# Source code for qutip.control.dynamics

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# @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 numpy as np
import scipy.linalg as la
from six import string_types
# QuTiP logging
import qutip.logging 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

[docs]class Dynamics:
"""
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 any of the methods
can be used.

Attributes
----------
log_level : integer
level of messaging output from the logger.
Options are attributes of qutip.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
Note value should be set using set_log_level

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

num_tslots : integer
Number of timeslots, aka timeslices

num_ctrls : integer
Number of controls.
Note this is set when get_num_ctrls is called based on the
length of ctrl_dyn_gen

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
Drift or system dynamics generator
Matrix defining the underlying dynamics of the system

ctrl_dyn_gen : List of Qobj
Control dynamics generator: ctrl_dyn_gen ()
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

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

self.initial_ctrl_offset = 0.0
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
Array  of matrices 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.

evo_init2t : 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

evo_t2end : 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

evo_t2targ : 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

decomp_curr : List of boolean
Indicates whether the diagonalisation for the timeslot is fresh,
it is set to false when the dyn_gen for the timeslot is changed
Only used when the PropagatorComputer uses diagonalisation

dyn_gen_eigenvectors : List of array[drift_dyn_gen.shape]
Eigenvectors of the dynamics generators
Used for calculating the propagators and their gradients
Only used when the PropagatorComputer uses diagonalisation

prop_eigen : List of array[drift_dyn_gen.shape]
Propagator in diagonalised basis of the combined dynamics generator
Used for calculating the propagators and their gradients
Only used when the PropagatorComputer uses diagonalisation

dyn_gen_factormatrix : List of array[drift_dyn_gen.shape]
Matrix of scaling factors calculated duing the decomposition
Used for calculating the propagator gradients
Only used when the PropagatorComputer uses diagonalisation

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

"""
def __init__(self, optimconfig):
self.config = optimconfig
self.reset()

def reset(self):
# Main functional attributes
self.evo_time = 0
self.num_tslots = 0
self.tau = None
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.dyn_gen = None
self.prop = None
self.evo_init2t = None
self.evo_t2end = None
self.evo_t2targ = None
# Atrributes used in diagonalisation
self.decomp_curr = None
self.prop_eigen = None
self.dyn_gen_eigenvectors = 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.set_log_level(self.config.log_level)
# Internal flags
self._dyn_gen_mapped = False
self._ctrls_initialized = False

# Create the computing objects
self._create_computers()

self.clear()

[docs]    def set_log_level(self, lvl):
"""
Set the log_level attribute and set the level of the logger
that is call logger.setLevel(lvl)
"""
self.log_level = lvl
logger.setLevel(lvl)

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.amp_update_mode == '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()

[docs]    def init_time_slots(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.tau is None:
self.tau = np.ones(self.num_tslots, dtype='f') * \
self.evo_time/self.num_tslots
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]

def _init_lists(self):
"""
Create the container lists / arrays for the:
dynamics generations, propagators, and evolutions etc
Set the time slices and cumulative time
"""

# Create containers for control Hamiltonian etc
shp = self.drift_dyn_gen.shape
# set H to be just empty float arrays with the shape of H
self.dyn_gen = [np.empty(shp, dtype=complex)
for x in range(self.num_tslots)]
# the exponetiation of H. Just empty float arrays with the shape of H
self.prop = [np.empty(shp, dtype=complex)
for x in range(self.num_tslots)]
dtype=np.ndarray)
# Time evolution operator (forward propagation)
self.evo_init2t = [np.empty(shp, dtype=complex)
for x in range(self.num_tslots + 1)]
self.evo_init2t[0] = self.initial
if self.fid_computer.uses_evo_t2end:
# Time evolution operator (onward propagation)
self.evo_t2end = [np.empty(shp, dtype=complex)
for x in range(self.num_tslots)]
if self.fid_computer.uses_evo_t2targ:
# Onward propagation overlap with inverse target
self.evo_t2targ = [np.empty(shp, dtype=complex)
for x in range(self.num_tslots + 1)]
self.evo_t2targ[-1] = self.get_owd_evo_target()

if isinstance(self.prop_computer, propcomp.PropCompDiag):
self._create_decomp_lists()

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
"""
shp = self.drift_dyn_gen.shape
n_ts = self.num_tslots
self.decomp_curr = [False for x in range(n_ts)]
self.prop_eigen = \
[np.empty(shp[0], dtype=complex) for x in range(n_ts)]
self.dyn_gen_eigenvectors = \
[np.empty(shp, dtype=complex) for x in range(n_ts)]
self.dyn_gen_factormatrix = \
[np.empty(shp, dtype=complex) for x in range(n_ts)]

def _check_test_out_files(self):
cfg = self.config
if cfg.any_test_files():
if not cfg.check_create_test_out_dir():
cfg.reset_test_out_files()
else:
if self.stats is None:
logger.warn("Cannot output test files when stats"
" attribute is not set.")
self.config.test_out_amps = False
self.config.test_out_prop = False
self.config.test_out_evo = False

[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
"""
self._check_test_out_files()

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.FideliyComputer):
raise errors.UsageError(
"No fid_computer (Fidelity computer)"
" set. A default should be assigned by the Dynamics subclass")

self.ctrl_amps = None
# Note this call is made just to initialise the num_ctrls attrib
self.get_num_ctrls()

if init_tslots:
self.init_time_slots()
self._init_lists()
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 isinstance(times, string_types):
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))

if not self.tslot_computer.compare_amps(new_amps):
if self.config.test_out_amps:
fname = "amps_{}_{}_{}_call{}{}".format(
self.id_text,
self.prop_computer.id_text,
self.fid_computer.id_text,
self.config.test_out_f_ext)

fpath = os.path.join(self.config.test_out_dir, fname)
self.save_amps(fpath, verbose=True)

[docs]    def flag_system_changed(self):
"""
Flag eveolution, 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 not isinstance(self.drift_dyn_gen, np.ndarray):
raise TypeError("Cannot get drift dimension, "
"as drift not set (correctly).")
return self.drift_dyn_gen.shape[0]

[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
"""
self.num_ctrls = len(self.ctrl_dyn_gen)
return self.num_ctrls

[docs]    def get_owd_evo_target(self):
"""
Get the inverse of the target.
Used for calculating the 'backward' evolution
"""
return la.inv(self.target)

[docs]    def combine_dyn_gen(self, k):
"""
Computes the dynamics generator for a given timeslot
The is the combined Hamiltion for unitary systems
"""
dg = np.asarray(self.drift_dyn_gen)
for j in range(self.get_num_ctrls()):
dg = dg + self.ctrl_amps[k, j]*np.asarray(self.ctrl_dyn_gen[j])
return 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
"""
raise errors.UsageError("Not implemented in the baseclass."
" Choose a subclass")

[docs]    def get_ctrl_dyn_gen(self, j):
"""
Get the dynamics generator for the control
Not implemented in the base class. Choose a subclass
"""
raise errors.UsageError("Not implemented in the baseclass."
" Choose a subclass")

[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

[docs]    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)

[docs]    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
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")

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, Limbladian
"""
def reset(self):
Dynamics.reset(self)
self.id_text = 'GEN_MAT'

def get_dyn_gen(self, k):
"""
Get the combined dynamics generator for the timeslot
This base class method simply returns dyn_gen[k]
other subclass methods will include some factor
"""
return self.dyn_gen[k]

def get_ctrl_dyn_gen(self, j):
"""
Get the dynamics generator for the control
This base class method simply returns ctrl_dyn_gen[j]
other subclass methods will include some factor
"""
return self.ctrl_dyn_gen[j]

[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

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.amp_update_mode == '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)

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

[docs]    def get_dyn_gen(self, k):
"""
Get the combined dynamics generator for the timeslot
including the -i factor
"""
return -1j*self.dyn_gen[k]

[docs]    def get_ctrl_dyn_gen(self, j):
"""
Get the dynamics generator for the control
including the -i factor
"""
return -1j*self.ctrl_dyn_gen[j]

def get_num_ctrls(self):
if not self._dyn_gen_mapped:
self._map_dyn_gen_to_ham()
return Dynamics.get_num_ctrls(self)

def get_owd_evo_target(self):
return self.target.conj().T

[docs]    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
"""
H = self.H[k]
# assuming H is an nxn matrix, find n
n = H.shape[0]
# returns row vector of eigen values,
# columns with the eigenvectors
eig_val, eig_vec = np.linalg.eig(H)

# 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
factors = prop_eig_diffs / eig_val_diffs
# for degenerate eigenvalues the factor is just the exponent

# Store eigenvals and eigenvectors for use by other functions, e.g.
self.decomp_curr[k] = True
self.prop_eigen[k] = prop_eig
self.dyn_gen_eigenvectors[k] = eig_vec
self.dyn_gen_factormatrix[k] = factors

[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

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.amp_update_mode == '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 get_omega(self):
if self.omega is None:
n = self.drift_dyn_gen.shape[0] // 2
self.omega = sympl.calc_omega(n)

return self.omega

[docs]    def get_dyn_gen(self, k):
"""
Get the combined dynamics generator for the timeslot
multiplied by omega
"""
o = self.get_omega()
return self.dyn_gen[k].dot(o)

[docs]    def get_ctrl_dyn_gen(self, j):
"""
Get the dynamics generator for the control
multiplied by omega
"""
o = self.get_omega()
return self.ctrl_dyn_gen[j].dot(o)