def _mesolve_QobjEvo(H, c_ops, tlist, args, opt):
"""
Prepare the system for the solver, H can be an QobjEvo.
"""
H_td = QobjEvo(H, args, tlist=tlist)
if not issuper(H_td.cte):
L_td = liouvillian(H_td)
else:
L_td = H_td
for op in c_ops:
op_td = QobjEvo(op, args, tlist=tlist)
if not issuper(op_td.cte):
op_td = lindblad_dissipator(op_td)
L_td += op_td
if opt.rhs_with_state:
L_td._check_old_with_state()
nthread = opt.openmp_threads if opt.use_openmp else 0
L_td.compile(omp=nthread)
ss = SolverSystem()
ss.H = L_td
ss.makefunc = _qobjevo_set
solver_safe["mesolve"] = ss
return ss
def _generate_A_ops_Euler(sc, L, dt): """ combine precomputed operators in one long operator for the Euler method """ A_len = len(sc) out = [] out += [spre(c).data + spost(c.dag()).data for c in sc] out += [(L + np.sum([lindblad_dissipator(c, data_only=True) for c in sc], axis=0))*dt] out1 = [[sp.vstack(out).tocsr(), sc[0].shape[0]]] #the following hack is required for compatibility with old A_ops out1 += [[] for n in xrange(A_len-1)] return out1
def test_lindblad_dissipator_td(self):
"Superoperator: lindblad_dissipator, time-dependent"
assert_(lindblad_dissipator(self.t2)(.5) ==
lindblad_dissipator(self.t2(.5)))
assert_(lindblad_dissipator(self.t2, self.q1)(.5) ==
lindblad_dissipator(self.t2(.5), self.q1))
assert_(lindblad_dissipator(self.q1, self.t2)(.5) ==
lindblad_dissipator(self.q1, self.t2(.5)))
def test_lindblad_dissipator_td(self):
"Superoperator: lindblad_dissipator, time-dependent"
assert_(lindblad_dissipator(self.t2)(.5) ==
lindblad_dissipator(self.t2(.5)))
assert_(lindblad_dissipator(self.t2, self.q1)(.5) ==
lindblad_dissipator(self.t2(.5), self.q1))
assert_(lindblad_dissipator(self.q1, self.t2)(.5) ==
lindblad_dissipator(self.q1, self.t2(.5)))
def _generate_rho_A_ops(sc, L, dt):
"""
pre-compute superoperator operator combinations that are commonly needed
when evaluating the RHS of stochastic master equations
"""
out = []
for c_idx, c in enumerate(sc):
n = c.dag() * c
out.append([spre(c).data, spost(c).data,
spre(c.dag()).data, spost(c.dag()).data,
spre(n).data, spost(n).data, (spre(c) * spost(c.dag())).data,
lindblad_dissipator(c, data_only=True)])
return out
def _generate_A_ops_Milstein(sc, L, dt): """ combine precomputed operators in one long operator for the Milstein method with commuting stochastic jump operators. """ A_len = len(sc) temp = [spre(c).data + spost(c.dag()).data for c in sc] out = [] out += temp out += [temp[n]*temp[n] for n in xrange(A_len)] out += [temp[n]*temp[m] for (n,m) in np.ndindex(A_len,A_len) if n > m] out += [(L + np.sum([lindblad_dissipator(c, data_only=True) for c in sc], axis=0))*dt] out1 = [[sp.vstack(out).tocsr(), sc[0].shape[0]]] #the following hack is required for compatibility with old A_ops out1 += [[] for n in xrange(A_len-1)] return out1
def _mesolve_func_td(L_func, c_op_list, rho0, tlist, args, opt):
"""
Evolve the density matrix using an ODE solver with time dependent
Hamiltonian.
"""
if type(c_op_list) is list:
c_ops = []
for op in c_op_list:
op_td = QobjEvo(op, args, tlist=tlist, copy=False)
if not issuper(op_td.cte):
c_ops += [lindblad_dissipator(op_td)]
else:
c_ops += [op_td]
if c_op_list:
c_ops_ = [sum(c_ops)]
else:
c_ops_ = []
elif callable(c_op_list):
c_ops_ = c_op_list
if opt.rhs_with_state:
state0 = rho0.full().ravel("F")
obj = L_func(0., state0, args)
if not issuper(obj):
L_func = _LiouvillianFromFunc(L_func, c_ops_).H2L_with_state
else:
L_func = _LiouvillianFromFunc(L_func, c_ops_).L_with_state
else:
obj = L_func(0., args)
if callable(c_ops_):
if not issuper(obj):
L_func = _LiouvillianFromFunc(L_func, c_ops_).H2L_c
else:
L_func = _LiouvillianFromFunc(L_func, c_ops_).L_c
else:
if not issuper(obj):
L_func = _LiouvillianFromFunc(L_func, c_ops_).H2L
else:
L_func = _LiouvillianFromFunc(L_func, c_ops_).L
ss = SolverSystem()
ss.L = L_func
ss.makefunc = _Lfunc_set
solver_safe["mesolve"] = ss
return ss
def _mesolve_func_td(L_func, c_op_list, rho0, tlist, args, opt):
"""
Evolve the density matrix using an ODE solver with time dependent
Hamiltonian.
"""
c_ops = []
for op in c_op_list:
td = QobjEvo(op, args, tlist=tlist, copy=False)
c_ops.append(td if td.cte.issuper else lindblad_dissipator(td))
c_ops_ = [sum(c_ops)] if c_op_list else []
L_api = _LiouvillianFromFunc(L_func, c_ops_, rho0.dims)
if opt.rhs_with_state:
obj = L_func(0., rho0.full().ravel("F"), args)
L_func = L_api.L_with_state if issuper(obj) else L_api.H2L_with_state
else:
obj = L_func(0., args)
L_func = L_api.L if issuper(obj) else L_api.H2L
ss = SolverSystem()
ss.L = L_func
ss.makefunc = _Lfunc_set
solver_safe["mesolve"] = ss
return ss
def _mesolve_QobjEvo(H, c_ops, tlist, args, opt):
"""
Prepare the system for the solver, H can be an QobjEvo.
"""
H_td = QobjEvo(H, args, tlist=tlist)
if not issuper(H_td.cte):
L_td = liouvillian(H_td)
else:
L_td = H_td
for op in c_ops:
# We want to avoid passing tlist where it isn't necessary, to allow a
# Hamiltonian/Liouvillian which already _has_ time-dependence not equal
# to the mesolve evaluation times to be used in conjunction with
# time-independent c_ops. If we _always_ pass it, it may appear to
# QobjEvo that there is a tlist mismatch, even though it is not used.
if isinstance(op, Qobj):
op_td = QobjEvo(op)
elif isinstance(op, QobjEvo):
op_td = QobjEvo(op, args)
else:
op_td = QobjEvo(op, args, tlist=tlist)
if not issuper(op_td.cte):
op_td = lindblad_dissipator(op_td)
L_td += op_td
if opt.rhs_with_state:
L_td._check_old_with_state()
nthread = opt.openmp_threads if opt.use_openmp else 0
L_td.compile(omp=nthread)
ss = SolverSystem()
ss.H = L_td
ss.makefunc = _qobjevo_set
solver_safe["mesolve"] = ss
return ss
def smesolve_generic(ssdata, options, progress_bar):
"""
internal
.. note::
Experimental.
"""
if debug:
print(inspect.stack()[0][3])
N_store = len(ssdata.tlist)
N_substeps = ssdata.nsubsteps
N = N_store * N_substeps
dt = (ssdata.tlist[1] - ssdata.tlist[0]) / N_substeps
NT = ssdata.ntraj
data = Odedata()
data.solver = "smesolve"
data.times = ssdata.tlist
data.expect = np.zeros((len(ssdata.e_ops), N_store), dtype=complex)
data.ss = np.zeros((len(ssdata.e_ops), N_store), dtype=complex)
data.noise = []
data.measurement = []
# pre-compute suporoperator operator combinations that are commonly needed
# when evaluating the RHS of stochastic master equations
A_ops = []
for c_idx, c in enumerate(ssdata.sc_ops):
n = c.dag() * c
A_ops.append([spre(c).data, spost(c).data,
spre(c.dag()).data, spost(c.dag()).data,
spre(n).data, spost(n).data,
(spre(c) * spost(c.dag())).data,
lindblad_dissipator(c, data_only=True)])
s_e_ops = [spre(e) for e in ssdata.e_ops]
# Liouvillian for the deterministic part.
# needs to be modified for TD systems
L = liouvillian_fast(ssdata.H, ssdata.c_ops)
progress_bar.start(ssdata.ntraj)
for n in range(ssdata.ntraj):
progress_bar.update(n)
rho_t = mat2vec(ssdata.state0.full()).ravel()
noise = ssdata.noise[n] if ssdata.noise else None
states_list, dW, m = _smesolve_single_trajectory(
L, dt, ssdata.tlist, N_store, N_substeps,
rho_t, A_ops, s_e_ops, data, ssdata.rhs,
ssdata.d1, ssdata.d2, ssdata.d2_len, ssdata.homogeneous,
ssdata.distribution, ssdata.args,
store_measurement=ssdata.store_measurement,
store_states=ssdata.store_states, noise=noise)
data.states.append(states_list)
data.noise.append(dW)
data.measurement.append(m)
progress_bar.finished()
# average density matrices
if options.average_states and np.any(data.states):
data.states = [sum(state_list).unit() for state_list in data.states]
# 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(ssdata.e_ops)]
return data
def smesolve_generic(ssdata, options, progress_bar):
"""
internal
.. note::
Experimental.
"""
if debug:
print(inspect.stack()[0][3])
N_store = len(ssdata.tlist)
N_substeps = ssdata.nsubsteps
N = N_store * N_substeps
dt = (ssdata.tlist[1] - ssdata.tlist[0]) / N_substeps
NT = ssdata.ntraj
data = Odedata()
data.solver = "smesolve"
data.times = ssdata.tlist
data.expect = np.zeros((len(ssdata.e_ops), N_store), dtype=complex)
data.ss = np.zeros((len(ssdata.e_ops), N_store), dtype=complex)
data.noise = []
data.measurement = []
# pre-compute suporoperator operator combinations that are commonly needed
# when evaluating the RHS of stochastic master equations
A_ops = []
for c_idx, c in enumerate(ssdata.sc_ops):
n = c.dag() * c
A_ops.append([spre(c).data, spost(c).data,
spre(c.dag()).data, spost(c.dag()).data,
spre(n).data, spost(n).data,
(spre(c) * spost(c.dag())).data,
lindblad_dissipator(c, data_only=True)])
s_e_ops = [spre(e) for e in ssdata.e_ops]
# Liouvillian for the deterministic part.
# needs to be modified for TD systems
L = liouvillian_fast(ssdata.H, ssdata.c_ops)
progress_bar.start(ssdata.ntraj)
for n in range(ssdata.ntraj):
progress_bar.update(n)
rho_t = mat2vec(ssdata.state0.full()).ravel()
noise = ssdata.noise[n] if ssdata.noise else None
states_list, dW, m = _smesolve_single_trajectory(
L, dt, ssdata.tlist, N_store, N_substeps,
rho_t, A_ops, s_e_ops, data, ssdata.rhs,
ssdata.d1, ssdata.d2, ssdata.d2_len, ssdata.homogeneous,
ssdata.distribution, ssdata.args,
store_measurement=ssdata.store_measurement,
store_states=ssdata.store_states, noise=noise)
data.states.append(states_list)
data.noise.append(dW)
data.measurement.append(m)
progress_bar.finished()
# average density matrices
if options.average_states and np.any(data.states):
data.states = [sum(state_list).unit() for state_list in data.states]
# 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(ssdata.e_ops)]
return data