def test_lindblad_singlequbit(self):
ham = random_hermitian_matrix(2, seed=56)
lindblad_ops = np.array([
[[0, 0.1], [0, 0]],
[[0, 0], [0, 0.33]],
])
t1 = 10
t2 = 25
b1 = (bases.general(2), )
b2 = (bases.gell_mann(2), )
op1 = Operation.from_lindblad_form(t1,
b1,
b2,
hamiltonian=ham,
lindblad_ops=lindblad_ops)
op2 = Operation.from_lindblad_form(t2,
b2,
b1,
hamiltonian=ham,
lindblad_ops=lindblad_ops)
op = Operation.from_lindblad_form(t1 + t2,
b1,
hamiltonian=ham,
lindblad_ops=lindblad_ops)
dm = random_hermitian_matrix(2, seed=3)
state1 = PauliVector.from_dm(dm, b1)
state2 = PauliVector.from_dm(dm, b1)
op1(state1, 0)
op2(state1, 0)
op(state2, 0)
assert np.allclose(state1.to_pv(), state2.to_pv())
def test_lindblad_time_inverse(self):
ham = random_hermitian_matrix(2, seed=4)
b = (bases.general(2), )
op_plus = Operation.from_lindblad_form(20, b, hamiltonian=ham)
op_minus = Operation.from_lindblad_form(20, b, hamiltonian=-ham)
dm = random_hermitian_matrix(2, seed=5)
state = PauliVector.from_dm(dm, b)
op_plus(state, 0)
op_minus(state, 0)
assert np.allclose(state.to_dm(), dm)
def test_lindblad_two_qubit(self):
b = (bases.general(2), )
id = np.array([[1, 0], [0, 1]])
ham1 = random_hermitian_matrix(2, seed=6)
ham2 = random_hermitian_matrix(2, seed=7)
ham = np.kron(ham1, id).reshape(2, 2, 2, 2) + \
np.kron(id, ham2).reshape(2, 2, 2, 2)
dm = random_hermitian_matrix(4, seed=3)
op1 = Operation.from_lindblad_form(25, b, hamiltonian=ham1)
op2 = Operation.from_lindblad_form(25, b, hamiltonian=ham2)
op = Operation.from_lindblad_form(25, b * 2, hamiltonian=ham)
state1 = PauliVector.from_dm(dm, b * 2)
state2 = PauliVector.from_dm(dm, b * 2)
op1(state1, 0)
op2(state1, 1)
op(state2, 0, 1)
assert np.allclose(state1.to_pv(), state2.to_pv())
ops1 = np.array([
[[0, 0.1], [0, 0]],
[[0, 0], [0, 0.33]],
])
ops2 = np.array([
[[0, 0.15], [0, 0]],
[[0, 0], [0, 0.17]],
])
ops = [np.kron(op, id).reshape(2, 2, 2, 2) for op in ops1] +\
[np.kron(id, op).reshape(2, 2, 2, 2) for op in ops2]
op1 = Operation.from_lindblad_form(25, b, lindblad_ops=ops1)
op2 = Operation.from_lindblad_form(25, b, lindblad_ops=ops2)
op = Operation.from_lindblad_form(25, b * 2, lindblad_ops=ops)
state1 = PauliVector.from_dm(dm, b * 2)
state2 = PauliVector.from_dm(dm, b * 2)
op1(state1, 0)
op2(state1, 1)
op(state2, 0, 1)
assert np.allclose(state1.to_pv(), state2.to_pv())
op1 = Operation.from_lindblad_form(25,
b,
hamiltonian=ham1,
lindblad_ops=ops1)
op2 = Operation.from_lindblad_form(25,
b,
hamiltonian=ham2,
lindblad_ops=ops2)
op = Operation.from_lindblad_form(25,
b * 2,
hamiltonian=ham,
lindblad_ops=ops)
state1 = PauliVector.from_dm(dm, b * 2)
state2 = PauliVector.from_dm(dm, b * 2)
op1(state1, 0)
op2(state1, 1)
op(state2, 0, 1)
assert np.allclose(state1.to_pv(), state2.to_pv())
def idle(duration, t1, t2, anharmonicity=0.):
if np.isfinite(t1) and np.isfinite(t2):
t_phi = 1. / (1. / t2 - 0.5 / t1)
if t_phi < 0:
raise ValueError('t2 must be less than 2*t1')
elif np.allclose(t_phi, 0):
ops_t2 = []
else:
ops_t2 = [(8. / (9 * t_phi))**0.5 *
np.array([[1, 0, 0], [0, 0, 0], [0, 0, -1]]),
(2. / (9 * t_phi))**0.5 *
np.array([[1, 0, 0], [0, -1, 0], [0, 0, 0]]),
(2. / (9 * t_phi))**0.5 *
np.array([[0, 0, 0], [0, 1, 0], [0, 0, -1]])]
else:
ops_t2 = []
op_t1 = t1**-0.5 * np.array([[0, 1, 0], [0, 0, np.sqrt(2)], [0, 0, 0]])
if not np.allclose(anharmonicity, 0.):
ham = np.array([
[0., 0., 0.],
[0., 0., 0.],
[0., 0., anharmonicity],
])
else:
ham = None
return Operation.from_lindblad_form(duration, (bases.general(3), ),
hamiltonian=ham,
lindblad_ops=[op_t1, *ops_t2])
def idle(duration, t1, t2, anharmonicity=0.):
t_phi = 1./(1./t2 - 0.5/t1)
op_t1 = t1**-0.5 * np.array([
[0, 1, 0],
[0, 0, np.sqrt(2)],
[0, 0, 0]
])
ops_t2 = [
(8. / (9*t_phi))**0.5 * np.array([
[1, 0, 0],
[0, 0, 0],
[0, 0, -1]
]),
(2. / (9*t_phi))**0.5 * np.array([
[1, 0, 0],
[0, -1, 0],
[0, 0, 0]
]),
(2. / (9*t_phi))**0.5 * np.array([
[0, 0, 0],
[0, 1, 0],
[0, 0, -1]
])
]
if not np.allclose(anharmonicity, 0.):
ham = np.array([
[0., 0., 0.],
[0., 0., 0.],
[0., 0., anharmonicity],
])
else:
ham = None
return Operation.from_lindblad_form(
duration, bases.general(3),
hamiltonian=ham,
lindblad_ops=[op_t1, *ops_t2])