def build_initial_state(self, initial_state=[]):
""" Build the initial density matrix for the atom.
The default is for all of the population to be in |0> <0|.
Args:
rho0: a list or array of populations, length num_states.
Returns:
Qu.Qobj: A density matrix representing the initial
Notes:
- The elements must sum to 1 (as this will be the trace of the
density matrix).
"""
if initial_state:
if len(initial_state) != self.num_states:
raise ValueError(
'initial_state must have num_states elements.')
self.initial_state = qu.qzero(self.num_states)
for i, g in enumerate(initial_state):
self.initial_state += g * self.sigma(i, i)
else:
self.initial_state = self.sigma(0, 0)
if not np.isclose(self.initial_state.tr(), 1.0):
raise ValueError(
'initial_state must have diagonal elements sum to 1.')
# Initialise rho
self.rho = self.initial_state
return self.initial_state
def get_frem_Hs(qubits, part):
"""
Turns input H and partition into valid
QuTip Hx and Hz for both F and R partition.
Input: isingH Hamiltonian and part(ition) dictionary
Output: (HFx, HFz, HRx, HRz)
"""
num_q = len(qubits)
Rqubits = part['Rqubits']
HF = part['HF']
HFx = qt.tensor(*[qt.qzero(2) for n in range(num_q)])
HFz = HFx.copy()
HR = part['HR']
HRx = HFx.copy()
HRz = HFx.copy()
for key in HR.keys():
if key[0] == key[1]:
if key[0] in Rqubits:
HRx += nqubit_1pauli(qt.sigmax(), key[0], num_q)
HRz += HR[key] * nqubit_1pauli(qt.sigmaz(), key[0], num_q)
else:
HFx += nqubit_1pauli(qt.sigmax(), key[0], num_q)
HFz += HF[key] * nqubit_1pauli(qt.sigmaz(), key[0], num_q)
else:
HRz += HR[key] * nqubit_2pauli(qt.sigmaz(), qt.sigmaz(), key[0], key[1], num_q)
HFz += HF[key] * nqubit_2pauli(qt.sigmaz(), qt.sigmaz(), key[0], key[1], num_q)
return (HFx, HFz, HRx, HRz)
def _parametrize_solver_coefficients(metafunc):
"""
Perform the parametrisation for test cases using a solver and some
time-dependent coefficients. This is necessary because not all solvers can
accept all combinations of time-dependence specifications.
"""
size = 10
times = np.linspace(0, 5, 50)
c_ops = [qutip.qzero(size)]
solvers = [
(qutip.sesolve, 'sesolve'),
(functools.partial(qutip.mesolve, c_ops=c_ops), 'mesolve'),
(functools.partial(qutip.mcsolve, c_ops=c_ops), "mcsolve"),
(qutip.brmesolve, 'brmesolve'),
]
# A list of (reference, test) pairs, where the reference is in function
# form because that's the fastest, and the test is named type.
coefficients = [
([_real_cos.spline(times)], "real-spline"),
([_real_cos.string(), _real_sin.spline(times)], "real-string,spline"),
([_real_cos.spline(times),
_real_sin.function()], "real-spline,function"),
([_complex_pos.spline(times),
_complex_neg.string()], "complex-spline,string"),
]
def _valid_case(solver_id, coefficient_id):
invalids = [
"brmesolve" in solver_id and "function" in coefficient_id,
]
return not any(invalids)
def _make_case(solver, solver_id, coefficients, coefficient_id):
marks = []
if "brmesolve" in solver_id:
# We must use the string as the reference type instead of the
# function if brmesolve is in use.
marks.append(pytest.mark.requires_cython)
coefficients = [(c.string_coefficient, other)
for c, other in coefficients]
id_ = "-".join([solver_id, coefficient_id])
return pytest.param(solver,
coefficients,
size,
times,
id=id_,
marks=marks)
cases = [
_make_case(solver, solver_id, coefficients_, coefficient_id)
for solver, solver_id in solvers
for coefficients_, coefficient_id in coefficients
if _valid_case(solver_id, coefficient_id)
]
metafunc.parametrize(["solver", "coefficients", "size", "times"], cases)
def test_commutator():
A = qutip.qeye(N)
B = qutip.destroy(N)
assert qutip.commutator(A, B) == qutip.qzero(N)
sx = qutip.sigmax()
sy = qutip.sigmay()
assert qutip.commutator(sx, sy) / 2 == (qutip.sigmaz() * 1j)
A = qutip.qeye(N)
B = qutip.destroy(N)
assert qutip.commutator(A, B, 'anti') == qutip.destroy(N) * 2
sx = qutip.sigmax()
sy = qutip.sigmay()
assert qutip.commutator(sx, sy, 'anti') == qutip.qzero(2)
with pytest.raises(TypeError) as e:
qutip.commutator(sx, sy, 'something')
assert str(e.value).startswith("Unknown commutator kind")
def compute_free_evolution_hamiltonian(nb_qubits, nb_drives, omega, omega0,
hbar):
H_res = qt.qzero([[2, 2]])
for index_qubit in range(nb_qubits):
H_qubit_tmp = qt.Qobj(np.zeros((2, 2)))
for index_drive in range(nb_drives):
delta = omega[index_drive] - omega0[index_qubit]
H_qubit_tmp += -hbar * delta * (qt.sigmam() * qt.sigmap())
H_res = H_res + compute_multiqbt_hamil(H_qubit_tmp, nb_qubits,
index_qubit, 2)
return H_res
def test_coefficient_c_ops_3ls(self, dependence_3ls):
# Calculate zero-delay HOM cross-correlation for incoherently pumped
# three-level system, g2_ab[0] with gamma = 1.
dimension = 3
H = qutip.qzero(dimension)
start = qutip.basis(dimension, 2)
times = _3ls_times
project_0_1 = qutip.projection(dimension, 0, 1)
project_1_2 = qutip.projection(dimension, 1, 2)
population_1 = qutip.projection(dimension, 1, 1)
# Define the pi pulse to be when 99% of the population is transferred.
rabi = np.sqrt(-np.log(0.01) / (_3ls_args['tp'] * np.sqrt(np.pi)))
c_ops = [project_0_1, [rabi * project_1_2, dependence_3ls]]
forwards = qutip.correlation_2op_2t(H,
start,
times,
times,
c_ops,
project_0_1.dag(),
project_0_1,
args=_3ls_args)
backwards = qutip.correlation_2op_2t(H,
start,
times,
times,
c_ops,
project_0_1.dag(),
project_0_1,
args=_3ls_args,
reverse=True)
n_expect = qutip.mesolve(H,
start,
times,
c_ops,
args=_3ls_args,
e_ops=[population_1]).expect[0]
correlation_ab = -forwards * backwards + _n_correlation(
times, n_expect)
g2_ab_0 = _trapz_2d(np.real(correlation_ab), times)
assert abs(g2_ab_0 - 0.185) < 1e-2
def __init__(self, op):
# Operator decomposition
dims = op.dims[0]
op_decomposition = []
for N in range(len(dims)+1):
# N = 0 -> constant term
# N = 1 -> single mode terms
# N = 2 -> 2 mode interaction
# and so forth...
for inds in combinations(iterable=range(len(dims)), r=N):
if inds: # This if statement is just there because ptrace and tensor does not work if inds is empty
h = op.ptrace(inds) / prod([d for i,d in enumerate(dims) if not i in inds])
# Figuring out tensor re-ordering
new_dims_order = [i for i in inds] + [j for j in range(len(dims)) if not j in inds] # This is the new order (inds[0], ind[1],..., notInds[0],...)
reorder = [new_dims_order.index(i) for i in range(len(new_dims_order))] # This restores old order
h_tensor = tensor([h]+[qeye(d) for i,d in enumerate(dims) if i not in inds]).permute(reorder) # Tensor product made in new_dims_order. Reordered by permute
else:
h = op.tr()/prod(dims)
h_tensor = h*qeye(list(dims))
op -= h_tensor
op_decomposition.append([inds,h,h_tensor])
if not op.tidyup()==qzero(list(dims)):
warnings.warn("Decomposition seems to be bad!")
self.decomp = op_decomposition
def test_zero_type():
"Operator CSR Type: zero_oper"
op = qzero(5)
assert_equal(isspmatrix_csr(op.data), True)
def test_zero_type():
"Operator CSR Type: zero_oper"
op = qzero(5, [[5], [5]])
assert_equal(isspmatrix_csr(op.data), True)
@pytest.mark.repeat(20)
@pytest.mark.parametrize("hermitian", [False, True], ids=['complex', 'real'])
def test_equivalent_to_matrix_element(hermitian):
dimension = 20
state = qutip.rand_ket(dimension, 0.3)
op = qutip.rand_herm(dimension, 0.2)
if not hermitian:
op = op + 1j * qutip.rand_herm(dimension, 0.1)
expected = (state.dag() * op * state).data[0, 0]
assert abs(qutip.expect(op, state) - expected) < 1e-14
@pytest.mark.parametrize("solve", [
pytest.param(qutip.sesolve, id="sesolve"),
pytest.param(functools.partial(qutip.mesolve, c_ops=[qutip.qzero(2)]),
id="mesolve"),
])
def test_compatibility_with_solver(solve):
e_ops = [getattr(qutip, 'sigma' + x)() for x in 'xyzmp']
h = qutip.sigmax()
state = qutip.basis(2, 0)
times = np.linspace(0, 10, 101)
options = qutip.Options(store_states=True)
result = solve(h, state, times, e_ops=e_ops, options=options)
direct, states = result.expect, result.states
indirect = qutip.expect(e_ops, states)
assert len(direct) == len(indirect)
for direct_, indirect_ in zip(direct, indirect):
assert len(direct_) == len(indirect_)
assert isinstance(direct_, np.ndarray)
def zero(self):
"""Returns the zero operator for the space
"""
return qt.qzero(self.dims())
def zero(self):
"""Returns the <code>Qobj</code> representation of the zero operator
for the space, which takes any state identically to zero
"""
return qt.qzero(self.dims())