def test_invariant_under_unitary_transformation(self, dimension):
rho1 = rand_dm(dimension, 0.25)
rho2 = rand_dm(dimension, 0.25)
U = rand_unitary(dimension, 0.25)
F = fidelity(rho1, rho2)
FU = fidelity(U * rho1 * U.dag(), U * rho2 * U.dag())
assert F == pytest.approx(FU, rel=1e-5)
def testNoise(self):
"""
Test for Processor with noise
"""
# setup and fidelity without noise
init_state = qubit_states(2, [0, 0, 0, 0])
tlist = np.array([0., np.pi / 2.])
a = destroy(2)
proc = Processor(N=2)
proc.add_control(sigmax(), targets=1, label="sx")
proc.set_all_coeffs({"sx": np.array([1.])})
proc.set_all_tlist(tlist)
result = proc.run_state(init_state=init_state)
assert_allclose(fidelity(result.states[-1],
qubit_states(2, [0, 1, 0, 0])),
1,
rtol=1.e-7)
# decoherence noise
dec_noise = DecoherenceNoise([0.25 * a], targets=1)
proc.add_noise(dec_noise)
result = proc.run_state(init_state=init_state)
assert_allclose(fidelity(result.states[-1],
qubit_states(2, [0, 1, 0, 0])),
0.981852,
rtol=1.e-3)
# white random noise
proc.model._noise = []
white_noise = RandomNoise(0.2, np.random.normal, loc=0.1, scale=0.1)
proc.add_noise(white_noise)
result = proc.run_state(init_state=init_state)
def test_hadamard_pulse(self):
system = self.system
q0 = system.q0
q1 = system.q1
init_state = system.fock()
target_fidelity = 1 - 1e-6
for i, qubit in enumerate([q0, q1]):
seq = QasmSequence(system)
# h
ideal = qubit.hadamard()
seq.qasm(f"h q[{i}];", unitary=False, append=True)
result = seq.run(init_state)
state = result.states[-1]
self.assertGreater(
fidelity(state, ideal * init_state) ** 2, target_fidelity
)
seq.clear()
# U2(0, \pi) = H
ideal = qubit.hadamard()
seq.qasm(f"u2(0,pi) q[{i}];", unitary=False, append=True)
result = seq.run(init_state)
state = result.states[-1]
self.assertGreater(
fidelity(state, ideal * init_state) ** 2, target_fidelity
)
seq.clear()
def test_ry_pulse(self):
system = self.system
q0 = system.q0
q1 = system.q1
init_state = system.fock()
target_fidelity = 1 - 1e-6
for i, qubit in enumerate([q0, q1]):
seq = QasmSequence(system)
for denom in [1, 2, 3, 4]:
ideal = qubit.Ry(-np.pi / denom)
seq.qasm(f"ry(-pi/{denom}) q[{i}];", unitary=False, append=True)
result = seq.run(init_state)
state = result.states[-1]
self.assertGreater(
fidelity(state, ideal * init_state) ** 2, target_fidelity
)
seq.clear()
# U(\theta, 0, 0) = R_y(\theta)
ideal = qubit.Ry(np.pi / denom)
seq.qasm(f"U(pi/{denom},0,0) q[{i}];", unitary=False, append=True)
result = seq.run(init_state)
state = result.states[-1]
self.assertGreater(
fidelity(state, ideal * init_state) ** 2, target_fidelity
)
seq.clear()
def get_fidelity_with(self,
target_state: Union[str, Qobj] = "ghz") -> float:
"""
:param target_state: One of "ghz", "ghz_antisymmetric", "ground", and "excited"
:return:
"""
assert (self.solve_result is not None
), "solve_result attribute cannot be None (call solve method)"
final_state = self.solve_result.states[-1]
if target_state == "ghz":
return fidelity(final_state,
self.ghz_state.get_state_tensor(symmetric=True))**2
elif target_state == "ghz_antisymmetric":
return fidelity(
final_state,
self.ghz_state.get_state_tensor(symmetric=False))**2
elif target_state == "ground":
return fidelity(final_state, tensor(*get_ground_states(self.N)))**2
elif target_state == "excited":
return fidelity(final_state,
tensor(*get_excited_states(self.N)))**2
elif isinstance(target_state, Qobj):
return fidelity(final_state, target_state)**2
else:
raise ValueError(
f"target_state has to be one of 'ghz', 'ground', or 'excited', not {target_state}."
)
def test_rotations_pulse(self):
q0 = Transmon("q0", levels=2)
q1 = Transmon("q1", levels=3, kerr=-200e-3)
q0.gaussian_pulse.sigma = 40
q1.gaussian_pulse.sigma = 40
system = System("system", modes=[q0, q1])
init_state = system.fock()
for qubit in [q0, q1]:
for _ in range(1):
_ = tune_rabi(system,
init_state=init_state,
mode_name=qubit.name,
verify=False)
angles = np.linspace(-np.pi, np.pi, 5)
for angle in angles:
for qubit in [q0, q1]:
seq = get_sequence(system)
qubit.rotate_x(angle)
unitary = qubit.rotate_x(angle, unitary=True)
result = seq.run(init_state)
fidelity = qutip.fidelity(result.states[-1],
unitary * init_state)**2
self.assertGreater(fidelity, 1 - 1e-2)
seq = get_sequence(system)
qubit.rotate_y(angle)
unitary = qubit.rotate_y(angle, unitary=True)
result = seq.run(init_state)
fidelity = qutip.fidelity(result.states[-1],
unitary * init_state)**2
self.assertGreater(fidelity, 1 - 1e-2)
def test_env_error(self):
print("----------Test env dephasing-----------")
n_steps = 10
rho_noise1 = errs.env_error(rho_test, 20, .3, 25e-6, 2, [0, 1])
rho_noise2 = errs.env_error(rho_test, 0, .3, 25e-6, 2, [0, 1])
# print(rho_noise1)
# print(rho_noise.tr())
print(qt.fidelity(rho_noise1, psi_test))
print(qt.fidelity(rho_noise2, psi_test))
def fitfunc(x):
L = len(x) / 3
x_noinit = x[0:L]
x_up = x[L:2 * L]
x_down = x[2 * L:3 * L]
### Initial states
rho_c1 = F1() * rho0 + (1 - F1()) * rho1
rho_c2_up = F2() * rho0 + (1 - F2()) * rho1
rho_c2_down = (1 - F2()) * rho0 + F2() * rho1
rho_c2_noinit = 0.5 * rho0 + 0.5 * rho1
rho_up = qutip.tensor(rhox, rho_c1, rho_c2_up)
rho_down = qutip.tensor(rhox, rho_c1, rho_c2_down)
rho_noinit = qutip.tensor(rhox, rho_c1, rho_c2_noinit)
### Hamiltonian
H = 2 * np.pi * (det() * qutip.tensor(szz, Id, Id) + 430e3 *
(qutip.tensor(Id, sz, Id) + qutip.tensor(Id, Id, sz))
+ A_par_1() * qutip.tensor(szz, sz, Id) +
A_perp_1() * qutip.tensor(szz, sx, Id) +
A_par_2() * qutip.tensor(szz, Id, sz) +
A_perp_2() * qutip.tensor(szz, Id, sx))
Fid_up = np.zeros(len(x_up))
Fid_down = np.zeros(len(x_down))
Fid_noinit = np.zeros(len(x_noinit))
for ii, tau in enumerate(x_up):
expH = (-1j * H * tau).expm()
### State evolution
rho_final_up = expH * rho_up * expH.dag()
rho_final_down = expH * rho_down * expH.dag()
rho_final_noinit = expH * rho_noinit * expH.dag()
### Trace out the electron
rho_el_final_up = rho_final_up.ptrace(
0) # Trace out the nuclear spins
rho_el_final_down = rho_final_down.ptrace(
0) # Trace out the nuclear spins
rho_el_final_noinit = rho_final_noinit.ptrace(
0) # Trace out the nuclear spins
### Final fidelity
Fid_up[ii] = 0.5 + 0.5 * (2 * qutip.fidelity(
rhox, rho_el_final_up)**2 - 1) * np.exp(-(tau / t())**2)
Fid_down[ii] = 0.5 + 0.5 * (2 * qutip.fidelity(
rhox, rho_el_final_down)**2 - 1) * np.exp(-(tau / t())**2)
Fid_noinit[ii] = 0.5 + 0.5 * (2 * qutip.fidelity(
rhox, rho_el_final_noinit)**2 - 1) * np.exp(-(tau / t())**2)
Fid = np.r_[Fid_noinit, Fid_up, Fid_down]
return Fid
def test_qasm_circuit_pulse(self):
qreg = self.qreg
n = len(qreg.active_modes)
QASM_CIRCUIT = [
"OPENQASM 2.0;",
'include "qelib1.inc";',
f"qreg q[{n}];",
"h q[0];",
"barrier;",
]
QASM_CIRCUIT.extend([f"CX q[0],q[{i}];" for i in range(1, n)])
QASM_CIRCUIT = "\n\t".join([""] + QASM_CIRCUIT)
print("Running the following QASM circuit:")
print(QASM_CIRCUIT)
seq = QasmSequence(qreg)
seq.qasm_circuit(QASM_CIRCUIT, unitary=False, append=True)
_ = seq.plot_coefficients(subplots=False)
result = seq.run(qreg.ground_state())
fid = fidelity(result.states[-1], self.ideal_state) ** 2
print(
f"Pulsed qasm_circuit Bell state fidelity "
f"(n = {len(qreg.active_modes)}): {fid:.7f}."
)
self.assertLess(1 - fid, 1e-6)
def timescan(self, nT=100, **kwargs):
# do a gate dynamics time scan
# !!! If parameters are not separately specified, chooses optimal gate parameters
# for programmed gate detuning
self.set_custom_parameters(**kwargs)
# initialize result vectors
end_populations_dndn = []
end_populations_upup = []
end_populations_updn = []
end_populations_dnup = []
fidelities = []
times, final_rhos = self.do_gate(nT=nT)
for ii in range(len(times)):
end_populations_upup.append(expect(self.spin_upup, final_rhos[ii]))
end_populations_dndn.append(expect(self.spin_dndn, final_rhos[ii]))
end_populations_updn.append(expect(self.spin_updn, final_rhos[ii]))
end_populations_dnup.append(expect(self.spin_dnup, final_rhos[ii]))
rho_target = 1 / 2 * (self.uu_uu + self.dd_dd - 1j * self.ud_ud +
1j * self.du_du)
fidelities.append(
fidelity(rho_target, ptrace(final_rhos[ii], [0, 1]))**2)
return times, end_populations_upup, end_populations_dndn, end_populations_updn, end_populations_dnup, fidelities
def extract_ft(ignore_percent, ghzs, times):
N = len(times)
ignore_number = int(N*ignore_percent/100)
indices_sorted = np.argsort(times)
t_sorted = times[indices_sorted]
if ignore_number != 0:
t_max = t_sorted[:-ignore_number][-1]
tavg = np.average(times[indices_sorted][:-ignore_number])
tstd = np.std(times[indices_sorted][:-ignore_number])
ghz = np.sum(ghzs[indices_sorted][:-ignore_number])
else:
t_max = t_sorted[-1]
tavg = np.average(times)
tstd = np.std(times)
ghz = np.sum(ghzs)
ghz = ghz/(N - ignore_number)
ghz = stab.twirl_ghz(ghz)
fidelity = qt.fidelity(ghz, ghz_ref)
print("_____________________________________________________")
print("N: ", N)
print("T_avg: ", tavg, tstd)
print("TIME_MAX:", t_max)
print("F: ", fidelity)
return fidelity, t_max
def plot_ghz_states_overlaps(self,
ax,
with_antisymmetric_ghz: bool,
plot_title: bool = True):
labelled_states = [(self.ghz_state.get_state_tensor(),
r"$\psi_{\mathrm{GHZ}}^{\mathrm{s}}$")]
if with_antisymmetric_ghz is not None:
labelled_states.append(
(self.ghz_state.get_state_tensor(symmetric=False),
r"$\psi_{\mathrm{GHZ}}^{\mathrm{a}}$"))
for _state, _label in labelled_states:
ax.plot(self.t_list, [
fidelity(_state, _instantaneous_state)**2
for _instantaneous_state in self.solve_result.states
],
label=_label,
lw=1,
alpha=0.8)
ax.set_ylabel("Fidelity")
if plot_title:
ax.set_title("Fidelity with GHZ states")
ax.set_ylim((-0.1, 1.1))
ax.yaxis.set_ticks([0, 0.5, 1])
ax.legend()
def test_two_qubit_error(self):
print("----------Test two qubit error-----------")
p = .09
rho_noise = errs.two_qubit_gate_noise(rho_test, p, 2, 0, 1)
print(rho_noise)
print(rho_noise.tr())
print(qt.fidelity(rho_noise, psi_test))
def test_score(params, x, y):
"""Calculates the average fidelity
between the predicted and output
kets for a given on the whole dataset.
Args:
params (obj:`np.ndarray`): parameters
:math:`\t` and :math:`\tau` in :math:
`U^{\dagger} U(\vec{t},\vec{\tau})`
inputs (obj:`np.ndarray`): input kets
:math:`|\psi_{l} \rangle` in the dataset
outputs (obj:`np.ndarray`): output kets
:math:`U(\vec{t}, \vec{\tau})
|ket_{input}\rangle` in the dataset
Returns:
float: fidelity between :math:`U(\vec{t},
\vec{\tau})|ket_{input} \rangle` and the output
(label) kets for parameters :math:`\vec{t},
\vec{\tau}` averaged over the entire training set.
"""
fidel = 0
for i in range(train_len):
pred = np.matmul(make_unitary(N, params), x[i])
step_fidel = fidelity(Qobj(pred), Qobj(y[i]))
fidel += step_fidel
return fidel / train_len
def scan_efficiency(self,
ndot=0,
fact_vec=[1, 2, 3, 4, 5],
tau_mot=0,
gamma_el=0,
gamma_ram=0,
tau_spin=0):
if self.species is not 'effic_test':
raise TypeError(
'Need species effic_test for this to work (factor not implemented for other ions species)'
)
# initialize result vectors
errors = []
efficiencies = []
rho_target = 1 / 2 * (self.uu_uu + self.dd_dd - 1j * self.ud_ud +
1j * self.du_du)
self.set_mot_dephasing_time(tau_mot)
self.set_el_deph_rate(gamma_el)
self.set_ram_scat_rate(gamma_ram)
self.set_spin_dephasing_time(tau_spin)
for factor in fact_vec:
self.set_eff_factor(factor)
self.set_heating_rate(ndot)
times, final_rhos = self.do_gate()
errors.append(
1 - fidelity(rho_target, ptrace(final_rhos[-1], [0, 1]))**2)
efficiencies.append(self.calc_gate_eff())
return fact_vec, errors, efficiencies
def test_multi_qubits(self):
"""
Test for multi-qubits system.
"""
N = 3
H_d = tensor([sigmaz()] * 3)
H_c = []
# test empty ctrls
num_tslots = 30
evo_time = 10
test = OptPulseProcessor(N)
test.add_drift(H_d, [0, 1, 2])
test.add_control(tensor([sigmax(), sigmax()]), cyclic_permutation=True)
# test periodically adding ctrls
sx = sigmax()
iden = identity(2)
assert (len(test.get_control_labels()) == 3)
test.add_control(sigmax(), cyclic_permutation=True)
test.add_control(sigmay(), cyclic_permutation=True)
# test pulse genration for cnot gate, with kwargs
qc = [tensor([identity(2), cnot()])]
test.load_circuit(qc,
num_tslots=num_tslots,
evo_time=evo_time,
min_fid_err=1.0e-6)
rho0 = qubit_states(3, [1, 1, 1])
rho1 = qubit_states(3, [1, 1, 0])
result = test.run_state(rho0, options=SolverOptions(store_states=True))
assert_(fidelity(result.states[-1], rho1) > 1 - 1.0e-6)
def test_simple_hadamard(self):
"""
Test for optimizing a simple hadamard gate
"""
N = 1
H_d = sigmaz()
H_c = sigmax()
qc = QubitCircuit(N)
qc.add_gate("SNOT", 0)
# test load_circuit, with verbose info
num_tslots = 10
evo_time = 10
test = OptPulseProcessor(N, drift=H_d)
test.add_control(H_c, targets=0)
tlist, coeffs = test.load_circuit(qc,
num_tslots=num_tslots,
evo_time=evo_time,
verbose=True)
# test run_state
rho0 = qubit_states(1, [0])
plus = (qubit_states(1, [0]) + qubit_states(1, [1])).unit()
result = test.run_state(rho0)
assert_allclose(fidelity(result.states[-1], plus), 1, rtol=1.0e-6)
def get_fid(self, args=None, phi_tgt=None):
if args is not None:
self.run(args)
if phi_tgt is not None:
self.phi_tgt = phi_tgt
self.fid = np.square(fidelity(self.final_state, self.phi_tgt))
return self.fid
def test_multi_gates(self):
N = 2
H_d = tensor([sigmaz()]*2)
H_c = []
test = OptPulseProcessor(N)
test.add_drift(H_d, [0, 1])
test.add_control(sigmax(), cyclic_permutation=True)
test.add_control(sigmay(), cyclic_permutation=True)
test.add_control(tensor([sigmay(), sigmay()]))
# qubits circuit with 3 gates
setting_args = {"SNOT": {"num_tslots": 10, "evo_time": 1},
"SWAP": {"num_tslots": 30, "evo_time": 3},
"CNOT": {"num_tslots": 30, "evo_time": 3}}
qc = QubitCircuit(N)
qc.add_gate("SNOT", 0)
qc.add_gate("SWAP", targets=[0, 1])
qc.add_gate('CNOT', controls=1, targets=[0])
test.load_circuit(qc, setting_args=setting_args,
merge_gates=False)
rho0 = rand_ket(4) # use random generated ket state
rho0.dims = [[2, 2], [1, 1]]
U = gate_sequence_product(qc.propagators())
rho1 = U * rho0
result = test.run_state(rho0)
assert_(fidelity(result.states[-1], rho1) > 1-1.0e-6)
def test_u2_pulse(self):
system = self.system
q0 = system.q0
q1 = system.q1
init_state = system.fock()
target_fidelity = 1 - 1e-6
for i, qubit in enumerate([q0, q1]):
# U2(\phi, \lambda) = RZ(\phi) RY(\frac{\pi}{2}) RZ(\lambda)
for phi_denom in [1, 2, 3, 4]:
for lam_denom in [1, 2, 3, 4]:
seq = QasmSequence(system)
ideal = (
qubit.Rz(np.pi / phi_denom)
* qubit.Ry(np.pi / 2)
* qubit.Rz(np.pi / lam_denom)
)
seq.qasm(
f"u2(pi/{phi_denom},pi/{lam_denom}) q[{i}];",
unitary=False,
append=True,
)
result = seq.run(init_state)
state = result.states[-1]
self.assertGreater(
fidelity(state, ideal * init_state) ** 2, target_fidelity
)
def detuning_scan(self, delta_g_vec, delta_g_0=None, **kwargs):
# do a gate dynamics frequency scan
# !!! If parameters are not separately specified, chooses optimal gate parameters
# for programmed gate detuning
self.set_custom_parameters(delta_g=delta_g_0, **kwargs)
# initialize result vectors
end_populations_dndn = []
end_populations_upup = []
end_populations_updn = []
end_populations_dnup = []
fidelities = []
for delta_g in delta_g_vec:
self.set_gate_detuning(delta_g)
times, final_rhos = self.do_gate(nT=2)
end_populations_upup.append(expect(self.spin_upup, final_rhos[-1]))
end_populations_dndn.append(expect(self.spin_dndn, final_rhos[-1]))
end_populations_updn.append(expect(self.spin_updn, final_rhos[-1]))
end_populations_dnup.append(expect(self.spin_dnup, final_rhos[-1]))
rho_target = 1 / 2 * (self.uu_uu + self.dd_dd - 1j * self.ud_ud +
1j * self.du_du)
fidelities.append(
fidelity(rho_target, ptrace(final_rhos[-1], [0, 1]))**2)
return end_populations_upup, end_populations_dndn, end_populations_updn, end_populations_dnup, fidelities
def run_operator(state, QI_a, QQ_a, QI_c, QQ_c, show_fid_graph=False):
start_time = time.time_ns()
fid = []
prod = 1
for k in range(num_time_steps):
H = H0 + Ha_I * QI_a[k] + Ha_Q * QQ_a[k] + Hc_I * QI_c[
k] + Hc_Q * QQ_c[k]
U = ((-1j * dt) * H).expm()
prod = U * prod
bl.add_states(qt.ptrace(prod * state, 0))
fid.append(qt.fidelity(prod * state, state_target * state_init))
result = prod * state
if show_fid_graph:
fig, ax = plt.subplots(1, 1)
ax.plot(times, fid)
ax.set_title("Fidelity Over Time")
ax.set_xlabel('Time (sec)')
ax.set_ylabel('Fidelity')
print("- Simulating the system took",
str((time.time_ns() - start_time) * 1e-9)[0:4], "Seconds")
return result
def scan_tilt_angle(self,
angle_max=10 / 360 * 2 * pi,
angle_min=-10 / 360 * 2 * pi,
n_steps=10,
mode_name='rad_ip_l',
**kwargs):
# simulate gate fidelity for different heating rates
# initialize result vectors
self.set_custom_parameters(**kwargs)
errors = []
rho_target = tensor(self.dn_dn, self.dn_dn)
tilt_angles = np.linspace(angle_min, angle_max, n_steps)
self.set_ion_temp(self.modes.modes[mode_name].nbar)
detuning_offset = self.omega_z - self.modes.modes[mode_name].freq
self.set_gate_detuning(self.delta_g + detuning_offset)
for angle in tilt_angles:
self.set_lamb_dicke_factors(mode_name=mode_name,
raman_misalignment=angle)
times, final_rhos = self.do_gate()
errors.append(
1 - fidelity(rho_target, ptrace(final_rhos[-1], [0, 1]))**2)
return tilt_angles, errors
def test_N_level_system(self):
"""
Test for circuit with N-level system.
"""
mat3 = qp.rand_unitary_haar(3)
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)))
qc = QubitCircuit(2, dims=[3, 2])
qc.user_gates = {"CTRLMAT3": controlled_mat3}
qc.add_gate("CTRLMAT3", targets=[1, 0], arg_value=1)
props = qc.propagators()
final_fid = qp.average_gate_fidelity(mat3, ptrace(props[0], 0) - 1)
assert pytest.approx(final_fid, 1.0e-6) == 1
init_state = basis([3, 2], [0, 1])
result = qc.run(init_state)
final_fid = qp.fidelity(result, props[0] * init_state)
assert pytest.approx(final_fid, 1.0e-6) == 1.
def scan_t_g(self,
t_max=50e-6,
t_min=10e-6,
n_steps=10,
tau=0,
ndot=0,
factor=1,
gamma_el=0,
gamma_ram=0,
**kwargs):
# simulate gate fidelity for different gate pulse durations, with delta_g
# and Omega_R optimised for this t_g
# i.e. determines scaling of errors due to eg heating with t_g
errors = []
rho_target = 1 / 2 * (self.uu_uu + self.dd_dd - 1j * self.ud_ud +
1j * self.du_du)
ts = np.linspace(t_min, t_max, n_steps)
for t_g in ts:
delta_g = self.calc_ideal_gate_detuning(T=t_g, verbose=False)
self.set_custom_parameters(delta_g=delta_g, **kwargs)
times, final_rhos = self.do_gate()
errors.append(
1 - fidelity(rho_target, ptrace(final_rhos[-1], [0, 1]))**2)
return ts, errors
def random_benchmark(state, **kwargs):
target = root_iSWAP * state #.ptrace([1,2])
sim = Simulation(do_qt_mesolve, state=state, fname='2qtest.yaml')
states = sim.run_solver(nsteps=1000,
steps=1000,
tau=1e-8,
progress_bar=True)
return np.max([qt.fidelity(target, s) for s in states])
def test_orthogonal(self, left_dm, right_dm, dimension):
left = basis(dimension, 0)
right = basis(dimension, dimension // 2)
if left_dm:
left = left.proj()
if right_dm:
right = right.proj()
assert fidelity(left, right) == pytest.approx(0, abs=1e-6)
def fitfunc(x):
L = len(x)/3
x_noinit = x[0:L]
x_up = x[L:2*L]
x_down = x[2*L:3*L]
### Initial states
rho_c1 = F1()*rho0 + (1-F1())*rho1
rho_c2_up = F2()*rho0 + (1-F2())*rho1
rho_c2_down = (1-F2())*rho0 + F2()*rho1
rho_c2_noinit = 0.5*rho0 + 0.5*rho1
rho_up = qutip.tensor(rhox,rho_c1,rho_c2_up)
rho_down = qutip.tensor(rhox,rho_c1,rho_c2_down)
rho_noinit = qutip.tensor(rhox,rho_c1,rho_c2_noinit)
### Hamiltonian
H = 2*np.pi*(det()*qutip.tensor(szz,Id,Id) + 431.9e3*(qutip.tensor(Id,sz,Id) + qutip.tensor(Id,Id,sz)) +
A_par_1()*qutip.tensor(szz,sz,Id) + A_perp_1()*qutip.tensor(szz,sx,Id) +
A_par_2()*qutip.tensor(szz,Id,sz) + A_perp_2()*qutip.tensor(szz,Id,sx) )
Fid_up = np.zeros(len(x_up))
Fid_down = np.zeros(len(x_down))
Fid_noinit = np.zeros(len(x_noinit))
for ii, tau in enumerate(x_up):
expH = (-1j*H*tau).expm()
### State evolution
rho_final_up = expH * rho_up * expH.dag()
rho_final_down = expH * rho_down * expH.dag()
rho_final_noinit = expH * rho_noinit * expH.dag()
### Trace out the electron
rho_el_final_up = rho_final_up.ptrace(0) # Trace out the nuclear spins
rho_el_final_down = rho_final_down.ptrace(0) # Trace out the nuclear spins
rho_el_final_noinit = rho_final_noinit.ptrace(0) # Trace out the nuclear spins
### Final fidelity
Fid_up[ii] = O() + 0.5*(2*qutip.fidelity(rhox, rho_el_final_up)**2 -1)* np.exp(-(tau/t()/1e-6)**2)
Fid_down[ii] = O() + 0.5*(2*qutip.fidelity(rhox, rho_el_final_down)**2 -1)* np.exp(-(tau/t()/1e-6)**2)
Fid_noinit[ii] = O() + 0.5*(2*qutip.fidelity(rhox, rho_el_final_noinit)**2 -1)* np.exp(-(tau/t()/1e-6)**2)
Fid = np.r_[Fid_noinit, Fid_up, Fid_down]
return Fid
def dis(state1,state2):
(n,m)=state1.shape
if state1.type is not 'ket' or state2.type is not 'ket':
print("Error: One or more input to the distance function is not a ket." )
p_0=0
else:
fid=qt.fidelity(state1,state2)
p_0 = 1/n + (n-1)*fid/n
return p_0
def fidelity(self):
"""
Calculates fidelity of current and goal state/unitary.
Return:
fid (float): fidelity measure
"""
if self.is_unitary:
assert self.current_unitary.shape == self.goal_unitary.shape
fid = fidelity(
Qobj(self.current_unitary) * self.basis_state,
Qobj(self.goal_unitary) * self.basis_state)
else:
assert len(self.current_state) == len(self.goal_state)
fid = fidelity(Qobj([self.current_state]), Qobj([self.goal_state]))
return fid
def report_stats(result: OptimResult, N: int):
result.stats.report()
target_state = StandardGHZState(N).get_state_tensor()
final_fidelity = qutip.fidelity(target_state, result.evo_full_final)**2
print(f"final_fidelity: {final_fidelity:.5f}")
print(f"Final gradient normal {result.grad_norm_final:.3e}")
print(f"Terminated due to {result.termination_reason}")
q1 = qt.basis(2,0)
q2 = (qt.basis(2,1))#+qt.basis(2,0)).unit()
# L1 = 0.01 * qt.tensor(qt.qeye(5),qt.destroy(2),I)
# L2 = 0.01 * qt.tensor(qt.qeye(5),I,qt.destroy(2))
# lindblads = [L1,L2]
if __name__ == '__main__':
# cav = thermal_state(5e9,20e-3)
sim = Simulation(do_qt_mesolve, state=qt.tensor(cav, q1, q2),
fname='time_dependent.yaml')
# sim.append_L(cavity_loss(10000, sim.w_c, 20e-3, sim.dims))
# sim.append_L(thermal_in(10000, sim.w_c, 20e-3, sim.dims))
# sim.append_L(relaxation(1,sim.dims,1))
# sim.append_L(relaxation(1,sim.dims,2))
# sim.append_L(decoherence(1e2,sim.dims,1))
# sim.append_L(decoherence(1e2,sim.dims,2))
states = sim.run_solver(nsteps=1000, steps=10000, tau=1e-9,
progress_bar=True)
target = root_iSWAP * qt.tensor(q1, q2)
fids1 = [qt.fidelity(target, state.ptrace([1,2])) for state in states]
# print(np.max(fids1),np.argmax(fids1)*1e-9)
# sim = Simulation(do_qt_mesolve, state=qt.tensor(q1, q2),
# fname='2qtest.yaml')
# states = sim.run_solver(nsteps=1000,steps=2500,tau=1e-7,progress_bar=True)
# target = root_iSWAP * qt.tensor(q1, q2)
# fids2 = [qt.fidelity(target, state) for state in states]
# print(np.max(fids1),np.argmax(fids1)*1e-7)
plt.plot(1e-7*np.arange(len(fids1)), fids1, 'r')
# # 1e-7*np.arange(len(fids2)), fids2, 'b')
plt.show()
def random_benchmark(state, **kwargs):
target = root_iSWAP * state#.ptrace([1,2])
sim = Simulation(do_qt_mesolve, state=state, fname='2qtest.yaml')
states = sim.run_solver(nsteps=1000, steps=1000, tau=1e-8,
progress_bar=True)
return np.max([qt.fidelity(target, s) for s in states])
def random_purity_benchmark(state, **kwargs):
target = root_iSWAP * state.ptrace([1,2])
sim = Simulation(do_qt_mesolve, state=state, fname='time_dependent.yaml')
states = sim.run_solver(nsteps=2000, steps=10000, tau=1e-7, rhs_reuse=True)
print('Done a state')
return qt.fidelity(target, states[-1].ptrace([1,2]))
def fidelitycheck(self, out1, out2, rho0vec):
fid = np.zeros(len(out1.states))
for i, E in enumerate(out2.states):
rhot = vector_to_operator(E * rho0vec)
fid[i] = fidelity(out1.states[i], rhot)
return fid
print(Best_A)
print(Best_B)
Sin_terms = np.sin(np.outer(time, Freqs))
Cos_terms = np.cos(np.outer(time, Freqs))
f_t = np.add(np.dot(Sin_terms, Best_A), np.dot(Cos_terms, Best_B))
plt.figure(1)
plt.plot(time, f_t)
def func_t(t, args):
S_terms = np.sin(np.outer(t, args['w']))
C_terms = np.cos(np.outer(t, args['w']))
return np.add(np.dot(S_terms, args['A']), np.dot(C_terms, args['B']))
Hamiltonian = [H0, [H1, func_t]]
arguments = {'w':Freqs, 'A':Best_A, 'B':Best_B}
Evolution = qutip.mesolve(Hamiltonian, Rho_ini, time, [np.sqrt(0.5)*qutip.tensor(qutip.sigmax(),qutip.sigmax())], [], args = arguments)
fidelity = []
for i in range (len(time)) :
fidelity.append(qutip.fidelity(Rho_fi, Evolution.states[i]))
plt.figure(2)
plt.plot(time, fidelity)
print(fidelity[-1])
def Cost(x) : #Function to be minimized using scipy.optimize
a = x[0:Nc:1] #Returns 1 - Fidelity
b = x[Nc:2*Nc:1]
args = {'w' : np.hstack((w, Frequencies)), 'A' : np.hstack((a, Best_parameters_A)), 'B' : np.hstack((b, Best_parameters_B))}
temp = qutip.mesolve(H, Initial_density, Time_steps, [np.sqrt(0.5)*qutip.tensor(qutip.sigmax(),qutip.sigmax())], [], args = args)
return 1. - qutip.fidelity(Final_density, temp.states[len(Time_steps) - 1])