def test_depolarizing_representation_with_choi(gate: Gate, noise: float):
"""Tests the representation by comparing exact Choi matrices."""
qreg = LineQubit.range(gate.num_qubits())
ideal_choi = _operation_to_choi(gate.on(*qreg))
op_rep = represent_operation_with_global_depolarizing_noise(
Circuit(gate.on(*qreg)),
noise,
)
choi_components = []
for noisy_op, coeff in op_rep.basis_expansion.items():
implementable_circ = noisy_op.circuit()
# Apply noise after each sequence.
# NOTE: noise is not applied after each operation.
depolarizing_op = DepolarizingChannel(noise, len(qreg))(*qreg)
implementable_circ.append(depolarizing_op)
sequence_choi = _circuit_to_choi(implementable_circ)
choi_components.append(coeff * sequence_choi)
combination_choi = np.sum(choi_components, axis=0)
assert np.allclose(ideal_choi, combination_choi, atol=10**-6)
def test_sample_circuit_choi():
"""Tests the sample_circuit by comparing the exact Choi matrices."""
# A simple 2-qubit circuit
qreg = cirq.LineQubit.range(2)
ideal_circ = cirq.Circuit(
cirq.X.on(qreg[0]),
cirq.I.on(qreg[1]),
cirq.CNOT.on(*qreg),
)
noisy_circuit = ideal_circ.with_noise(cirq.depolarize(BASE_NOISE))
ideal_choi = _circuit_to_choi(ideal_circ)
noisy_choi = _operation_to_choi(noisy_circuit)
rep_list = represent_operations_in_circuit_with_local_depolarizing_noise(
ideal_circuit=ideal_circ,
noise_level=BASE_NOISE,
)
choi_unbiased_estimates = []
rng = np.random.RandomState(1)
for _ in range(500):
imp_circs, signs, norm = sample_circuit(ideal_circ,
rep_list,
random_state=rng)
noisy_imp_circ = imp_circs[0].with_noise(cirq.depolarize(BASE_NOISE))
sequence_choi = _circuit_to_choi(noisy_imp_circ)
choi_unbiased_estimates.append(norm * signs[0] * sequence_choi)
choi_pec_estimate = np.average(choi_unbiased_estimates, axis=0)
noise_error = np.linalg.norm(ideal_choi - noisy_choi)
pec_error = np.linalg.norm(ideal_choi - choi_pec_estimate)
assert pec_error < noise_error
assert np.allclose(ideal_choi, choi_pec_estimate, atol=0.05)