def set_up_ops(self, N):
"""
Generate the Hamiltonians for the spinchain model and save them in the
attribute `ctrls`.
Parameters
----------
N: int
The number of qubits in the system.
"""
self.pulse_dict = {}
index = 0
# sx_ops
for m in range(N):
self.pulses.append(
Pulse(sigmax(), m, spline_kind=self.spline_kind))
self.pulse_dict["sx" + str(m)] = index
index += 1
# sz_ops
for m in range(N):
self.pulses.append(
Pulse(sigmaz(), m, spline_kind=self.spline_kind))
self.pulse_dict["sz" + str(m)] = index
index += 1
# sxsy_ops
operator = tensor([sigmax(), sigmax()]) + tensor([sigmay(), sigmay()])
for n in range(N - 1):
self.pulses.append(
Pulse(operator, [n, n+1], spline_kind=self.spline_kind))
self.pulse_dict["g" + str(n)] = index
index += 1
def set_up_ops(self, N):
"""
Generate the Hamiltonians for the spinchain model and save them in the
attribute `ctrls`.
Parameters
----------
N: int
The number of qubits in the system.
"""
# single qubit terms
self.a = tensor(destroy(self.num_levels))
self.pulses.append(
Pulse(self.a.dag() * self.a, [0], spline_kind=self.spline_kind))
for m in range(N):
self.pulses.append(
Pulse(sigmax(), [m + 1], spline_kind=self.spline_kind))
for m in range(N):
self.pulses.append(
Pulse(sigmaz(), [m + 1], spline_kind=self.spline_kind))
# interaction terms
a_full = tensor([destroy(self.num_levels)] +
[identity(2) for n in range(N)])
for n in range(N):
sm = tensor(
[identity(self.num_levels)] +
[destroy(2) if m == n else identity(2) for m in range(N)])
self.pulses.append(
Pulse(a_full.dag() * sm + a_full * sm.dag(),
list(range(N + 1)),
spline_kind=self.spline_kind))
self.psi_proj = tensor([basis(self.num_levels, 0)] +
[identity(2) for n in range(N)])
def add_control(self,
qobj,
targets=None,
cyclic_permutation=False,
label=None):
"""
Add a control Hamiltonian to the processor. It creates a new
:class:`qutip.qip.Pulse`
object for the device that is turned off
(``tlist = None``, ``coeff = None``). To activate the pulse, one
can set its `tlist` and `coeff`.
Parameters
----------
qobj: :class:`qutip.Qobj`
The Hamiltonian for the control pulse..
targets: list, optional
The indices of the target qubits
(or subquantum system of other dimensions).
cyclic_permutation: bool, optional
If true, the Hamiltonian will be expanded for
all cyclic permutation of the target qubits.
label: str, optional
The label (name) of the pulse
"""
# Check validity of ctrl
if not isinstance(qobj, Qobj):
raise TypeError("The control Hamiltonian must be a qutip.Qobj.")
if not qobj.isherm:
raise ValueError("The control Hamiltonian must be Hermitian.")
num_qubits = len(qobj.dims[0])
if targets is None:
targets = list(range(num_qubits))
if not isinstance(targets, list):
targets = [targets]
if cyclic_permutation:
for i in range(self.N):
temp_targets = [(t + i) % self.N for t in targets]
if label is not None:
temp_label = label + "_" + str(temp_targets)
temp_label = label
self.pulses.append(
Pulse(qobj,
temp_targets,
spline_kind=self.spline_kind,
label=temp_label))
else:
self.pulses.append(
Pulse(qobj, targets, spline_kind=self.spline_kind,
label=label))
def test_id_with_T1_T2(self):
"""
Test for identity evolution with relaxation t1 and t2
"""
# setup
a = destroy(2)
Hadamard = hadamard_transform(1)
ex_state = basis(2, 1)
mines_state = (basis(2, 1) - basis(2, 0)).unit()
end_time = 2.
tlist = np.arange(0, end_time + 0.02, 0.02)
t1 = 1.
t2 = 0.5
# test t1
test = Processor(1, t1=t1)
# zero ham evolution
test.add_pulse(Pulse(identity(2), 0, tlist, False))
result = test.run_state(ex_state, e_ops=[a.dag() * a])
assert_allclose(result.expect[0][-1],
np.exp(-1. / t1 * end_time),
rtol=1e-5,
err_msg="Error in t1 time simulation")
# test t2
test = Processor(1, t2=t2)
test.add_pulse(Pulse(identity(2), 0, tlist, False))
result = test.run_state(init_state=mines_state,
e_ops=[Hadamard * a.dag() * a * Hadamard])
assert_allclose(result.expect[0][-1],
np.exp(-1. / t2 * end_time) * 0.5 + 0.5,
rtol=1e-5,
err_msg="Error in t2 time simulation")
# test t1 and t2
t1 = np.random.rand(1) + 0.5
t2 = np.random.rand(1) * 0.5 + 0.5
test = Processor(1, t1=t1, t2=t2)
test.add_pulse(Pulse(identity(2), 0, tlist, False))
result = test.run_state(init_state=mines_state,
e_ops=[Hadamard * a.dag() * a * Hadamard])
assert_allclose(result.expect[0][-1],
np.exp(-1. / t2 * end_time) * 0.5 + 0.5,
rtol=1e-5,
err_msg="Error in t1 & t2 simulation, "
"with t1={} and t2={}".format(t1, t2))
def TestDrift(self):
"""
Test for the drift Hamiltonian
"""
processor = Processor(N=1)
processor.add_drift(sigmaz(), 0)
tlist = np.array([0., 1., 2.])
processor.add_pulse(Pulse(identity(2), 0, tlist, False))
ideal_qobjevo, _ = processor.get_qobjevo(noisy=True)
assert_equal(ideal_qobjevo.cte, sigmaz())
def process_noise(pulses,
noise_list,
dims,
t1=None,
t2=None,
device_noise=False):
"""
Apply noise to the input list of pulses. It does not modify the input
pulse, but return a new one containing the noise.
Parameters
----------
pulses: list of :class:`qutip.qip.Pulse`
The input pulses, on which the noise object will be applied.
noise_list: list of :class:`qutip.qip.noise`
A list of noise objects.
dims: int or list
Dimension of the system.
If int, we assume it is the number of qubits in the system.
If list, it is the dimension of the component systems.
t1: list or float, optional
Characterize the decoherence of amplitude damping for
each qubit. A list of size `N` or a float for all qubits.
t2: list of float, optional
Characterize the decoherence of dephasing for
each qubit. A list of size `N` or a float for all qubits.
device_noise: bool
If pulse independent noise such as relaxation are included.
Default is False.
Returns
-------
noisy_pulses: list of :class:`qutip.qip.Pulse`
The noisy pulses, including the system noise.
"""
noisy_pulses = deepcopy(pulses)
systematic_noise = Pulse(None, None, label="systematic_noise")
if (t1 is not None) or (t2 is not None):
noise_list.append(RelaxationNoise(t1, t2))
for noise in noise_list:
if isinstance(noise, (DecoherenceNoise, RelaxationNoise)) \
and not device_noise:
pass
else:
noisy_pulses, systematic_noise = noise._apply_noise(
dims=dims,
pulses=noisy_pulses,
systematic_noise=systematic_noise)
if device_noise:
return noisy_pulses + [systematic_noise]
else:
return noisy_pulses
def get_noisy_dynamics(self, dims):
"""
Return a list of Pulse object with only trivial ideal pulse (H=0) but
non-trivial lindblad noise.
Parameters
----------
dims: list, optional
The dimension of the components system, the default value is
[2,2...,2] for qubits system.
Returns
-------
lindblad_noise: list of :class:`qutip.qip.Pulse`
A list of Pulse object with only trivial ideal pulse (H=0) but
non-trivial lindblad noise.
"""
if isinstance(dims, list):
N = len(dims)
else:
N = dims
# time-independent
if (self.coeff is None) and (self.tlist is None):
self.coeff = True
lindblad_noise = Pulse(None, None)
for c_op in self.c_ops:
if self.all_qubits:
for targets in range(N):
lindblad_noise.add_lindblad_noise(c_op, targets,
self.tlist, self.coeff)
else:
lindblad_noise.add_lindblad_noise(c_op, self.targets,
self.tlist, self.coeff)
return lindblad_noise
def TestUserNoise(self):
"""
Test for the user-defined noise object
"""
dr_noise = DriftNoise(sigmax())
proc = Processor(1)
proc.add_noise(dr_noise)
tlist = np.array([0, np.pi / 2.])
proc.add_pulse(Pulse(identity(2), 0, tlist, False))
result = proc.run_state(init_state=basis(2, 0))
assert_allclose(fidelity(result.states[-1], basis(2, 1)),
1,
rtol=1.0e-6)
def TestControlAmpNoise(self):
"""
Test for the control amplitude noise
"""
tlist = np.array([1, 2, 3, 4, 5, 6])
coeff = np.array([1, 1, 1, 1, 1, 1])
# use proc_qobjevo
pulses = [Pulse(sigmaz(), 0, tlist, coeff)]
connoise = ControlAmpNoise(coeff=coeff, tlist=tlist)
noisy_pulses = connoise.get_noisy_dynamics(pulses=pulses)
assert_allclose(noisy_pulses[0].coherent_noise[0].qobj, sigmaz())
assert_allclose(noisy_pulses[0].coherent_noise[0].coeff, coeff)
def test_id_evolution(self):
"""
Test for identity evolution
"""
N = 1
proc = Processor(N=N)
init_state = rand_ket(2)
tlist = [0., 1., 2.]
proc.add_pulse(Pulse(identity(2), 0, tlist, False))
result = proc.run_state(
init_state, options=Options(store_final_state=True))
global_phase = init_state.data[0, 0]/result.final_state.data[0, 0]
assert_allclose(global_phase*result.final_state, init_state)
def get_noisy_dynamics(self, dims):
"""
Return a list of Pulse object with only trivial ideal pulse (H=0) but
non-trivial relaxation noise.
Parameters
----------
dims: list, optional
The dimension of the components system, the default value is
[2,2...,2] for qubits system.
Returns
-------
lindblad_noise: list of :class:`qutip.qip.Pulse`
A list of Pulse object with only trivial ideal pulse (H=0) but
non-trivial relaxation noise.
"""
if isinstance(dims, list):
for d in dims:
if d != 2:
raise ValueError(
"Relaxation noise is defined only for qubits system")
N = len(dims)
else:
N = dims
self.t1 = self._T_to_list(self.t1, N)
self.t2 = self._T_to_list(self.t2, N)
if len(self.t1) != N or len(self.t2) != N:
raise ValueError(
"Length of t1 or t2 does not match N, "
"len(t1)={}, len(t2)={}".format(
len(self.t1), len(self.t2)))
lindblad_noise = Pulse(None, None)
if self.targets is None:
targets = range(N)
else:
targets = self.targets
for qu_ind in targets:
t1 = self.t1[qu_ind]
t2 = self.t2[qu_ind]
if t1 is not None:
op = 1/np.sqrt(t1) * destroy(2)
lindblad_noise.add_lindblad_noise(op, qu_ind, coeff=True)
if t2 is not None:
# Keep the total dephasing ~ exp(-t/t2)
if t1 is not None:
if 2*t1 < t2:
raise ValueError(
"t1={}, t2={} does not fulfill "
"2*t1>t2".format(t1, t2))
T2_eff = 1./(1./t2-1./2./t1)
else:
T2_eff = t2
op = 1/np.sqrt(2*T2_eff) * sigmaz()
lindblad_noise.add_lindblad_noise(op, qu_ind, coeff=True)
return lindblad_noise
def test_relaxation_noise(self):
"""
Test for the relaxation noise
"""
# only t1
a = destroy(2)
dims = [2] * 3
relnoise = RelaxationNoise(t1=[1., 1., 1.], t2=None)
systematic_noise = Pulse(None, None, label="system")
pulses, systematic_noise = relnoise.get_noisy_dynamics(
dims=dims, systematic_noise=systematic_noise)
noisy_qu, c_ops = systematic_noise.get_noisy_qobjevo(dims=dims)
assert_(len(c_ops) == 3)
assert_allclose(c_ops[1].cte, tensor([qeye(2), a, qeye(2)]))
# no relaxation
dims = [2] * 2
relnoise = RelaxationNoise(t1=None, t2=None)
systematic_noise = Pulse(None, None, label="system")
pulses, systematic_noise = relnoise.get_noisy_dynamics(
dims=dims, systematic_noise=systematic_noise)
noisy_qu, c_ops = systematic_noise.get_noisy_qobjevo(dims=dims)
assert_(len(c_ops) == 0)
# only t2
relnoise = RelaxationNoise(t1=None, t2=[0.2, 0.7])
systematic_noise = Pulse(None, None, label="system")
pulses, systematic_noise = relnoise.get_noisy_dynamics(
dims=dims, systematic_noise=systematic_noise)
noisy_qu, c_ops = systematic_noise.get_noisy_qobjevo(dims=dims)
assert_(len(c_ops) == 2)
# t1+t2 and systematic_noise = None
relnoise = RelaxationNoise(t1=[1., 1.], t2=[0.5, 0.5])
pulses, systematic_noise = relnoise.get_noisy_dynamics(dims=dims)
noisy_qu, c_ops = systematic_noise.get_noisy_qobjevo(dims=dims)
assert_(len(c_ops) == 4)
def set_up_ops(self, N):
"""
Generate the Hamiltonians for the spinchain model and save them in the
attribute `ctrls`.
Parameters
----------
N: int
The number of qubits in the system.
"""
self.pulse_dict = {}
index = 0
# single qubit terms
for m in range(N):
self.pulses.append(
Pulse(sigmax(), [m + 1], spline_kind=self.spline_kind))
self.pulse_dict["sx" + str(m)] = index
index += 1
for m in range(N):
self.pulses.append(
Pulse(sigmaz(), [m + 1], spline_kind=self.spline_kind))
self.pulse_dict["sz" + str(m)] = index
index += 1
# coupling terms
a = tensor([destroy(self.num_levels)] +
[identity(2) for n in range(N)])
for n in range(N):
sm = tensor(
[identity(self.num_levels)] +
[destroy(2) if m == n else identity(2) for m in range(N)])
self.pulses.append(
Pulse(a.dag() * sm + a * sm.dag(),
list(range(N + 1)),
spline_kind=self.spline_kind))
self.pulse_dict["g" + str(n)] = index
index += 1
def testDrift(self):
"""
Test for the drift Hamiltonian
"""
processor = Processor(N=1)
processor.add_drift(sigmax() / 2, 0)
tlist = np.array([0., np.pi, 2 * np.pi, 3 * np.pi])
processor.add_pulse(Pulse(None, None, tlist, False))
ideal_qobjevo, _ = processor.get_qobjevo(noisy=True)
assert_equal(ideal_qobjevo.cte, sigmax() / 2)
init_state = basis(2)
propagators = processor.run_analytically()
analytical_result = init_state
for unitary in propagators:
analytical_result = unitary * analytical_result
fid = fidelity(sigmax() * init_state, analytical_result)
assert ((1 - fid) < 1.0e-6)
def test_random_noise(self):
"""
Test for the white noise
"""
tlist = np.array([1, 2, 3, 4, 5, 6])
coeff = np.array([1, 1, 1, 1, 1, 1])
dummy_qobjevo = QobjEvo(sigmaz(), tlist=tlist)
mean = 0.
std = 0.5
pulses = [
Pulse(sigmaz(), 0, tlist, coeff),
Pulse(sigmax(), 0, tlist, coeff * 2),
Pulse(sigmay(), 0, tlist, coeff * 3)
]
# random noise with operators from proc_qobjevo
gaussnoise = RandomNoise(dt=0.1,
rand_gen=np.random.normal,
loc=mean,
scale=std)
noisy_pulses, systematic_noise = \
gaussnoise.get_noisy_dynamics(pulses=pulses)
assert_allclose(noisy_pulses[2].qobj, sigmay())
assert_allclose(noisy_pulses[1].coherent_noise[0].qobj, sigmax())
assert_allclose(len(noisy_pulses[0].coherent_noise[0].tlist),
len(noisy_pulses[0].coherent_noise[0].coeff))
# random noise with dt and other random number generator
pulses = [
Pulse(sigmaz(), 0, tlist, coeff),
Pulse(sigmax(), 0, tlist, coeff * 2),
Pulse(sigmay(), 0, tlist, coeff * 3)
]
gaussnoise = RandomNoise(lam=0.1, dt=0.2, rand_gen=np.random.poisson)
assert_(gaussnoise.rand_gen is np.random.poisson)
noisy_pulses, systematic_noise = \
gaussnoise.get_noisy_dynamics(pulses=pulses)
assert_allclose(noisy_pulses[0].coherent_noise[0].tlist,
np.linspace(1, 6,
int(5 / 0.2) + 1))
assert_allclose(noisy_pulses[1].coherent_noise[0].tlist,
np.linspace(1, 6,
int(5 / 0.2) + 1))
assert_allclose(noisy_pulses[2].coherent_noise[0].tlist,
np.linspace(1, 6,
int(5 / 0.2) + 1))
def get_noisy_dynamics(self,
dims=None,
pulses=None,
systematic_noise=None):
if systematic_noise is None:
systematic_noise = Pulse(None, None, label="system")
N = len(dims)
# time-independent
if (self.coeff is None) and (self.tlist is None):
self.coeff = True
for c_op in self.c_ops:
if self.all_qubits:
for targets in range(N):
systematic_noise.add_lindblad_noise(
c_op, targets, self.tlist, self.coeff)
else:
systematic_noise.add_lindblad_noise(c_op, self.targets,
self.tlist, self.coeff)
return pulses, systematic_noise
def TestCoherentNoise():
"""
Test for pulse genration with coherent noise.
"""
coeff = np.array([0.1, 0.2, 0.3, 0.4])
tlist = np.array([0., 1., 2., 3.])
ham = sigmaz()
pulse1 = Pulse(ham, 1, tlist, coeff)
# Add coherent noise with the same tlist
pulse1.add_coherent_noise(sigmay(), 0, tlist, coeff)
assert_allclose(
pulse1.get_ideal_qobjevo(2).ops[0].qobj, tensor(identity(2), sigmaz()))
assert_(len(pulse1.coherent_noise) == 1)
noise_qu, c_ops = pulse1.get_noisy_qobjevo(2)
assert_allclose(c_ops, [])
assert_allclose(noise_qu.tlist, np.array([0., 1., 2., 3.]))
qobj_list = [ele.qobj for ele in noise_qu.ops]
assert_(tensor(identity(2), sigmaz()) in qobj_list)
assert_(tensor(sigmay(), identity(2)) in qobj_list)
for ele in noise_qu.ops:
assert_allclose(ele.coeff, coeff)
def get_noisy_dynamics(self,
dims=None,
pulses=None,
systematic_noise=None):
if systematic_noise is None:
systematic_noise = Pulse(None, None, label="system")
N = len(dims)
self.t1 = self._T_to_list(self.t1, N)
self.t2 = self._T_to_list(self.t2, N)
if len(self.t1) != N or len(self.t2) != N:
raise ValueError("Length of t1 or t2 does not match N, "
"len(t1)={}, len(t2)={}".format(
len(self.t1), len(self.t2)))
if self.targets is None:
targets = range(N)
else:
targets = self.targets
for qu_ind in targets:
t1 = self.t1[qu_ind]
t2 = self.t2[qu_ind]
if t1 is not None:
op = 1 / np.sqrt(t1) * destroy(dims[qu_ind])
systematic_noise.add_lindblad_noise(op, qu_ind, coeff=True)
if t2 is not None:
# Keep the total dephasing ~ exp(-t/t2)
if t1 is not None:
if 2 * t1 < t2:
raise ValueError("t1={}, t2={} does not fulfill "
"2*t1>t2".format(t1, t2))
T2_eff = 1. / (1. / t2 - 1. / 2. / t1)
else:
T2_eff = t2
op = 1 / np.sqrt(2 * T2_eff) * 2 * num(dims[qu_ind])
systematic_noise.add_lindblad_noise(op, qu_ind, coeff=True)
return pulses, systematic_noise
def TestPulseConstructor():
"""
Test for creating empty Pulse, Pulse with constant coefficients etc.
"""
coeff = np.array([0.1, 0.2, 0.3, 0.4])
tlist = np.array([0., 1., 2., 3.])
ham = sigmaz()
# Special ways of initializing pulse
pulse2 = Pulse(sigmax(), 0, tlist, True)
assert_allclose(pulse2.get_ideal_qobjevo(2).ops[0].qobj,
tensor(sigmax(), identity(2)))
pulse3 = Pulse(sigmay(), 0)
assert_allclose(pulse3.get_ideal_qobjevo(2).cte.norm(), 0.)
pulse4 = Pulse(None, None) # Dummy empty ham
assert_allclose(pulse4.get_ideal_qobjevo(2).cte.norm(), 0.)
tlist_noise = np.array([1., 2.5, 3.])
coeff_noise = np.array([0.5, 0.1, 0.5])
tlist_noise2 = np.array([0.5, 2, 3.])
coeff_noise2 = np.array([0.1, 0.2, 0.3])
# Pulse with different dims
random_qobj = Qobj(np.random.random((3, 3)))
pulse5 = Pulse(sigmaz(), 1, tlist, True)
pulse5.add_coherent_noise(sigmay(), 1, tlist_noise, coeff_noise)
pulse5.add_lindblad_noise(
random_qobj, 0, tlist=tlist_noise2, coeff=coeff_noise2)
qu, c_ops = pulse5.get_noisy_qobjevo(dims=[3, 2])
assert_allclose(qu.ops[0].qobj, tensor([identity(3), sigmaz()]))
assert_allclose(qu.ops[1].qobj, tensor([identity(3), sigmay()]))
assert_allclose(c_ops[0].ops[0].qobj, tensor([random_qobj, identity(2)]))
def get_noisy_dynamics(self, ctrl_pulses, dims=None):
dummy = Pulse(None, None)
dummy.add_coherent_noise(self.qobj, 0, coeff=True)
return ctrl_pulses + [dummy]
def TestBasicPulse():
"""
Test for basic pulse generation and attributes.
"""
coeff = np.array([0.1, 0.2, 0.3, 0.4])
tlist = np.array([0., 1., 2., 3.])
ham = sigmaz()
# Basic tests
pulse1 = Pulse(ham, 1, tlist, coeff)
assert_allclose(
pulse1.get_ideal_qobjevo(2).ops[0].qobj, tensor(identity(2), sigmaz()))
pulse1.tlist = 2 * tlist
assert_allclose(pulse1.tlist, 2 * tlist)
pulse1.tlist = tlist
pulse1.coeff = 2 * coeff
assert_allclose(pulse1.coeff, 2 * coeff)
pulse1.coeff = coeff
pulse1.qobj = 2 * sigmay()
assert_allclose(pulse1.qobj, 2 * sigmay())
pulse1.qobj = ham
pulse1.targets = 3
assert_allclose(pulse1.targets, 3)
pulse1.targets = 1
assert_allclose(pulse1.get_ideal_qobj(2), tensor(identity(2), sigmaz()))
def set_up_ops(self, N):
super(CircularSpinChain, self).set_up_ops(N)
operator = tensor([sigmax(), sigmax()]) + tensor([sigmay(), sigmay()])
self.pulses.append(
Pulse(operator, [N-1, 0], spline_kind=self.spline_kind))
self.pulse_dict["g" + str(N-1)] = len(self.pulses) - 1
def TestNoisyPulse():
"""
Test for lindblad noise and different tlist
"""
coeff = np.array([0.1, 0.2, 0.3, 0.4])
tlist = np.array([0., 1., 2., 3.])
ham = sigmaz()
pulse1 = Pulse(ham, 1, tlist, coeff)
# Add coherent noise and lindblad noise with different tlist
pulse1.spline_kind = "step_func"
tlist_noise = np.array([1., 2.5, 3.])
coeff_noise = np.array([0.5, 0.1, 0.5])
pulse1.add_coherent_noise(sigmay(), 0, tlist_noise, coeff_noise)
tlist_noise2 = np.array([0.5, 2, 3.])
coeff_noise2 = np.array([0.1, 0.2, 0.3])
pulse1.add_lindblad_noise(sigmax(), 1, coeff=True)
pulse1.add_lindblad_noise(
sigmax(), 0, tlist=tlist_noise2, coeff=coeff_noise2)
assert_allclose(
pulse1.get_ideal_qobjevo(2).ops[0].qobj, tensor(identity(2), sigmaz()))
noise_qu, c_ops = pulse1.get_noisy_qobjevo(2)
assert_allclose(noise_qu.tlist, np.array([0., 0.5, 1., 2., 2.5, 3.]))
for ele in noise_qu.ops:
if ele.qobj == tensor(identity(2), sigmaz()):
assert_allclose(
ele.coeff, np.array([0.1, 0.1, 0.2, 0.3, 0.3, 0.4]))
elif ele.qobj == tensor(sigmay(), identity(2)):
assert_allclose(
ele.coeff, np.array([0., 0., 0.5, 0.5, 0.1, 0.5]))
for c_op in c_ops:
if len(c_op.ops) == 0:
assert_allclose(c_ops[0].cte, tensor(identity(2), sigmax()))
else:
assert_allclose(
c_ops[1].ops[0].qobj, tensor(sigmax(), identity(2)))
assert_allclose(
c_ops[1].tlist, np.array([0., 0.5, 1., 2., 2.5, 3.]))
assert_allclose(
c_ops[1].ops[0].coeff, np.array([0., 0.1, 0.1, 0.2, 0.2, 0.3]))