def test_simdiag(num_mat):
N = 10
U = qutip.rand_unitary(N)
commuting_matrices = [
U * qutip.qdiags(np.random.rand(N), 0) * U.dag()
for _ in range(num_mat)
]
all_evals, evecs = qutip.simdiag(commuting_matrices)
for matrix, evals in zip(commuting_matrices, all_evals):
for eval, evec in zip(evals, evecs):
assert matrix * evec == evec * eval
def test_simdiag_degen_large():
N = 20
U = qutip.rand_unitary(N)
commuting_matrices = [
U * qutip.qdiags(np.random.randint(0, 3, N), 0) * U.dag()
for _ in range(5)
]
all_evals, evecs = qutip.simdiag(commuting_matrices, tol=1e-12)
for matrix, evals in zip(commuting_matrices, all_evals):
for eval, evec in zip(evals, evecs):
np.testing.assert_allclose((matrix * evec).full(),
(evec * eval).full())
def test_simdiag_degen():
N = 10
U = qutip.rand_unitary(N)
commuting_matrices = [
U * qutip.qdiags([0, 0, 0, 1, 1, 1, 2, 2, 3, 4], 0) * U.dag(),
U * qutip.qdiags([0, 0, 0, 1, 2, 2, 2, 2, 2, 2], 0) * U.dag(),
U * qutip.qdiags([0, 0, 2, 1, 1, 2, 2, 3, 3, 4], 0) * U.dag(),
]
all_evals, evecs = qutip.simdiag(commuting_matrices)
for matrix, evals in zip(commuting_matrices, all_evals):
for eval, evec in zip(evals, evecs):
np.testing.assert_allclose((matrix * evec).full(),
(evec * eval).full())
def test_simdiag_no_evals(num_mat):
N = 10
U = qutip.rand_unitary(N)
commuting_matrices = [
U * qutip.qdiags(np.random.rand(N), 0) * U.dag()
for _ in range(num_mat)
]
evecs = qutip.simdiag(commuting_matrices, evals=False)
for matrix in commuting_matrices:
for evec in evecs:
Mvec = matrix * evec
eval = Mvec.norm() / evec.norm()
assert matrix * evec == evec * eval
def sim_diag(self, r_matrices):
r_qt_ob = []
for r_matrix in r_matrices:
r_qt_ob.append(qt.Qobj(r_matrix))
r_mat_diag = qt.simdiag(r_qt_ob)
# r_mat_diag = qt.simdiag(r_matrices)
r_mat_evals = r_mat_diag[0]
# r_mat_evals = r_mat_evals[np.argsort(np.sum(np.where(np.round(r_mat_evals,10)==-1.0,r_mat_evals,np.zeros(np.shape(r_mat_evals))),axis=1))[::-1],:]
v_matrix = np.hstack([
r_mat_diag[1][i].data.toarray() for i in range(self.fer_op.modes)
])
# print(v_matrix)
print("checking the v matrix...")
is_identity = np.allclose(np.dot(v_matrix,
v_matrix.conj().T),
np.identity(self.fer_op.modes))
print("v matrix is {} unitary.".format("" if is_identity else "NOT"))
return [r_mat_evals, v_matrix]
def find_symmetry_ops(r_matrices):
"""
Args:
r_matrices (list[numpy.ndarray]): a list of rotation matrices.
Returns:
numpy.ndarray: the V matrix
list[Operator]: symmetry paulis
list[Operator]: cliffords, composed of symmetries and single-qubit op
list[int]: position of the single-qubit operators that anticommute
with the cliffords
"""
modes = r_matrices[0].shape[0]
g_matrices = []
for r_matrix in r_matrices:
g_matrix = -1j * scila.logm(r_matrix)
g_matrices.append(g_matrix)
sim_dia = []
for g_matrix in g_matrices:
sim_dia.append(qt.Qobj(g_matrix))
d_v = qt.simdiag(sim_dia)
d_matrices = d_v[0]
v_matrix = np.hstack([d_v[1][i].data.toarray() for i in range(modes)])
# check the build d_matrix
for eig in d_matrices.flatten():
print(eig)
if not (np.isclose(eig, 0.0) or np.isclose(eig, np.pi)):
# print(np.where(d_matrices.flatten()==eig))
raise ValueError('The specified R matrix is invalid. \
Eigenvalues of G includes: {}'.format(
eig))
single_qubit_list = []
cliffords = []
pauli_symmetries = []
existed_pi_locs = []
# pdb.set_trace()
for d_idx in range(len(d_matrices)):
pi_index = np.where(np.isclose(d_matrices[d_idx], np.pi))[0]
single_qubit_pauli = ['I'] * modes
pi_loc = 0
for i in pi_index:
if i not in existed_pi_locs:
pi_loc = i
existed_pi_locs.extend(pi_index.tolist())
break
single_qubit_pauli[pi_loc] = 'X'
single_qubit_pauli = ''.join(single_qubit_pauli)
single_qubit_op = Operator(
paulis=[[1.0, Pauli.from_label(single_qubit_pauli[::-1])]])
single_qubit_list.append(pi_loc)
symmetries_pauli_label = ''
for i in range(modes):
symmetries_pauli_label += 'I' if i not in pi_index else 'Z'
sym_pauli = Pauli.from_label(symmetries_pauli_label[::-1])
pauli_symmetries.append(sym_pauli)
symmetries_op = Operator(paulis=[[1.0, sym_pauli]])
clifford_op = single_qubit_op + symmetries_op
clifford_op.scaling_coeff(1.0 / np.sqrt(2))
cliffords.append(clifford_op)
return v_matrix, pauli_symmetries, cliffords, single_qubit_list
def test_simdiag_errors(ops, error):
with pytest.raises(TypeError) as err:
qutip.simdiag(ops)
assert error in str(err.value)
def test_simdiag_no_input():
with pytest.raises(ValueError):
qutip.simdiag([])