def test_initial_guess_in_minimize_one_norm():
for noise_level in [0.7, 0.9]:
depo_kraus = global_depolarizing_kraus(noise_level, num_qubits=1)
depo_super = kraus_to_super(depo_kraus)
ideal_matrix = kraus_to_super(kraus(H))
basis_matrices = [
depo_super @ kraus_to_super(kraus(gate)) @ ideal_matrix
for gate in [I, X, Y, Z, H]
]
optimal_coeffs = minimize_one_norm(
ideal_matrix,
basis_matrices,
initial_guess=[1.0, 1.0, 1.0, 1.0, 1.0],
)
represented_mat = sum(
[eta * mat for eta, mat in zip(optimal_coeffs, basis_matrices)]
)
assert np.allclose(ideal_matrix, represented_mat)
# Test bad argument
with raises(ValueError, match="shapes"):
minimize_one_norm(
ideal_matrix,
basis_matrices,
initial_guess=[1],
)
def test_initial_guess_in_minimize_one_norm():
for noise_level in [0.7, 0.9]:
depo_kraus = global_depolarizing_kraus(noise_level, num_qubits=1)
depo_super = kraus_to_super(depo_kraus)
ideal_matrix = kraus_to_super(channel(H))
basis_matrices = [
depo_super @ kraus_to_super(channel(gate)) @ ideal_matrix
for gate in [I, X, Y, Z, H]
]
optimal_coeffs = minimize_one_norm(
ideal_matrix,
basis_matrices,
initial_guess=[1.0, 1.0, 1.0, 1.0, 1.0],
)
represented_mat = sum(
[eta * mat for eta, mat in zip(optimal_coeffs, basis_matrices)])
assert np.allclose(ideal_matrix, represented_mat)
# With a very bad guess it should fail
with raises(RuntimeError, match="optimal representation failed"):
minimize_one_norm(
ideal_matrix,
basis_matrices,
initial_guess=[-1.0e9, 1.0e9, -1.0e9, +1.0e9, -1.0e9],
)
def test_minimize_one_norm_with_depolarized_superoperators():
for noise_level in [0.01, 0.02, 0.03]:
depo_kraus = global_depolarizing_kraus(noise_level, num_qubits=1)
depo_super = kraus_to_super(depo_kraus)
ideal_matrix = kraus_to_super(channel(H))
basis_matrices = [
depo_super @ kraus_to_super(channel(gate)) @ ideal_matrix
for gate in [I, X, Y, Z, H]
]
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)
eps = 4.0 / 3.0 * noise_level
expected = (1.0 + 0.5 * eps) / (1.0 - eps)
assert np.isclose(np.linalg.norm(optimal_coeffs, 1), expected)
def test_minimize_one_norm_tolerance():
depo_kraus = global_depolarizing_kraus(noise_level=0.1, num_qubits=1)
depo_super = kraus_to_super(depo_kraus)
ideal_matrix = kraus_to_super(channel(H))
basis_matrices = [
depo_super @ kraus_to_super(channel(gate)) @ ideal_matrix
for gate in [I, X, Y, Z]
]
previous_minimum = 0.0
previous_error = 1.0
for tol in [1.0e-2, 1.0e-4, 1.0e-6, 1.0e-8]:
optimal_coeffs = minimize_one_norm(ideal_matrix, basis_matrices, tol)
represented_mat = sum(
[eta * mat for eta, mat in zip(optimal_coeffs, basis_matrices)])
worst_case_error = np.max(abs(ideal_matrix - represented_mat))
minimum = np.linalg.norm(optimal_coeffs, 1)
# Reducing "tol" should decrease the worst case error
# and should also increase the objective function
assert worst_case_error < previous_error
assert minimum > previous_minimum
previous_error = worst_case_error
previous_minimum = minimum