def floquet_master_equation_tensor(Alist, f_energies):
"""
Construct a tensor that represents the master equation in the floquet
basis (with constant Hamiltonian and collapse operators).
Simplest RWA approximation [Grifoni et al, Phys.Rep. 304 229 (1998)]
Parameters
----------
Alist : list
A list of Floquet-Markov master equation rate matrices.
f_energies : array
The Floquet energies.
Returns
-------
output : array
The Floquet-Markov master equation tensor `R`.
"""
if isinstance(Alist, list):
# Alist can be a list of rate matrices corresponding
# to different operators that couple to the environment
N, M = np.shape(Alist[0])
else:
# or a simple rate matrix, in which case we put it in a list
Alist = [Alist]
N, M = np.shape(Alist[0])
R = Qobj(scipy.sparse.csr_matrix((N * N, N * N)), [[N, N], [N, N]],
[N * N, N * N])
R.data = R.data.tolil()
for I in range(N * N):
a, b = vec2mat_index(N, I)
for J in range(N * N):
c, d = vec2mat_index(N, J)
R.data[I, J] = -1.0j * (f_energies[a] - f_energies[b]) * \
(a == c) * (b == d)
for A in Alist:
s1 = s2 = 0
for n in range(N):
s1 += A[a, n] * (n == c) * (n == d) - A[n, a] * \
(a == c) * (a == d)
s2 += (A[n, a] + A[n, b]) * (a == c) * (b == d)
dR = (a == b) * s1 - 0.5 * (1 - (a == b)) * s2
if dR != 0.0:
R.data[I, J] += dR
R.data = R.data.tocsr()
return R
def vector_to_operator(op):
"""
Create a matrix representation given a quantum operator in
vector form.
"""
q = Qobj()
q.dims = op.dims[0]
q.data = sp_reshape(op.data.T, q.shape).T
return q
def operator_to_vector(op):
"""
Create a vector representation of a quantum operator given
the matrix representation.
"""
q = Qobj()
q.dims = [op.dims, [1]]
q.data = sp_reshape(op.data.T, (np.prod(op.shape), 1))
return q
def vector_to_operator(op):
"""
Create a matrix representation given a quantum operator in
vector form.
"""
q = Qobj()
q.dims = op.dims[0]
n = int(np.sqrt(op.shape[0]))
q.data = sp_reshape(op.data.T, (n, n)).T
return q
def steadystate_nonlinear(L_func, rho0, args={}, maxiter=10,
random_initial_state=False, tol=1e-6, itertol=1e-5,
use_umfpack=True, verbose=False):
"""
Steady state for the evolution subject to the nonlinear Liouvillian
(which depends on the density matrix).
.. note:: Experimental. Not at all certain that the inverse power method
works for state-dependent Liouvillian operators.
"""
use_solver(assumeSortedIndices=True, useUmfpack=use_umfpack)
if random_initial_state:
rhoss = rand_dm(rho0.shape[0], 1.0, dims=rho0.dims)
elif isket(rho0):
rhoss = ket2dm(rho0)
else:
rhoss = Qobj(rho0)
v = mat2vec(rhoss.full())
n = prod(rhoss.shape)
tr_vec = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
tr_vec = tr_vec.reshape((1, n))
it = 0
while it < maxiter:
L = L_func(rhoss, args)
L = L.data.tocsc() - (tol ** 2) * sp.eye(n, n, format='csc')
L.sort_indices()
v = spsolve(L, v, use_umfpack=use_umfpack)
v = v / la.norm(v, np.inf)
data = v / sum(tr_vec.dot(v))
data = reshape(data, (rhoss.shape[0], rhoss.shape[1])).T
rhoss.data = sp.csr_matrix(data)
it += 1
if la.norm(L * v, np.inf) <= tol:
break
if it >= maxiter:
raise ValueError('Failed to find steady state after ' +
str(maxiter) + ' iterations')
rhoss = 0.5 * (rhoss + rhoss.dag())
return rhoss.tidyup() if qset.auto_tidyup else rhoss
def _steadystate_power(L, maxiter=10, tol=1e-6, itertol=1e-5,
verbose=False):
"""
Inverse power method for steady state solving.
"""
if verbose:
print('Starting iterative power method Solver...')
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
rhoss.shape = [prod(rhoss.dims[0]), prod(rhoss.dims[1])]
else:
rhoss.dims = [L.dims[0], 1]
rhoss.shape = [prod(rhoss.dims[0]), 1]
n = prod(rhoss.shape)
L = L.data.tocsc() - (tol ** 2) * sp.eye(n, n, format='csc')
L.sort_indices()
v = mat2vec(rand_dm(rhoss.shape[0], 0.5 / rhoss.shape[0] + 0.5).full())
if verbose:
start_time = time.time()
it = 0
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
v = spsolve(L, v)
v = v / la.norm(v, np.inf)
it += 1
if it >= maxiter:
raise Exception('Failed to find steady state after ' +
str(maxiter) + ' iterations')
# normalise according to type of problem
if sflag:
trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
trow = sp_reshape(trow, (1, n))
data = v / sum(trow.dot(v))
else:
data = data / la.norm(v)
data = sp.csr_matrix(vec2mat(data))
rhoss.data = 0.5 * (data + data.conj().T)
rhoss.isherm = True
if verbose:
print('Power solver time: ', time.time() - start_time)
if qset.auto_tidyup:
return rhoss.tidyup()
else:
return rhoss
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
if settings.debug:
print('Starting iterative power method Solver...')
tol=ss_args['tol']
maxiter=ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = prod(rhoss.shape)
L = L.data.tocsc() - (tol ** 2) * sp.eye(n, n, format='csc')
L.sort_indices()
v = mat2vec(rand_dm(rhoss.shape[0], 0.5 / rhoss.shape[0] + 0.5).full())
it = 0
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
v = spsolve(L, v)
v = v / la.norm(v, np.inf)
it += 1
if it >= maxiter:
raise Exception('Failed to find steady state after ' +
str(maxiter) + ' iterations')
# normalise according to type of problem
if sflag:
trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
trow = sp_reshape(trow, (1, n))
data = v / sum(trow.dot(v))
else:
data = data / la.norm(v)
data = sp.csr_matrix(vec2mat(data))
rhoss.data = 0.5 * (data + data.conj().T)
rhoss.isherm = True
return rhoss
def spre(A):
"""Superoperator formed from pre-multiplication by operator A.
Parameters
----------
A : qobj
Quantum operator for pre-multiplication.
Returns
--------
super :qobj
Superoperator formed from input quantum object.
"""
if not isinstance(A, Qobj):
raise TypeError('Input is not a quantum object')
if not A.isoper:
raise TypeError('Input is not a quantum operator')
S = Qobj(isherm=A.isherm, superrep='super')
S.dims = [[A.dims[0], A.dims[1]], [A.dims[0], A.dims[1]]]
S.data = sp.kron(sp.identity(np.prod(A.shape[1])), A.data, format='csr')
return S
def spost(A):
"""Superoperator formed from post-multiplication by operator A
Parameters
----------
A : qobj
Quantum operator for post multiplication.
Returns
-------
super : qobj
Superoperator formed from input qauntum object.
"""
if not isinstance(A, Qobj):
raise TypeError('Input is not a quantum object')
if not A.isoper:
raise TypeError('Input is not a quantum operator')
S = Qobj(isherm=A.isherm, superrep='super')
S.dims = [[A.dims[0], A.dims[1]], [A.dims[0], A.dims[1]]]
S.data = zcsr_kron(A.data.T,
fast_identity(np.prod(A.shape[0])))
return S
def tensor(*args):
"""Calculates the tensor product of input operators.
Parameters
----------
args : array_like
``list`` or ``array`` of quantum objects for tensor product.
Returns
--------
obj : qobj
A composite quantum object.
Examples
--------
>>> tensor([sigmax(), sigmax()])
Quantum object: dims = [[2, 2], [2, 2]], shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]]
"""
if not args:
raise TypeError("Requires at least one input argument")
num_args=len(args)
step=0
for n in range(num_args):
if isinstance(args[n],Qobj):
qos=args[n]
if step==0:
dat=qos.data
dim=qos.dims
shp=qos.shape
step=1
else:
dat=sp.kron(dat,qos.data, format='csr') #sparse Kronecker product
dim=[dim[0]+qos.dims[0],dim[1]+qos.dims[1]] #append dimensions of Qobjs
shp=[dat.shape[0],dat.shape[1]] #new shape of matrix
elif isinstance(args[n],(list,ndarray)):#checks if input is list/array of Qobjs
qos=args[n]
items=len(qos) #number of inputs
if not all([isinstance(k,Qobj) for k in qos]): #raise error if one of the inputs is not a quantum object
raise TypeError("One of inputs is not a quantum object")
if items==1:# if only one Qobj, do nothing
if step==0:
dat=qos[0].data
dim=qos[0].dims
shp=qos[0].shape
step=1
else:
dat=sp.kron(dat,qos[0].data, format='csr') #sparse Kronecker product
dim=[dim[0]+qos[0].dims[0],dim[1]+qos[0].dims[1]] #append dimensions of Qobjs
shp=[dat.shape[0],dat.shape[1]] #new shape of matrix
elif items!=1:
if step==0:
dat=qos[0].data
dim=qos[0].dims
shp=qos[0].shape
step=1
for k in range(items-1): #cycle over all items
dat=sp.kron(dat,qos[k+1].data, format='csr') #sparse Kronecker product
dim=[dim[0]+qos[k+1].dims[0],dim[1]+qos[k+1].dims[1]] #append dimensions of Qobjs
shp=[dat.shape[0],dat.shape[1]] #new shape of matrix
out=Qobj()
out.data=dat
out.dims=dim
out.shape=shp
if qutip.settings.auto_tidyup:
return Qobj(out).tidyup() #returns tidy Qobj
else:
return Qobj(out)
def _td_brmesolve(H, psi0, tlist, a_ops=[], e_ops=[], c_ops=[], args={},
use_secular=True, sec_cutoff=0.1,
tol=qset.atol, options=None,
progress_bar=None,_safe_mode=True,
verbose=False,
_prep_time=0):
if isket(psi0):
rho0 = ket2dm(psi0)
else:
rho0 = psi0
nrows = rho0.shape[0]
H_terms = []
H_td_terms = []
H_obj = []
A_terms = []
A_td_terms = []
C_terms = []
C_td_terms = []
CA_obj = []
spline_count = [0,0]
coupled_ops = []
coupled_lengths = []
coupled_spectra = []
if isinstance(H, Qobj):
H_terms.append(H.full('f'))
H_td_terms.append('1')
else:
for kk, h in enumerate(H):
if isinstance(h, Qobj):
H_terms.append(h.full('f'))
H_td_terms.append('1')
elif isinstance(h, list):
H_terms.append(h[0].full('f'))
if isinstance(h[1], Cubic_Spline):
H_obj.append(h[1].coeffs)
spline_count[0] += 1
H_td_terms.append(h[1])
else:
raise Exception('Invalid Hamiltonian specification.')
for kk, c in enumerate(c_ops):
if isinstance(c, Qobj):
C_terms.append(c.full('f'))
C_td_terms.append('1')
elif isinstance(c, list):
C_terms.append(c[0].full('f'))
if isinstance(c[1], Cubic_Spline):
CA_obj.append(c[1].coeffs)
spline_count[0] += 1
C_td_terms.append(c[1])
else:
raise Exception('Invalid collapse operator specification.')
coupled_offset = 0
for kk, a in enumerate(a_ops):
if isinstance(a, list):
if isinstance(a[0], Qobj):
A_terms.append(a[0].full('f'))
A_td_terms.append(a[1])
if isinstance(a[1], tuple):
if not len(a[1])==2:
raise Exception('Tuple must be len=2.')
if isinstance(a[1][0],Cubic_Spline):
spline_count[1] += 1
if isinstance(a[1][1],Cubic_Spline):
spline_count[1] += 1
elif isinstance(a[0], tuple):
if not isinstance(a[1], tuple):
raise Exception('Invalid bath-coupling specification.')
if (len(a[0])+1) != len(a[1]):
raise Exception('BR a_ops tuple lengths not compatible.')
coupled_ops.append(kk+coupled_offset)
coupled_lengths.append(len(a[0]))
coupled_spectra.append(a[1][0])
coupled_offset += len(a[0])-1
if isinstance(a[1][0],Cubic_Spline):
spline_count[1] += 1
for nn, _a in enumerate(a[0]):
A_terms.append(_a.full('f'))
A_td_terms.append(a[1][nn+1])
if isinstance(a[1][nn+1],Cubic_Spline):
CA_obj.append(a[1][nn+1].coeffs)
spline_count[1] += 1
else:
raise Exception('Invalid bath-coupling specification.')
string_list = []
for kk,_ in enumerate(H_td_terms):
string_list.append("H_terms[{0}]".format(kk))
for kk,_ in enumerate(H_obj):
string_list.append("H_obj[{0}]".format(kk))
for kk,_ in enumerate(C_td_terms):
string_list.append("C_terms[{0}]".format(kk))
for kk,_ in enumerate(CA_obj):
string_list.append("CA_obj[{0}]".format(kk))
for kk,_ in enumerate(A_td_terms):
string_list.append("A_terms[{0}]".format(kk))
#Add nrows to parameters
string_list.append('nrows')
for name, value in args.items():
if isinstance(value, np.ndarray):
raise TypeError('NumPy arrays not valid args for BR solver.')
else:
string_list.append(str(value))
parameter_string = ",".join(string_list)
if verbose:
print('BR prep time:', time.time()-_prep_time)
#
# generate and compile new cython code if necessary
#
if not options.rhs_reuse or config.tdfunc is None:
if options.rhs_filename is None:
config.tdname = "rhs" + str(os.getpid()) + str(config.cgen_num)
else:
config.tdname = opt.rhs_filename
if verbose:
_st = time.time()
cgen = BR_Codegen(h_terms=len(H_terms),
h_td_terms=H_td_terms, h_obj=H_obj,
c_terms=len(C_terms),
c_td_terms=C_td_terms, c_obj=CA_obj,
a_terms=len(A_terms), a_td_terms=A_td_terms,
spline_count=spline_count,
coupled_ops = coupled_ops,
coupled_lengths = coupled_lengths,
coupled_spectra = coupled_spectra,
config=config, sparse=False,
use_secular = use_secular,
sec_cutoff = sec_cutoff,
args=args,
use_openmp=options.use_openmp,
omp_thresh=qset.openmp_thresh if qset.has_openmp else None,
omp_threads=options.num_cpus,
atol=tol)
cgen.generate(config.tdname + ".pyx")
code = compile('from ' + config.tdname + ' import cy_td_ode_rhs',
'<string>', 'exec')
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
if verbose:
print('BR compile time:', time.time()-_st)
initial_vector = mat2vec(rho0.full()).ravel()
_ode = scipy.integrate.ode(config.tdfunc)
code = compile('_ode.set_f_params(' + parameter_string + ')',
'<string>', 'exec')
_ode.set_integrator('zvode', method=options.method,
order=options.order, atol=options.atol,
rtol=options.rtol, nsteps=options.nsteps,
first_step=options.first_step,
min_step=options.min_step,
max_step=options.max_step)
_ode.set_initial_value(initial_vector, tlist[0])
exec(code, locals())
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "brmesolve"
output.times = tlist
if options.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
options.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
if type(progress_bar)==BaseProgressBar and verbose:
_run_time = time.time()
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not _ode.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
if options.store_states or expt_callback:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(_ode.y), rho.shape[0], rho.shape[1])
if options.store_states:
output.states.append(Qobj(rho, isherm=True))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(e_sops_data[m],
_ode.y, 0)
else:
output.expect[m][t_idx] = expect_rho_vec(e_sops_data[m],
_ode.y, 1)
if t_idx < n_tsteps - 1:
_ode.integrate(_ode.t + dt[t_idx])
progress_bar.finished()
if type(progress_bar)==BaseProgressBar and verbose:
print('BR runtime:', time.time()-_run_time)
if (not options.rhs_reuse) and (config.tdname is not None):
_cython_build_cleanup(config.tdname)
if options.store_final_state:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(_ode.y), rho.shape[0], rho.shape[1])
output.final_state = Qobj(rho, dims=rho0.dims, isherm=True)
return output
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
logger.debug('Starting iterative inverse-power method solver.')
tol = ss_args['tol']
mtol = ss_args['mtol']
if mtol is None:
mtol = max(0.1*tol, 1e-15)
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = L.shape[0]
# Build Liouvillian
if ss_args['solver'] == 'mkl' and ss_args['method'] == 'power':
has_mkl = 1
else:
has_mkl = 0
L, perm, perm2, rev_perm, ss_args = _steadystate_power_liouvillian(L,
ss_args,
has_mkl)
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
v = v[np.ix_(perm2,)]
# Do preconditioning
if ss_args['solver'] == 'scipy':
if ss_args['M'] is None and ss_args['use_precond'] and \
ss_args['method'] in ['power-gmres',
'power-lgmres',
'power-bicgstab']:
ss_args['M'], ss_args = _iterative_precondition(L, int(np.sqrt(n)),
ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
_power_start = time.time()
# Get LU factors
if ss_args['method'] == 'power':
if ss_args['solver'] == 'mkl':
lu = mkl_splu(L, max_iter_refine=ss_args['max_iter_refine'],
scaling_vectors=ss_args['scaling_vectors'],
weighted_matching=ss_args['weighted_matching'])
else:
lu = splu(L, permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
logger.debug('L NNZ: %i ; U NNZ: %i' % (L_nnz, U_nnz))
logger.debug('Fill factor: %f' % ((L_nnz+U_nnz)/orig_nnz))
it = 0
# FIXME: These atol keyword except checks can be removed once scipy 1.1
# is a minimum requirement
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
check = 0
if ss_args['method'] == 'power':
v = lu.solve(v)
elif ss_args['method'] == 'power-gmres':
try:
v, check = gmres(L, v, tol=mtol, atol=ss_args['matol'],
M=ss_args['M'], x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = gmres(L, v, tol=mtol,
M=ss_args['M'], x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-lgmres':
try:
v, check = lgmres(L, v, tol=mtol, atol=ss_args['matol'],
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = lgmres(L, v, tol=mtol,
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-bicgstab':
try:
v, check = bicgstab(L, v, tol=mtol, atol=ss_args['matol'],
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = bicgstab(L, v, tol=mtol,
M=ss_args['M'], x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
if check > 0:
raise Exception("{} failed to find solution in "
"{} iterations.".format(ss_args['method'],
check))
if check < 0:
raise Exception("Breakdown in {}".format(ss_args['method']))
v = v / la.norm(v, np.inf)
it += 1
if ss_args['method'] == 'power' and ss_args['solver'] == 'mkl':
lu.delete()
if ss_args['return_info']:
ss_args['info']['max_iter_refine'] = ss_args['max_iter_refine']
ss_args['info']['scaling_vectors'] = ss_args['scaling_vectors']
ss_args['info']['weighted_matching'] = ss_args['weighted_matching']
if it >= maxiter:
raise Exception('Failed to find steady state after ' +
str(maxiter) + ' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end-_power_start
ss_args['info']['iterations'] = it
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(L*v, np.inf)
if settings.debug:
logger.debug('Number of iterations: %i' % it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm,)]
# normalise according to type of problem
if sflag:
trow = v[::rhoss.shape[0]+1]
data = v / np.sum(trow)
else:
data = data / la.norm(v)
data = dense2D_to_fastcsr_fmode(vec2mat(data),
rhoss.shape[0],
rhoss.shape[0])
rhoss.data = 0.5 * (data + data.H)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
print('Starting iterative inverse-power method solver...')
tol = ss_args['tol']
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = prod(rhoss.shape)
L = L.data.tocsc() - (1e-15) * sp.eye(n, n, format='csc')
L.sort_indices()
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n,dtype=complex)
if ss_args['use_rcm']:
if settings.debug:
old_band = sp_bandwidth(L)[0]
print('Original bandwidth:', old_band)
perm = reverse_cuthill_mckee(L)
rev_perm = np.argsort(perm)
L = sp_permute(L, perm, perm, 'csc')
v = v[np.ix_(perm,)]
if settings.debug:
new_band = sp_bandwidth(L)[0]
print('RCM bandwidth:', new_band)
print('Bandwidth reduction factor:', round(old_band/new_band, 2))
# Get LU factors
lu = splu(L, permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
print('L NNZ:', L_nnz, ';', 'U NNZ:', U_nnz)
print('Fill factor:', (L_nnz+U_nnz)/orig_nnz)
_power_start = time.time()
it = 0
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
v = lu.solve(v)
v = v / la.norm(v, np.inf)
it += 1
if it >= maxiter:
raise Exception('Failed to find steady state after ' +
str(maxiter) + ' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end-_power_start
ss_args['info']['iterations'] = it
if settings.debug:
print('Number of iterations:', it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm,)]
# normalise according to type of problem
if sflag:
trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
trow = sp_reshape(trow, (1, n))
data = v / sum(trow.dot(v))
else:
data = data / la.norm(v)
data = sp.csr_matrix(vec2mat(data))
rhoss.data = 0.5 * (data + data.conj().T)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar):
"""
Internal function for solving ME. Solve an ODE which solver parameters
already setup (r). Calculate the required expectation values or invoke
callback function at each time step.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "mesolve"
output.times = tlist
if opt.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
break
if opt.store_states or expt_callback:
rho.data = vec2mat(r.y)
if opt.store_states:
output.states.append(Qobj(rho))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 0)
else:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 1)
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if not opt.rhs_reuse and config.tdname is not None:
try:
os.remove(config.tdname + ".pyx")
except:
pass
if opt.store_final_state:
rho.data = vec2mat(r.y)
output.final_state = Qobj(rho)
return output
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
logger.debug('Starting iterative inverse-power method solver.')
tol = ss_args['tol']
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = L.shape[0]
# Build Liouvillian
if settings.has_mkl and ss_args['method'] == 'power':
has_mkl = 1
else:
has_mkl = 0
L, perm, perm2, rev_perm, ss_args = _steadystate_power_liouvillian(L,
ss_args, has_mkl)
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
v = v[np.ix_(perm2,)]
# Do preconditioning
if ss_args['M'] is None and ss_args['use_precond'] and \
ss_args['method'] in ['power-gmres',
'power-lgmres', 'power-bicgstab']:
ss_args['M'], ss_args = _iterative_precondition(L, int(np.sqrt(n)), ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
_power_start = time.time()
# Get LU factors
if ss_args['method'] == 'power':
if settings.has_mkl:
lu = mkl_splu(L)
else:
lu = splu(L, permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
logger.debug('L NNZ: %i ; U NNZ: %i' % (L_nnz, U_nnz))
logger.debug('Fill factor: %f' % ((L_nnz+U_nnz)/orig_nnz))
it = 0
_tol = max(ss_args['tol']/10, 1e-15) # Should make this user accessible
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
if ss_args['method'] == 'power':
v = lu.solve(v)
elif ss_args['method'] == 'power-gmres':
v, check = gmres(L, v, tol=_tol, M=ss_args['M'],
x0=ss_args['x0'], restart=ss_args['restart'],
maxiter=ss_args['maxiter'], callback=_iter_count)
elif ss_args['method'] == 'power-lgmres':
v, check = lgmres(L, v, tol=_tol, M=ss_args['M'],
x0=ss_args['x0'], maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-bicgstab':
v, check = bicgstab(L, v, tol=_tol, M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'], callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
v = v / la.norm(v, np.inf)
it += 1
if ss_args['method'] == 'power' and settings.has_mkl:
lu.delete()
if it >= maxiter:
raise Exception('Failed to find steady state after ' +
str(maxiter) + ' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end-_power_start
ss_args['info']['iterations'] = it
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(L*v)
if settings.debug:
logger.debug('Number of iterations: %i' % it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm,)]
# normalise according to type of problem
if sflag:
trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
trow = sp_reshape(trow, (1, n))
data = v / sum(trow.dot(v))
else:
data = data / la.norm(v)
data = sp.csr_matrix(vec2mat(data))
rhoss.data = 0.5 * (data + data.conj().T)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def _td_brmesolve(H,
psi0,
tlist,
a_ops=[],
e_ops=[],
c_ops=[],
args={},
use_secular=True,
sec_cutoff=0.1,
tol=qset.atol,
options=None,
progress_bar=None,
_safe_mode=True,
verbose=False,
_prep_time=0):
if isket(psi0):
rho0 = ket2dm(psi0)
else:
rho0 = psi0
nrows = rho0.shape[0]
H_terms = []
H_td_terms = []
H_obj = []
A_terms = []
A_td_terms = []
C_terms = []
C_td_terms = []
CA_obj = []
spline_count = [0, 0]
coupled_ops = []
coupled_lengths = []
coupled_spectra = []
if isinstance(H, Qobj):
H_terms.append(H.full('f'))
H_td_terms.append('1')
else:
for kk, h in enumerate(H):
if isinstance(h, Qobj):
H_terms.append(h.full('f'))
H_td_terms.append('1')
elif isinstance(h, list):
H_terms.append(h[0].full('f'))
if isinstance(h[1], Cubic_Spline):
H_obj.append(h[1].coeffs)
spline_count[0] += 1
H_td_terms.append(h[1])
else:
raise Exception('Invalid Hamiltonian specification.')
for kk, c in enumerate(c_ops):
if isinstance(c, Qobj):
C_terms.append(c.full('f'))
C_td_terms.append('1')
elif isinstance(c, list):
C_terms.append(c[0].full('f'))
if isinstance(c[1], Cubic_Spline):
CA_obj.append(c[1].coeffs)
spline_count[0] += 1
C_td_terms.append(c[1])
else:
raise Exception('Invalid collapse operator specification.')
coupled_offset = 0
for kk, a in enumerate(a_ops):
if isinstance(a, list):
if isinstance(a[0], Qobj):
A_terms.append(a[0].full('f'))
A_td_terms.append(a[1])
if isinstance(a[1], tuple):
if not len(a[1]) == 2:
raise Exception('Tuple must be len=2.')
if isinstance(a[1][0], Cubic_Spline):
spline_count[1] += 1
if isinstance(a[1][1], Cubic_Spline):
spline_count[1] += 1
elif isinstance(a[0], tuple):
if not isinstance(a[1], tuple):
raise Exception('Invalid bath-coupling specification.')
if (len(a[0]) + 1) != len(a[1]):
raise Exception('BR a_ops tuple lengths not compatible.')
coupled_ops.append(kk + coupled_offset)
coupled_lengths.append(len(a[0]))
coupled_spectra.append(a[1][0])
coupled_offset += len(a[0]) - 1
if isinstance(a[1][0], Cubic_Spline):
spline_count[1] += 1
for nn, _a in enumerate(a[0]):
A_terms.append(_a.full('f'))
A_td_terms.append(a[1][nn + 1])
if isinstance(a[1][nn + 1], Cubic_Spline):
CA_obj.append(a[1][nn + 1].coeffs)
spline_count[1] += 1
else:
raise Exception('Invalid bath-coupling specification.')
string_list = []
for kk, _ in enumerate(H_td_terms):
string_list.append("H_terms[{0}]".format(kk))
for kk, _ in enumerate(H_obj):
string_list.append("H_obj[{0}]".format(kk))
for kk, _ in enumerate(C_td_terms):
string_list.append("C_terms[{0}]".format(kk))
for kk, _ in enumerate(CA_obj):
string_list.append("CA_obj[{0}]".format(kk))
for kk, _ in enumerate(A_td_terms):
string_list.append("A_terms[{0}]".format(kk))
#Add nrows to parameters
string_list.append('nrows')
for name, value in args.items():
if isinstance(value, np.ndarray):
raise TypeError('NumPy arrays not valid args for BR solver.')
else:
string_list.append(str(value))
parameter_string = ",".join(string_list)
if verbose:
print('BR prep time:', time.time() - _prep_time)
#
# generate and compile new cython code if necessary
#
if not options.rhs_reuse or config.tdfunc is None:
if options.rhs_filename is None:
config.tdname = "rhs" + str(os.getpid()) + str(config.cgen_num)
else:
config.tdname = opt.rhs_filename
if verbose:
_st = time.time()
cgen = BR_Codegen(
h_terms=len(H_terms),
h_td_terms=H_td_terms,
h_obj=H_obj,
c_terms=len(C_terms),
c_td_terms=C_td_terms,
c_obj=CA_obj,
a_terms=len(A_terms),
a_td_terms=A_td_terms,
spline_count=spline_count,
coupled_ops=coupled_ops,
coupled_lengths=coupled_lengths,
coupled_spectra=coupled_spectra,
config=config,
sparse=False,
use_secular=use_secular,
sec_cutoff=sec_cutoff,
args=args,
use_openmp=options.use_openmp,
omp_thresh=qset.openmp_thresh if qset.has_openmp else None,
omp_threads=options.num_cpus,
atol=tol)
cgen.generate(config.tdname + ".pyx")
code = compile('from ' + config.tdname + ' import cy_td_ode_rhs',
'<string>', 'exec')
exec(code, globals())
config.tdfunc = cy_td_ode_rhs
if verbose:
print('BR compile time:', time.time() - _st)
initial_vector = mat2vec(rho0.full()).ravel()
_ode = scipy.integrate.ode(config.tdfunc)
code = compile('_ode.set_f_params(' + parameter_string + ')', '<string>',
'exec')
_ode.set_integrator('zvode',
method=options.method,
order=options.order,
atol=options.atol,
rtol=options.rtol,
nsteps=options.nsteps,
first_step=options.first_step,
min_step=options.min_step,
max_step=options.max_step)
_ode.set_initial_value(initial_vector, tlist[0])
exec(code, locals())
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "brmesolve"
output.times = tlist
if options.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
options.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
if type(progress_bar) == BaseProgressBar and verbose:
_run_time = time.time()
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not _ode.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
if options.store_states or expt_callback:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(_ode.y), rho.shape[0],
rho.shape[1])
if options.store_states:
output.states.append(Qobj(rho, isherm=True))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], _ode.y, 0)
else:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], _ode.y, 1)
if t_idx < n_tsteps - 1:
_ode.integrate(_ode.t + dt[t_idx])
progress_bar.finished()
if type(progress_bar) == BaseProgressBar and verbose:
print('BR runtime:', time.time() - _run_time)
if (not options.rhs_reuse) and (config.tdname is not None):
_cython_build_cleanup(config.tdname)
if options.store_final_state:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(_ode.y), rho.shape[0],
rho.shape[1])
output.final_state = Qobj(rho, dims=rho0.dims, isherm=True)
return output
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
print('Starting iterative inverse-power method solver...')
tol = ss_args['tol']
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = prod(rhoss.shape)
L = L.data.tocsc() - (1e-15) * sp.eye(n, n, format='csc')
L.sort_indices()
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
if settings.debug:
old_band = sp_bandwidth(L)[0]
print('Original bandwidth:', old_band)
perm = reverse_cuthill_mckee(L)
rev_perm = np.argsort(perm)
L = sp_permute(L, perm, perm, 'csc')
v = v[np.ix_(perm, )]
if settings.debug:
new_band = sp_bandwidth(L)[0]
print('RCM bandwidth:', new_band)
print('Bandwidth reduction factor:', round(old_band / new_band, 2))
# Get LU factors
lu = splu(L,
permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
print('L NNZ:', L_nnz, ';', 'U NNZ:', U_nnz)
print('Fill factor:', (L_nnz + U_nnz) / orig_nnz)
_power_start = time.time()
it = 0
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
v = lu.solve(v)
v = v / la.norm(v, np.inf)
it += 1
if it >= maxiter:
raise Exception('Failed to find steady state after ' + str(maxiter) +
' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end - _power_start
ss_args['info']['iterations'] = it
if settings.debug:
print('Number of iterations:', it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm, )]
# normalise according to type of problem
if sflag:
trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
trow = sp_reshape(trow, (1, n))
data = v / sum(trow.dot(v))
else:
data = data / la.norm(v)
data = sp.csr_matrix(vec2mat(data))
rhoss.data = 0.5 * (data + data.conj().T)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar):
"""
Internal function for solving ME. Solve an ODE which solver parameters
already setup (r). Calculate the required expectation values or invoke
callback function at each time step.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "mesolve"
output.times = tlist
if opt.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
if opt.store_states or expt_callback:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(r.y), rho.shape[0],
rho.shape[1])
if opt.store_states:
output.states.append(Qobj(rho, isherm=True))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 0)
else:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 1)
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if (not opt.rhs_reuse) and (config.tdname is not None):
_cython_build_cleanup(config.tdname)
if opt.store_final_state:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(r.y), rho.shape[0],
rho.shape[1])
output.final_state = Qobj(rho, dims=rho0.dims, isherm=True)
return output
def _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar):
"""
Internal function for solving ME. Solve an ODE which solver parameters
already setup (r). Calculate the required expectation values or invoke
callback function at each time step.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "mesolve"
output.times = tlist
if opt.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
if opt.store_states or expt_callback:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(r.y), rho.shape[0], rho.shape[1])
if opt.store_states:
output.states.append(Qobj(rho, isherm=True))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(e_sops_data[m],
r.y, 0)
else:
output.expect[m][t_idx] = expect_rho_vec(e_sops_data[m],
r.y, 1)
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if (not opt.rhs_reuse) and (config.tdname is not None):
_cython_build_cleanup(config.tdname)
if opt.store_final_state:
rho.data = dense2D_to_fastcsr_fmode(vec2mat(r.y), rho.shape[0], rho.shape[1])
output.final_state = Qobj(rho, dims=rho0.dims, isherm=True)
return output
def tensor(*args):
"""Calculates the tensor product of input operators.
Parameters
----------
args : array_like
``list`` or ``array`` of quantum objects for tensor product.
Returns
-------
obj : qobj
A composite quantum object.
Examples
--------
>>> tensor([sigmax(), sigmax()])
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]]
"""
if not args:
raise TypeError("Requires at least one input argument")
if len(args) == 1 and isinstance(args[0], (list, np.ndarray)):
# this is the case when tensor is called on the form:
# tensor([q1, q2, q3, ...])
qlist = args[0]
elif len(args) == 1 and isinstance(args[0], Qobj):
# tensor is called with a single Qobj as an argument, do nothing
return args[0]
else:
# this is the case when tensor is called on the form:
# tensor(q1, q2, q3, ...)
qlist = args
if not all([isinstance(q, Qobj) for q in qlist]):
# raise error if one of the inputs is not a quantum object
raise TypeError("One of inputs is not a quantum object")
out = Qobj()
if qlist[0].issuper:
out.superrep = qlist[0].superrep
if not all([q.superrep == out.superrep for q in qlist]):
raise TypeError("In tensor products of superroperators, all must" +
"have the same representation")
out.isherm = True
for n, q in enumerate(qlist):
if n == 0:
out.data = q.data
out.dims = q.dims
else:
out.data = sp.kron(out.data, q.data, format='csr')
out.dims = [out.dims[0] + q.dims[0], out.dims[1] + q.dims[1]]
out.isherm = out.isherm and q.isherm
if not out.isherm:
out._isherm = None
return out.tidyup() if qutip.settings.auto_tidyup else out
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
logger.debug('Starting iterative inverse-power method solver.')
tol = ss_args['tol']
mtol = ss_args['mtol']
if mtol is None:
mtol = max(0.1 * tol, 1e-15)
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = L.shape[0]
# Build Liouvillian
if ss_args['solver'] == 'mkl' and ss_args['method'] == 'power':
has_mkl = 1
else:
has_mkl = 0
L, perm, perm2, rev_perm, ss_args = _steadystate_power_liouvillian(
L, ss_args, has_mkl)
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
v = v[np.ix_(perm2, )]
# Do preconditioning
if ss_args['solver'] == 'scipy':
if ss_args['M'] is None and ss_args['use_precond'] and \
ss_args['method'] in ['power-gmres',
'power-lgmres',
'power-bicgstab']:
ss_args['M'], ss_args = _iterative_precondition(
L, int(np.sqrt(n)), ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
_power_start = time.time()
# Get LU factors
if ss_args['method'] == 'power':
if ss_args['solver'] == 'mkl':
lu = mkl_splu(L,
max_iter_refine=ss_args['max_iter_refine'],
scaling_vectors=ss_args['scaling_vectors'],
weighted_matching=ss_args['weighted_matching'])
else:
lu = splu(L,
permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
logger.debug('L NNZ: %i ; U NNZ: %i' % (L_nnz, U_nnz))
logger.debug('Fill factor: %f' % ((L_nnz + U_nnz) / orig_nnz))
it = 0
# FIXME: These atol keyword except checks can be removed once scipy 1.1
# is a minimum requirement
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
check = 0
if ss_args['method'] == 'power':
v = lu.solve(v)
elif ss_args['method'] == 'power-gmres':
try:
v, check = gmres(L,
v,
tol=mtol,
atol=ss_args['matol'],
M=ss_args['M'],
x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = gmres(L,
v,
tol=mtol,
M=ss_args['M'],
x0=ss_args['x0'],
restart=ss_args['restart'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-lgmres':
try:
v, check = lgmres(L,
v,
tol=mtol,
atol=ss_args['matol'],
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = lgmres(L,
v,
tol=mtol,
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-bicgstab':
try:
v, check = bicgstab(L,
v,
tol=mtol,
atol=ss_args['matol'],
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
except TypeError as e:
if "unexpected keyword argument 'atol'" in str(e):
v, check = bicgstab(L,
v,
tol=mtol,
M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'],
callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
if check > 0:
raise Exception("{} failed to find solution in "
"{} iterations.".format(ss_args['method'], check))
if check < 0:
raise Exception("Breakdown in {}".format(ss_args['method']))
v = v / la.norm(v, np.inf)
it += 1
if ss_args['method'] == 'power' and ss_args['solver'] == 'mkl':
lu.delete()
if ss_args['return_info']:
ss_args['info']['max_iter_refine'] = ss_args['max_iter_refine']
ss_args['info']['scaling_vectors'] = ss_args['scaling_vectors']
ss_args['info']['weighted_matching'] = ss_args['weighted_matching']
if it >= maxiter:
raise Exception('Failed to find steady state after ' + str(maxiter) +
' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end - _power_start
ss_args['info']['iterations'] = it
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(L * v, np.inf)
if settings.debug:
logger.debug('Number of iterations: %i' % it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm, )]
# normalise according to type of problem
if sflag:
trow = v[::rhoss.shape[0] + 1]
data = v / np.sum(trow)
else:
data = data / la.norm(v)
data = dense2D_to_fastcsr_fmode(vec2mat(data), rhoss.shape[0],
rhoss.shape[0])
rhoss.data = 0.5 * (data + data.H)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def floquet_markov_mesolve(R, ekets, rho0, tlist, e_ops, f_modes_table=None,
options=None, floquet_basis=True):
"""
Solve the dynamics for the system using the Floquet-Markov master equation.
"""
if options is None:
opt = Options()
else:
opt = options
if opt.tidy:
R.tidyup()
#
# check initial state
#
if isket(rho0):
# Got a wave function as initial state: convert to density matrix.
rho0 = ket2dm(rho0)
#
# prepare output array
#
n_tsteps = len(tlist)
dt = tlist[1] - tlist[0]
output = Result()
output.solver = "fmmesolve"
output.times = tlist
if isinstance(e_ops, FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
output.states = []
else:
if not f_modes_table:
raise TypeError("The Floquet mode table has to be provided " +
"when requesting expectation values.")
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
if op.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# transform the initial density matrix to the eigenbasis: from
# computational basis to the floquet basis
#
if ekets is not None:
rho0 = rho0.transform(ekets)
#
# setup integrator
#
initial_vector = mat2vec(rho0.full())
r = scipy.integrate.ode(cy_ode_rhs)
r.set_f_params(R.data.data, R.data.indices, R.data.indptr)
r.set_integrator('zvode', method=opt.method, order=opt.order,
atol=opt.atol, rtol=opt.rtol, max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
#
# start evolution
#
rho = Qobj(rho0)
t_idx = 0
for t in tlist:
if not r.successful():
break
rho.data = vec2mat(r.y)
if expt_callback:
# use callback method
if floquet_basis:
e_ops(t, Qobj(rho))
else:
f_modes_table_t, T = f_modes_table
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
e_ops(t, Qobj(rho).transform(f_modes_t, True))
else:
# calculate all the expectation values, or output rho if
# no operators
if n_expt_op == 0:
if floquet_basis:
output.states.append(Qobj(rho))
else:
f_modes_table_t, T = f_modes_table
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
output.states.append(Qobj(rho).transform(f_modes_t, True))
else:
f_modes_table_t, T = f_modes_table
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
for m in range(0, n_expt_op):
output.expect[m][t_idx] = \
expect(e_ops[m], rho.transform(f_modes_t, False))
r.integrate(r.t + dt)
t_idx += 1
return output
def _steadystate_power(L, ss_args):
"""
Inverse power method for steady state solving.
"""
ss_args['info'].pop('weight', None)
if settings.debug:
logger.debug('Starting iterative inverse-power method solver.')
tol = ss_args['tol']
maxiter = ss_args['maxiter']
use_solver(assumeSortedIndices=True)
rhoss = Qobj()
sflag = issuper(L)
if sflag:
rhoss.dims = L.dims[0]
else:
rhoss.dims = [L.dims[0], 1]
n = L.shape[0]
# Build Liouvillian
L, perm, perm2, rev_perm, ss_args = _steadystate_power_liouvillian(L, ss_args)
orig_nnz = L.nnz
# start with all ones as RHS
v = np.ones(n, dtype=complex)
if ss_args['use_rcm']:
v = v[np.ix_(perm2,)]
# Do preconditioning
if ss_args['M'] is None and ss_args['use_precond'] and \
ss_args['method'] in ['power-gmres',
'power-lgmres', 'power-bicgstab']:
ss_args['M'], ss_args = _iterative_precondition(L, int(np.sqrt(n)), ss_args)
if ss_args['M'] is None:
warnings.warn("Preconditioning failed. Continuing without.",
UserWarning)
ss_iters = {'iter': 0}
def _iter_count(r):
ss_iters['iter'] += 1
return
_power_start = time.time()
# Get LU factors
if ss_args['method'] == 'power':
lu = splu(L, permc_spec=ss_args['permc_spec'],
diag_pivot_thresh=ss_args['diag_pivot_thresh'],
options=dict(ILU_MILU=ss_args['ILU_MILU']))
if settings.debug and _scipy_check:
L_nnz = lu.L.nnz
U_nnz = lu.U.nnz
logger.debug('L NNZ: %i ; U NNZ: %i' % (L_nnz, U_nnz))
logger.debug('Fill factor: %f' % ((L_nnz+U_nnz)/orig_nnz))
it = 0
_tol = np.max(ss_args['tol']/10,1e-15) # Should make this user accessible
while (la.norm(L * v, np.inf) > tol) and (it < maxiter):
if ss_args['method'] == 'power':
v = lu.solve(v)
elif ss_args['method'] == 'power-gmres':
v, check = gmres(L, v, tol=_tol, M=ss_args['M'],
x0=ss_args['x0'], restart=ss_args['restart'],
maxiter=ss_args['maxiter'], callback=_iter_count)
elif ss_args['method'] == 'power-lgmres':
v, check = lgmres(L, v, tol=_tol, M=ss_args['M'],
x0=ss_args['x0'], maxiter=ss_args['maxiter'],
callback=_iter_count)
elif ss_args['method'] == 'power-bicgstab':
v, check = bicgstab(L, v, tol=_tol, M=ss_args['M'],
x0=ss_args['x0'],
maxiter=ss_args['maxiter'], callback=_iter_count)
else:
raise Exception("Invalid iterative solver method.")
v = v / la.norm(v, np.inf)
it += 1
if it >= maxiter:
raise Exception('Failed to find steady state after ' +
str(maxiter) + ' iterations')
_power_end = time.time()
ss_args['info']['solution_time'] = _power_end-_power_start
ss_args['info']['iterations'] = it
if ss_args['return_info']:
ss_args['info']['residual_norm'] = la.norm(L*v)
if settings.debug:
logger.debug('Number of iterations: %i' % it)
if ss_args['use_rcm']:
v = v[np.ix_(rev_perm,)]
# normalise according to type of problem
if sflag:
trow = sp.eye(rhoss.shape[0], rhoss.shape[0], format='coo')
trow = sp_reshape(trow, (1, n))
data = v / sum(trow.dot(v))
else:
data = data / la.norm(v)
data = sp.csr_matrix(vec2mat(data))
rhoss.data = 0.5 * (data + data.conj().T)
rhoss.isherm = True
if ss_args['return_info']:
return rhoss, ss_args['info']
else:
return rhoss
def generic_ode_solve_checkpoint(r, rho0, tlist, e_ops, opt, progress_bar,
save, subdir):
"""
Internal function for solving ME. Solve an ODE which solver parameters
already setup (r). Calculate the required expectation values or invoke
callback function at each time step.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "mesolve"
output.times = tlist
if opt.store_states:
output.states = []
e_ops_dict = e_ops
e_ops = [e for e in e_ops_dict.values()]
headings = [key for key in e_ops_dict.keys()]
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
results_row = np.zeros(n_expt_op)
#
# start evolution
#
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dims = rho.dims
dt = np.diff(tlist)
end_time = tlist[-1]
for t_idx, t in tqdm(enumerate(tlist)):
progress_bar.update(t_idx)
if not r.successful():
raise Exception("ODE integration error: Try to increase "
"the allowed number of substeps by increasing "
"the nsteps parameter in the Options class.")
if opt.store_states or expt_callback:
rho.data = vec2mat(r.y)
if opt.store_states:
output.states.append(Qobj(rho))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 0)
results_row[m] = output.expect[m][t_idx]
else:
output.expect[m][t_idx] = expect_rho_vec(
e_sops_data[m], r.y, 1)
results_row[m] = output.expect[m][t_idx]
results = pd.DataFrame(results_row).T
results.columns = headings
results.index = [t]
results.index.name = 'times'
if t == 0:
first_row = True
else:
first_row = False
if save:
rho_checkpoint = Qobj(vec2mat(r.y))
rho_checkpoint.dims = dims
if t_idx % 200 == 0:
rho_c = rho_checkpoint.ptrace(0)
with open('./cavity_states.pkl', 'ab') as f:
pickle.dump(rho_c, f)
with open('./results.csv', 'a') as file:
results.to_csv(file, header=first_row, float_format='%.15f')
qsave(rho_checkpoint, './state_checkpoint')
save = True
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if not opt.rhs_reuse and config.tdname is not None:
_cython_build_cleanup(config.tdname)
return output
def _generic_ode_solve(r, rho0, tlist, e_ops, opt, progress_bar):
"""
Internal function for solving ME. Solve an ODE which solver parameters
already setup (r). Calculate the required expectation values or invoke
callback function at each time step.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
e_sops_data = []
output = Result()
output.solver = "mesolve"
output.times = tlist
if opt.store_states:
output.states = []
if isinstance(e_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
# fall back on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
e_sops_data.append(spre(op).data)
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
dt = np.diff(tlist)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
break
if opt.store_states or expt_callback:
rho.data = vec2mat(r.y)
if opt.store_states:
output.states.append(Qobj(rho))
if expt_callback:
# use callback method
e_ops(t, rho)
for m in range(n_expt_op):
if output.expect[m].dtype == complex:
output.expect[m][t_idx] = expect_rho_vec(e_sops_data[m], r.y, 0)
else:
output.expect[m][t_idx] = expect_rho_vec(e_sops_data[m], r.y, 1)
if t_idx < n_tsteps - 1:
r.integrate(r.t + dt[t_idx])
progress_bar.finished()
if not opt.rhs_reuse and config.tdname is not None:
try:
os.remove(config.tdname + ".pyx")
except:
pass
if opt.store_final_state:
rho.data = vec2mat(r.y)
output.final_state = Qobj(rho)
return output
def liouvillian(H, c_ops=[], data_only=False, chi=None):
"""Assembles the Liouvillian superoperator from a Hamiltonian
and a ``list`` of collapse operators. Like liouvillian, but with an
experimental implementation which avoids creating extra Qobj instances,
which can be advantageous for large systems.
Parameters
----------
H : Qobj or QobjEvo
System Hamiltonian.
c_ops : array_like of Qobj or QobjEvo
A ``list`` or ``array`` of collapse operators.
Returns
-------
L : Qobj or QobjEvo
Liouvillian superoperator.
"""
if isinstance(c_ops, (Qobj, QobjEvo)):
c_ops = [c_ops]
if chi and len(chi) != len(c_ops):
raise ValueError('chi must be a list with same length as c_ops')
h = None
if H is not None:
if isinstance(H, QobjEvo):
h = H.cte
else:
h = H
if h.isoper:
op_dims = h.dims
op_shape = h.shape
elif h.issuper:
op_dims = h.dims[0]
op_shape = [np.prod(op_dims[0]), np.prod(op_dims[0])]
else:
raise TypeError("Invalid type for Hamiltonian.")
else:
# no hamiltonian given, pick system size from a collapse operator
if isinstance(c_ops, list) and len(c_ops) > 0:
if isinstance(c_ops[0], QobjEvo):
c = c_ops[0].cte
else:
c = c_ops[0]
if c.isoper:
op_dims = c.dims
op_shape = c.shape
elif c.issuper:
op_dims = c.dims[0]
op_shape = [np.prod(op_dims[0]), np.prod(op_dims[0])]
else:
raise TypeError("Invalid type for collapse operator.")
else:
raise TypeError("Either H or c_ops must be given.")
sop_dims = [[op_dims[0], op_dims[0]], [op_dims[1], op_dims[1]]]
sop_shape = [np.prod(op_dims), np.prod(op_dims)]
spI = fast_identity(op_shape[0])
td = False
L = None
if isinstance(H, QobjEvo):
td = True
def H2L(H):
if H.isoper:
return -1.0j * (spre(H) - spost(H))
else:
return H
L = H.apply(H2L)
data = L.cte.data
elif isinstance(H, Qobj):
if H.isoper:
Ht = H.data.T
data = -1j * zcsr_kron(spI, H.data)
data += 1j * zcsr_kron(Ht, spI)
else:
data = H.data
else:
data = fast_csr_matrix(shape=(sop_shape[0], sop_shape[1]))
td_c_ops = []
for idx, c_op in enumerate(c_ops):
if isinstance(c_op, QobjEvo):
td = True
if c_op.const:
c_ = c_op.cte
elif chi:
td_c_ops.append(lindblad_dissipator(c_op, chi=chi[idx]))
continue
else:
td_c_ops.append(lindblad_dissipator(c_op))
continue
else:
c_ = c_op
if c_.issuper:
data = data + c_.data
else:
cd = c_.data.H
c = c_.data
if chi:
data = data + np.exp(1j * chi[idx]) * \
zcsr_kron(c.conj(), c)
else:
data = data + zcsr_kron(c.conj(), c)
cdc = cd * c
cdct = cdc.T
data = data - 0.5 * zcsr_kron(spI, cdc)
data = data - 0.5 * zcsr_kron(cdct, spI)
if not td:
if data_only:
return data
else:
L = Qobj()
L.dims = sop_dims
L.data = data
L.superrep = 'super'
return L
else:
if not L:
l = Qobj()
l.dims = sop_dims
l.data = data
l.superrep = 'super'
L = QobjEvo(l)
else:
L.cte.data = data
for c_op in td_c_ops:
L += c_op
return L
def _generic_ode_solve(r, rho0, tlist, expt_ops, opt, progress_bar):
"""
Internal function for solving ME.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
dt = tlist[1] - tlist[0]
output = Odedata()
output.solver = "mesolve"
output.times = tlist
if opt.store_states:
output.states = []
if isinstance(expt_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(expt_ops, list):
n_expt_op = len(expt_ops)
expt_callback = False
if n_expt_op == 0:
# fallback on storing states
output.states = []
opt.store_states = True
else:
output.expect = []
output.num_expect = n_expt_op
for op in expt_ops:
if op.isherm and rho0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
progress_bar.start(n_tsteps)
rho = Qobj(rho0)
for t_idx, t in enumerate(tlist):
progress_bar.update(t_idx)
if not r.successful():
break
rho.data = vec2mat(r.y)
if opt.store_states:
output.states.append(Qobj(rho))
if expt_callback:
# use callback method
expt_ops(t, Qobj(rho))
for m in range(n_expt_op):
output.expect[m][t_idx] = expect(expt_ops[m], rho)
r.integrate(r.t + dt)
progress_bar.finished()
if not opt.rhs_reuse and odeconfig.tdname is not None:
try:
os.remove(odeconfig.tdname + ".pyx")
except:
pass
if opt.store_final_state:
output.final_state = Qobj(rho)
return output
def tensor(*args):
"""Calculates the tensor product of input operators.
Parameters
----------
args : array_like
``list`` or ``array`` of quantum objects for tensor product.
Returns
--------
obj : qobj
A composite quantum object.
Examples
--------
>>> tensor([sigmax(), sigmax()])
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]]
"""
if not args:
raise TypeError("Requires at least one input argument")
num_args = len(args)
step = 0
for n in range(num_args):
if isinstance(args[n], Qobj):
qos = args[n]
if step == 0:
dat = qos.data
dim = qos.dims
shp = qos.shape
step = 1
else:
dat = sp.kron(dat, qos.data, format='csr')
dim = [dim[0] + qos.dims[0],
dim[1] + qos.dims[1]] # append dimensions of Qobjs
shp = [dat.shape[0], dat.shape[1]] # new shape of matrix
elif isinstance(args[n], (list, ndarray)):
qos = args[n]
items = len(qos) # number of inputs
if not all([isinstance(k, Qobj) for k in qos]):
# raise error if one of the inputs is not a quantum object
raise TypeError("One of inputs is not a quantum object")
if items == 1: # if only one Qobj, do nothing
if step == 0:
dat = qos[0].data
dim = qos[0].dims
shp = qos[0].shape
step = 1
else:
dat = sp.kron(dat, qos[0].data, format='csr')
dim = [dim[0] + qos[0].dims[0],
dim[1] + qos[0].dims[1]] # append dimensions of qos
shp = [dat.shape[0], dat.shape[1]] # new shape of matrix
elif items != 1:
if step == 0:
dat = qos[0].data
dim = qos[0].dims
shp = qos[0].shape
step = 1
for k in range(items - 1): # cycle over all items
dat = sp.kron(dat, qos[k + 1].data, format='csr')
dim = [
dim[0] + qos[k + 1].dims[0],
dim[1] + qos[k + 1].dims[1]
]
shp = [dat.shape[0], dat.shape[1]] # new shape of matrix
out = Qobj()
out.data = dat
out.dims = dim
out.shape = shp
if qutip.settings.auto_tidyup:
return Qobj(out).tidyup() # returns tidy Qobj
else:
return Qobj(out)
def floquet_markov_mesolve(R, ekets, rho0, tlist, e_ops, f_modes_table=None,
options=None, floquet_basis=True):
"""
Solve the dynamics for the system using the Floquet-Markov master equation.
"""
if options is None:
opt = Options()
else:
opt = options
if opt.tidy:
R.tidyup()
#
# check initial state
#
if isket(rho0):
# Got a wave function as initial state: convert to density matrix.
rho0 = ket2dm(rho0)
#
# prepare output array
#
n_tsteps = len(tlist)
dt = tlist[1] - tlist[0]
output = Result()
output.solver = "fmmesolve"
output.times = tlist
if isinstance(e_ops, FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
output.states = []
else:
if not f_modes_table:
raise TypeError("The Floquet mode table has to be provided " +
"when requesting expectation values.")
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
if op.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# transform the initial density matrix to the eigenbasis: from
# computational basis to the floquet basis
#
if ekets is not None:
rho0 = rho0.transform(ekets)
#
# setup integrator
#
initial_vector = mat2vec(rho0.full())
r = scipy.integrate.ode(cy_ode_rhs)
r.set_f_params(R.data.data, R.data.indices, R.data.indptr)
r.set_integrator('zvode', method=opt.method, order=opt.order,
atol=opt.atol, rtol=opt.rtol, max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
#
# start evolution
#
rho = Qobj(rho0)
t_idx = 0
for t in tlist:
if not r.successful():
break
rho.data = vec2mat(r.y)
if expt_callback:
# use callback method
if floquet_basis:
e_ops(t, Qobj(rho))
else:
f_modes_table_t, T = f_modes_table
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
e_ops(t, Qobj(rho).transform(f_modes_t, True))
else:
# calculate all the expectation values, or output rho if
# no operators
if n_expt_op == 0:
if floquet_basis:
output.states.append(Qobj(rho))
else:
f_modes_table_t, T = f_modes_table
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
output.states.append(Qobj(rho).transform(f_modes_t, True))
else:
f_modes_table_t, T = f_modes_table
f_modes_t = floquet_modes_t_lookup(f_modes_table_t, t, T)
for m in range(0, n_expt_op):
output.expect[m][t_idx] = \
expect(e_ops[m], rho.transform(f_modes_t, False))
r.integrate(r.t + dt)
t_idx += 1
return output
def bloch_redfield_solve(R, ekets, rho0, tlist, e_ops=[], options=None):
"""
Evolve the ODEs defined by Bloch-Redfield master equation. The
Bloch-Redfield tensor can be calculated by the function
:func:`bloch_redfield_tensor`.
Parameters
----------
R : :class:`qutip.qobj`
Bloch-Redfield tensor.
ekets : array of :class:`qutip.qobj`
Array of kets that make up a basis tranformation for the eigenbasis.
rho0 : :class:`qutip.qobj`
Initial density matrix.
tlist : *list* / *array*
List of times for :math:`t`.
e_ops : list of :class:`qutip.qobj` / callback function
List of operators for which to evaluate expectation values.
options : :class:`qutip.Qdeoptions`
Options for the ODE solver.
Returns
-------
output: :class:`qutip.odedata`
An instance of the class :class:`qutip.odedata`, which contains either
an *array* of expectation values for the times specified by `tlist`.
"""
if options is None:
options = Odeoptions()
options.nsteps = 2500
if options.tidy:
R.tidyup()
#
# check initial state
#
if isket(rho0):
# Got a wave function as initial state: convert to density matrix.
rho0 = rho0 * rho0.dag()
#
# prepare output array
#
n_e_ops = len(e_ops)
n_tsteps = len(tlist)
dt = tlist[1] - tlist[0]
if n_e_ops == 0:
result_list = []
else:
result_list = []
for op in e_ops:
if op.isherm and rho0.isherm:
result_list.append(np.zeros(n_tsteps))
else:
result_list.append(np.zeros(n_tsteps, dtype=complex))
#
# transform the initial density matrix and the e_ops opterators to the
# eigenbasis
#
if ekets is not None:
rho0 = rho0.transform(ekets)
for n in arange(len(e_ops)):
e_ops[n] = e_ops[n].transform(ekets, False)
#
# setup integrator
#
initial_vector = mat2vec(rho0.full())
r = scipy.integrate.ode(cy_ode_rhs)
r.set_f_params(R.data.data, R.data.indices, R.data.indptr)
r.set_integrator('zvode', method=options.method, order=options.order,
atol=options.atol, rtol=options.rtol,
#nsteps=options.nsteps,
#first_step=options.first_step, min_step=options.min_step,
max_step=options.max_step)
r.set_initial_value(initial_vector, tlist[0])
#
# start evolution
#
rho = Qobj(rho0)
t_idx = 0
for t in tlist:
if not r.successful():
break
rho.data = vec2mat(r.y)
# calculate all the expectation values, or output rho if no operators
if n_e_ops == 0:
result_list.append(Qobj(rho))
else:
for m in range(0, n_e_ops):
result_list[m][t_idx] = expect(e_ops[m], rho)
r.integrate(r.t + dt)
t_idx += 1
return result_list
def tensor(*args):
"""Calculates the tensor product of input operators.
Parameters
----------
args : array_like
``list`` or ``array`` of quantum objects for tensor product.
Returns
-------
obj : qobj
A composite quantum object.
Examples
--------
>>> tensor([sigmax(), sigmax()])
Quantum object: dims = [[2, 2], [2, 2]], \
shape = [4, 4], type = oper, isHerm = True
Qobj data =
[[ 0.+0.j 0.+0.j 0.+0.j 1.+0.j]
[ 0.+0.j 0.+0.j 1.+0.j 0.+0.j]
[ 0.+0.j 1.+0.j 0.+0.j 0.+0.j]
[ 1.+0.j 0.+0.j 0.+0.j 0.+0.j]]
"""
if not args:
raise TypeError("Requires at least one input argument")
if len(args) == 1 and isinstance(args[0], (list, np.ndarray)):
# this is the case when tensor is called on the form:
# tensor([q1, q2, q3, ...])
qlist = args[0]
elif len(args) == 1 and isinstance(args[0], Qobj):
# tensor is called with a single Qobj as an argument, do nothing
return args[0]
else:
# this is the case when tensor is called on the form:
# tensor(q1, q2, q3, ...)
qlist = args
if not all([isinstance(q, Qobj) for q in qlist]):
# raise error if one of the inputs is not a quantum object
raise TypeError("One of inputs is not a quantum object")
out = Qobj()
if qlist[0].issuper:
out.superrep = qlist[0].superrep
if not all([q.superrep == out.superrep for q in qlist]):
raise TypeError("In tensor products of superroperators, all must" +
"have the same representation")
out.isherm = True
for n, q in enumerate(qlist):
if n == 0:
out.data = q.data
out.dims = q.dims
else:
out.data = sp.kron(out.data, q.data, format='csr')
out.dims = [out.dims[0] + q.dims[0], out.dims[1] + q.dims[1]]
out.isherm = out.isherm and q.isherm
if not out.isherm:
out._isherm = None
return out.tidyup() if qutip.settings.auto_tidyup else out
def floquet_markov_mesolve(R, ekets, rho0, tlist, e_ops, options=None):
"""
Solve the dynamics for the system using the Floquet-Markov master equation.
"""
if options is None:
opt = Odeoptions()
else:
opt = options
if opt.tidy:
R.tidyup()
#
# check initial state
#
if isket(rho0):
# Got a wave function as initial state: convert to density matrix.
rho0 = ket2dm(rho0)
#
# prepare output array
#
n_tsteps = len(tlist)
dt = tlist[1] - tlist[0]
output = Odedata()
output.times = tlist
if isinstance(e_ops, FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(e_ops, list):
n_expt_op = len(e_ops)
expt_callback = False
if n_expt_op == 0:
output.states = []
else:
output.expect = []
output.num_expect = n_expt_op
for op in e_ops:
if op.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# transform the initial density matrix and the e_ops opterators to the
# eigenbasis: from computational basis to the floquet basis
#
if ekets is not None:
rho0 = rho0.transform(ekets, True)
if isinstance(e_ops, list):
for n in np.arange(len(e_ops)): # not working
e_ops[n] = e_ops[n].transform(ekets)
#
# setup integrator
#
initial_vector = mat2vec(rho0.full())
r = scipy.integrate.ode(cyq_ode_rhs)
r.set_f_params(R.data.data, R.data.indices, R.data.indptr)
r.set_integrator("zvode", method=opt.method, order=opt.order, atol=opt.atol, rtol=opt.rtol, max_step=opt.max_step)
r.set_initial_value(initial_vector, tlist[0])
#
# start evolution
#
rho = Qobj(rho0)
t_idx = 0
for t in tlist:
if not r.successful():
break
rho.data = vec2mat(r.y)
if expt_callback:
# use callback method
e_ops(t, Qobj(rho))
else:
# calculate all the expectation values, or output rho if
# no operators
if n_expt_op == 0:
output.states.append(Qobj(rho)) # copy psi/rho
else:
for m in range(0, n_expt_op):
output.expect[m][t_idx] = expect(e_ops[m], rho) # basisOK?
r.integrate(r.t + dt)
t_idx += 1
return output
def liouvillian(H, c_ops=[], data_only=False, chi=None):
"""Assembles the Liouvillian superoperator from a Hamiltonian
and a ``list`` of collapse operators. Like liouvillian, but with an
experimental implementation which avoids creating extra Qobj instances,
which can be advantageous for large systems.
Parameters
----------
H : qobj
System Hamiltonian.
c_ops : array_like
A ``list`` or ``array`` of collapse operators.
Returns
-------
L : qobj
Liouvillian superoperator.
"""
if chi and len(chi) != len(c_ops):
raise ValueError('chi must be a list with same length as c_ops')
if H is not None:
if H.isoper:
op_dims = H.dims
op_shape = H.shape
elif H.issuper:
op_dims = H.dims[0]
op_shape = [np.prod(op_dims[0]), np.prod(op_dims[0])]
else:
raise TypeError("Invalid type for Hamiltonian.")
else:
# no hamiltonian given, pick system size from a collapse operator
if isinstance(c_ops, list) and len(c_ops) > 0:
c = c_ops[0]
if c.isoper:
op_dims = c.dims
op_shape = c.shape
elif c.issuper:
op_dims = c.dims[0]
op_shape = [np.prod(op_dims[0]), np.prod(op_dims[0])]
else:
raise TypeError("Invalid type for collapse operator.")
else:
raise TypeError("Either H or c_ops must be given.")
sop_dims = [[op_dims[0], op_dims[0]], [op_dims[1], op_dims[1]]]
sop_shape = [np.prod(op_dims), np.prod(op_dims)]
spI = sp.identity(op_shape[0], format='csr')
if H:
if H.isoper:
data = -1j * (sp.kron(spI, H.data, format='csr')
- sp.kron(H.data.T, spI, format='csr'))
else:
data = H.data
else:
data = sp.csr_matrix((sop_shape[0], sop_shape[1]), dtype=complex)
for idx, c_op in enumerate(c_ops):
if c_op.issuper:
data = data + c_op.data
else:
cd = c_op.data.T.conj()
c = c_op.data
if chi:
data = data + np.exp(1j * chi[idx]) * sp.kron(cd.T, c,
format='csr')
else:
data = data + sp.kron(cd.T, c, format='csr')
cdc = cd * c
data = data - 0.5 * sp.kron(spI, cdc, format='csr')
data = data - 0.5 * sp.kron(cdc.T, spI, format='csr')
if data_only:
return data
else:
L = Qobj()
L.dims = sop_dims
L.data = data
L.isherm = False
L.superrep = 'super'
return L
def _generic_ode_solve(r, psi0, tlist, expt_ops, opt,
state_vectorize, state_norm_func=None):
"""
Internal function for solving ODEs.
"""
#
# prepare output array
#
n_tsteps = len(tlist)
dt = tlist[1] - tlist[0]
output = Odedata()
output.solver = "mesolve"
output.times = tlist
if isinstance(expt_ops, types.FunctionType):
n_expt_op = 0
expt_callback = True
elif isinstance(expt_ops, list):
n_expt_op = len(expt_ops)
expt_callback = False
if n_expt_op == 0:
output.states = []
else:
output.expect = []
output.num_expect = n_expt_op
for op in expt_ops:
if op.isherm and psi0.isherm:
output.expect.append(np.zeros(n_tsteps))
else:
output.expect.append(np.zeros(n_tsteps, dtype=complex))
else:
raise TypeError("Expectation parameter must be a list or a function")
#
# start evolution
#
psi = Qobj(psi0)
t_idx = 0
for t in tlist:
if not r.successful():
break
if state_norm_func:
psi.data = state_vectorize(r.y)
state_norm = state_norm_func(psi.data)
psi.data = psi.data / state_norm
r.set_initial_value(r.y / state_norm, r.t)
else:
psi.data = state_vectorize(r.y)
if expt_callback:
# use callback method
expt_ops(t, Qobj(psi))
else:
# calculate all the expectation values,
# or output rho if no operators
if n_expt_op == 0:
output.states.append(Qobj(psi)) # copy psi/rho
else:
for m in range(0, n_expt_op):
output.expect[m][t_idx] = expect(expt_ops[m], psi)
r.integrate(r.t + dt)
t_idx += 1
if not opt.rhs_reuse and odeconfig.tdname is not None:
try:
os.remove(odeconfig.tdname + ".pyx")
except:
pass
return output
