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import numpy as np
import scipy.sparse as sp
from qutip.cy.stochastic import (SSESolver, SMESolver, PcSSESolver, PcSMESolver,
PmSMESolver, GenericSSolver, Solvers)
from qutip.qobj import Qobj, isket, isoper, issuper
from qutip.states import ket2dm
from qutip.solver import Result
from qutip.qobjevo import QobjEvo
from qutip.superoperator import (spre, spost, mat2vec, vec2mat,
liouvillian, lindblad_dissipator)
from qutip.solver import Options, _solver_safety_check
from qutip.parallel import serial_map
from qutip.ui.progressbar import TextProgressBar
from qutip.pdpsolve import main_ssepdpsolve, main_smepdpsolve
__all__ = ['ssesolve', 'photocurrent_sesolve', 'smepdpsolve',
'smesolve', 'photocurrent_mesolve', 'ssepdpsolve',
'stochastic_solvers', 'general_stochastic']
def stochastic_solvers():
"""Available solvers for ssesolve and smesolve
euler-maruyama:
A simple generalization of the Euler method for ordinary
differential equations to stochastic differential equations.
Only solver which could take non-commuting sc_ops. *not tested*
-Order 0.5
-Code: 'euler-maruyama', 'euler', 0.5
milstein, Order 1.0 strong Taylor scheme:
Better approximate numerical solution to stochastic
differential equations.
-Order strong 1.0
-Code: 'milstein', 1.0
Numerical Solution of Stochastic Differential Equations
Chapter 10.3 Eq. (3.1), By Peter E. Kloeden, Eckhard Platen
milstein-imp, Order 1.0 implicit strong Taylor scheme:
Implicit milstein scheme for the numerical simulation of stiff
stochastic differential equations.
-Order strong 1.0
-Code: 'milstein-imp'
Numerical Solution of Stochastic Differential Equations
Chapter 12.2 Eq. (2.9), By Peter E. Kloeden, Eckhard Platen
predictor-corrector:
Generalization of the trapezoidal method to stochastic
differential equations. More stable than explicit methods.
-Order strong 0.5, weak 1.0
Only the stochastic part is corrected.
(alpha = 0, eta = 1/2)
-Code: 'pred-corr', 'predictor-corrector', 'pc-euler'
Both the deterministic and stochastic part corrected.
(alpha = 1/2, eta = 1/2)
-Code: 'pc-euler-imp', 'pc-euler-2', 'pred-corr-2'
Numerical Solution of Stochastic Differential Equations
Chapter 15.5 Eq. (5.4), By Peter E. Kloeden, Eckhard Platen
platen:
Explicit scheme, create the milstein using finite difference instead of
derivatives. Also contain some higher order terms, thus converge better
than milstein while staying strong order 1.0.
Do not require derivatives, therefore usable for
:func:`qutip.stochastic.general_stochastic`
-Order strong 1.0, weak 2.0
-Code: 'platen', 'platen1', 'explicit1'
The Theory of Open Quantum Systems
Chapter 7 Eq. (7.47), H.-P Breuer, F. Petruccione
rouchon:
Scheme keeping the positivity of the density matrix. (smesolve only)
-Order strong 1.0?
-Code: 'rouchon', 'Rouchon'
Eq. 4 of arXiv:1410.5345 with eta=1
Efficient Quantum Filtering for Quantum Feedback Control
Pierre Rouchon, Jason F. Ralph
arXiv:1410.5345 [quant-ph]
taylor1.5, Order 1.5 strong Taylor scheme:
Solver with more terms of the Ito-Taylor expansion.
Default solver for smesolve and ssesolve.
-Order strong 1.5
-Code: 'taylor1.5', 'taylor15', 1.5, None
Numerical Solution of Stochastic Differential Equations
Chapter 10.4 Eq. (4.6), By Peter E. Kloeden, Eckhard Platen
taylor1.5-imp, Order 1.5 implicit strong Taylor scheme:
implicit Taylor 1.5 (alpha = 1/2, beta = doesn't matter)
-Order strong 1.5
-Code: 'taylor1.5-imp', 'taylor15-imp'
Numerical Solution of Stochastic Differential Equations
Chapter 12.2 Eq. (2.18), By Peter E. Kloeden, Eckhard Platen
explicit1.5, Explicit Order 1.5 Strong Schemes:
Reproduce the order 1.5 strong Taylor scheme using finite difference
instead of derivatives. Slower than taylor15 but usable by
:func:`qutip.stochastic.general_stochastic`
-Order strong 1.5
-Code: 'explicit1.5', 'explicit15', 'platen15'
Numerical Solution of Stochastic Differential Equations
Chapter 11.2 Eq. (2.13), By Peter E. Kloeden, Eckhard Platen
taylor2.0, Order 2 strong Taylor scheme:
Solver with more terms of the Stratonovich expansion.
-Order strong 2.0
-Code: 'taylor2.0', 'taylor20', 2.0
Numerical Solution of Stochastic Differential Equations
Chapter 10.5 Eq. (5.2), By Peter E. Kloeden, Eckhard Platen
---All solvers, except taylor2.0, are usable in both smesolve and ssesolve
and for both heterodyne and homodyne. taylor2.0 only work for 1 stochastic
operator not dependent of time with the homodyne method.
The :func:`qutip.stochastic.general_stochastic` only accept derivatives
free solvers: ['euler', 'platen', 'explicit1.5'].
Available solver for photocurrent_sesolve and photocurrent_mesolve:
Photocurrent use ordinary differential equations between
stochastic "jump/collapse".
euler:
Euler method for ordinary differential equations between jumps.
Only 1 jumps per time interval.
Default solver
-Order 1.0
-Code: 'euler'
Quantum measurement and control
Chapter 4, Eq 4.19, 4.40, By Howard M. Wiseman, Gerard J. Milburn
predictor–corrector:
predictor–corrector method (PECE) for ordinary differential equations.
Use poisson distribution to obtain the number of jump at each timestep.
-Order 2.0
-Code: 'pred-corr'
"""
pass
[docs]class StochasticSolverOptions:
"""Class of options for stochastic solvers such as
:func:`qutip.stochastic.ssesolve`, :func:`qutip.stochastic.smesolve`, etc.
The stochastic solvers :func:`qutip.stochastic.general_stochastic`,
:func:`qutip.stochastic.ssesolve`, :func:`qutip.stochastic.smesolve`,
:func:`qutip.stochastic.photocurrent_sesolve` and
:func:`qutip.stochastic.photocurrent_mesolve`
all take the same keyword arguments as
the constructor of these class, and internally they use these arguments to
construct an instance of this class, so it is rarely needed to explicitly
create an instance of this class.
Attributes
----------
H : :class:`qutip.Qobj`, time-dependent Qobj as a list*
System Hamiltonian.
state0 : :class:`qutip.Qobj`
Initial state vector (ket) or density matrix.
times : *list* / *array*
List of times for :math:`t`. Must be uniformly spaced.
c_ops : list of :class:`qutip.Qobj`, :class:`qutip.QobjEvo` or [Qobj, coeff*]
List of deterministic collapse operators.
sc_ops : list of :class:`qutip.Qobj`, :class:`qutip.QobjEvo` or [Qobj, coeff*]
List of stochastic collapse operators. Each stochastic collapse
operator will give a deterministic and stochastic contribution
to the equation of motion according to how the d1 and d2 functions
are defined.
e_ops : list of :class:`qutip.Qobj`
Single operator or list of operators for which to evaluate
expectation values.
m_ops : list of :class:`qutip.Qobj`
List of operators representing the measurement operators. The expected
format is a nested list with one measurement operator for each
stochastic increament, for each stochastic collapse operator.
args : dict
Dictionary of parameters for time dependent systems.
tol : float
Tolerance of the solver for implicit methods.
ntraj : int
Number of trajectors.
nsubsteps : int
Number of sub steps between each time-spep given in `times`.
dW_factors : array
Array of length len(sc_ops), containing scaling factors for each
measurement operator in m_ops.
solver : string
Name of the solver method to use for solving the stochastic
equations. Valid values are:
order 1/2 algorithms: 'euler-maruyama', 'pc-euler', 'pc-euler-imp'
order 1 algorithms: 'milstein', 'platen', 'milstein-imp', 'rouchon'
order 3/2 algorithms: 'taylor1.5', 'taylor1.5-imp', 'explicit1.5'
order 2 algorithms: 'taylor2.0'
call help of :func:`qutip.stochastic.stochastic_solvers`
for a description of the solvers.
Implicit methods can adjust tolerance via the kw 'tol'
default is {'tol':1e-6}
method : string ('homodyne', 'heterodyne')
The name of the type of measurement process that give rise to the
stochastic equation to solve.
store_all_expect : bool (default False)
Whether or not to store the e_ops expect values for all paths.
store_measurement : bool (default False)
Whether or not to store the measurement results in the
:class:`qutip.solver.Result` instance returned by the solver.
noise : int, array[int, 1d], array[double, 4d]
int : seed of the noise
array[int, 1d], length = ntraj, seeds for each trajectories
array[double, 4d] (ntraj, len(times), nsubsteps, len(sc_ops)*[1|2])
vector for the noise, the len of the last dimensions is doubled for
solvers of order 1.5. The correspond to results.noise
noiseDepth : int
Number of terms kept of the truncated series used to create the
noise used by taylor2.0 solver.
normalize : bool
(default True for (photo)ssesolve, False for (photo)smesolve)
Whether or not to normalize the wave function during the evolution.
Normalizing density matrices introduce numerical errors.
options : :class:`qutip.solver.Options`
Generic solver options. Only options.average_states and
options.store_states are used.
map_func: function
A map function or managing the calls to single-trajactory solvers.
map_kwargs: dictionary
Optional keyword arguments to the map_func function function.
progress_bar : :class:`qutip.ui.BaseProgressBar`
Optional progress bar class instance.
*
time-dependent Qobj can be used for H, c_ops and sc_ops.
The format for time-dependent system hamiltonian is:
H = [Qobj0,[Qobj1,coeff1],[Qobj2,coeff2],...]
= Qobj0 + Qobj1 * coeff1(t) + Qobj2 * coeff2(t)
coeff function can be:
function: coeff(t, args) -> complex
str: "sin(1j*w*t)"
np.array[complex, 1d] of length equal to the times array
The argument args for the function coeff is the args keyword argument of
the stochastic solver.
Likewisem in str cases, the parameters ('w' in this case) are taken from
the args keywords argument.
*While mixing coeff type does not results in errors, it is not recommended.*
For the collapse operators (c_ops, sc_ops):
Each operators can only be composed of 1 Qobj.
c_ops = [c_op1, c_op2, ...]
where, c_opN = Qobj or [Qobj,coeff]
The coeff format is the same as for the Hamiltonian.
"""
def __init__(self, me, H=None, c_ops=[], sc_ops=[], state0=None,
e_ops=[], m_ops=None, store_all_expect=False,
store_measurement=False, dW_factors=None,
solver=None, method="homodyne", normalize=None,
times=None, nsubsteps=1, ntraj=1, tol=None,
generate_noise=None, noise=None,
progress_bar=None, map_func=None, map_kwargs=None,
args={}, options=None, noiseDepth=20):
if options is None:
options = Options()
if progress_bar is None:
progress_bar = TextProgressBar()
# System
# Cast to QobjEvo so the code has only one version for both the
# constant and time-dependent case.
self.me = me
if H is not None:
try:
self.H = QobjEvo(H, args=args, tlist=times)
except:
raise Exception("The hamiltonian format is not valid")
else:
self.H = H
if sc_ops:
try:
self.sc_ops = [QobjEvo(op, args=args, tlist=times)
for op in sc_ops]
except:
raise Exception("The sc_ops format is not valid.\n" +
"[ Qobj / QobjEvo / [Qobj,coeff]]")
else:
self.sc_ops = sc_ops
if c_ops:
try:
self.c_ops = [QobjEvo(op, args=args, tlist=times)
for op in c_ops]
except:
raise Exception("The c_ops format is not valid.\n" +
"[ Qobj / QobjEvo / [Qobj,coeff]]")
else:
self.c_ops = c_ops
self.state0 = state0
self.rho0 = mat2vec(state0.full()).ravel()
# Observation
self.e_ops = e_ops
self.m_ops = m_ops
self.store_measurement = store_measurement
self.store_all_expect = store_all_expect
self.store_states = options.store_states
self.dW_factors = dW_factors
# Solver
self.solver = solver
self.method = method
if normalize is None and me:
self.normalize = 0
elif normalize is None and not me:
self.normalize = 1
elif normalize:
self.normalize = 1
else:
self.normalize = 0
self.times = times
self.nsubsteps = nsubsteps
self.dt = (times[1] - times[0]) / self.nsubsteps
self.ntraj = ntraj
if tol is not None:
self.tol = tol
elif "tol" in args:
self.tol = args["tol"]
else:
self.tol = 1e-7
# Noise
if noise is not None:
if isinstance(noise, int):
# noise contain a seed
np.random.seed(noise)
noise = np.random.randint(0, 2**32, ntraj)
noise = np.array(noise)
if len(noise.shape) == 1:
if noise.shape[0] < ntraj:
raise Exception("'noise' does not have enought seeds" +
"len(noise) >= ntraj")
# numpy seed must be between 0 and 2**32-1
# 'u4': unsigned 32bit int
self.noise = noise.astype("u4")
self.noise_type = 0
elif len(noise.shape) == 4:
# taylor case not included
dw_len = (2 if method == "heterodyne" else 1)
dw_len_str = (" * 2" if method == "heterodyne" else "")
if noise.shape[0] < ntraj:
raise Exception("'noise' does not have the right shape" +
"shape[0] >= ntraj")
if noise.shape[1] < len(times):
raise Exception("'noise' does not have the right shape" +
"shape[1] >= len(times)")
if noise.shape[2] < nsubsteps:
raise Exception("'noise' does not have the right shape" +
"shape[2] >= nsubsteps")
if noise.shape[3] < len(self.sc_ops) * dw_len:
raise Exception("'noise' does not have the right shape: " +
"shape[3] >= len(self.sc_ops)" +
dw_len_str)
self.noise_type = 1
self.noise = noise
else:
self.noise = np.random.randint(0, 2**32, ntraj).astype("u4")
self.noise_type = 0
# Map
self.progress_bar = progress_bar
if self.ntraj > 1 and map_func:
self.map_func = map_func
else:
self.map_func = serial_map
self.map_kwargs = map_kwargs if map_kwargs is not None else {}
# Other
self.options = options
self.args = args
self.set_solver()
self.p = noiseDepth
def set_solver(self):
if self.solver in ['euler-maruyama', 'euler', 50, 0.5]:
self.solver_code = 50
self.solver = 'euler-maruyama'
elif self.solver in ['platen', 'platen1', 'explicit1', 100]:
self.solver_code = 100
self.solver = 'platen'
elif self.solver in ['pred-corr', 'predictor-corrector',
'pc-euler', 101]:
self.solver_code = 101
self.solver = 'pred-corr'
elif self.solver in ['milstein', 102, 1.0]:
self.solver_code = 102
self.solver = 'milstein'
elif self.solver in ['milstein-imp', 103]:
self.solver_code = 103
self.solver = 'milstein-imp'
elif self.solver in ['pred-corr-2', 'pc-euler-2', 'pc-euler-imp', 104]:
self.solver_code = 104
self.solver = 'pred-corr-2'
elif self.solver in ['Rouchon', 'rouchon', 120]:
self.solver_code = 120
self.solver = 'rouchon'
if not all((op.const for op in self.sc_ops)):
raise Exception("Rouchon only work with constant sc_ops")
elif self.solver in ['platen15', 'explicit1.5', 'explicit15', 150]:
self.solver_code = 150
self.solver = 'explicit1.5'
elif self.solver in ['taylor15', 'taylor1.5', None, 1.5, 152]:
self.solver_code = 152
self.solver = 'taylor1.5'
elif self.solver in ['taylor15-imp', 'taylor1.5-imp', 153]:
self.solver_code = 153
self.solver = 'taylor1.5-imp'
elif self.solver in ['taylor2.0', 'taylor20', 2.0, 202]:
self.solver_code = 202
self.solver = 'taylor2.0'
if not len(self.sc_ops) == 1 or \
not self.sc_ops[0].const or \
not self.method == "homodyne":
raise Exception("Taylor2.0 only work with 1 constant sc_ops " +
"and for homodyne method")
else:
raise Exception("The solver should be one of " +
"[None, 'euler-maruyama', 'platen', 'pc-euler', " +
"'pc-euler-imp', 'milstein', 'milstein-imp', " +
"'rouchon', " +
"'taylor1.5', 'taylor1.5-imp', 'explicit1.5' " +
"'taylor2.0']")
class StochasticSolverOptionsPhoto(StochasticSolverOptions):
"""
Attributes
----------
solver : string
Name of the solver method to use for solving the evolution
of the system.*
order 1 algorithms: 'euler'
order 2 algorithms: 'pred-corr'
In photocurrent evolution
"""
def set_solver(self):
if self.solver in [None, 'euler', 1, 60]:
self.solver_code = 60
self.solver = 'euler'
elif self.solver in ['pred-corr', 'predictor-corrector', 110, 2]:
self.solver_code = 110
self.solver = 'pred-corr'
else:
raise Exception("The solver should be one of " +
"[None, 'euler', 'predictor-corrector']")
[docs]def smesolve(H, rho0, times, c_ops=[], sc_ops=[], e_ops=[],
_safe_mode=True, args={}, **kwargs):
"""
Solve stochastic master equation. Dispatch to specific solvers
depending on the value of the `solver` keyword argument.
Parameters
----------
H : :class:`qutip.Qobj`, or time dependent system.
System Hamiltonian.
Can depend on time, see StochasticSolverOptions help for format.
rho0 : :class:`qutip.Qobj`
Initial density matrix or state vector (ket).
times : *list* / *array*
List of times for :math:`t`. Must be uniformly spaced.
c_ops : list of :class:`qutip.Qobj`, or time dependent Qobjs.
Deterministic collapse operator which will contribute with a standard
Lindblad type of dissipation.
Can depend on time, see StochasticSolverOptions help for format.
sc_ops : list of :class:`qutip.Qobj`, or time dependent Qobjs.
List of stochastic collapse operators. Each stochastic collapse
operator will give a deterministic and stochastic contribution
to the eqaution of motion according to how the d1 and d2 functions
are defined.
Can depend on time, see StochasticSolverOptions help for format.
e_ops : list of :class:`qutip.Qobj`
single operator or list of operators for which to evaluate
expectation values.
kwargs : *dictionary*
Optional keyword arguments. See
:class:`qutip.stochastic.StochasticSolverOptions`.
Returns
-------
output: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`.
"""
if "method" in kwargs and kwargs["method"] == "photocurrent":
print("stochastic solver with photocurrent method has been moved to "
"it's own function: photocurrent_mesolve")
return photocurrent_mesolve(H, rho0, times, c_ops=c_ops, sc_ops=sc_ops,
e_ops=e_ops, _safe_mode=_safe_mode,
args=args, **kwargs)
if isket(rho0):
rho0 = ket2dm(rho0)
if isinstance(e_ops, dict):
e_ops_dict = e_ops
e_ops = [e for e in e_ops.values()]
else:
e_ops_dict = None
sso = StochasticSolverOptions(True, H=H, state0=rho0, times=times,
c_ops=c_ops, sc_ops=sc_ops, e_ops=e_ops,
args=args, **kwargs)
if _safe_mode:
_safety_checks(sso)
if sso.solver_code == 120:
return _positive_map(sso, e_ops_dict)
sso.LH = liouvillian(sso.H, c_ops=sso.sc_ops + sso.c_ops) * sso.dt
if sso.method == 'homodyne' or sso.method is None:
if sso.m_ops is None:
sso.m_ops = [op + op.dag() for op in sso.sc_ops]
sso.sops = [spre(op) + spost(op.dag()) for op in sso.sc_ops]
if not isinstance(sso.dW_factors, list):
sso.dW_factors = [1] * len(sso.m_ops)
elif len(sso.dW_factors) != len(sso.m_ops):
raise Exception("The len of dW_factors is not the same as m_ops")
elif sso.method == 'heterodyne':
if sso.m_ops is None:
m_ops = []
sso.sops = []
for c in sso.sc_ops:
if sso.m_ops is None:
m_ops += [c + c.dag(), -1j * c - c.dag()]
sso.sops += [(spre(c) + spost(c.dag())) / np.sqrt(2),
(spre(c) - spost(c.dag())) * -1j / np.sqrt(2)]
sso.m_ops = m_ops
if not isinstance(sso.dW_factors, list):
sso.dW_factors = [np.sqrt(2)] * len(sso.sops)
elif len(sso.dW_factors) == len(sso.m_ops):
pass
elif len(sso.dW_factors) == len(sso.sc_ops):
dW_factors = []
for fact in sso.dW_factors:
dW_factors += [np.sqrt(2) * fact, np.sqrt(2) * fact]
sso.dW_factors = dW_factors
elif len(sso.dW_factors) != len(sso.m_ops):
raise Exception("The len of dW_factors is not the same as sc_ops")
elif sso.method == "photocurrent":
raise NotImplementedError("Moved to 'photocurrent_mesolve'")
else:
raise Exception("The method must be one of None, homodyne, heterodyne")
sso.ce_ops = [QobjEvo(spre(op)) for op in sso.e_ops]
sso.cm_ops = [QobjEvo(spre(op)) for op in sso.m_ops]
sso.LH.compile()
[op.compile() for op in sso.sops]
[op.compile() for op in sso.cm_ops]
[op.compile() for op in sso.ce_ops]
if sso.solver_code in [103, 153]:
sso.imp = 1 - sso.LH * 0.5
sso.imp.compile()
sso.solver_obj = SMESolver
sso.solver_name = "smesolve_" + sso.solver
res = _sesolve_generic(sso, sso.options, sso.progress_bar)
if e_ops_dict:
res.expect = {e: res.expect[n]
for n, e in enumerate(e_ops_dict.keys())}
return res
[docs]def ssesolve(H, psi0, times, sc_ops=[], e_ops=[],
_safe_mode=True, args={}, **kwargs):
"""
Solve stochastic schrodinger equation. Dispatch to specific solvers
depending on the value of the `solver` keyword argument.
Parameters
----------
H : :class:`qutip.Qobj`, or time dependent system.
System Hamiltonian.
Can depend on time, see StochasticSolverOptions help for format.
psi0 : :class:`qutip.Qobj`
State vector (ket).
times : *list* / *array*
List of times for :math:`t`. Must be uniformly spaced.
sc_ops : list of :class:`qutip.Qobj`, or time dependent Qobjs.
List of stochastic collapse operators. Each stochastic collapse
operator will give a deterministic and stochastic contribution
to the eqaution of motion according to how the d1 and d2 functions
are defined.
Can depend on time, see StochasticSolverOptions help for format.
e_ops : list of :class:`qutip.Qobj`
single operator or list of operators for which to evaluate
expectation values.
kwargs : *dictionary*
Optional keyword arguments. See
:class:`qutip.stochastic.StochasticSolverOptions`.
Returns
-------
output: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`.
"""
if "method" in kwargs and kwargs["method"] == "photocurrent":
print("stochastic solver with photocurrent method has been moved to "
"it's own function: photocurrent_sesolve")
return photocurrent_sesolve(H, psi0, times, c_ops=c_ops,
e_ops=e_ops, _safe_mode=_safe_mode,
args=args, **kwargs)
if isinstance(e_ops, dict):
e_ops_dict = e_ops
e_ops = [e for e in e_ops.values()]
else:
e_ops_dict = None
sso = StochasticSolverOptions(False, H=H, state0=psi0, times=times,
sc_ops=sc_ops, e_ops=e_ops,
args=args, **kwargs)
if _safe_mode:
_safety_checks(sso)
if sso.solver_code == 120:
raise Exception("rouchon only work with smesolve")
if sso.method == 'homodyne' or sso.method is None:
if sso.m_ops is None:
sso.m_ops = [op + op.dag() for op in sso.sc_ops]
sso.sops = [[op, op + op.dag()] for op in sso.sc_ops]
if not isinstance(sso.dW_factors, list):
sso.dW_factors = [1] * len(sso.sops)
elif len(sso.dW_factors) != len(sso.sops):
raise Exception("The len of dW_factors is not the same as sc_ops")
elif sso.method == 'heterodyne':
if sso.m_ops is None:
m_ops = []
sso.sops = []
for c in sso.sc_ops:
if sso.m_ops is None:
m_ops += [c + c.dag(), -1j * (c - c.dag())]
c1 = c / np.sqrt(2)
c2 = c * (-1j / np.sqrt(2))
sso.sops += [[c1, c1 + c1.dag()],
[c2, c2 + c2.dag()]]
sso.m_ops = m_ops
if not isinstance(sso.dW_factors, list):
sso.dW_factors = [np.sqrt(2)] * len(sso.sops)
elif len(sso.dW_factors) == len(sso.sc_ops):
dW_factors = []
for fact in sso.dW_factors:
dW_factors += [np.sqrt(2) * fact, np.sqrt(2) * fact]
sso.dW_factors = dW_factors
elif len(sso.dW_factors) != len(sso.sops):
raise Exception("The len of dW_factors is not the same as sc_ops")
elif sso.method == "photocurrent":
NotImplementedError("Moved to 'photocurrent_sesolve'")
else:
raise Exception("The method must be one of None, homodyne, heterodyne")
sso.LH = sso.H * (-1j*sso.dt)
for ops in sso.sops:
sso.LH -= ops[0]._cdc()*0.5*sso.dt
sso.ce_ops = [QobjEvo(op) for op in sso.e_ops]
sso.cm_ops = [QobjEvo(op) for op in sso.m_ops]
sso.LH.compile()
[[op.compile() for op in ops] for ops in sso.sops]
[op.compile() for op in sso.cm_ops]
[op.compile() for op in sso.ce_ops]
sso.solver_obj = SSESolver
sso.solver_name = "ssesolve_" + sso.solver
res = _sesolve_generic(sso, sso.options, sso.progress_bar)
if e_ops_dict:
res.expect = {e: res.expect[n]
for n, e in enumerate(e_ops_dict.keys())}
return res
def _positive_map(sso, e_ops_dict):
if sso.method == 'homodyne' or sso.method is None:
sops = sso.sc_ops
if sso.m_ops is None:
sso.m_ops = [op + op.dag() for op in sso.sc_ops]
if not isinstance(sso.dW_factors, list):
sso.dW_factors = [1] * len(sops)
elif len(sso.dW_factors) != len(sops):
raise Exception("The len of dW_factors is not the same as sc_ops")
elif sso.method == 'heterodyne':
if sso.m_ops is None:
m_ops = []
sops = []
for c in sso.sc_ops:
if sso.m_ops is None:
m_ops += [c + c.dag(), -1j * c - c.dag()]
sops += [c / np.sqrt(2), -1j / np.sqrt(2) * c]
sso.m_ops = m_ops
if not isinstance(sso.dW_factors, list):
sso.dW_factors = [np.sqrt(2)] * len(sops)
elif len(sso.dW_factors) == len(sso.sc_ops):
dW_factors = []
for fact in sso.dW_factors:
dW_factors += [np.sqrt(2) * fact, np.sqrt(2) * fact]
sso.dW_factors = dW_factors
elif len(sso.dW_factors) != len(sops):
raise Exception("The len of dW_factors is not the same as sc_ops")
else:
raise Exception("The method must be one of homodyne or heterodyne")
LH = 1 - (sso.H * 1j * sso.dt)
sso.pp = spre(sso.H) * 0
sso.sops = []
sso.preops = []
sso.postops = []
sso.preops2 = []
sso.postops2 = []
def _prespostdag(op):
return spre(op) * spost(op.dag())
for op in sso.c_ops:
LH -= op._cdc() * sso.dt * 0.5
sso.pp += op.apply(_prespostdag)._f_norm2() * sso.dt
for i, op in enumerate(sops):
LH -= op._cdc() * sso.dt * 0.5
sso.sops += [(spre(op) + spost(op.dag())) * sso.dt]
sso.preops += [spre(op)]
sso.postops += [spost(op.dag())]
for op2 in sops[i:]:
sso.preops2 += [spre(op * op2)]
sso.postops2 += [spost(op.dag() * op2.dag())]
sso.ce_ops = [QobjEvo(spre(op)) for op in sso.e_ops]
sso.cm_ops = [QobjEvo(spre(op)) for op in sso.m_ops]
sso.preLH = spre(LH)
sso.postLH = spost(LH.dag())
sso.preLH.compile()
sso.postLH.compile()
sso.pp.compile()
[op.compile() for op in sso.sops]
[op.compile() for op in sso.preops]
[op.compile() for op in sso.postops]
[op.compile() for op in sso.preops2]
[op.compile() for op in sso.postops2]
[op.compile() for op in sso.cm_ops]
[op.compile() for op in sso.ce_ops]
sso.solver_obj = PmSMESolver
sso.solver_name = "smesolve_" + sso.solver
res = _sesolve_generic(sso, sso.options, sso.progress_bar)
if e_ops_dict:
res.expect = {e: res.expect[n]
for n, e in enumerate(e_ops_dict.keys())}
return res
def photocurrent_mesolve(H, rho0, times, c_ops=[], sc_ops=[], e_ops=[],
_safe_mode=True, args={}, **kwargs):
"""
Solve stochastic master equation using the photocurrent method.
Parameters
----------
H : :class:`qutip.Qobj`, or time dependent system.
System Hamiltonian.
Can depend on time, see StochasticSolverOptions help for format.
rho0 : :class:`qutip.Qobj`
Initial density matrix or state vector (ket).
times : *list* / *array*
List of times for :math:`t`. Must be uniformly spaced.
c_ops : list of :class:`qutip.Qobj`, or time dependent Qobjs.
Deterministic collapse operator which will contribute with a standard
Lindblad type of dissipation.
Can depend on time, see StochasticSolverOptions help for format.
sc_ops : list of :class:`qutip.Qobj`, or time dependent Qobjs.
List of stochastic collapse operators. Each stochastic collapse
operator will give a deterministic and stochastic contribution
to the eqaution of motion according to how the d1 and d2 functions
are defined.
Can depend on time, see StochasticSolverOptions help for format.
e_ops : list of :class:`qutip.Qobj` / callback function single
single operator or list of operators for which to evaluate
expectation values.
kwargs : *dictionary*
Optional keyword arguments. See
:class:`qutip.stochastic.StochasticSolverOptions`.
Returns
-------
output: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`.
"""
if isket(rho0):
rho0 = ket2dm(rho0)
if isinstance(e_ops, dict):
e_ops_dict = e_ops
e_ops = [e for e in e_ops.values()]
else:
e_ops_dict = None
sso = StochasticSolverOptionsPhoto(True, H=H, state0=rho0, times=times,
c_ops=c_ops, sc_ops=sc_ops, e_ops=e_ops,
args=args, **kwargs)
if _safe_mode:
_safety_checks(sso)
if sso.m_ops is None:
sso.m_ops = [op * 0 for op in sso.sc_ops]
if not isinstance(sso.dW_factors, list):
sso.dW_factors = [1] * len(sso.sc_ops)
elif len(sso.dW_factors) != len(sso.sc_ops):
raise Exception("The len of dW_factors is not the same as sc_ops")
sso.solver_obj = PcSMESolver
sso.solver_name = "photocurrent_mesolve"
sso.LH = liouvillian(sso.H, c_ops=sso.c_ops) * sso.dt
def _prespostdag(op):
return spre(op) * spost(op.dag())
sso.sops = [[spre(op._cdc()) + spost(op._cdc()),
spre(op._cdc()),
op.apply(_prespostdag)._f_norm2()] for op in sso.sc_ops]
sso.ce_ops = [QobjEvo(spre(op)) for op in sso.e_ops]
sso.cm_ops = [QobjEvo(spre(op)) for op in sso.m_ops]
sso.LH.compile()
[[op.compile() for op in ops] for ops in sso.sops]
[op.compile() for op in sso.cm_ops]
[op.compile() for op in sso.ce_ops]
res = _sesolve_generic(sso, sso.options, sso.progress_bar)
res.num_collapse = [np.count_nonzero(noise) for noise in res.noise]
if e_ops_dict:
res.expect = {e: res.expect[n]
for n, e in enumerate(e_ops_dict.keys())}
return res
def photocurrent_sesolve(H, psi0, times, sc_ops=[], e_ops=[],
_safe_mode=True, args={}, **kwargs):
"""
Solve stochastic schrodinger equation using the photocurrent method.
Parameters
----------
H : :class:`qutip.Qobj`, or time dependent system.
System Hamiltonian.
Can depend on time, see StochasticSolverOptions help for format.
psi0 : :class:`qutip.Qobj`
Initial state vector (ket).
times : *list* / *array*
List of times for :math:`t`. Must be uniformly spaced.
sc_ops : list of :class:`qutip.Qobj`, or time dependent Qobjs.
List of stochastic collapse operators. Each stochastic collapse
operator will give a deterministic and stochastic contribution
to the eqaution of motion according to how the d1 and d2 functions
are defined.
Can depend on time, see StochasticSolverOptions help for format.
e_ops : list of :class:`qutip.Qobj` / callback function single
single operator or list of operators for which to evaluate
expectation values.
kwargs : *dictionary*
Optional keyword arguments. See
:class:`qutip.stochastic.StochasticSolverOptions`.
Returns
-------
output: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`.
"""
if isinstance(e_ops, dict):
e_ops_dict = e_ops
e_ops = [e for e in e_ops.values()]
else:
e_ops_dict = None
sso = StochasticSolverOptionsPhoto(False, H=H, state0=psi0, times=times,
sc_ops=sc_ops, e_ops=e_ops,
args=args, **kwargs)
if _safe_mode:
_safety_checks(sso)
if sso.m_ops is None:
sso.m_ops = [op * 0 for op in sso.sc_ops]
if not isinstance(sso.dW_factors, list):
sso.dW_factors = [1] * len(sso.sc_ops)
elif len(sso.dW_factors) != len(sso.sc_ops):
raise Exception("The len of dW_factors is not the same as sc_ops")
sso.solver_obj = PcSSESolver
sso.solver_name = "photocurrent_sesolve"
sso.sops = [[op, op._cdc()] for op in sso.sc_ops]
sso.LH = sso.H * (-1j*sso.dt)
for ops in sso.sops:
sso.LH -= ops[0]._cdc()*0.5*sso.dt
sso.ce_ops = [QobjEvo(op) for op in sso.e_ops]
sso.cm_ops = [QobjEvo(op) for op in sso.m_ops]
sso.LH.compile()
[[op.compile() for op in ops] for ops in sso.sops]
[op.compile() for op in sso.cm_ops]
[op.compile() for op in sso.ce_ops]
res = _sesolve_generic(sso, sso.options, sso.progress_bar)
res.num_collapse = [np.count_nonzero(noise) for noise in res.noise]
if e_ops_dict:
res.expect = {e: res.expect[n]
for n, e in enumerate(e_ops_dict.keys())}
return res
def general_stochastic(state0, times, d1, d2, e_ops=[], m_ops=[],
_safe_mode=True, len_d2=1, args={}, **kwargs):
"""
Solve stochastic general equation. Dispatch to specific solvers
depending on the value of the `solver` keyword argument.
Parameters
----------
state0 : :class:`qutip.Qobj`
Initial state vector (ket) or density matrix as a vector.
times : *list* / *array*
List of times for :math:`t`. Must be uniformly spaced.
d1 : function, callable class
Function representing the deterministic evolution of the system.
def d1(time (double), state (as a np.array vector)):
return 1d np.array
d2 : function, callable class
Function representing the stochastic evolution of the system.
def d2(time (double), state (as a np.array vector)):
return 2d np.array (N_sc_ops, len(state0))
len_d2 : int
Number of output vector produced by d2
e_ops : list of :class:`qutip.Qobj`
single operator or list of operators for which to evaluate
expectation values.
Must be a superoperator if the state vector is a density matrix.
kwargs : *dictionary*
Optional keyword arguments. See
:class:`qutip.stochastic.StochasticSolverOptions`.
Returns
-------
output: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`.
"""
if isinstance(e_ops, dict):
e_ops_dict = e_ops
e_ops = [e for e in e_ops.values()]
else:
e_ops_dict = None
if "solver" not in kwargs:
kwargs["solver"] = 50
sso = StochasticSolverOptions(False, H=None, state0=state0, times=times,
e_ops=e_ops, args=args, **kwargs)
if sso.solver_code not in [50, 100, 150]:
raise Exception("Only Euler, platen, platen15 can be " +
"used for the general stochastic solver")
sso.d1 = d1
sso.d2 = d2
if _safe_mode:
l_vec = sso.rho0.shape[0]
try:
out_d1 = d1(0., sso.rho0)
except Exception as e:
raise Exception("d1(0., mat2vec(state0.full()).ravel()) failed:\n"+
str(e))
except:
raise Exception("d1(0., mat2vec(state0.full()).ravel()) failed")
try:
out_d2 = d2(0., sso.rho0)
except Exception as e:
raise Exception("d2(0., mat2vec(state0.full()).ravel()) failed:\n"+
str(e))
except:
raise Exception("d2(0., mat2vec(state0.full()).ravel()) failed")
if out_d1.shape[0] != l_vec or len(out_d1.shape) != 1:
raise Exception("d1 must return an 1d numpy array with "+
"the same number of element than the " +
"initial state as a vector")
if len(out_d2.shape) != 2 and out_d2.shape[1] != l_vec and \
out_d2.shape[0] != len_d2:
raise Exception("d2 must return an 2d numpy array with the shape" +
" (l2_len, len(mat2vec(state0.full()).ravel()) )")
if out_d1.dtype != np.dtype('complex128') or \
out_d2.dtype != np.dtype('complex128'):
raise Exception("d1 and d2 must return complex numpy array")
for op in sso.e_ops:
shape_op = op.shape
if sso.me:
if shape_op[0]**2 != l_vec or shape_op[1]**2 != l_vec:
raise Exception("The size of the e_ops does "
"not fit the intial state")
else:
if shape_op[0] != l_vec or shape_op[1] != l_vec:
raise Exception("The size of the e_ops does "
"not fit the intial state")
sso.m_ops = []
sso.cm_ops = []
if sso.store_measurement:
if not m_ops:
raise Exception("General stochastic need explicit " +
"m_ops to store measurement")
sso.m_ops = m_ops
sso.cm_ops = [QobjEvo(op) for op in sso.m_ops]
[op.compile() for op in sso.cm_ops]
if sso.dW_factors is None:
sso.dW_factors = [1.] * len(sso.m_ops)
elif len(sso.dW_factors) == 1:
sso.dW_factors = sso.dW_factors * len(sso.m_ops)
elif len(sso.dW_factors) != len(sso.m_ops):
raise Exception("The number of dW_factors must fit"
" the number of m_ops")
if sso.dW_factors is None:
sso.dW_factors = [1.] * len_d2
sso.sops = [None] * len_d2
sso.ce_ops = [QobjEvo(op) for op in sso.e_ops]
[op.compile() for op in sso.ce_ops]
sso.solver_obj = GenericSSolver
sso.solver_name = "general_stochastic_solver_" + sso.solver
ssolver = GenericSSolver()
# ssolver.set_data(sso)
ssolver.set_solver(sso)
res = _sesolve_generic(sso, sso.options, sso.progress_bar)
if e_ops_dict:
res.expect = {e: res.expect[n]
for n, e in enumerate(e_ops_dict.keys())}
return res
def _safety_checks(sso):
l_vec = sso.rho0.shape[0]
if sso.H.cte.issuper:
if not sso.me:
raise
shape_op = sso.H.cte.shape
if shape_op[0] != l_vec or shape_op[1] != l_vec:
raise Exception("The size of the hamiltonian does "
"not fit the intial state")
else:
shape_op = sso.H.cte.shape
if sso.me:
if shape_op[0]**2 != l_vec or shape_op[1]**2 != l_vec:
raise Exception("The size of the hamiltonian does "
"not fit the intial state")
else:
if shape_op[0] != l_vec or shape_op[1] != l_vec:
raise Exception("The size of the hamiltonian does "
"not fit the intial state")
for op in sso.sc_ops:
if op.cte.issuper:
if not sso.me:
raise
shape_op = op.cte.shape
if shape_op[0] != l_vec or shape_op[1] != l_vec:
raise Exception("The size of the sc_ops does "
"not fit the intial state")
else:
shape_op = op.cte.shape
if sso.me:
if shape_op[0]**2 != l_vec or shape_op[1]**2 != l_vec:
raise Exception("The size of the sc_ops does "
"not fit the intial state")
else:
if shape_op[0] != l_vec or shape_op[1] != l_vec:
raise Exception("The size of the sc_ops does "
"not fit the intial state")
for op in sso.c_ops:
if op.cte.issuper:
if not sso.me:
raise
shape_op = op.cte.shape
if shape_op[0] != l_vec or shape_op[1] != l_vec:
raise Exception("The size of the c_ops does "
"not fit the intial state")
else:
shape_op = op.cte.shape
if sso.me:
if shape_op[0]**2 != l_vec or shape_op[1]**2 != l_vec:
raise Exception("The size of the c_ops does "
"not fit the intial state")
else:
if shape_op[0] != l_vec or shape_op[1] != l_vec:
raise Exception("The size of the c_ops does "
"not fit the intial state")
for op in sso.e_ops:
shape_op = op.shape
if sso.me:
if shape_op[0]**2 != l_vec or shape_op[1]**2 != l_vec:
raise Exception("The size of the e_ops does "
"not fit the intial state")
else:
if shape_op[0] != l_vec or shape_op[1] != l_vec:
raise Exception("The size of the e_ops does "
"not fit the intial state")
if sso.m_ops is not None:
for op in sso.m_ops:
shape_op = op.shape
if sso.me:
if shape_op[0]**2 != l_vec or shape_op[1]**2 != l_vec:
raise Exception("The size of the m_ops does "
"not fit the intial state")
else:
if shape_op[0] != l_vec or shape_op[1] != l_vec:
raise Exception("The size of the m_ops does "
"not fit the intial state")
def _sesolve_generic(sso, options, progress_bar):
"""
Internal function. See smesolve.
"""
data = Result()
data.times = sso.times
data.expect = np.zeros((len(sso.e_ops), len(sso.times)), dtype=complex)
data.ss = np.zeros((len(sso.e_ops), len(sso.times)), dtype=complex)
data.measurement = []
data.solver = sso.solver_name
data.ntraj = sso.ntraj
data.num_expect = len(sso.e_ops)
nt = sso.ntraj
task = _single_trajectory
map_kwargs = {'progress_bar': sso.progress_bar}
map_kwargs.update(sso.map_kwargs)
task_args = (sso,)
task_kwargs = {}
results = sso.map_func(task, list(range(sso.ntraj)),
task_args, task_kwargs, **map_kwargs)
noise = []
for result in results:
states_list, dW, m, expect = result
data.states.append(states_list)
noise.append(dW)
data.measurement.append(m)
data.expect += expect
data.ss += expect * expect
data.noise = np.stack(noise)
if sso.store_all_expect:
paths_expect = []
for result in results:
paths_expect.append(result[3])
data.runs_expect = np.stack(paths_expect)
# average density matrices
if options.average_states and np.any(data.states):
data.states = [sum([data.states[mm][n] for mm in range(nt)]).unit()
for n in range(len(data.times))]
# average
data.expect = data.expect / nt
# standard error
if nt > 1:
data.se = (data.ss - nt * (data.expect ** 2)) / (nt * (nt - 1))
else:
data.se = None
# convert complex data to real if hermitian
data.expect = [np.real(data.expect[n, :])
if e.isherm else data.expect[n, :]
for n, e in enumerate(sso.e_ops)]
return data
def _single_trajectory(i, sso):
# Only one step?
ssolver = sso.solver_obj()
#ssolver.set_data(sso)
ssolver.set_solver(sso)
result = ssolver.cy_sesolve_single_trajectory(i)#, sso)
return result
# The code for ssepdpsolve have been moved to the file pdpsolve.
# The call is still in stochastic for consistance.
[docs]def ssepdpsolve(H, psi0, times, c_ops, e_ops, **kwargs):
"""
A stochastic (piecewse deterministic process) PDP solver for wavefunction
evolution. For most purposes, use :func:`qutip.mcsolve` instead for quantum
trajectory simulations.
Parameters
----------
H : :class:`qutip.Qobj`
System Hamiltonian.
psi0 : :class:`qutip.Qobj`
Initial state vector (ket).
times : *list* / *array*
List of times for :math:`t`. Must be uniformly spaced.
c_ops : list of :class:`qutip.Qobj`
Deterministic collapse operator which will contribute with a standard
Lindblad type of dissipation.
e_ops : list of :class:`qutip.Qobj` / callback function single
single operator or list of operators for which to evaluate
expectation values.
kwargs : *dictionary*
Optional keyword arguments. See
:class:`qutip.stochastic.StochasticSolverOptions`.
Returns
-------
output: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`.
"""
return main_ssepdpsolve(H, psi0, times, c_ops, e_ops, **kwargs)
# The code for smepdpsolve have been moved to the file pdpsolve.
# The call is still in stochastic for consistance.
[docs]def smepdpsolve(H, rho0, times, c_ops, e_ops, **kwargs):
"""
A stochastic (piecewse deterministic process) PDP solver for density matrix
evolution.
Parameters
----------
H : :class:`qutip.Qobj`
System Hamiltonian.
rho0 : :class:`qutip.Qobj`
Initial density matrix.
times : *list* / *array*
List of times for :math:`t`. Must be uniformly spaced.
c_ops : list of :class:`qutip.Qobj`
Deterministic collapse operator which will contribute with a standard
Lindblad type of dissipation.
sc_ops : list of :class:`qutip.Qobj`
List of stochastic collapse operators. Each stochastic collapse
operator will give a deterministic and stochastic contribution
to the eqaution of motion according to how the d1 and d2 functions
are defined.
e_ops : list of :class:`qutip.Qobj` / callback function single
single operator or list of operators for which to evaluate
expectation values.
kwargs : *dictionary*
Optional keyword arguments. See
:class:`qutip.stochastic.StochasticSolverOptions`.
Returns
-------
output: :class:`qutip.solver.Result`
An instance of the class :class:`qutip.solver.Result`.
"""
return main_smepdpsolve(H, rho0, times, c_ops, e_ops, **kwargs)