._prop_eigen = [object for x in range(n_ts)]
self._dyn_gen_eigenvectors = [object for x in range(n_ts)]
if self.cache_dyn_gen_eigenvectors_adj:
self._dyn_gen_eigenvectors_adj = [object for x in range(n_ts)]
self._dyn_gen_factormatrix = [object for x in range(n_ts)]
[docs] def initialize_controls(self, amps, init_tslots=True):
"""
Set the initial control amplitudes and time slices
Note this must be called after the configuration is complete
before any dynamics can be calculated
"""
if not isinstance(self.prop_computer, propcomp.PropagatorComputer):
raise errors.UsageError(
"No prop_computer (propagator computer) "
"set. A default should be assigned by the Dynamics subclass")
if not isinstance(self.tslot_computer, tslotcomp.TimeslotComputer):
raise errors.UsageError(
"No tslot_computer (Timeslot computer)"
" set. A default should be assigned by the Dynamics class")
if not isinstance(self.fid_computer, fidcomp.FidelityComputer):
raise errors.UsageError(
"No fid_computer (Fidelity computer)"
" set. A default should be assigned by the Dynamics subclass")
self.ctrl_amps = None
if not self._timeslots_initialized:
init_tslots = True
if init_tslots:
self.init_timeslots()
self._init_evo()
self.tslot_computer.init_comp()
self.fid_computer.init_comp()
self._ctrls_initialized = True
self.update_ctrl_amps(amps)
def check_ctrls_initialized(self):
if not self._ctrls_initialized:
raise errors.UsageError(
"Controls not initialised. "
"Ensure Dynamics.initialize_controls has been "
"executed with the initial control amplitudes.")
def get_amp_times(self):
return self.time[:self.num_tslots]
[docs] def save_amps(self, file_name=None, times=None, amps=None, verbose=False):
"""
Save a file with the current control amplitudes in each timeslot
The first column in the file will be the start time of the slot
Parameters
----------
file_name : string
Name of the file
If None given the def_amps_fname attribuite will be used
times : List type (or string)
List / array of the start times for each slot
If None given this will be retrieved through get_amp_times()
If 'exclude' then times will not be saved in the file, just
the amplitudes
amps : Array[num_tslots, num_ctrls]
Amplitudes to be saved
If None given the ctrl_amps attribute will be used
verbose : Boolean
If True then an info message will be logged
"""
self.check_ctrls_initialized()
inctimes = True
if file_name is None:
file_name = self.def_amps_fname
if amps is None:
amps = self.ctrl_amps
if times is None:
times = self.get_amp_times()
else:
if _is_string(times):
if times.lower() == 'exclude':
inctimes = False
else:
logger.warn("Unknown option for times '{}' "
"when saving amplitudes".format(times))
times = self.get_amp_times()
try:
if inctimes:
shp = amps.shape
data = np.empty([shp[0], shp[1] + 1], dtype=float)
data[:, 0] = times
data[:, 1:] = amps
else:
data = amps
np.savetxt(file_name, data, delimiter='\t', fmt='%14.6g')
if verbose:
logger.info("Amplitudes saved to file: " + file_name)
except Exception as e:
logger.error("Failed to save amplitudes due to underling "
"error: {}".format(e))
[docs] def update_ctrl_amps(self, new_amps):
"""
Determine if any amplitudes have changed. If so, then mark the
timeslots as needing recalculation
The actual work is completed by the compare_amps method of the
timeslot computer
"""
if self.log_level <= logging.DEBUG_INTENSE:
logger.log(logging.DEBUG_INTENSE, "Updating amplitudes...\n"
"Current control amplitudes:\n" + str(self.ctrl_amps) +
"\n(potenially) new amplitudes:\n" + str(new_amps))
self.tslot_computer.compare_amps(new_amps)
[docs] def flag_system_changed(self):
"""
Flag evolution, fidelity and gradients as needing recalculation
"""
self.evo_current = False
self.fid_computer.flag_system_changed()
[docs] def get_drift_dim(self):
"""
Returns the size of the matrix that defines the drift dynamics
that is assuming the drift is NxN, then this returns N
"""
if self.dyn_shape is None:
self.refresh_drift_attribs()
return self.dyn_shape[0]
[docs] def refresh_drift_attribs(self):
"""Reset the dyn_shape, dyn_dims and time_depend_drift attribs"""
if isinstance(self.drift_dyn_gen, (list, tuple)):
d0 = self.drift_dyn_gen[0]
self.time_depend_drift = True
else:
d0 = self.drift_dyn_gen
self.time_depend_drift = False
if not isinstance(d0, Qobj):
raise TypeError("Unable to determine drift attributes, "
"because drift_dyn_gen is not Qobj (nor list of)")
self.dyn_shape = d0.shape
self.dyn_dims = d0.dims
[docs] def get_num_ctrls(self):
"""
calculate the of controls from the length of the control list
sets the num_ctrls property, which can be used alternatively
subsequently
"""
_func_deprecation("'get_num_ctrls' has been replaced by "
"'num_ctrls' property")
return self.num_ctrls
def _get_num_ctrls(self):
if not self._ctrl_dyn_gen_checked:
self.ctrl_dyn_gen = _check_ctrls_container(self.ctrl_dyn_gen)
self._ctrl_dyn_gen_checked = True
if isinstance(self.ctrl_dyn_gen, np.ndarray):
self._num_ctrls = self.ctrl_dyn_gen.shape[1]
self.time_depend_ctrl_dyn_gen = True
else:
self._num_ctrls = len(self.ctrl_dyn_gen)
return self._num_ctrls
@property
def num_ctrls(self):
"""
calculate the of controls from the length of the control list
sets the num_ctrls property, which can be used alternatively
subsequently
"""
if self._num_ctrls is None:
self._num_ctrls = self._get_num_ctrls()
return self._num_ctrls
@property
def onto_evo_target(self):
if self._onto_evo_target is None:
self._get_onto_evo_target()
if self._onto_evo_target_qobj is None:
if isinstance(self._onto_evo_target, Qobj):
self._onto_evo_target_qobj = self._onto_evo_target
else:
rev_dims = [self.sys_dims[1], self.sys_dims[0]]
self._onto_evo_target_qobj = Qobj(self._onto_evo_target,
dims=rev_dims)
return self._onto_evo_target_qobj
def get_owd_evo_target(self):
_func_deprecation("'get_owd_evo_target' has been replaced by "
"'onto_evo_target' property")
return self.onto_evo_target
def _get_onto_evo_target(self):
"""
Get the inverse of the target.
Used for calculating the 'onto target' evolution
This is actually only relevant for unitary dynamics where
the target.dag() is what is required
However, for completeness, in general the inverse of the target
operator is is required
For state-to-state, the bra corresponding to the is required ket
"""
if self.target.shape[0] == self.target.shape[1]:
#Target is operator
targ = la.inv(self.target.full())
if self.oper_dtype == Qobj:
self._onto_evo_target = Qobj(targ)
elif self.oper_dtype == np.ndarray:
self._onto_evo_target = targ
elif self.oper_dtype == sp.csr_matrix:
self._onto_evo_target = sp.csr_matrix(targ)
else:
targ_cls = self._target.__class__
self._onto_evo_target = targ_cls(targ)
else:
if self.oper_dtype == Qobj:
self._onto_evo_target = self.target.dag()
elif self.oper_dtype == np.ndarray:
self._onto_evo_target = self.target.dag().full()
elif self.oper_dtype == sp.csr_matrix:
self._onto_evo_target = self.target.dag().data
else:
targ_cls = self._target.__class__
self._onto_evo_target = targ_cls(self.target.dag().full())
return self._onto_evo_target
[docs] def combine_dyn_gen(self, k):
"""
Computes the dynamics generator for a given timeslot
The is the combined Hamiltion for unitary systems
"""
_func_deprecation("'combine_dyn_gen' has been replaced by "
"'_combine_dyn_gen'")
self._combine_dyn_gen(k)
return self._dyn_gen(k)
def _combine_dyn_gen(self, k):
"""
Computes the dynamics generator for a given timeslot
The is the combined Hamiltion for unitary systems
Also applies the phase (if any required by the propagation)
"""
if self.time_depend_drift:
dg = self._drift_dyn_gen[k]
else:
dg = self._drift_dyn_gen
for j in range(self._num_ctrls):
if self.time_depend_ctrl_dyn_gen:
dg = dg + self.ctrl_amps[k, j]*self._ctrl_dyn_gen[k, j]
else:
dg = dg + self.ctrl_amps[k, j]*self._ctrl_dyn_gen[j]
self._dyn_gen[k] = dg
if self.cache_phased_dyn_gen:
self._phased_dyn_gen[k] = self._apply_phase(dg)
[docs] def get_dyn_gen(self, k):
"""
Get the combined dynamics generator for the timeslot
Not implemented in the base class. Choose a subclass
"""
_func_deprecation("'get_dyn_gen' has been replaced by "
"'_get_phased_dyn_gen'")
return self._get_phased_dyn_gen(k)
def _get_phased_dyn_gen(self, k):
if self.dyn_gen_phase is None:
return self._dyn_gen[k]
else:
if self._phased_dyn_gen is None:
return self._apply_phase(self._dyn_gen[k])
else:
return self._phased_dyn_gen[k]
[docs] def get_ctrl_dyn_gen(self, j):
"""
Get the dynamics generator for the control
Not implemented in the base class. Choose a subclass
"""
_func_deprecation("'get_ctrl_dyn_gen' has been replaced by "
"'_get_phased_ctrl_dyn_gen'")
return self._get_phased_ctrl_dyn_gen(0, j)
def _get_phased_ctrl_dyn_gen(self, k, j):
if self._phased_ctrl_dyn_gen is not None:
if self.time_depend_ctrl_dyn_gen:
return self._phased_ctrl_dyn_gen[k, j]
else:
return self._phased_ctrl_dyn_gen[j]
else:
if self.time_depend_ctrl_dyn_gen:
if self.dyn_gen_phase is None:
return self._ctrl_dyn_gen[k, j]
else:
return self._apply_phase(self._ctrl_dyn_gen[k, j])
else:
if self.dyn_gen_phase is None:
return self._ctrl_dyn_gen[j]
else:
return self._apply_phase(self._ctrl_dyn_gen[j])
@property
def dyn_gen(self):
"""
List of combined dynamics generators (Qobj) for each timeslot
"""
if self._dyn_gen is not None:
if self._dyn_gen_qobj is None:
if self.oper_dtype == Qobj:
self._dyn_gen_qobj = self._dyn_gen
else:
self._dyn_gen_qobj = [Qobj(dg, dims=self.dyn_dims)
for dg in self._dyn_gen]
return self._dyn_gen_qobj
@property
def prop(self):
"""
List of propagators (Qobj) for each timeslot
"""
if self._prop is not None:
if self._prop_qobj is None:
if self.oper_dtype == Qobj:
self._prop_qobj = self._prop
else:
self._prop_qobj = [Qobj(dg, dims=self.dyn_dims)
for dg in self._prop]
return self._prop_qobj
@property
def prop_grad(self):
"""
Array of propagator gradients (Qobj) for each timeslot, control
"""
if self._prop_grad is not None:
if self._prop_grad_qobj is None:
if self.oper_dtype == Qobj:
self._prop_grad_qobj = self._prop_grad
else:
self._prop_grad_qobj = np.empty(
[self.num_tslots, self.num_ctrls],
dtype=object)
for k in range(self.num_tslots):
for j in range(self.num_ctrls):
self._prop_grad_qobj[k, j] = Qobj(
self._prop_grad[k, j],
dims=self.dyn_dims)
return self._prop_grad_qobj
def _get_prop_grad(self, k, j):
if self.cache_prop_grad:
prop_grad = self._prop_grad[k, j]
else:
prop_grad = self.prop_computer._compute_prop_grad(k, j,
compute_prop = False)
return prop_grad
@property
def evo_init2t(self):
_attrib_deprecation(
"'evo_init2t' has been replaced by '_fwd_evo'")
return self._fwd_evo
@property
def fwd_evo(self):
"""
List of evolution operators (Qobj) from the initial to the given
timeslot
"""
if self._fwd_evo is not None:
if self._fwd_evo_qobj is None:
if self.oper_dtype == Qobj:
self._fwd_evo_qobj = self._fwd_evo
else:
self._fwd_evo_qobj = [self.initial]
for k in range(1, self.num_tslots+1):
self._fwd_evo_qobj.append(Qobj(self._fwd_evo[k],
dims=self.sys_dims))
return self._fwd_evo_qobj
def _get_full_evo(self):
return self._fwd_evo[self._num_tslots]
@property
def full_evo(self):
"""Full evolution - time evolution at final time slot"""
return self.fwd_evo[self.num_tslots]
@property
def evo_t2end(self):
_attrib_deprecation(
"'evo_t2end' has been replaced by '_onwd_evo'")
return self._onwd_evo
@property
def onwd_evo(self):
"""
List of evolution operators (Qobj) from the initial to the given
timeslot
"""
if self._onwd_evo is not None:
if self._onwd_evo_qobj is None:
if self.oper_dtype == Qobj:
self._onwd_evo_qobj = self._fwd_evo
else:
self._onwd_evo_qobj = [Qobj(dg, dims=self.sys_dims)
for dg in self._onwd_evo]
return self._onwd_evo_qobj
@property
def evo_t2targ(self):
_attrib_deprecation(
"'evo_t2targ' has been replaced by '_onto_evo'")
return self._onto_evo
@property
def onto_evo(self):
"""
List of evolution operators (Qobj) from the initial to the given
timeslot
"""
if self._onto_evo is not None:
if self._onto_evo_qobj is None:
if self.oper_dtype == Qobj:
self._onto_evo_qobj = self._onto_evo
else:
self._onto_evo_qobj = []
for k in range(0, self.num_tslots):
self._onto_evo_qobj.append(Qobj(self._onto_evo[k],
dims=self.sys_dims))
self._onto_evo_qobj.append(self.onto_evo_target)
return self._onto_evo_qobj
[docs] def compute_evolution(self):
"""
Recalculate the time evolution operators
Dynamics generators (e.g. Hamiltonian) and
prop (propagators) are calculated as necessary
Actual work is completed by the recompute_evolution method
of the timeslot computer
"""
# Check if values are already current, otherwise calculate all values
if not self.evo_current:
if self.log_level <= logging.DEBUG_VERBOSE:
logger.log(logging.DEBUG_VERBOSE, "Computing evolution")
self.tslot_computer.recompute_evolution()
self.evo_current = True
return True
else:
return False
def _ensure_decomp_curr(self, k):
"""
Checks to see if the diagonalisation has been completed since
the last update of the dynamics generators
(after the amplitude update)
If not then the diagonlisation is completed
"""
if self._decomp_curr is None:
raise errors.UsageError("Decomp lists have not been created")
if not self._decomp_curr[k]:
self._spectral_decomp(k)
def _spectral_decomp(self, k):
"""
Calculate the diagonalization of the dynamics generator
generating lists of eigenvectors, propagators in the diagonalised
basis, and the 'factormatrix' used in calculating the propagator
gradient
Not implemented in this base class, because the method is specific
to the matrix type
"""
raise errors.UsageError("Decomposition cannot be completed by "
"this class. Try a(nother) subclass")
def _is_unitary(self, A):
"""
Checks whether operator A is unitary
A can be either Qobj or ndarray
"""
if isinstance(A, Qobj):
unitary = np.allclose(np.eye(A.shape[0]), A*A.dag().full(),
atol=self.unitarity_tol)
else:
unitary = np.allclose(np.eye(len(A)), A.dot(A.T.conj()),
atol=self.unitarity_tol)
return unitary
def _calc_unitary_err(self, A):
if isinstance(A, Qobj):
err = np.sum(abs(np.eye(A.shape[0]) - A*A.dag().full()))
else:
err = np.sum(abs(np.eye(len(A)) - A.dot(A.T.conj())))
return err
[docs] def unitarity_check(self):
"""
Checks whether all propagators are unitary
"""
for k in range(self.num_tslots):
if not self._is_unitary(self._prop[k]):
logger.warning(
"Progator of timeslot {} is not unitary".format(k))
[docs]class DynamicsGenMat(Dynamics):
"""
This sub class can be used for any system where no additional
operator is applied to the dynamics generator before calculating
the propagator, e.g. classical dynamics, Lindbladian
"""
def reset(self):
Dynamics.reset(self)
self.id_text = 'GEN_MAT'
self.apply_params()
[docs]class DynamicsUnitary(Dynamics):
"""
This is the subclass to use for systems with dynamics described by
unitary matrices. E.g. closed systems with Hermitian Hamiltonians
Note a matrix diagonalisation is used to compute the exponent
The eigen decomposition is also used to calculate the propagator gradient.
The method is taken from DYNAMO (see file header)
Attributes
----------
drift_ham : Qobj
This is the drift Hamiltonian for unitary dynamics
It is mapped to drift_dyn_gen during initialize_controls
ctrl_ham : List of Qobj
These are the control Hamiltonians for unitary dynamics
It is mapped to ctrl_dyn_gen during initialize_controls
H : List of Qobj
The combined drift and control Hamiltonians for each timeslot
These are the dynamics generators for unitary dynamics.
It is mapped to dyn_gen during initialize_controls
"""
def reset(self):
Dynamics.reset(self)
self.id_text = 'UNIT'
self.drift_ham = None
self.ctrl_ham = None
self.H = None
self._dyn_gen_phase = -1j
self._phase_application = 'preop'
self.apply_params()
def _create_computers(self):
"""
Create the default timeslot, fidelity and propagator computers
"""
# The time slot computer. By default it is set to _UpdateAll
# can be set to _DynUpdate in the configuration
# (see class file for details)
if self.config.tslot_type == 'DYNAMIC':
self.tslot_computer = tslotcomp.TSlotCompDynUpdate(self)
else:
self.tslot_computer = tslotcomp.TSlotCompUpdateAll(self)
# set the default fidelity computer
self.fid_computer = fidcomp.FidCompUnitary(self)
# set the default propagator computer
self.prop_computer = propcomp.PropCompDiag(self)
[docs] def initialize_controls(self, amplitudes, init_tslots=True):
# Either the _dyn_gen or _ham names can be used
# This assumes that one or other has been set in the configuration
self._map_dyn_gen_to_ham()
Dynamics.initialize_controls(self, amplitudes, init_tslots=init_tslots)
#self.H = self._dyn_gen
def _map_dyn_gen_to_ham(self):
if self.drift_dyn_gen is None:
self.drift_dyn_gen = self.drift_ham
else:
self.drift_ham = self.drift_dyn_gen
if self.ctrl_dyn_gen is None:
self.ctrl_dyn_gen = self.ctrl_ham
else:
self.ctrl_ham = self.ctrl_dyn_gen
self._dyn_gen_mapped = True
@property
def num_ctrls(self):
if not self._dyn_gen_mapped:
self._map_dyn_gen_to_ham()
if self._num_ctrls is None:
self._num_ctrls = self._get_num_ctrls()
return self._num_ctrls
def _get_onto_evo_target(self):
"""
Get the adjoint of the target.
Used for calculating the 'backward' evolution
"""
if self.oper_dtype == Qobj:
self._onto_evo_target = self.target.dag()
else:
self._onto_evo_target = self._target.T.conj()
return self._onto_evo_target
def _spectral_decomp(self, k):
"""
Calculates the diagonalization of the dynamics generator
generating lists of eigenvectors, propagators in the diagonalised
basis, and the 'factormatrix' used in calculating the propagator
gradient
"""
if self.oper_dtype == Qobj:
H = self._dyn_gen[k]
# Returns eigenvalues as array (row)
# and eigenvectors as rows of an array
eig_val, eig_vec = sp_eigs(H.data, H.isherm,
sparse=self.sparse_eigen_decomp)
eig_vec = eig_vec.T
elif self.oper_dtype == np.ndarray:
H = self._dyn_gen[k]
# returns row vector of eigenvals, columns with the eigenvecs
eig_val, eig_vec = np.linalg.eigh(H)
else:
if sparse:
H = self._dyn_gen[k].toarray()
else:
H = self._dyn_gen[k]
# returns row vector of eigenvals, columns with the eigenvecs
eig_val, eig_vec = la.eigh(H)
# assuming H is an nxn matrix, find n
n = self.get_drift_dim()
# Calculate the propagator in the diagonalised basis
eig_val_tau = -1j*eig_val*self.tau[k]
prop_eig = np.exp(eig_val_tau)
# Generate the factor matrix through the differences
# between each of the eigenvectors and the exponentiations
# create nxn matrix where each eigen val is repeated n times
# down the columns
o = np.ones([n, n])
eig_val_cols = eig_val_tau*o
# calculate all the differences by subtracting it from its transpose
eig_val_diffs = eig_val_cols - eig_val_cols.T
# repeat for the propagator
prop_eig_cols = prop_eig*o
prop_eig_diffs = prop_eig_cols - prop_eig_cols.T
# the factor matrix is the elementwise quotient of the
# differeneces between the exponentiated eigen vals and the
# differences between the eigen vals
# need to avoid division by zero that would arise due to denegerate
# eigenvalues and the diagonals
degen_mask = np.abs(eig_val_diffs) < self.fact_mat_round_prec
eig_val_diffs[degen_mask] = 1
factors = prop_eig_diffs / eig_val_diffs
# for degenerate eigenvalues the factor is just the exponent
factors[degen_mask] = prop_eig_cols[degen_mask]
# Store eigenvectors, propagator and factor matric
# for use in propagator computations
self._decomp_curr[k] = True
if isinstance(factors, np.ndarray):
self._dyn_gen_factormatrix[k] = factors
else:
self._dyn_gen_factormatrix[k] = np.array(factors)
if self.oper_dtype == Qobj:
self._prop_eigen[k] = Qobj(np.diagflat(prop_eig),
dims=self.dyn_dims)
self._dyn_gen_eigenvectors[k] = Qobj(eig_vec,
dims=self.dyn_dims)
# The _dyn_gen_eigenvectors_adj list is not used in
# memory optimised modes
if self._dyn_gen_eigenvectors_adj is not None:
self._dyn_gen_eigenvectors_adj[k] = \
self._dyn_gen_eigenvectors[k].dag()
else:
self._prop_eigen[k] = np.diagflat(prop_eig)
self._dyn_gen_eigenvectors[k] = eig_vec
# The _dyn_gen_eigenvectors_adj list is not used in
# memory optimised modes
if self._dyn_gen_eigenvectors_adj is not None:
self._dyn_gen_eigenvectors_adj[k] = \
self._dyn_gen_eigenvectors[k].conj().T
def _get_dyn_gen_eigenvectors_adj(self, k):
# The _dyn_gen_eigenvectors_adj list is not used in
# memory optimised modes
if self._dyn_gen_eigenvectors_adj is not None:
return self._dyn_gen_eigenvectors_adj[k]
else:
if self.oper_dtype == Qobj:
return self._dyn_gen_eigenvectors[k].dag()
else:
return self._dyn_gen_eigenvectors[k].conj().T
[docs] def check_unitarity(self):
"""
Checks whether all propagators are unitary
For propagators found not to be unitary, the potential underlying
causes are investigated.
"""
for k in range(self.num_tslots):
prop_unit = self._is_unitary(self._prop[k])
if not prop_unit:
logger.warning(
"Progator of timeslot {} is not unitary".format(k))
if not prop_unit or self.unitarity_check_level > 1:
# Check Hamiltonian
H = self._dyn_gen[k]
if isinstance(H, Qobj):
herm = H.isherm
else:
diff = np.abs(H.T.conj() - H)
herm = False if np.any(diff > settings.atol) else True
eigval_unit = self._is_unitary(self._prop_eigen[k])
eigvec_unit = self._is_unitary(self._dyn_gen_eigenvectors[k])
if self._dyn_gen_eigenvectors_adj is not None:
eigvecadj_unit = self._is_unitary(
self._dyn_gen_eigenvectors_adj[k])
else:
eigvecadj_unit = None
msg = ("prop unit: {}; H herm: {}; "
"eigval unit: {}; eigvec unit: {}; "
"eigvecadj_unit: {}".format(
prop_unit, herm, eigval_unit, eigvec_unit,
eigvecadj_unit))
logger.info(msg)
[docs]class DynamicsSymplectic(Dynamics):
"""
Symplectic systems
This is the subclass to use for systems where the dynamics is described
by symplectic matrices, e.g. coupled oscillators, quantum optics
Attributes
----------
omega : array[drift_dyn_gen.shape]
matrix used in the calculation of propagators (time evolution)
with symplectic systems.
"""
def reset(self):
Dynamics.reset(self)
self.id_text = 'SYMPL'
self._omega = None
self._omega_qobj = None
self._phase_application = 'postop'
self.grad_exact = True
self.apply_params()
def _create_computers(self):
"""
Create the default timeslot, fidelity and propagator computers
"""
# The time slot computer. By default it is set to _UpdateAll
# can be set to _DynUpdate in the configuration
# (see class file for details)
if self.config.tslot_type == 'DYNAMIC':
self.tslot_computer = tslotcomp.TSlotCompDynUpdate(self)
else:
self.tslot_computer = tslotcomp.TSlotCompUpdateAll(self)
self.prop_computer = propcomp.PropCompFrechet(self)
self.fid_computer = fidcomp.FidCompTraceDiff(self)
@property
def omega(self):
if self._omega is None:
self._get_omega()
if self._omega_qobj is None:
self._omega_qobj = Qobj(self._omega, dims=self.dyn_dims)
return self._omega_qobj
def _get_omega(self):
if self._omega is None:
n = self.get_drift_dim() // 2
omg = sympl.calc_omega(n)
if self.oper_dtype == Qobj:
self._omega = Qobj(omg, dims=self.dyn_dims)
self._omega_qobj = self._omega
elif self.oper_dtype == sp.csr_matrix:
self._omega = sp.csr_matrix(omg)
else:
self._omega = omg
return self._omega
def _set_phase_application(self, value):
Dynamics._set_phase_application(self, value)
if self._evo_initialized:
phase = self._get_dyn_gen_phase()
if phase is not None:
self._dyn_gen_phase = phase
def _get_dyn_gen_phase(self):
if self._phase_application == 'postop':
phase = -self._get_omega()
elif self._phase_application == 'preop':
phase = self._get_omega()
elif self._phase_application == 'custom':
phase = None
# Assume phase set by user
else:
raise ValueError("No option for phase_application "
"'{}'".format(self._phase_application))
return phase
@property
def dyn_gen_phase(self):
"""
The phasing operator for the symplectic group generators
usually refered to as \Omega
By default this is applied as 'postop' dyn_gen*-\Omega
If phase_application is 'preop' it is applied as \Omega*dyn_gen
"""
# Cannot be calculated until the dyn_shape is set
# that is after the drift dyn gen has been set.
if self._dyn_gen_phase is None:
self._dyn_gen_phase = self._get_dyn_gen_phase()
return self._dyn_gen_phase