def e_ops_gen(params):
projectors = gen_projectors(params)
sm = tensor(sigmam(), qeye(params.c_levels))
a = tensor(qeye(2), destroy(params.c_levels))
base_e_ops = {'a': a, 'sm': sm, 'n': a.dag() * a}
e_ops = base_e_ops.copy()
for key, item in base_e_ops.items():
for i in range(2):
for j in range(2):
e_ops[key + '_' + str(i) + str(j)] = projectors[i] * item * projectors[j]
for n in range(2):
e_ops['p_q' + str(n)] = tensor(fock_dm(2, n), qeye(params.c_levels))
for n in range(params.c_levels):
e_ops['p_c' + str(n)] = tensor(qeye(2), fock_dm(params.c_levels, n))
e_ops['P_0'] = projectors[0]
e_ops['P_1'] = projectors[1]
e_ops['P_01'] = projectors[0] * projectors[1]
return e_ops
def controlled_mat3(arg_value):
"""
A qubit control an operator acting on a 3 level system
"""
control_value = arg_value
dim = mat3.dims[0][0]
return (tensor(fock_dm(2, control_value), mat3) +
tensor(fock_dm(2, 1 - control_value), identity(dim)))
def adc_choi(x):
kraus = [
np.sqrt(1 - x) * qeye(2),
np.sqrt(x) * destroy(2),
np.sqrt(x) * fock_dm(2, 0),
]
return kraus_to_choi(kraus)
def __init__(self, nbrOfQubits=4, FockDim=3):
self.nbrOfQubits = nbrOfQubits
self.FockDim = FockDim
self.qubits = []
for i in range(nbrOfQubits):
self.qubits.append(qt.fock_dm(FockDim, 0))
def __init__(self, resonance_freq, anharmonicity, T1=0, T2=0):
self.resonance_freq = resonance_freq
self.anharmonicity = anharmonicity
self.T1 = T1
self.T2 = T2
self.state = qt.fock_dm(3,
0) # 3-level qubit initialized in ground state
def testFockDensityMatrix(self):
"""
states: Fock density matrix
"""
N = 10
for i in range(N):
rho = fock_dm(N, i)
# make sure rho has trace close to 1.0
assert_(abs(rho.tr() - 1.0) < 1e-12)
assert_(rho.data[i, i] == 1.0)
def testFockDensityMatrix(self):
"""
states: Fock density matrix
"""
N = 10
for i in range(N):
rho = fock_dm(N, i)
# make sure rho has trace close to 1.0
assert_(abs(rho.tr() - 1.0) < 1e-12)
assert_(rho.data[i, i] == 1.0)
def test_smesolve_homodyne_methods():
"Stochastic: smesolve: homodyne methods with single jump operator"
def arccoth(x):
return 0.5*np.log((1.+x)/(x-1.))
th = 0.1 # Interaction parameter
alpha = np.cos(th)
beta = np.sin(th)
gamma = 1.
N = 30 # number of Fock states
Id = qeye(N)
a = destroy(N)
s = 0.5*((alpha+beta)*a + (alpha-beta)*a.dag())
x = (a + a.dag()) * 2**-0.5
H = Id
c_op = [gamma**0.5 * a]
sc_op = [s]
e_op = [x, x*x]
rho0 = fock_dm(N,0) # initial vacuum state
T = 6. # final time
N_store = 200 # number of time steps for which we save the expectation values
Nsub = 5
tlist = np.linspace(0, T, N_store)
ddt = (tlist[1]-tlist[0])
#### Analytic solution
y0 = 0.5
A = (gamma**2 + alpha**2 * (beta**2 + 4*gamma) - 2*alpha*beta*gamma)**0.5
B = arccoth((-4*alpha**2*y0 + alpha*beta - gamma)/A)
y_an = (alpha*beta - gamma + A / np.tanh(0.5*A*tlist - B))/(4*alpha**2)
list_methods_tol = [['euler-maruyama', 2e-2],
['fast-euler-maruyama', 2e-2],
['pc-euler', 2e-3],
['milstein', 1e-3],
['fast-milstein', 1e-3],
['milstein-imp', 1e-3],
['taylor15', 1e-4],
['taylor15-imp', 1e-4]
]
for n_method in list_methods_tol:
sol = smesolve(H, rho0, tlist, c_op, sc_op, e_op,
nsubsteps=Nsub, method='homodyne', solver = n_method[0])
sol2 = smesolve(H, rho0, tlist, c_op, sc_op, e_op,
nsubsteps=Nsub, method='homodyne', solver = n_method[0],
noise = sol.noise)
err = 1/T * np.sum(np.abs(y_an - (sol.expect[1]-sol.expect[0]*sol.expect[0].conj())))*ddt
print(n_method[0], ': deviation =', err, ', tol =', n_method[1])
assert_(err < n_method[1])
assert_(np.all(sol.noise == sol2.noise))# just to check that noise is not affected by smesolve
assert_(np.all(sol.expect[0] == sol2.expect[0]))
def cphase(theta, N=2, control=0, target=1):
"""
Returns quantum object representing the controlled phase shift gate.
Parameters
----------
theta : float
Phase rotation angle.
N : integer
The number of qubits in the target space.
control : integer
The index of the control qubit.
target : integer
The index of the target qubit.
Returns
-------
U : qobj
Quantum object representation of controlled phase gate.
"""
if N < 1 or target < 0 or control < 0:
raise ValueError("Minimum value: N=1, control=0 and target=0")
if control >= N or target >= N:
raise ValueError("control and target need to be smaller than N")
U_list1 = [identity(2)] * N
U_list2 = [identity(2)] * N
U_list1[control] = fock_dm(2, 1)
U_list1[target] = phasegate(theta)
U_list2[control] = fock_dm(2, 0)
U = tensor(U_list1) + tensor(U_list2)
return U
def test_result_states():
N = 5
a = qutip.destroy(N)
coefficient = np.random.random() + 1j * np.random.random()
H = a.dag() * a + coefficient * a + np.conj(coefficient) * a.dag()
H_brme = [[H, '1']]
psi0 = qutip.fock_dm(N, 2)
times = np.linspace(0, 10, 10)
me = qutip.mesolve(H, psi0, times).states
brme = qutip.brmesolve(H_brme, psi0, times).states
assert max(
np.abs((me_state - brme_state).full()).max()
for me_state, brme_state in zip(me, brme)) < 1e-5
def test_thermal():
N = 10
beta = 0.5
assert qutip.thermal_dm(N, 0) == qutip.fock_dm(N, 0)
thermal_operator = qutip.thermal_dm(N, beta)
thermal_analytic = qutip.thermal_dm(N, beta, method="analytic")
np.testing.assert_allclose(thermal_operator.full(),
thermal_analytic.full(), atol=2e-5)
with pytest.raises(ValueError) as e:
qutip.thermal_dm(N, beta, method="other")
assert str(e.value) == ("The method option can only take "
"values 'operator' or 'analytic'")
def single_crosstalk_simulation(num_gates):
""" A single simulation, with num_gates representing the number of rotations.
Args:
num_gates (int): The number of random gates to add in the simulation.
Returns:
result (qutip.solver.Result): A qutip Result object obtained from any of the
solver methods such as mesolve.
"""
num_qubits = 2 # Qubit-0 is the target qubit. Qubit-1 suffers from crosstalk.
myprocessor = ModelProcessor(model=MyModel(num_qubits))
# Add qubit frequency detuning 1.852MHz for the second qubit.
myprocessor.add_drift(2 * np.pi * (sigmaz() + 1) / 2 * 1.852, targets=1)
myprocessor.native_gates = None # Remove the native gates
mycompiler = MyCompiler(num_qubits, {
"pulse_amplitude": 0.02,
"duration": 25
})
myprocessor.add_noise(ClassicalCrossTalk(1.0))
# Define a randome circuit.
gates_set = [
Gate("ROT", 0, arg_value=0),
Gate("ROT", 0, arg_value=np.pi / 2),
Gate("ROT", 0, arg_value=np.pi),
Gate("ROT", 0, arg_value=np.pi / 2 * 3),
]
circuit = QubitCircuit(num_qubits)
for ind in np.random.randint(0, 4, num_gates):
circuit.add_gate(gates_set[ind])
# Simulate the circuit.
myprocessor.load_circuit(circuit, compiler=mycompiler)
init_state = tensor(
[Qobj([[init_fid, 0], [0, 0.025]]),
Qobj([[init_fid, 0], [0, 0.025]])])
options = SolverOptions(nsteps=10000) # increase the maximal allowed steps
e_ops = [tensor([qeye(2), fock_dm(2)])] # observable
# compute results of the run using a solver of choice with custom options
result = myprocessor.run_state(init_state,
solver="mesolve",
options=options,
e_ops=e_ops)
result = result.expect[0][-1] # measured expectation value at the end
return result
def osc_relax():
w = 1.0 # oscillator frequency
kappa = 0.1 # relaxation rate
a = destroy(10) # oscillator annihilation operator
rho0 = fock_dm(10, 5) # initial state, fock state with 5 photons
H = w * a.dag() * a # Hamiltonian
# A list of collapse operators
c_ops = [sqrt(kappa) * a]
tlist = linspace(0, 50, 100)
# request that the solver return the expectation value of the photon number state operator a.dag() * a
result = mesolve(H, rho0, tlist, c_ops, [a.dag() * a])
print result
fig, axes = plt.subplots(1,1)
axes.plot(tlist, result.expect[0])
axes.set_xlabel(r'$t$', fontsize=20)
axes.set_ylabel(r"Photon number", fontsize=16);
def __init__(self, resonance_freq, anharmonicity, fock_dim=3):
self.fock_dim = fock_dim
self.resonance_freq = resonance_freq
self.anharmonicity = anharmonicity
self.state = qt.fock_dm(fock_dim, 0)
def run_sim_full_and_approx(p):
"""
TODO:
-Should get separate the approximate (rotating wave) evolution into its own function. Then the plotting routines should take a list
of results, using different
-Double check that coupling of higher qudit levels scales as standard lowering/rasing ops to a good approximation.
-Add co-rotating terms evolution to approximate RF results.
IMPORTANT:
the passed in options 'p' should not be changed inside this function if one wants to run things in parallel via multiprocessing.Pool.map()
Otherwise, in particular if p gets entries with new objects, can lead to things break down in non-trivial way.
"""
# if p.show_approx_evolution:
# print("The codebase for the approx evolution needs a couple of minor updates with the recent changes...\n\n\n")
# return None
if p.N_q > 2 and p.show_approx_evolution:
#Need to generalize the approximate treatment to more levels
print(
"ERROR: The approximate evolution (in terms of J_m functions) for now only handles a 2 level qudit...\n\
... set p.show_approx_evolution=False in order to look at the full evolution instead.\n"
)
return None
#make sure the config is sane
assert (len(p.mode_freqs) == len(p.mode_q_coupling_freqs) == len(
p.mode_decay_rates))
assert (p.N_q == len(p.q_level_freqs) == len(p.q_level_freqs_time_dep) ==
len(p.q_level_dephasing_rate) == (len(p.q_level_decay_rate) + 1))
assert (p.non_rwa_terms == 0 or p.non_rwa_terms == 1)
results = DictExtended()
#keep a reference to the specific options/parameters that were used in the simulation along with the results
results.p = DictExtended(p)
#qubit lowering operator
c = q.tensor(q.destroy(p.N_q),
*[q.qeye(p.N_m) for i in xrange(p.mode_count)])
#mode lowering operators; a[j], gives the lowering operator for the jth mode (first is the 0th indexed)
a = []
for j in xrange(p.mode_count):
#prettier way to do this?
temp_op_list = [q.qeye(p.N_q)]
for i in xrange(p.mode_count):
if i == j:
temp_op_list.append(q.destroy(p.N_m))
else:
temp_op_list.append(q.qeye(p.N_m))
a.append(q.tensor(*temp_op_list))
#keep a reference to the key operators of our system
results.op = DictExtended(a=a, c=c)
#Build the total Hamiltonian of our system
H_rest_list = []
for i in xrange(p.mode_count):
H_rest_list.append(p.mode_freqs[i] * a[i].dag() * a[i])
H_rest_list.append(p.mode_q_coupling_freqs[i] *
(a[i].dag() * c + a[i] * c.dag()) +
p.non_rwa_terms * p.mode_q_coupling_freqs[i] *
(a[i].dag() * c.dag() + a[i] * c))
H_rest_static = np.sum(H_rest_list)
H_q_static = q.tensor(q.Qobj(np.diag(p.q_level_freqs)),
*[q.qeye(p.N_m) for i in xrange(p.mode_count)])
H_q_t_list = []
#then time dependence...
for lvl in xrange(p.N_q):
h_matrix = q.tensor(q.fock_dm(p.N_q, lvl),
*[q.qeye(p.N_m) for i in xrange(p.mode_count)])
H_q_t_list.append([
h_matrix, p.q_level_freqs_time_dep[lvl](p.tlist, p.epsilon,
p.omega_drive)
])
H_static = H_q_static + H_rest_static
results.H = [H_static] + H_q_t_list
# print(H)
#Get the eigenvalues/vectors of static portion of the Hamiltonian
eigen_system = H_static.eigenstates()
results.eigen_vals = eigen_system[0]
results.eigen_vecs = eigen_system[1]
if p.print_extra_info:
print("Eigen frequencies:")
print(
map(lambda item: "%0.9g" % item,
(results.eigen_vals - results.eigen_vals[0]) / (2.0 * np.pi)))
print("Consecutive differences in eigen frequencies:")
print(
map(lambda item: "%0.9g" % item,
(results.eigen_vals[1:] - results.eigen_vals[:-1]) /
(2.0 * np.pi)))
print("Differences between mode and 1st excited qubit freqs")
print((np.array(p.mode_freqs) - p.q_level_freqs[1]) / (2.0 * np.pi))
if p.only_show_ev:
#in case we only want to see the eigenvalues/extra_info
return None
#Here we generate a whole bunch of states that might be of interest... but later we'll only consider some subset of those that we want to plot
#...this could be streamlined... in reality no need to create all these states if they are not to be used... but this portion of the code is fast anyway
#WE ASSUME that the initial state is one of those states defined here
#Generate the single excitation states in bare basis
results.states_collection = generate_single_excitation_states(p)
# print(states_collection)
#add the ground state
results.states_collection['state_0'] = fock_state(p, 0, [])
#add the systems's eigenstates
eigenvectors_count = p.N_q * p.N_m * p.mode_count
for m in xrange(eigenvectors_count):
results.states_collection[
"state_v%d" %
m] = results.eigen_vecs[m] * results.eigen_vecs[m].dag()
# results.states_collection["state_pv%d" % m]= results.eigen_vecs[m]*results.eigen_vecs[m].dag()
#add some other fun states
results.states_collection["g"] = q.tensor(
q.fock_dm(p.N_q, 0), *[q.qeye(p.N_m) for i in xrange(p.mode_count)])
results.states_collection["e"] = q.tensor(
q.fock_dm(p.N_q, 1), *[q.qeye(p.N_m) for i in xrange(p.mode_count)])
results.states_collection["sup_v1-v2"] = 0.5 * (
results.states_collection["state_v1"] +
results.states_collection["state_v2"])
#get the right states whose expectation values we want to plot
results.e_ops = [
results.states_collection[state_name]
for state_name in p.states_to_evolve
]
#initial state
results.rho0 = results.states_collection[p.rho0_name]
results.c_op_list = []
#qubit dephasing
if np.count_nonzero(p.q_level_dephasing_rate) > 0:
dis_op = q.tensor(
q.Qobj(np.diag(np.sqrt(2.0) * np.sqrt(p.q_level_dephasing_rate))),
*[q.qeye(p.N_m) for i in xrange(p.mode_count)])
if p.dissipators_in_dressed_basis:
dis_op = dis_op.transform(results.eigen_vecs, inverse=False)
# dis_op=dis_op.transform(results.eigen_vecs, inverse=True)
results.c_op_list.append(dis_op)
#TESTING
#reverse which state "feels" the phase shift
# rev_dephasing=np.array(p.q_level_dephasing_rate)[::-1]
# results.c_op_list.append(q.tensor(q.Qobj(np.diag( np.sqrt(2.0) * np.sqrt(rev_dephasing) ) ), *[q.ket2dm(q.basis(p.N_m,0)) for i in xrange(p.mode_count)]))
# results.c_op_list.append(q.tensor(q.Qobj(np.diag( np.sqrt(2.0) * np.sqrt(rev_dephasing) ) ), *[q.qeye(p.N_m) for i in xrange(p.mode_count)]))
# results.c_op_list.append(q.tensor(q.Qobj(np.diag( np.sqrt(2.0) * np.sqrt(p.q_level_dephasing_rate) ) ), *[q.ket2dm(q.basis(p.N_m,0)) for i in xrange(p.mode_count)]))
#qubit decay
if np.count_nonzero(p.q_level_decay_rate) > 0:
dis_op = q.tensor(q.Qobj(np.diag(np.sqrt(p.q_level_decay_rate), 1)),
*[q.qeye(p.N_m) for i in xrange(p.mode_count)])
if p.dissipators_in_dressed_basis:
dis_op = dis_op.transform(results.eigen_vecs, inverse=False)
# dis_op=dis_op.transform(results.eigen_vecs, inverse=True)
results.c_op_list.append(dis_op)
#TESTING
# results.c_op_list.append(q.tensor(q.Qobj(np.diag( np.sqrt(p.q_level_decay_rate), 1 ) ), *[q.ket2dm(q.basis(p.N_m,0)) for i in xrange(p.mode_count)]))
#mode decay
for i, entry in enumerate(p.mode_decay_rates):
if entry != 0:
dis_op = np.sqrt(entry) * a[i]
if p.dissipators_in_dressed_basis:
dis_op = dis_op.transform(results.eigen_vecs, inverse=False)
# dis_op=dis_op.transform(results.eigen_vecs, inverse=True)
results.c_op_list.append(dis_op)
# print(results.c_op_list)
results.output = q.mesolve(results.H,
results.rho0,
p.tlist,
results.c_op_list,
results.e_ops,
options=p.odeoptions,
progress_bar={
False: None,
True: True
}[p.show_progress_bar])
if p.show_approx_evolution:
if p.N_q > 2:
#Need to generalize the approximate (i.e. rotating frame) treatment to more levels
print(
"ERROR: The approximate (in terms of J_m functions) for now only handles a 2 level qudit...\n\n\n"
)
return None
if p.omega_drive == 0:
#the rotated frame we've chosen assumes p.omega_drive is not zero, because we end up with a 1/p.omega_drive in the arugment
#of the Bessel functions.
print(
"ERROR: The approximate expression for the Hamiltonian (in terms of Bessel functions) assumes that omega_drive is not zero. \
If the drive is not needed, simply set its amplitude to zero. Full numerics if of course possible with omega_drive==0."
)
return results
#TODO: double check minus signs, etc and generalize to many qudit levels
def Utrans(t):
return ((+1.0j) * (
(p.q_level_freqs[1] - p.q_level_freqs[0]) * t - p.epsilon /
(1.0 * p.omega_drive) * np.cos(p.omega_drive * t)) * c.dag() *
c +
np.sum([(+1.0j) * t * p.mode_freqs[i] * a[i].dag() * a[i]
for i in xrange(p.mode_count)])).expm()
results.Utrans = Utrans
zero_ops = [q.Qobj(np.zeros((p.N_q, p.N_q)))] + [
q.Qobj(np.zeros((p.N_m, p.N_m))) for i in xrange(p.mode_count)
]
zero_H = q.tensor(*zero_ops)
results.H_rf = []
results.H_rf.append(
zero_H
) #dirrtyyy... seems like qutip wants at least one time independent Hamiltonian portion... just give it all zeros.
for i in xrange(p.mode_count):
ham_coeff_time_array = np.zeros(np.array(p.tlist).shape)
for m in p.bessel_indices:
ham_coeff_time_array = ham_coeff_time_array + (
(1.0j)**m * p.mode_q_coupling_freqs[i] * sc.special.jv(
m, p.epsilon / (1.0 * p.omega_drive)) * np.exp(
(1.0j) *
(p.mode_freqs[i] -
(p.q_level_freqs[1] - p.q_level_freqs[0]) -
m * p.omega_drive) * p.tlist))
matrix_components = [c * a[i].dag(), ham_coeff_time_array]
results.H_rf.append(matrix_components)
results.H_rf.append([
matrix_components[0].dag(),
np.conjugate(matrix_components[1])
])
if p.non_rwa_terms != 0: #do the same but for the non-rwa terms
ham_coeff_time_array = np.zeros(np.array(p.tlist).shape)
for m in p.bessel_indices:
ham_coeff_time_array = ham_coeff_time_array + (
(1.0j)**m * p.mode_q_coupling_freqs[i] * sc.special.jv(
m, p.epsilon / (1.0 * p.omega_drive)) * np.exp(
(1.0j) *
(p.mode_freqs[i] +
(p.q_level_freqs[1] - p.q_level_freqs[0]) -
m * p.omega_drive) * p.tlist))
matrix_components = [
c.dag() * a[i].dag(), ham_coeff_time_array
]
results.H_rf.append(matrix_components)
results.H_rf.append([
matrix_components[0].dag(),
np.conjugate(matrix_components[1])
])
results.rho0_rf = Utrans(0) * results.rho0 * Utrans(0).dag()
#In general we have to be careful about how the dissipators transform in the rotated frame...
#take them as the same as in lab frame, which should be true in our case
# results.c_op_list = []
#If the "measurement operators" (i.e. ones we calculate the expectation values of) do not commute with the unitary transformation
#that defines the rotating frame, we need to transform the resulting density matrix before calculating expectation values if we
#want to compare the results to the full lab frame evolution
if p.transform_before_measurement:
def e_ops_func(t, rho, transformation=Utrans, e_ops=results.e_ops):
"""Transform the density matrix into the lab frame, and calculate the expectation values.
TODO: this could probably be streamlined... need to look into qutip's code
"""
rho_lab_frame = Utrans(t).dag() * q.Qobj(rho) * Utrans(t)
for i, e_operator in enumerate(e_ops):
expectation_values[i][e_ops_func.idx] = q.expect(
e_operator, rho_lab_frame).real
e_ops_func.idx += 1
e_ops_func.idx = 0
expectation_values = [
np.zeros(len(p.tlist)) for i in xrange(len(results.e_ops))
]
results.output_rf = q.mesolve(results.H_rf,
results.rho0_rf,
p.tlist,
results.c_op_list,
e_ops_func,
options=p.odeoptions,
progress_bar={
False: None,
True: True
}[p.show_progress_bar])
results.output_rf.expect = expectation_values
else:
results.output_rf = q.mesolve(results.H_rf,
results.rho0_rf,
p.tlist,
results.c_op_list,
results.e_ops,
options=p.odeoptions,
progress_bar={
False: None,
True: True
}[p.show_progress_bar])
print("p.epsilon / ( p.omega_drive )=%f, " %
(p.epsilon / (1.0 * p.omega_drive), ) + ",".join([
"J_%d()=%f" %
(m, sc.special.jv(m, (p.epsilon / (1.0 * p.omega_drive))))
for m in p.bessel_indices
]))
if p.show_plots:
plot_results(p, results)
return results
def vacuum_ket(self):
kets = []
for m in self.modes():
kets.append(qt.fock_dm(self.nfock(m)))
return qt.tensor(kets)
def __init__(self,
nHO=15,
nbar_mode=0.0,
delta_g=2 * pi * 40e3,
Omega_R=2 * pi * 80e3,
T=25e-6,
two_loops=True,
species='8888',
ion_spacing=-1,
mode=1,
factor=1,
tau_mot=0,
tau_spin=0,
gamma_el=0,
gamma_ram=0,
Delta_ca=-2 * pi * 10e12,
Delta_sr=2 * pi * 30e12,
Omega_R_2=2 * pi * 80e3,
phase_insensitive=False,
sq_factor=1.0,
qudpl_and_raman=False,
on_radial_modes=False,
nbars=[0.1, 0.1, 5, 5, 5, 5],
mode_freqs=None):
''' nHO: dimension of HO space which is simulated
nbar_mode: mean thermal population of motional mode
delta_g: gate detuning
Omega_R: Rabi frequency
T: elapsed time
two loops: do two-loop (True) or single loop (false) gate
species: ion species of crystal
ion-spacing: integer (+1) or half-integer (-1) standing wavelengths
mode: ip (1) or oop (-1), this code assumes gate is performed an axial mode
factor: square-root of ratio of Rabi frequencies for efficiency tests
tau_mot: motional coherence time, =0 for intinity
tau_spin: spin coherence time, =0 for intinity
gamma_el: Rayleigh elastic dephasing rate
gamma_ram: Raman scattering rate
Delta_ca: calcium Raman detuning, from 397
Delta_sr: strontium Raman detuning, from 422
sq_factor: relative area offset of single qubit pulses (i.e. to simulate if
Ramsey pi/2 and pi pulses aren't calibrated properly)
Only for MS gate:
Omega_R_2: Rabi frequency for second ion, for mixed species gate driven with different lasers
phase_insensitive: wraps gate in single qubit operations driven by gate laser, to make it insensitive
relative to phase of other single qubit operations
qudpl_and_raman: use two different lasers for MS gate, with different lamb-dicke factors
on_radial_modes: does gate on radial modes, but still sets it up for axial modes,
this is used for simulating off-resonant excitation of radial modes for a tilted ion crystal
nbars: temperature of all modes, this is only used for calculating errors from off-resonantly exciting other modes
! Note that most gate parameters are class objects, and therefore parameters
are changed by previously run scans !
'''
self.nq = 2 # number of qubit states
self.nHO = nHO
self.nbar_mode = nbar_mode
self.delta_g = delta_g
self.Omega_R = Omega_R
self.Omega_R_2 = Omega_R_2
self.T = T
self.two_loops = two_loops
self.species = species
self.ion_spacing = ion_spacing
self.mode = mode
self.factor = factor
self.tau_mot = tau_mot
self.tau_spin = tau_spin
self.gamma_el = gamma_el
self.gamma_ram = gamma_ram
self.Delta_ca = Delta_ca # detuning from 397 transition
self.Delta_sr = Delta_sr # detuning from 422 transition!! (not 408, would require different matrix elements)
self.delta_LS = 0 # frequency offset due to light shift
self.ampl_asym_1 = 0 # amplitude asymmetry in sidebands
self.ampl_asym_2 = 0 # amplitude asymmetry in sidebands of second species laser
self.species_Rabi_asym_MS = 0 # Rabi frequency asymmetry btw the two species, for MS gate
self.phase_insensitive = phase_insensitive # surround gate pulse with pi/2 pulses so that can use analysis pulse that is not phase-stabilised to gate
self.sq_factor = sq_factor
self.qudpl_and_raman = qudpl_and_raman
self.on_radial_modes = on_radial_modes
self.nbars = nbars
# single qubit operators
self.up_up = fock_dm(2, 0) # |up><up|
self.dn_dn = fock_dm(2, 1) # |dn><dn|
self.sz = self.up_up - self.dn_dn
self.up = basis(2, 0) # |up>
self.dn = basis(2, 1) # |dn>
self.pl = (self.up + self.dn) / 2 # |+>
self.mn = (self.up - self.dn) / 2 # |->
self.pp = self.pl * self.pl.dag() # |+><+|
self.mm = self.mn * self.mn.dag() # |+><+|
self.pm = self.pl * self.mn.dag() # |+><+|
self.mp = self.mn * self.pl.dag() # |+><+|
# two qubit operators
self.uu_uu = tensor(self.up_up, self.up_up) # |up,up><up,up|
self.dd_dd = tensor(self.dn_dn, self.dn_dn) # |dn,dn><dn,dn|
self.ud_ud = tensor(sigmap(), sigmap()) # |up,dn><up,dn|
self.du_du = tensor(sigmam(), sigmam()) # |dn,up><dn,up|
self.pp_pp = tensor(self.pp, self.pp) # |+,+><+,+|
self.mm_mm = tensor(self.mm, self.mm) # |-,-><-,-|
self.pm_pm = tensor(self.pm, self.pm) # |+,-><+,-|
self.mp_mp = tensor(self.mp, self.mp) # |-,+><-,+|
# two qubit operators with HO, o* means tensor product
self.uu_id = tensor(self.up_up, qeye(self.nq),
qeye(self.nHO)) # |up><up| o* id
self.id_uu = tensor(qeye(self.nq), self.up_up,
qeye(self.nHO)) # id o* |up><up|
self.dd_id = tensor(self.dn_dn, qeye(self.nq),
qeye(self.nHO)) # |dn><dn| o* id
self.id_dd = tensor(qeye(self.nq), self.dn_dn,
qeye(self.nHO)) # id o* |dn><dn|
self.sp_id = tensor(sigmap(), qeye(self.nq),
qeye(self.nHO)) # |up><up| o* id
self.id_sp = tensor(qeye(self.nq), sigmap(),
qeye(self.nHO)) # id o* |up><up|
self.sm_id = tensor(sigmam(), qeye(self.nq),
qeye(self.nHO)) # |dn><dn| o* id
self.id_sm = tensor(qeye(self.nq), sigmam(),
qeye(self.nHO)) # id o* |dn><dn|
# readout projection operators
self.spin_dndn = tensor(self.dn_dn, self.dn_dn, qeye(self.nHO))
self.spin_upup = tensor(self.up_up, self.up_up, qeye(self.nHO))
self.spin_updn_dnup = tensor(self.up_up, self.dn_dn, qeye(
self.nHO)) + tensor(self.dn_dn, self.up_up, qeye(self.nHO))
self.spin_updn = tensor(self.up_up, self.dn_dn, qeye(self.nHO))
self.spin_dnup = tensor(self.dn_dn, self.up_up, qeye(self.nHO))
self.spin_pp = tensor(self.pp, self.pp, qeye(self.nHO))
self.spin_mm = tensor(self.mm, self.mm, qeye(self.nHO))
self.spin_pm = tensor(self.pp, self.mm, qeye(self.nHO))
self.spin_mp = tensor(self.mm, self.pp, qeye(self.nHO))
# annihilation operator
self.a = tensor(qeye(self.nq), qeye(self.nq), destroy(self.nHO))
self.ad = self.a.dag()
self.mw_offset_phase_1 = random.random(
) * 2 * pi # use this phase offset for mw pulses because they don't have a fixed phase relationship to gate lasers
self.phi_sum_1 = random.random(
) * 2 * pi # sum frequency of phases of two sidebands, ie the phase that determines phi in sigma_phi
self.phi_diff_1 = random.random(
) * 2 * pi # difference frequency of phases of two sidebands, constant and ~0 for our frequency geometry
self.setup_mode_structure(mode_freqs)
self.set_ion_parameters()
tau = 0.6 steps = 2e4 sigma = 0.01 gamma_1 = (1000. * tau)**-1. #ridic low, just trying for stability gamma_phi = (1000. * tau)**-1. #ridic low, just trying for stability delta = 2. * np.pi * 1600. g = 2. * np.pi * 50. kappa = 2. * np.pi * 5. omega_cav = 2. * np.pi * 7400. n_c = 60 #number of cavity states n_q = 1 zero_state = qt.fock_dm(2, 0) one_state = qt.fock_dm(2, 1) vacuum = qt.fock_dm(n_c, 0) zero_ket = qt.fock(2, 0) one_ket = qt.fock(2, 1) vacuum_ket = qt.fock(n_c, 0) sz = jc.s_z(n_c, n_q, 0) rest_ham = delta * (-sz / 2.) a = jc.ann(n_c, n_q) a_dag = a.dag() sp = jc.s_p(n_c, n_q, 0) sm = sp.dag() jc_ham = g * (a * sp + a_dag * sm) rabi_ham = [
def test_fockdm_type():
"State CSR Type: fock_dm"
st = fock_dm(5,3)
assert_equal(isspmatrix_csr(st.data), True)
# Similarly,
print("Basis with {N} states, where state {n} is occupied:\n".format(N=4, n=2),
fock(4, 2))
print()
# Generating a Coherent State
print(
"Coherent State with {N} fock states in hilbert space and eigenvalue = {alpha} \n"
.format(N=10, alpha=1.0), coherent(N=10, alpha=1.0))
print()
# Fock state (as a density matrix)
print(
"Fock State as a Density Matrix with hilbert space size = {dim} and occupied state = {n} \n"
.format(dim=5, n=2), fock_dm(5, 2))
print()
print(
"Coherent State as a Density Matrix with number of fock states = {N} and eigenvalue = {alpha}"
.format(N=8, alpha=1.0), coherent_dm(N=8, alpha=1.0))
print()
n = 1 # average number of thermal photons
print(
"Thermal State as Density Matrix with with number of basis states in hilbert space = {N} and expectation value for number of particles in thermal state = {n}\n"
.format(N=8, n=n), thermal_dm(8, n))
wait()
""" --------------- </Operators> --------------- """
wa = 1.0 * 2 * pi # atom frequency
g = 0.05 * 2 * pi # coupling strength
kappa = 0.005 # cavity dissipation rate
gamma = 0.05 # atom dissipation rate
N = 15 # number of cavity fock states
n_th_a = 0.0 # avg number of thermal bath excitation
use_rwa = True
tlist = linspace(0, 100, 10000)
qt.Options(nsteps=1e10)
# intial state
psi0 = qt.tensor(qt.basis(N, 0), qt.basis(2, 0)) # start with an excited atom
e_cav = qt.tensor(qt.fock_dm(N, 1), qt.fock_dm(2, 0))
e_qb = qt.tensor(qt.fock_dm(N, 0), qt.fock_dm(2, 1))
# operators
a = qt.tensor(qt.destroy(N), qt.qeye(2))
sm = qt.tensor(qt.qeye(N), qt.destroy(2))
# Hamiltonian
if use_rwa:
H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() * sm +
a * sm.dag())
else:
H = wc * a.dag() * a + wa * sm.dag() * sm + g * (a.dag() + a) * (sm +
sm.dag())
c_ops = []
def evolve(self, rho, omegas, detuning, detuning_percent, detuning_fixed,
dephasing, dephasing_sigma, timestep):
"""
Constant state evolution of the system, for a single timestep, using the STIRAP
hamiltonian as in arXiv:1901.06603v1.
:params:
--------
rho: (np.array) Input state of the systems (from either the previous timestep or the initial
state)
omegas: (np.array) An array of size 2 containing the constant pulse values for the pump and stokes
pulse respectively.
omega_max: (float) Maximum value for the pulses
detuning: (bool) True for inclusion of random detuning in the interval [-detuning_percent,detuning_percent]*omega_max
detuning_percent: (float) Value between 0 and 1 defining the interval from which detuning is randomly sampled.
:returns:
---------
rho_out: (np.array) State of the system after the evolution.
reduced_rho_out: (np.array) Array containing only the diagonal elements of rho_out.
"""
tlist = [0.0, timestep]
# Turn the listform of rho into a proper qobj for the solver
rho_proper = qt.Qobj(rho.reshape(self.num_levels, self.num_levels))
# Initialize an empty array to fill with the pulse values to make the hamiltonian.
ham_array = np.zeros((self.num_levels, self.num_levels))
for i in range(self.num_levels):
for j in range(self.num_levels):
if i == j + 1:
ham_array[i, j] = 0.5 * omegas[j]
elif j == i + 1:
ham_array[i, j] = 0.5 * omegas[i]
hamiltonian = qt.Qobj(ham_array)
# If the detuning kwarg = True we introduce uniformly random detuning into
# each timestep.
if detuning_fixed == False:
delta1 = np.random.uniform(low=-detuning_percent * self.omega_max,
high=detuning_percent * self.omega_max)
delta2 = 0
elif detuning_fixed == True:
delta2 = detuning_percent * self.omega_max
delta1 = detuning_percent * self.omega_max
elif detuning_fixed == "pierpaolo":
delta2 = detuning_percent * self.omega_max
delta1 = -23.5 * delta2
detuning_hamiltonian = qt.Qobj([[0, 0, 0], [0, delta1, 0],
[0, 0, delta2]])
# Currently only compatablibe with num_levels = 3
if detuning == True:
H = hamiltonian + detuning_hamiltonian
#print(H)
else:
H = hamiltonian
#print(H)
# Dephasing section:
Sigma = dephasing_sigma * self.omega_max
c0 = np.sqrt(Sigma) * qt.fock_dm(3, 0)
c1 = np.sqrt(Sigma) * qt.fock_dm(3, 1)
c2 = np.sqrt(Sigma) * qt.fock_dm(3, 2)
collapse_operators = [c0, c1, c2]
# Pass the (stepwise constant) hamiltonian into the mesolve function to evolve the
# state and access the resultant state using the .states attribute.
if dephasing == True:
rho_out = qt.mesolve(H,
rho_proper,
tlist,
c_ops=collapse_operators)
elif dephasing == False:
rho_out = qt.mesolve(H, rho_proper, tlist)
x = rho_out.states[-1]
# flatten the resultant state back into an array again. Also return a reduced_rho
# containing only the diagonal elements of the density matrix.
rho_final = x.full().reshape((self.num_levels**2, ))
reduced_rho_final = x.diag()
return rho_final, reduced_rho_final
axes.plot(kappa_arr, np.absolute(max_pts), '--b*')
axes.set_xlabel("$\kappa$")
axes.set_ylabel("Radius of Wigner Function")
axes.set_title("$nbar(\omega)=%f$" % nbar_omega)
if __name__ == "__main__":
gamma1 = 1 # TODO
gamma2 = 0.5 # 0.1 # TODO
nbar_omega = 0.1 # Temperature dependence
tlist = np.linspace(0.0, 20.0, tN)
nbar_omega = (0.1, 0.4, 0.7)
kappa = np.linspace(0, 1, 3)
kappa = np.append(kappa, np.linspace(1, 1.25, 10))
kappa = np.append(kappa, np.linspace(1.5, 3, 4))
rho0 = qutip.fock_dm(N, 0)
print(kappa)
results = [[0 for j in kappa] for i in nbar_omega]
fig1, axes = plt.subplots(1, len(nbar_omega), figsize=(16, 3))
for i, nb in enumerate(nbar_omega):
for j, kap in enumerate(kappa):
results[i][j] = solve_lindblad(gamma1, gamma2, nb, nb, kap, rho0, tlist, 0)
print("solved for nbar_omega=%f and kappa=%f" % (nb, kap))
plot_max_W_func(kappa, nb, results[i], axes[i])
# plt.hold(True)
# plt.plot(kappa)
plt.show()
print("Eseries 1 + Eseries 2\n", es1 + es2, end="\n\n")
print("Eseries 1 - Eseries 2\n", es1 - es2, end="\n\n")
print("Eseries 1 * Eseries 2\n", es1 * es2, end="\n\n")
print("Eseries: (es1 + es2) * (es1 - es2) \n", (es1 + es2) * (es1 - es2),
end="\n\n")
wait()
""" --------------- </Expecation Values of eseries> --------------- """
es3 = eseries([0.5 * sigmaz(), 0.5 * sigmaz()], [1j, -1j]) + eseries(
[-0.5j * sigmax(), 0.5 * sigmax()], [1j, -1j])
print("*Eseries:\n", es3)
print("Eseries' Value at t = 0.0:\n", es3.value(0.0))
print("Eseries' Value at t = pi/2:\n", es3.value(pi / 2))
rho = fock_dm(2, 1)
es3_expect = expect(rho, es3)
print(
"For fock density matrix(2,1) Expectation of fock density matrix(2,1) on the state given above (*Eseries)\n",
es3_expect)
print("Expectation values at times 0 and pi/2 are:\n",
es3_expect.value([0.0, pi / 2]))
wait()
""" --------------- </Software Versions> --------------- """
"""
Software Version
QuTiP 4.6.2
Numpy 1.21.4
SciPy 1.7.2
def test_smesolve_homodyne_methods():
"Stochastic: smesolve: homodyne methods with single jump operator"
def arccoth(x):
return 0.5 * np.log((1. + x) / (x - 1.))
th = 0.1 # Interaction parameter
alpha = np.cos(th)
beta = np.sin(th)
gamma = 1.
N = 30 # number of Fock states
Id = qeye(N)
a = destroy(N)
s = 0.5 * ((alpha + beta) * a + (alpha - beta) * a.dag())
x = (a + a.dag()) * 2**-0.5
H = Id
c_op = [gamma**0.5 * a]
sc_op = [s]
e_op = [x, x * x]
rho0 = fock_dm(N, 0) # initial vacuum state
T = 6. # final time
N_store = 200 # number of time steps for which we save the expectation values
Nsub = 5
tlist = np.linspace(0, T, N_store)
ddt = (tlist[1] - tlist[0])
#### Analytic solution
y0 = 0.5
A = (gamma**2 + alpha**2 * (beta**2 + 4 * gamma) -
2 * alpha * beta * gamma)**0.5
B = arccoth((-4 * alpha**2 * y0 + alpha * beta - gamma) / A)
y_an = (alpha * beta - gamma +
A / np.tanh(0.5 * A * tlist - B)) / (4 * alpha**2)
list_methods_tol = [['euler-maruyama', 2e-2],
['fast-euler-maruyama', 2e-2], ['pc-euler', 2e-3],
['milstein', 1e-3], ['fast-milstein', 1e-3],
['milstein-imp', 1e-3], ['taylor15', 1e-4],
['taylor15-imp', 1e-4]]
for n_method in list_methods_tol:
sol = smesolve(H,
rho0,
tlist,
c_op,
sc_op,
e_op,
nsubsteps=Nsub,
method='homodyne',
solver=n_method[0])
sol2 = smesolve(H,
rho0,
tlist,
c_op,
sc_op,
e_op,
nsubsteps=Nsub,
method='homodyne',
solver=n_method[0],
noise=sol.noise)
err = 1 / T * np.sum(
np.abs(y_an - (sol.expect[1] -
sol.expect[0] * sol.expect[0].conj()))) * ddt
print(n_method[0], ': deviation =', err, ', tol =', n_method[1])
assert_(err < n_method[1])
assert_(np.all(sol.noise == sol2.noise)
) # just to check that noise is not affected by smesolve
assert_(np.all(sol.expect[0] == sol2.expect[0]))
def H_approx_Par(phi):
H = -np.exp(-phi**2 / 2) * sum(
eval_laguerre(n, phi**2) * qt.fock_dm(NFock, n) for n in range(NFock))
return H
def test_smesolve_homodyne_methods():
"Stochastic: smesolve: homodyne methods with single jump operator"
def arccoth(x):
return 0.5 * np.log((1. + x) / (x - 1.))
th = 0.1 # Interaction parameter
alpha = np.cos(th)
beta = np.sin(th)
gamma = 1.
N = 30 # number of Fock states
Id = qeye(N)
a = destroy(N)
s = 0.5 * ((alpha + beta) * a + (alpha - beta) * a.dag())
x = (a + a.dag()) * 2**-0.5
H = Id
c_op = [gamma**0.5 * a]
sc_op = [s]
e_op = [x, x * x]
rho0 = fock_dm(N, 0) # initial vacuum state
T = 3. # final time
# number of time steps for which we save the expectation values
N_store = 121
Nsub = 10
tlist = np.linspace(0, T, N_store)
ddt = (tlist[1] - tlist[0])
#### Analytic solution
y0 = 0.5
A = (gamma**2 + alpha**2 * (beta**2 + 4 * gamma) -
2 * alpha * beta * gamma)**0.5
B = arccoth((-4 * alpha**2 * y0 + alpha * beta - gamma) / A)
y_an = (alpha * beta - gamma +
A / np.tanh(0.5 * A * tlist - B)) / (4 * alpha**2)
list_methods_tol = [['euler-maruyama', 2e-2], ['pc-euler', 2e-3],
['pc-euler-2', 2e-3], ['platen', 1e-3],
['milstein', 1e-3], ['milstein-imp', 1e-3],
['rouchon', 1e-3], ['taylor1.5', 1e-4],
['taylor1.5-imp', 1e-4], ['explicit1.5', 1e-4],
['taylor2.0', 1e-4]]
for n_method in list_methods_tol:
sol = smesolve(H,
rho0,
tlist,
c_op,
sc_op,
e_op,
nsubsteps=Nsub,
method='homodyne',
solver=n_method[0])
sol2 = smesolve(H,
rho0,
tlist,
c_op,
sc_op,
e_op,
store_measurement=0,
nsubsteps=Nsub,
method='homodyne',
solver=n_method[0],
noise=sol.noise)
sol3 = smesolve(H,
rho0,
tlist,
c_op,
sc_op,
e_op,
nsubsteps=Nsub * 5,
method='homodyne',
solver=n_method[0],
tol=1e-8)
err = 1/T * np.sum(np.abs(y_an - \
(sol.expect[1]-sol.expect[0]*sol.expect[0].conj())))*ddt
err3 = 1/T * np.sum(np.abs(y_an - \
(sol3.expect[1]-sol3.expect[0]*sol3.expect[0].conj())))*ddt
print(n_method[0], ': deviation =', err, ', tol =', n_method[1])
assert_(err < n_method[1])
# 5* more substep should decrease the error
assert_(err3 < err)
# just to check that noise is not affected by smesolve
assert_(np.all(sol.noise == sol2.noise))
assert_(np.all(sol.expect[0] == sol2.expect[0]))
sol = smesolve(H,
rho0,
tlist[:2],
c_op,
sc_op,
e_op,
noise=10,
ntraj=2,
nsubsteps=Nsub,
method='homodyne',
solver='euler',
store_measurement=1)
sol2 = smesolve(H,
rho0,
tlist[:2],
c_op,
sc_op,
e_op,
noise=10,
ntraj=2,
nsubsteps=Nsub,
method='homodyne',
solver='euler',
store_measurement=0)
sol3 = smesolve(H,
rho0,
tlist[:2],
c_op,
sc_op,
e_op,
noise=11,
ntraj=2,
nsubsteps=Nsub,
method='homodyne',
solver='euler')
# sol and sol2 have the same seed, sol3 differ.
assert_(np.all(sol.noise == sol2.noise))
assert_(np.all(sol.noise != sol3.noise))
assert_(not np.all(sol.measurement[0] == 0. + 0j))
assert_(np.all(sol2.measurement[0] == 0. + 0j))
sol = smesolve(H,
rho0,
tlist[:2],
c_op,
sc_op,
e_op,
noise=np.array([1, 2]),
ntraj=2,
nsubsteps=Nsub,
method='homodyne',
solver='euler')
sol2 = smesolve(H,
rho0,
tlist[:2],
c_op,
sc_op,
e_op,
noise=np.array([2, 1]),
ntraj=2,
nsubsteps=Nsub,
method='homodyne',
solver='euler')
# sol and sol2 have the seed of traj 1 and 2 reversed.
assert_(np.all(sol.noise[0, :, :, :] == sol2.noise[1, :, :, :]))
assert_(np.all(sol.noise[1, :, :, :] == sol2.noise[0, :, :, :]))
def test_smesolve_homodyne_methods():
"Stochastic: smesolve: homodyne methods with single jump operator"
def arccoth(x):
return 0.5*np.log((1.+x)/(x-1.))
th = 0.1 # Interaction parameter
alpha = np.cos(th)
beta = np.sin(th)
gamma = 1.
N = 30 # number of Fock states
Id = qeye(N)
a = destroy(N)
s = 0.5*((alpha+beta)*a + (alpha-beta)*a.dag())
x = (a + a.dag()) * 2**-0.5
H = Id
c_op = [gamma**0.5 * a]
sc_op = [s]
e_op = [x, x*x]
rho0 = fock_dm(N,0) # initial vacuum state
T = 3. # final time
# number of time steps for which we save the expectation values
N_store = 121
Nsub = 10
tlist = np.linspace(0, T, N_store)
ddt = (tlist[1]-tlist[0])
#### Analytic solution
y0 = 0.5
A = (gamma**2 + alpha**2 * (beta**2 + 4*gamma) - 2*alpha*beta*gamma)**0.5
B = arccoth((-4*alpha**2*y0 + alpha*beta - gamma)/A)
y_an = (alpha*beta - gamma + A / np.tanh(0.5*A*tlist - B))/(4*alpha**2)
list_methods_tol = [['euler-maruyama', 2e-2],
['pc-euler', 2e-3],
['pc-euler-2', 2e-3],
['platen', 1e-3],
['milstein', 1e-3],
['milstein-imp', 1e-3],
['rouchon', 1e-3],
['taylor1.5', 1e-4],
['taylor1.5-imp', 1e-4],
['explicit1.5', 1e-4],
['taylor2.0', 1e-4]]
for n_method in list_methods_tol:
sol = smesolve(H, rho0, tlist, c_op, sc_op, e_op,
nsubsteps=Nsub, method='homodyne', solver = n_method[0])
sol2 = smesolve(H, rho0, tlist, c_op, sc_op, e_op, store_measurement=0,
nsubsteps=Nsub, method='homodyne', solver = n_method[0],
noise = sol.noise)
sol3 = smesolve(H, rho0, tlist, c_op, sc_op, e_op,
nsubsteps=Nsub*5, method='homodyne',
solver = n_method[0], tol=1e-8)
err = 1/T * np.sum(np.abs(y_an - \
(sol.expect[1]-sol.expect[0]*sol.expect[0].conj())))*ddt
err3 = 1/T * np.sum(np.abs(y_an - \
(sol3.expect[1]-sol3.expect[0]*sol3.expect[0].conj())))*ddt
print(n_method[0], ': deviation =', err, ', tol =', n_method[1])
assert_(err < n_method[1])
# 5* more substep should decrease the error
assert_(err3 < err)
# just to check that noise is not affected by smesolve
assert_(np.all(sol.noise == sol2.noise))
assert_(np.all(sol.expect[0] == sol2.expect[0]))
sol = smesolve(H, rho0, tlist[:2], c_op, sc_op, e_op, noise=10, ntraj=2,
nsubsteps=Nsub, method='homodyne', solver='euler',
store_measurement=1)
sol2 = smesolve(H, rho0, tlist[:2], c_op, sc_op, e_op, noise=10, ntraj=2,
nsubsteps=Nsub, method='homodyne', solver='euler',
store_measurement=0)
sol3 = smesolve(H, rho0, tlist[:2], c_op, sc_op, e_op, noise=11, ntraj=2,
nsubsteps=Nsub, method='homodyne', solver='euler')
# sol and sol2 have the same seed, sol3 differ.
assert_(np.all(sol.noise == sol2.noise))
assert_(np.all(sol.noise != sol3.noise))
assert_(not np.all(sol.measurement[0] == 0.+0j))
assert_(np.all(sol2.measurement[0] == 0.+0j))
sol = smesolve(H, rho0, tlist[:2], c_op, sc_op, e_op, noise=np.array([1,2]),
ntraj=2, nsubsteps=Nsub, method='homodyne', solver='euler')
sol2 = smesolve(H, rho0, tlist[:2], c_op, sc_op, e_op, noise=np.array([2,1]),
ntraj=2, nsubsteps=Nsub, method='homodyne', solver='euler')
# sol and sol2 have the seed of traj 1 and 2 reversed.
assert_(np.all(sol.noise[0,:,:,:] == sol2.noise[1,:,:,:]))
assert_(np.all(sol.noise[1,:,:,:] == sol2.noise[0,:,:,:]))
H = QubitHam4_MatterSitesQubits_nocounter_rot(6, 6, 0.1, 0.1, 17.0, 16.0,
74e-15, 67e-15, 30.0, 30.0e-15,
-0.212381034483)
H.tidyup(atol=1e-1)
psi_0 = qt.tensor(
[qt.basis(2, 1),
qt.basis(n, 0),
qt.basis(n, 1),
qt.basis(2, 0)])
tlist = np.linspace(0, 25, 500)
e_ops = []
# Create excitation states for qubits and oscillators
g_qb = qt.fock_dm(2, 0)
e_qb = qt.fock_dm(2, 1)
g_osc = qt.fock_dm(n, 0)
e_osc = qt.fock_dm(n, 1)
f_osc = qt.fock_dm(n, 2)
PG = qt.tensor([g_qb, g_osc, g_osc, g_qb])
P1 = qt.tensor([e_qb, g_osc, e_osc, g_qb])
P2 = qt.tensor([g_qb, e_osc, e_osc, g_qb])
P3 = qt.tensor([g_qb, e_osc, g_osc, e_qb])
P4 = qt.tensor([g_qb, g_osc, e_osc, e_qb])
P5 = qt.tensor([g_qb, f_osc, g_osc, g_qb])
P6 = qt.tensor([g_qb, g_osc, f_osc, g_qb])
#P_e1 = qt.tensor([e_qb,qt.qeye(n),qt.qeye(n),qt.qeye(2)])
def run_sim_full_and_approx(p):
"""
TODO:
-Should get separate the approximate (rotating wave) evolution into its own function. Then the plotting routines should take a list
of results, using different
-Double check that coupling of higher qudit levels scales as standard lowering/rasing ops to a good approximation.
-Add co-rotating terms evolution to approximate RF results.
IMPORTANT:
the passed in options 'p' should not be changed inside this function if one wants to run things in parallel via multiprocessing.Pool.map()
Otherwise, in particular if p gets entries with new objects, can lead to things break down in non-trivial way.
"""
# if p.show_approx_evolution:
# print("The codebase for the approx evolution needs a couple of minor updates with the recent changes...\n\n\n")
# return None
if p.N_q>2 and p.show_approx_evolution:
#Need to generalize the approximate treatment to more levels
print("ERROR: The approximate evolution (in terms of J_m functions) for now only handles a 2 level qudit...\n\
... set p.show_approx_evolution=False in order to look at the full evolution instead.\n")
return None
#make sure the config is sane
assert(len(p.mode_freqs)==len(p.mode_q_coupling_freqs)==len(p.mode_decay_rates))
assert(p.N_q==len(p.q_level_freqs)==len(p.q_level_freqs_time_dep)==len(p.q_level_dephasing_rate)==(len(p.q_level_decay_rate)+1))
assert(p.non_rwa_terms==0 or p.non_rwa_terms==1)
results=DictExtended()
#keep a reference to the specific options/parameters that were used in the simulation along with the results
results.p=DictExtended(p)
#qubit lowering operator
c=q.tensor(q.destroy(p.N_q), *[q.qeye(p.N_m) for i in xrange(p.mode_count)])
#mode lowering operators; a[j], gives the lowering operator for the jth mode (first is the 0th indexed)
a=[]
for j in xrange(p.mode_count):
#prettier way to do this?
temp_op_list=[q.qeye(p.N_q)]
for i in xrange(p.mode_count):
if i==j:
temp_op_list.append(q.destroy(p.N_m))
else:
temp_op_list.append(q.qeye(p.N_m))
a.append(q.tensor(*temp_op_list))
#keep a reference to the key operators of our system
results.op=DictExtended(a=a, c=c)
#Build the total Hamiltonian of our system
H_rest_list=[]
for i in xrange(p.mode_count):
H_rest_list.append(p.mode_freqs[i] * a[i].dag() * a[i])
H_rest_list.append(p.mode_q_coupling_freqs[i] * (a[i].dag()*c + a[i]*c.dag()) +
p.non_rwa_terms * p.mode_q_coupling_freqs[i] * (a[i].dag()*c.dag() + a[i]*c) )
H_rest_static=np.sum(H_rest_list)
H_q_static=q.tensor(q.Qobj(np.diag(p.q_level_freqs)), *[q.qeye(p.N_m) for i in xrange(p.mode_count)])
H_q_t_list=[]
#then time dependence...
for lvl in xrange(p.N_q):
h_matrix=q.tensor(q.fock_dm(p.N_q,lvl), *[q.qeye(p.N_m) for i in xrange(p.mode_count)])
H_q_t_list.append([h_matrix, p.q_level_freqs_time_dep[lvl](p.tlist, p.epsilon, p.omega_drive)])
H_static=H_q_static + H_rest_static
results.H=[H_static] + H_q_t_list
# print(H)
#Get the eigenvalues/vectors of static portion of the Hamiltonian
eigen_system=H_static.eigenstates()
results.eigen_vals=eigen_system[0]
results.eigen_vecs=eigen_system[1]
if p.print_extra_info:
print("Eigen frequencies:")
print(map(lambda item: "%0.9g" % item, (results.eigen_vals-results.eigen_vals[0])/(2.0*np.pi)))
print("Consecutive differences in eigen frequencies:")
print(map(lambda item: "%0.9g" % item, (results.eigen_vals[1:] - results.eigen_vals[:-1])/(2.0*np.pi)))
print("Differences between mode and 1st excited qubit freqs")
print((np.array(p.mode_freqs) - p.q_level_freqs[1])/(2.0*np.pi))
if p.only_show_ev:
#in case we only want to see the eigenvalues/extra_info
return None
#Here we generate a whole bunch of states that might be of interest... but later we'll only consider some subset of those that we want to plot
#...this could be streamlined... in reality no need to create all these states if they are not to be used... but this portion of the code is fast anyway
#WE ASSUME that the initial state is one of those states defined here
#Generate the single excitation states in bare basis
results.states_collection=generate_single_excitation_states(p)
# print(states_collection)
#add the ground state
results.states_collection['state_0']=fock_state(p, 0,[])
#add the systems's eigenstates
eigenvectors_count=p.N_q*p.N_m*p.mode_count
for m in xrange(eigenvectors_count):
results.states_collection["state_v%d" % m]=results.eigen_vecs[m]*results.eigen_vecs[m].dag()
# results.states_collection["state_pv%d" % m]= results.eigen_vecs[m]*results.eigen_vecs[m].dag()
#add some other fun states
results.states_collection["g"]=q.tensor(q.fock_dm(p.N_q, 0), *[q.qeye(p.N_m) for i in xrange(p.mode_count)])
results.states_collection["e"]=q.tensor(q.fock_dm(p.N_q, 1), *[q.qeye(p.N_m) for i in xrange(p.mode_count)])
results.states_collection["sup_v1-v2"]=0.5 * (results.states_collection["state_v1"] + results.states_collection["state_v2"])
#get the right states whose expectation values we want to plot
results.e_ops=[results.states_collection[state_name] for state_name in p.states_to_evolve]
#initial state
results.rho0 = results.states_collection[p.rho0_name]
results.c_op_list = []
#qubit dephasing
if np.count_nonzero(p.q_level_dephasing_rate)>0:
dis_op=q.tensor(q.Qobj(np.diag( np.sqrt(2.0) * np.sqrt(p.q_level_dephasing_rate) ) ), *[q.qeye(p.N_m) for i in xrange(p.mode_count)])
if p.dissipators_in_dressed_basis:
dis_op=dis_op.transform(results.eigen_vecs, inverse=False)
# dis_op=dis_op.transform(results.eigen_vecs, inverse=True)
results.c_op_list.append(dis_op)
#TESTING
#reverse which state "feels" the phase shift
# rev_dephasing=np.array(p.q_level_dephasing_rate)[::-1]
# results.c_op_list.append(q.tensor(q.Qobj(np.diag( np.sqrt(2.0) * np.sqrt(rev_dephasing) ) ), *[q.ket2dm(q.basis(p.N_m,0)) for i in xrange(p.mode_count)]))
# results.c_op_list.append(q.tensor(q.Qobj(np.diag( np.sqrt(2.0) * np.sqrt(rev_dephasing) ) ), *[q.qeye(p.N_m) for i in xrange(p.mode_count)]))
# results.c_op_list.append(q.tensor(q.Qobj(np.diag( np.sqrt(2.0) * np.sqrt(p.q_level_dephasing_rate) ) ), *[q.ket2dm(q.basis(p.N_m,0)) for i in xrange(p.mode_count)]))
#qubit decay
if np.count_nonzero(p.q_level_decay_rate)>0:
dis_op=q.tensor(q.Qobj(np.diag( np.sqrt(p.q_level_decay_rate), 1 ) ), *[q.qeye(p.N_m) for i in xrange(p.mode_count)])
if p.dissipators_in_dressed_basis:
dis_op=dis_op.transform(results.eigen_vecs, inverse=False)
# dis_op=dis_op.transform(results.eigen_vecs, inverse=True)
results.c_op_list.append(dis_op)
#TESTING
# results.c_op_list.append(q.tensor(q.Qobj(np.diag( np.sqrt(p.q_level_decay_rate), 1 ) ), *[q.ket2dm(q.basis(p.N_m,0)) for i in xrange(p.mode_count)]))
#mode decay
for i, entry in enumerate(p.mode_decay_rates):
if entry!=0:
dis_op=np.sqrt(entry) * a[i]
if p.dissipators_in_dressed_basis:
dis_op=dis_op.transform(results.eigen_vecs, inverse=False)
# dis_op=dis_op.transform(results.eigen_vecs, inverse=True)
results.c_op_list.append(dis_op)
# print(results.c_op_list)
results.output = q.mesolve(results.H, results.rho0, p.tlist, results.c_op_list, results.e_ops, options=p.odeoptions, progress_bar={False:None, True:True}[p.show_progress_bar])
if p.show_approx_evolution:
if p.N_q>2:
#Need to generalize the approximate (i.e. rotating frame) treatment to more levels
print("ERROR: The approximate (in terms of J_m functions) for now only handles a 2 level qudit...\n\n\n")
return None
if p.omega_drive==0:
#the rotated frame we've chosen assumes p.omega_drive is not zero, because we end up with a 1/p.omega_drive in the arugment
#of the Bessel functions.
print("ERROR: The approximate expression for the Hamiltonian (in terms of Bessel functions) assumes that omega_drive is not zero. \
If the drive is not needed, simply set its amplitude to zero. Full numerics if of course possible with omega_drive==0.")
return results
#TODO: double check minus signs, etc and generalize to many qudit levels
def Utrans(t):
return ( (+1.0j) * ( (p.q_level_freqs[1] - p.q_level_freqs[0]) * t - p.epsilon/(1.0 * p.omega_drive ) * np.cos(p.omega_drive * t) ) * c.dag()*c +
np.sum([ (+1.0j) * t * p.mode_freqs[i] * a[i].dag()*a[i] for i in xrange(p.mode_count)]) ).expm()
results.Utrans=Utrans
zero_ops=[q.Qobj(np.zeros((p.N_q, p.N_q)))] + [q.Qobj(np.zeros((p.N_m, p.N_m))) for i in xrange(p.mode_count)]
zero_H=q.tensor(*zero_ops)
results.H_rf=[]
results.H_rf.append(zero_H) #dirrtyyy... seems like qutip wants at least one time independent Hamiltonian portion... just give it all zeros.
for i in xrange(p.mode_count):
ham_coeff_time_array=np.zeros(np.array(p.tlist).shape)
for m in p.bessel_indices:
ham_coeff_time_array=ham_coeff_time_array + ( (1.0j)**m * p.mode_q_coupling_freqs[i] * sc.special.jv(m, p.epsilon / ( 1.0 * p.omega_drive )) * np.exp( (1.0j) * (p.mode_freqs[i] - (p.q_level_freqs[1] - p.q_level_freqs[0]) - m * p.omega_drive ) * p.tlist))
matrix_components=[c*a[i].dag(), ham_coeff_time_array]
results.H_rf.append(matrix_components)
results.H_rf.append([matrix_components[0].dag(), np.conjugate(matrix_components[1])])
if p.non_rwa_terms!=0: #do the same but for the non-rwa terms
ham_coeff_time_array=np.zeros(np.array(p.tlist).shape)
for m in p.bessel_indices:
ham_coeff_time_array=ham_coeff_time_array + ( (1.0j)**m * p.mode_q_coupling_freqs[i] * sc.special.jv(m, p.epsilon / ( 1.0 * p.omega_drive )) * np.exp( (1.0j) * (p.mode_freqs[i] + (p.q_level_freqs[1] - p.q_level_freqs[0]) - m * p.omega_drive ) * p.tlist))
matrix_components=[c.dag()*a[i].dag(), ham_coeff_time_array]
results.H_rf.append(matrix_components)
results.H_rf.append([matrix_components[0].dag(), np.conjugate(matrix_components[1])])
results.rho0_rf=Utrans(0)*results.rho0*Utrans(0).dag()
#In general we have to be careful about how the dissipators transform in the rotated frame...
#take them as the same as in lab frame, which should be true in our case
# results.c_op_list = []
#If the "measurement operators" (i.e. ones we calculate the expectation values of) do not commute with the unitary transformation
#that defines the rotating frame, we need to transform the resulting density matrix before calculating expectation values if we
#want to compare the results to the full lab frame evolution
if p.transform_before_measurement:
def e_ops_func(t, rho, transformation=Utrans, e_ops=results.e_ops):
"""Transform the density matrix into the lab frame, and calculate the expectation values.
TODO: this could probably be streamlined... need to look into qutip's code
"""
rho_lab_frame=Utrans(t).dag()*q.Qobj(rho)*Utrans(t)
for i, e_operator in enumerate(e_ops):
expectation_values[i][e_ops_func.idx]=q.expect(e_operator, rho_lab_frame).real
e_ops_func.idx+=1
e_ops_func.idx=0
expectation_values=[np.zeros(len(p.tlist)) for i in xrange(len(results.e_ops))]
results.output_rf=q.mesolve(results.H_rf, results.rho0_rf, p.tlist, results.c_op_list, e_ops_func, options=p.odeoptions, progress_bar={False:None, True:True}[p.show_progress_bar])
results.output_rf.expect=expectation_values
else:
results.output_rf=q.mesolve(results.H_rf, results.rho0_rf, p.tlist, results.c_op_list, results.e_ops, options=p.odeoptions, progress_bar={False:None, True:True}[p.show_progress_bar])
print("p.epsilon / ( p.omega_drive )=%f, " % (p.epsilon / ( 1.0 * p.omega_drive ), ) +
",".join([ "J_%d()=%f" % (m, sc.special.jv(m,(p.epsilon / ( 1.0 * p.omega_drive )))) for m in p.bessel_indices]) )
if p.show_plots:
plot_results(p, results)
return results
import matplotlib.pyplot as plt
import qutip
N = 25
taus = np.linspace(0, 25.0, 200)
a = qutip.destroy(N)
H = 2 * np.pi * a.dag() * a
kappa = 0.25
n_th = 2.0 # bath temperature in terms of excitation number
c_ops = [np.sqrt(kappa * (1 + n_th)) * a, np.sqrt(kappa * n_th) * a.dag()]
states = [
{'state': qutip.coherent_dm(N, np.sqrt(2)), 'label': "coherent state"},
{'state': qutip.thermal_dm(N, 2), 'label': "thermal state"},
{'state': qutip.fock_dm(N, 2), 'label': "Fock state"},
]
fig, ax = plt.subplots(1, 1)
for state in states:
rho0 = state['state']
# first calculate the occupation number as a function of time
n = qutip.mesolve(H, rho0, taus, c_ops, [a.dag() * a]).expect[0]
# calculate the correlation function G2 and normalize with n(0)n(t) to
# obtain g2
G2 = qutip.correlation_3op_1t(H, rho0, taus, c_ops, a.dag(), a.dag()*a, a)
g2 = G2 / (n[0] * n)