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_channel():
class NoDetailsGate(cirq.Gate):
def num_qubits(self) -> int:
return 1
assert not cirq.has_kraus(NoDetailsGate().with_probability(0.5))
assert cirq.kraus(NoDetailsGate().with_probability(0.5), None) is None
assert cirq.kraus(cirq.X.with_probability(sympy.Symbol('x')), None) is None
assert_channel_sums_to_identity(cirq.X.with_probability(0.25))
assert_channel_sums_to_identity(cirq.bit_flip(0.75).with_probability(0.25))
assert_channel_sums_to_identity(cirq.amplitude_damp(0.75).with_probability(0.25))
m = cirq.kraus(cirq.X.with_probability(0.25))
assert len(m) == 2
np.testing.assert_allclose(
m[0],
cirq.unitary(cirq.X) * np.sqrt(0.25),
atol=1e-8,
)
np.testing.assert_allclose(
m[1],
cirq.unitary(cirq.I) * np.sqrt(0.75),
atol=1e-8,
)
m = cirq.kraus(cirq.bit_flip(0.75).with_probability(0.25))
assert len(m) == 3
np.testing.assert_allclose(
m[0],
cirq.unitary(cirq.I) * np.sqrt(0.25) * np.sqrt(0.25),
atol=1e-8,
)
np.testing.assert_allclose(
m[1],
cirq.unitary(cirq.X) * np.sqrt(0.25) * np.sqrt(0.75),
atol=1e-8,
)
np.testing.assert_allclose(
m[2],
cirq.unitary(cirq.I) * np.sqrt(0.75),
atol=1e-8,
)
m = cirq.kraus(cirq.amplitude_damp(0.75).with_probability(0.25))
assert len(m) == 3
np.testing.assert_allclose(
m[0],
np.array([[1, 0], [0, np.sqrt(1 - 0.75)]]) * np.sqrt(0.25),
atol=1e-8,
)
np.testing.assert_allclose(
m[1],
np.array([[0, np.sqrt(0.75)], [0, 0]]) * np.sqrt(0.25),
atol=1e-8,
)
np.testing.assert_allclose(
m[2],
cirq.unitary(cirq.I) * np.sqrt(0.75),
atol=1e-8,
)
def test_measurement_channel():
np.testing.assert_allclose(
cirq.kraus(cirq.MeasurementGate(1, 'a')),
(np.array([[1, 0], [0, 0]]), np.array([[0, 0], [0, 1]])),
)
cirq.testing.assert_consistent_channel(cirq.MeasurementGate(1, 'a'))
assert not cirq.has_mixture(cirq.MeasurementGate(1, 'a'))
# yapf: disable
np.testing.assert_allclose(
cirq.kraus(cirq.MeasurementGate(2, 'a')),
(np.array([[1, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]),
np.array([[0, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]),
np.array([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 0]]),
np.array([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 1]])))
np.testing.assert_allclose(
cirq.kraus(cirq.MeasurementGate(2, 'a', qid_shape=(2, 3))),
(np.diag([1, 0, 0, 0, 0, 0]),
np.diag([0, 1, 0, 0, 0, 0]),
np.diag([0, 0, 1, 0, 0, 0]),
np.diag([0, 0, 0, 1, 0, 0]),
np.diag([0, 0, 0, 0, 1, 0]),
np.diag([0, 0, 0, 0, 0, 1])))
def test_noisy_moment_two_qubit():
q0, q1 = cirq.LineQubit.range(2)
model = ThermalNoiseModel(
qubits={q0, q1},
gate_durations_ns={cirq.PhasedXZGate: 25.0, cirq.CZPowGate: 25.0},
heat_rate_GHz={q0: 1e-5, q1: 2e-5},
cool_rate_GHz={q0: 1e-4, q1: 2e-4},
dephase_rate_GHz={q0: 3e-4, q1: 4e-4},
require_physical_tag=False,
)
gate = cirq.CZ**0.5
moment = cirq.Moment(gate.on(q0, q1))
noisy_moment = model.noisy_moment(moment, system_qubits=[q0, q1])
assert noisy_moment[0] == moment
assert len(noisy_moment[1]) == 2
noisy_choi_0 = cirq.kraus_to_choi(cirq.kraus(noisy_moment[1].operations[0]))
assert np.allclose(
noisy_choi_0,
[
[9.99750343e-01, 0, 0, 9.91164267e-01],
[0, 2.49656565e-03, 0, 0],
[0, 0, 2.49656565e-04, 0],
[9.91164267e-01, 0, 0, 9.97503434e-01],
],
)
noisy_choi_1 = cirq.kraus_to_choi(cirq.kraus(noisy_moment[1].operations[1]))
assert np.allclose(
noisy_choi_1,
[
[9.99501372e-01, 0, 0, 9.87330937e-01],
[0, 4.98627517e-03, 0, 0],
[0, 0, 4.98627517e-04, 0],
[9.87330937e-01, 0, 0, 9.95013725e-01],
],
)
def test_two_qubit_gates(op):
q0, q1 = cirq.LineQubit.range(2)
props = TestNoiseProperties(
**default_props([q0, q1], [(q0, q1), (q1, q0)]))
model = NoiseModelFromNoiseProperties(props)
circuit = cirq.Circuit(op)
noisy_circuit = circuit.with_noise(model)
assert len(noisy_circuit.moments) == 3
assert len(noisy_circuit.moments[0].operations) == 1
assert noisy_circuit.moments[0].operations[0] == op.with_tags(
PHYSICAL_GATE_TAG)
# Depolarizing noise
assert len(noisy_circuit.moments[1].operations) == 1
depol_op = noisy_circuit.moments[1].operations[0]
assert isinstance(depol_op.gate, cirq.DepolarizingChannel)
assert np.isclose(depol_op.gate.p, 0.00952008)
# Thermal noise
assert len(noisy_circuit.moments[2].operations) == 2
thermal_op_0 = noisy_circuit.moments[2].operation_at(q0)
thermal_op_1 = noisy_circuit.moments[2].operation_at(q1)
assert isinstance(thermal_op_0.gate, cirq.KrausChannel)
assert isinstance(thermal_op_1.gate, cirq.KrausChannel)
thermal_choi_0 = cirq.kraus_to_choi(cirq.kraus(thermal_op_0))
thermal_choi_1 = cirq.kraus_to_choi(cirq.kraus(thermal_op_1))
expected_thermal_choi = np.array([
[1, 0, 0, 9.99680051e-01],
[0, 3.19948805e-04, 0, 0],
[0, 0, 0, 0],
[9.99680051e-01, 0, 0, 9.99680051e-01],
])
assert np.allclose(thermal_choi_0, expected_thermal_choi)
assert np.allclose(thermal_choi_1, expected_thermal_choi)
def test_measurement_channel():
np.testing.assert_allclose(
cirq.kraus(cirq.MeasurementGate(1)),
(np.array([[1, 0], [0, 0]]), np.array([[0, 0], [0, 1]])),
)
# yapf: disable
np.testing.assert_allclose(
cirq.kraus(cirq.MeasurementGate(2)),
(np.array([[1, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]),
np.array([[0, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0]]),
np.array([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 0]]),
np.array([[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 0],
[0, 0, 0, 1]])))
np.testing.assert_allclose(
cirq.kraus(cirq.MeasurementGate(2, qid_shape=(2, 3))),
(np.diag([1, 0, 0, 0, 0, 0]),
np.diag([0, 1, 0, 0, 0, 0]),
np.diag([0, 0, 1, 0, 0, 0]),
np.diag([0, 0, 0, 1, 0, 0]),
np.diag([0, 0, 0, 0, 1, 0]),
np.diag([0, 0, 0, 0, 0, 1])))
def test_channel():
a = cirq.NamedQubit('a')
op = cirq.bit_flip(0.5).on(a)
np.testing.assert_allclose(cirq.kraus(op), cirq.kraus(op.gate))
assert cirq.has_kraus(op)
assert cirq.kraus(cirq.SingleQubitGate()(a), None) is None
assert not cirq.has_kraus(cirq.SingleQubitGate()(a))
def assert_not_implemented(val):
with pytest.raises(TypeError, match='returned NotImplemented'):
_ = cirq.kraus(val)
assert cirq.kraus(val, None) is None
assert cirq.kraus(val, NotImplemented) is NotImplemented
assert cirq.kraus(val, (1, )) == (1, )
assert cirq.kraus(val, LOCAL_DEFAULT) is LOCAL_DEFAULT
assert not cirq.has_kraus(val)
def test_unitary_returns_not_implemented():
class ReturnsNotImplemented:
def _unitary_(self):
return NotImplemented
with pytest.raises(TypeError, match='returned NotImplemented'):
_ = cirq.kraus(ReturnsNotImplemented())
assert cirq.kraus(ReturnsNotImplemented(), None) is None
assert cirq.kraus(ReturnsNotImplemented(), NotImplemented) is NotImplemented
assert cirq.kraus(ReturnsNotImplemented(), (1,)) == (1,)
assert cirq.kraus(ReturnsNotImplemented(), LOCAL_DEFAULT) is LOCAL_DEFAULT
def test_two_qubit_gates(op):
q0, q1 = cirq.LineQubit.range(2)
props = sample_noise_properties([q0, q1], [(q0, q1), (q1, q0)])
model = NoiseModelFromGoogleNoiseProperties(props)
circuit = cirq.Circuit(op)
noisy_circuit = circuit.with_noise(model)
assert len(noisy_circuit.moments) == 4
assert len(noisy_circuit.moments[0].operations) == 1
assert noisy_circuit.moments[0].operations[0] == op.with_tags(
PHYSICAL_GATE_TAG)
# Depolarizing noise
assert len(noisy_circuit.moments[1].operations) == 1
depol_op = noisy_circuit.moments[1].operations[0]
assert isinstance(depol_op.gate, cirq.DepolarizingChannel)
assert np.isclose(depol_op.gate.p, 0.00719705)
# FSim angle corrections
assert len(noisy_circuit.moments[2].operations) == 1
fsim_op = noisy_circuit.moments[2].operations[0]
assert isinstance(fsim_op.gate, cirq.PhasedFSimGate)
assert fsim_op == PhasedFSimGate(theta=0.01,
zeta=0.03,
chi=0.04,
gamma=0.05,
phi=0.02).on(q0, q1)
# Thermal noise
assert len(noisy_circuit.moments[3].operations) == 2
thermal_op_0 = noisy_circuit.moments[3].operation_at(q0)
thermal_op_1 = noisy_circuit.moments[3].operation_at(q1)
assert isinstance(thermal_op_0.gate, cirq.KrausChannel)
assert isinstance(thermal_op_1.gate, cirq.KrausChannel)
thermal_choi_0 = cirq.kraus_to_choi(cirq.kraus(thermal_op_0))
thermal_choi_1 = cirq.kraus_to_choi(cirq.kraus(thermal_op_1))
expected_thermal_choi = np.array([
[1, 0, 0, 9.99680051e-01],
[0, 3.19948805e-04, 0, 0],
[0, 0, 0, 0],
[9.99680051e-01, 0, 0, 9.99680051e-01],
])
assert np.allclose(thermal_choi_0, expected_thermal_choi)
assert np.allclose(thermal_choi_1, expected_thermal_choi)
# Pauli error for depol_op + fsim_op + thermal_op_(0|1) == total (0.01)
depol_pauli_err = 1 - cirq.qis.measures.entanglement_fidelity(depol_op)
fsim_pauli_err = 1 - cirq.qis.measures.entanglement_fidelity(fsim_op)
thermal0_pauli_err = 1 - cirq.qis.measures.entanglement_fidelity(
thermal_op_0)
thermal1_pauli_err = 1 - cirq.qis.measures.entanglement_fidelity(
thermal_op_1)
total_err = depol_pauli_err + thermal0_pauli_err + thermal1_pauli_err + fsim_pauli_err
assert np.isclose(total_err, TWO_QUBIT_ERROR)
def test_super_to_choi():
for noise_level in [0, 0.3, 1]:
super_damping = kraus_to_super(amplitude_damping_kraus(noise_level, 1))
# Apply Pauli Y to get some complex numbers
super_op = np.kron(kraus(Y)[0], kraus(Y)[0].conj()) @ super_damping
choi_state = super_to_choi(super_op)
# expected result
q = LineQubit(0)
choi_expected = _operation_to_choi(
[AmplitudeDampingChannel(noise_level)(q),
Y(q)])
assert np.allclose(choi_state, choi_expected)
def test_channel_no_methods():
class NoMethod:
pass
with pytest.raises(TypeError, match='no _kraus_ or _mixture_ or _unitary_ method'):
_ = cirq.kraus(NoMethod())
assert cirq.kraus(NoMethod(), None) is None
assert cirq.kraus(NoMethod, NotImplemented) is NotImplemented
assert cirq.kraus(NoMethod(), (1,)) == (1,)
assert cirq.kraus(NoMethod(), LOCAL_DEFAULT) is LOCAL_DEFAULT
assert not cirq.has_kraus(NoMethod())
def test_state_prep_channel_kraus_small():
gate = cirq.StatePreparationChannel(np.array([0.0,
1.0]))(cirq.LineQubit(0))
np.testing.assert_almost_equal(cirq.kraus(gate), (np.array(
[[0.0, 0.0], [1.0, 0.0]]), np.array([[0.0, 0.0], [0.0, 1.0]])))
assert cirq.has_kraus(gate)
assert not cirq.has_mixture(gate)
gate = cirq.StatePreparationChannel(np.array([1.0,
0.0]))(cirq.LineQubit(0))
np.testing.assert_almost_equal(cirq.kraus(gate), (np.array(
[[1.0, 0.0], [0.0, 0.0]]), np.array([[0.0, 1.0], [0.0, 0.0]])))
assert cirq.has_kraus(gate)
assert not cirq.has_mixture(gate)
def test_channel_fallback_to_unitary():
u = np.array([[1, 0], [1, 0]])
class ReturnsUnitary:
def _unitary_(self) -> np.ndarray:
return u
np.testing.assert_equal(cirq.kraus(ReturnsUnitary()), (u,))
np.testing.assert_equal(cirq.kraus(ReturnsUnitary(), None), (u,))
np.testing.assert_equal(cirq.kraus(ReturnsUnitary(), NotImplemented), (u,))
np.testing.assert_equal(cirq.kraus(ReturnsUnitary(), (1,)), (u,))
np.testing.assert_equal(cirq.kraus(ReturnsUnitary(), LOCAL_DEFAULT), (u,))
assert cirq.has_kraus(ReturnsUnitary())
def test_kraus():
I = np.eye(2)
X = np.array([[0, 1], [1, 0]])
Y = np.array([[0, -1j], [1j, 0]])
Z = np.diag([1, -1])
a, b = cirq.LineQubit.range(2)
m = cirq.Moment()
assert cirq.has_kraus(m)
k = cirq.kraus(m)
assert len(k) == 1
assert np.allclose(k[0], np.array([[1.0]]))
m = cirq.Moment(cirq.S(a))
assert cirq.has_kraus(m)
k = cirq.kraus(m)
assert len(k) == 1
assert np.allclose(k[0], np.diag([1, 1j]))
m = cirq.Moment(cirq.CNOT(a, b))
assert cirq.has_kraus(m)
k = cirq.kraus(m)
print(k[0])
assert len(k) == 1
assert np.allclose(
k[0], np.array([[1, 0, 0, 0], [0, 1, 0, 0], [0, 0, 0, 1], [0, 0, 1,
0]]))
p = 0.1
m = cirq.Moment(cirq.depolarize(p).on(a))
assert cirq.has_kraus(m)
k = cirq.kraus(m)
assert len(k) == 4
assert np.allclose(k[0], np.sqrt(1 - p) * I)
assert np.allclose(k[1], np.sqrt(p / 3) * X)
assert np.allclose(k[2], np.sqrt(p / 3) * Y)
assert np.allclose(k[3], np.sqrt(p / 3) * Z)
p = 0.2
q = 0.3
m = cirq.Moment(cirq.bit_flip(p).on(a), cirq.phase_flip(q).on(b))
assert cirq.has_kraus(m)
k = cirq.kraus(m)
assert len(k) == 4
assert np.allclose(k[0], np.sqrt((1 - p) * (1 - q)) * np.kron(I, I))
assert np.allclose(k[1], np.sqrt(q * (1 - p)) * np.kron(I, Z))
assert np.allclose(k[2], np.sqrt(p * (1 - q)) * np.kron(X, I))
assert np.allclose(k[3], np.sqrt(p * q) * np.kron(X, Z))
def test_noisy_moment_one_qubit():
q0, q1 = cirq.LineQubit.range(2)
model = ThermalNoiseModel(
qubits={q0, q1},
gate_durations_ns={cirq.PhasedXZGate: 25.0, cirq.CZPowGate: 25.0},
heat_rate_GHz={q0: 1e-5, q1: 2e-5},
cool_rate_GHz={q0: 1e-4, q1: 2e-4},
dephase_rate_GHz={q0: 3e-4, q1: 4e-4},
require_physical_tag=False,
)
gate = cirq.PhasedXZGate(x_exponent=1, z_exponent=0.5, axis_phase_exponent=0.25)
moment = cirq.Moment(gate.on(q0))
noisy_moment = model.noisy_moment(moment, system_qubits=[q0, q1])
assert noisy_moment[0] == moment
# Noise applies to both qubits, even if only one is acted upon.
assert len(noisy_moment[1]) == 2
noisy_choi = cirq.kraus_to_choi(cirq.kraus(noisy_moment[1].operations[0]))
assert np.allclose(
noisy_choi,
[
[9.99750343e-01, 0, 0, 9.91164267e-01],
[0, 2.49656565e-03, 0, 0],
[0, 0, 2.49656565e-04, 0],
[9.91164267e-01, 0, 0, 9.97503434e-01],
],
)
def test_wait_gates():
q0 = cirq.LineQubit(0)
props = sample_noise_properties([q0], [])
model = NoiseModelFromGoogleNoiseProperties(props)
op = cirq.wait(q0, nanos=100)
circuit = cirq.Circuit(op)
noisy_circuit = circuit.with_noise(model)
assert len(noisy_circuit.moments) == 2
assert noisy_circuit.moments[0].operations[0] == op.with_tags(PHYSICAL_GATE_TAG)
# No depolarizing noise because WaitGate has none.
assert len(noisy_circuit.moments[1].operations) == 1
thermal_op = noisy_circuit.moments[1].operations[0]
assert isinstance(thermal_op.gate, cirq.KrausChannel)
thermal_choi = cirq.kraus_to_choi(cirq.kraus(thermal_op))
assert np.allclose(
thermal_choi,
[
[1, 0, 0, 9.990005e-01],
[0, 9.99500167e-04, 0, 0],
[0, 0, 0, 0],
[9.990005e-01, 0, 0, 9.990005e-01],
],
)
def test_asymmetric_depolarizing_channel():
d = cirq.asymmetric_depolarize(0.1, 0.2, 0.3)
np.testing.assert_almost_equal(
cirq.kraus(d),
(np.sqrt(0.4) * np.eye(2), np.sqrt(0.1) * X, np.sqrt(0.2) * Y, np.sqrt(0.3) * Z),
)
assert cirq.has_kraus(d)
def test_from_matrix_close_kraus(unitary: np.ndarray):
gate = cirq.PhasedXZGate.from_matrix(unitary)
kraus = cirq.kraus(gate)
assert len(kraus) == 1
cirq.testing.assert_allclose_up_to_global_phase(kraus[0],
unitary,
atol=1e-8)
def test_noise_from_wait():
# Verify that wait-gate noise is duration-dependent.
q0 = cirq.LineQubit(0)
gate_durations = {cirq.ZPowGate: 25.0}
heat_rate_GHz = {q0: 1e-5}
cool_rate_GHz = {q0: 1e-4}
model = ThermalNoiseModel(
qubits={q0},
gate_durations_ns=gate_durations,
heat_rate_GHz=heat_rate_GHz,
cool_rate_GHz=cool_rate_GHz,
dephase_rate_GHz=None,
require_physical_tag=False,
skip_measurements=True,
)
moment = cirq.Moment(cirq.wait(q0, nanos=100))
noisy_moment = model.noisy_moment(moment, system_qubits=[q0])
assert noisy_moment[0] == moment
assert len(noisy_moment[1]) == 1
noisy_choi = cirq.kraus_to_choi(cirq.kraus(noisy_moment[1].operations[0]))
print(noisy_choi)
assert np.allclose(
noisy_choi,
[
[9.99005480e-01, 0, 0, 9.94515097e-01],
[0, 9.94520111e-03, 0, 0],
[0, 0, 9.94520111e-04, 0],
[9.94515097e-01, 0, 0, 9.90054799e-01],
],
)
def test_single_qubit_gates(op):
q0 = cirq.LineQubit(0)
props = TestNoiseProperties(**default_props([q0], []))
model = NoiseModelFromNoiseProperties(props)
circuit = cirq.Circuit(op)
noisy_circuit = circuit.with_noise(model)
assert len(noisy_circuit.moments) == 3
assert len(noisy_circuit.moments[0].operations) == 1
assert noisy_circuit.moments[0].operations[0] == op.with_tags(
PHYSICAL_GATE_TAG)
# Depolarizing noise
assert len(noisy_circuit.moments[1].operations) == 1
depol_op = noisy_circuit.moments[1].operations[0]
assert isinstance(depol_op.gate, cirq.DepolarizingChannel)
assert np.isclose(depol_op.gate.p, 0.00081252)
# Thermal noise
assert len(noisy_circuit.moments[2].operations) == 1
thermal_op = noisy_circuit.moments[2].operations[0]
assert isinstance(thermal_op.gate, cirq.KrausChannel)
thermal_choi = cirq.kraus_to_choi(cirq.kraus(thermal_op))
assert np.allclose(
thermal_choi,
[
[1, 0, 0, 9.99750031e-01],
[0, 2.49968753e-04, 0, 0],
[0, 0, 0, 0],
[9.99750031e-01, 0, 0, 9.99750031e-01],
],
)
def test_kraus_too_big():
m = cirq.Moment(cirq.IdentityGate(11).on(*cirq.LineQubit.range(11)))
assert not cirq.has_kraus(m)
assert not m._has_superoperator_()
assert m._kraus_() is NotImplemented
assert m._superoperator_() is NotImplemented
assert cirq.kraus(m, default=None) is None
def test_depolarizing_channel_two_qubits():
d = cirq.depolarize(0.15, n_qubits=2)
np.testing.assert_almost_equal(
cirq.kraus(d),
(
np.sqrt(0.85) * np.eye(4),
np.sqrt(0.01) * np.kron(np.eye(2), X),
np.sqrt(0.01) * np.kron(np.eye(2), Y),
np.sqrt(0.01) * np.kron(np.eye(2), Z),
np.sqrt(0.01) * np.kron(X, np.eye(2)),
np.sqrt(0.01) * np.kron(X, X),
np.sqrt(0.01) * np.kron(X, Y),
np.sqrt(0.01) * np.kron(X, Z),
np.sqrt(0.01) * np.kron(Y, np.eye(2)),
np.sqrt(0.01) * np.kron(Y, X),
np.sqrt(0.01) * np.kron(Y, Y),
np.sqrt(0.01) * np.kron(Y, Z),
np.sqrt(0.01) * np.kron(Z, np.eye(2)),
np.sqrt(0.01) * np.kron(Z, X),
np.sqrt(0.01) * np.kron(Z, Y),
np.sqrt(0.01) * np.kron(Z, Z),
),
)
assert cirq.has_kraus(d)
assert d.num_qubits() == 2
cirq.testing.assert_has_diagram(
cirq.Circuit(d(*cirq.LineQubit.range(2))),
"""
0: ───D(0.15)───
│
1: ───#2────────
""",
)
def compute_channel_matrix(channel: cirq.SupportsChannel) -> np.ndarray:
ks = cirq.kraus(channel)
d_out, d_in = ks[0].shape
m = np.zeros((d_out * d_out, d_in * d_in), dtype=np.complex128)
for k, e_in in enumerate(generate_standard_operator_basis(d_in, d_in)):
m[:, k] = np.reshape(apply_channel(channel, e_in), d_out * d_out)
return m
def test_explicit_kraus():
a0 = np.array([[0, 0], [1, 0]])
a1 = np.array([[1, 0], [0, 0]])
c = (a0, a1)
class ReturnsKraus:
def _kraus_(self) -> Sequence[np.ndarray]:
return c
assert cirq.kraus(ReturnsKraus()) is c
assert cirq.kraus(ReturnsKraus(), None) is c
assert cirq.kraus(ReturnsKraus(), NotImplemented) is c
assert cirq.kraus(ReturnsKraus(), (1, )) is c
assert cirq.kraus(ReturnsKraus(), LOCAL_DEFAULT) is c
assert cirq.has_kraus(ReturnsKraus())
def compute_choi(channel: cirq.SupportsChannel) -> np.ndarray:
ks = cirq.kraus(channel)
d_out, d_in = ks[0].shape
d = d_in * d_out
c = np.zeros((d, d), dtype=np.complex128)
for e in generate_standard_operator_basis(d_in, d_in):
c += np.kron(apply_channel(channel, e), e)
return c
def apply_channel(channel: cirq.SupportsChannel, rho: np.ndarray) -> np.ndarray:
ks = cirq.kraus(channel)
d_out, d_in = ks[0].shape
assert rho.shape == (d_in, d_in)
out = np.zeros((d_out, d_out), dtype=np.complex128)
for k in ks:
out += k @ rho @ k.conj().T
return out
def assert_channel_sums_to_identity(val):
m = cirq.kraus(val)
s = sum(np.conj(e.T) @ e for e in m)
np.testing.assert_allclose(s,
np.eye(
np.prod(cirq.qid_shape(val),
dtype=np.int64)),
atol=1e-8)
def find_optimal_representation(
ideal_operation: QPROGRAM,
noisy_basis: NoisyBasis,
tol: float = 1.0e-8,
initial_guess: Optional[np.ndarray] = None,
) -> OperationRepresentation:
r"""Returns the ``OperationRepresentaiton`` of the input ideal operation
which minimizes the one-norm of the associated quasi-probability
distribution.
More precicely, it solve the following optimization problem:
.. math::
\min_{{\eta_\alpha}} = \sum_\alpha |\eta_\alpha|,
\text{ such that }
\mathcal G = \sum_\alpha \eta_\alpha \mathcal O_\alpha,
where :math:`\{\mathcal O_j\}` is the input basis of noisy operations.
Args:
ideal_operation: The ideal operation to represent.
noisy_basis: The ``NoisyBasis`` in which the ``ideal_operation``
should be represented. It must contain ``NoisyOperation`` objects
which are initialized with a numerical superoperator matrix.
tol: The error tolerance for each matrix element
of the represented operation.
initial_guess: Optional initial guess for the coefficients
:math:`\{ \eta_\alpha \}``.
Returns: The optimal OperationRepresentation.
"""
ideal_cirq_circuit, _ = convert_to_mitiq(ideal_operation)
ideal_matrix = kraus_to_super(
cast(List[np.ndarray], kraus(ideal_cirq_circuit)))
basis_set = noisy_basis.elements
try:
basis_matrices = [noisy_op.channel_matrix for noisy_op in basis_set]
except ValueError as err:
if str(err) == "The channel matrix is unknown.":
raise ValueError(
"The input noisy_basis should contain NoisyOperation objects"
" which are initialized with a numerical superoperator matrix."
)
else:
raise err # pragma no cover
# Run numerical optimization problem
quasi_prob_dist = minimize_one_norm(
ideal_matrix,
basis_matrices,
tol=tol,
initial_guess=initial_guess,
)
basis_expansion = {op: eta for op, eta in zip(basis_set, quasi_prob_dist)}
return OperationRepresentation(ideal_operation, basis_expansion)
def test_depolarizing_channel():
d = cirq.depolarize(0.3)
np.testing.assert_almost_equal(
cirq.kraus(d),
(np.sqrt(0.7) * np.eye(2), np.sqrt(0.1) * X, np.sqrt(0.1) * Y,
np.sqrt(0.1) * Z),
)
cirq.testing.assert_consistent_channel(d)
cirq.testing.assert_consistent_mixture(d)