def test_minimize_one_norm_with_amp_damp_choi():
for noise_level in [0.01, 0.02, 0.03]:
q = LineQubit(0)
ideal_matrix = _operation_to_choi(H(q))
basis_matrices = [
_operation_to_choi(
[H(q), gate(q),
AmplitudeDampingChannel(noise_level)(q)]) for gate in [I, Z]
]
# Append reset channel
reset_kraus = channel(ResetChannel())
basis_matrices.append(kraus_to_choi(reset_kraus))
optimal_coeffs = minimize_one_norm(ideal_matrix, basis_matrices)
represented_mat = sum(
[eta * mat for eta, mat in zip(optimal_coeffs, basis_matrices)])
assert np.allclose(ideal_matrix, represented_mat)
# Optimal analytic result by Takagi (arXiv:2006.12509)
expected = (1.0 + noise_level) / (1.0 - noise_level)
assert np.isclose(np.linalg.norm(optimal_coeffs, 1), expected)
def test_minimize_one_norm_with_amp_damp_superoperators():
for noise_level in [0.01, 0.02, 0.03]:
damp_kraus = amplitude_damping_kraus(noise_level, num_qubits=1)
damp_super = kraus_to_super(damp_kraus)
ideal_matrix = kraus_to_super(channel(H))
basis_matrices = [
damp_super @ kraus_to_super(channel(gate)) @ ideal_matrix
for gate in [I, Z]
]
# Append reset channel
reset_kraus = channel(ResetChannel())
basis_matrices.append(kraus_to_super(reset_kraus))
optimal_coeffs = minimize_one_norm(ideal_matrix,
basis_matrices,
tol=1.0e-6)
represented_mat = sum(
[eta * mat for eta, mat in zip(optimal_coeffs, basis_matrices)])
assert np.allclose(ideal_matrix, represented_mat)
# Optimal analytic result by Takagi (arXiv:2006.12509)
expected = (1.0 + noise_level) / (1.0 - noise_level)
assert np.isclose(np.linalg.norm(optimal_coeffs, 1), expected)