def test_pauli_string_expectation_value_pure_state_with_coef():
qs = cirq.LineQubit.range(4)
qubit_index_map = {q: i for i, q in enumerate(qs)}
circuit = cirq.Circuit.from_ops(
cirq.X(qs[1]),
cirq.H(qs[2]),
cirq.X(qs[3]),
cirq.H(qs[3]),
)
wavefunction = circuit.apply_unitary_effect_to_state(qubit_order=qs)
density_matrix = np.outer(wavefunction, np.conj(wavefunction))
z0z1 = cirq.pauli_string_expectation(cirq.Z(qs[0]) * cirq.Z(qs[1]) * .123)
z0z2 = cirq.pauli_string_expectation(cirq.Z(qs[0]) * cirq.Z(qs[2]) * -1)
z1x2 = cirq.pauli_string_expectation(-cirq.Z(qs[1]) * cirq.X(qs[2]))
np.testing.assert_allclose(
z0z1.value_derived_from_wavefunction(wavefunction, qubit_index_map),
-0.123)
np.testing.assert_allclose(
z0z2.value_derived_from_wavefunction(wavefunction, qubit_index_map), 0)
np.testing.assert_allclose(
z1x2.value_derived_from_wavefunction(wavefunction, qubit_index_map), 1)
np.testing.assert_allclose(
z0z1.value_derived_from_density_matrix(density_matrix,
qubit_index_map), -0.123)
np.testing.assert_allclose(
z0z2.value_derived_from_density_matrix(density_matrix,
qubit_index_map), 0)
np.testing.assert_allclose(
z1x2.value_derived_from_density_matrix(density_matrix,
qubit_index_map), 1)
def test_compute_samples_displays(dtype):
a, b, c = cirq.LineQubit.range(3)
circuit = cirq.Circuit.from_ops(
cirq.X(a),
cirq.H(b),
cirq.X(c),
cirq.H(c),
cirq.pauli_string_expectation(cirq.PauliString({c: cirq.X}), key='x3'),
cirq.pauli_string_expectation(cirq.PauliString({
a: cirq.Z,
b: cirq.X
}),
num_samples=10,
key='approx_z1x2'),
cirq.pauli_string_expectation(cirq.PauliString({
a: cirq.Z,
c: cirq.X
}),
num_samples=10,
key='approx_z1x3'),
)
simulator = cirq.DensityMatrixSimulator(dtype=dtype)
result = simulator.compute_samples_displays(circuit)
assert 'x3' not in result.display_values
np.testing.assert_allclose(result.display_values['approx_z1x2'],
-1,
atol=1e-7)
np.testing.assert_allclose(result.display_values['approx_z1x3'],
1,
atol=1e-7)
def test_pauli_string_expectation_helper():
qubits = cirq.LineQubit.range(9)
qubit_pauli_map = {q: cirq.Pauli.by_index(q.x) for q in qubits}
pauli_string = cirq.PauliString(qubit_pauli_map, -1)
assert (cirq.pauli_string_expectation(pauli_string, key='a')
== cirq.pauli_string_expectation(pauli_string, key='a'))
assert (cirq.pauli_string_expectation(pauli_string, 5, key='a')
== cirq.pauli_string_expectation(pauli_string, 5, key='a'))
def test_with_qubits():
old_qubits = cirq.LineQubit.range(9)
new_qubits = cirq.LineQubit.range(9, 18)
qubit_pauli_map = {q: cirq.Pauli.by_index(q.x) for q in old_qubits}
pauli_string = cirq.PauliString(qubit_pauli_map, -1)
assert (cirq.pauli_string_expectation(pauli_string).with_qubits(
*new_qubits) == cirq.pauli_string_expectation(
pauli_string.with_qubits(*new_qubits)))
assert (cirq.pauli_string_expectation(
pauli_string, num_samples=1).with_qubits(
*new_qubits) == cirq.pauli_string_expectation(
pauli_string.with_qubits(*new_qubits), num_samples=1))
def test_properties():
qubits = cirq.LineQubit.range(9)
qubit_pauli_map = {q: cirq.Pauli.by_index(q.x) for q in qubits}
pauli_string = cirq.PauliString(qubit_pauli_map, -1)
pauli_string_expectation = cirq.pauli_string_expectation(pauli_string,
key='a')
assert pauli_string_expectation.qubits == tuple(qubits)
assert pauli_string_expectation.key == 'a'
approx_pauli_string_expectation = cirq.pauli_string_expectation(
pauli_string, num_samples=5, key='a')
assert approx_pauli_string_expectation.qubits == tuple(qubits)
assert approx_pauli_string_expectation.num_samples == 5
assert approx_pauli_string_expectation.key == 'a'
def test_pauli_string_expectation_value_mixed_state_linearity():
n_qubits = 10
wavefunction1 = cirq.testing.random_superposition(2**n_qubits)
wavefunction2 = cirq.testing.random_superposition(2**n_qubits)
rho1 = np.outer(wavefunction1, np.conj(wavefunction1))
rho2 = np.outer(wavefunction2, np.conj(wavefunction2))
density_matrix = rho1 + rho2
qubits = cirq.LineQubit.range(n_qubits)
qubit_index_map = {q: i for i, q in enumerate(qubits)}
paulis = [cirq.X, cirq.Y, cirq.Z]
pauli_string_expectation = cirq.pauli_string_expectation(
cirq.PauliString({q: np.random.choice(paulis)
for q in qubits}))
a = pauli_string_expectation.value_derived_from_wavefunction(
wavefunction1, qubit_index_map)
b = pauli_string_expectation.value_derived_from_wavefunction(
wavefunction2, qubit_index_map)
c = pauli_string_expectation.value_derived_from_density_matrix(
density_matrix, qubit_index_map)
np.testing.assert_allclose(a + b, c)
def test_approx_pauli_string_expectation_value_with_coef(
measurements, value, coefficient):
display = cirq.pauli_string_expectation(cirq.PauliString(
{}, coefficient=coefficient),
num_samples=1)
assert display.value_derived_from_samples(
measurements) == value * coefficient
def hhl_circuit(A, C, t, register_size, *input_prep_gates):
"""
Constructs the HHL circuit.
A is the input Hermitian matrix.
C and t are tunable parameters for the algorithm.
register_size is the size of the eigenvalue register.
input_prep_gates is a list of gates to be applied to |0> to generate the
desired input state |b>.
"""
ancilla = cirq.GridQubit(0, 0)
# to store eigenvalues of the matrix
register = [cirq.GridQubit(i + 1, 0) for i in range(register_size)]
# to store input and output vectors
memory = cirq.GridQubit(register_size + 1, 0)
c = cirq.Circuit()
hs = HamiltonianSimulation(A, t)
pe = PhaseEstimation(register_size + 1, hs)
c.append([gate(memory) for gate in input_prep_gates])
c.append([
pe(*(register + [memory])),
EigenRotation(register_size + 1, C, t)(*(register + [ancilla])),
pe(*(register + [memory]))**-1,
cirq.measure(ancilla)
])
# Pauli observable display
c.append([
cirq.pauli_string_expectation(cirq.PauliString({ancilla: cirq.Z}),
key='a'),
cirq.pauli_string_expectation(cirq.PauliString({memory: cirq.X}),
key='x'),
cirq.pauli_string_expectation(cirq.PauliString({memory: cirq.Y}),
key='y'),
cirq.pauli_string_expectation(cirq.PauliString({memory: cirq.Z}),
key='z'),
])
return c
def test_compute_displays(dtype):
qubits = cirq.LineQubit.range(4)
circuit = cirq.Circuit.from_ops(
cirq.pauli_string_expectation(
cirq.PauliString({qubits[3]: cirq.Z}),
key='z3'
),
cirq.X(qubits[1]),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[0]: cirq.Z,
qubits[1]: cirq.Z}),
key='z0z1'
),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[0]: cirq.Z,
qubits[1]: cirq.X}),
key='z0x1'
),
cirq.H(qubits[2]),
cirq.X(qubits[3]),
cirq.H(qubits[3]),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[1]: cirq.Z,
qubits[2]: cirq.X}),
key='z1x2'
),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[0]: cirq.X,
qubits[1]: cirq.Z}),
key='x0z1'
),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[3]: cirq.X}),
key='x3'
),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[1]: cirq.Z,
qubits[2]: cirq.X}),
num_samples=1,
key='approx_z1x2'
),
)
simulator = cirq.DensityMatrixSimulator(dtype=dtype)
initial_state = cirq.sim.density_matrix_utils.to_valid_density_matrix(
0, num_qubits=len(qubits), dtype=dtype)
result = simulator.compute_displays(circuit, initial_state=initial_state)
np.testing.assert_allclose(result.display_values['z3'], 1, atol=1e-7)
np.testing.assert_allclose(result.display_values['z0z1'], -1, atol=1e-7)
np.testing.assert_allclose(result.display_values['z0x1'], 0, atol=1e-7)
np.testing.assert_allclose(result.display_values['z1x2'], -1, atol=1e-7)
np.testing.assert_allclose(result.display_values['x0z1'], 0, atol=1e-7)
np.testing.assert_allclose(result.display_values['x3'], -1, atol=1e-7)
np.testing.assert_allclose(result.display_values['approx_z1x2'], -1,
atol=1e-7)
def test_compute_displays(dtype):
qubits = cirq.LineQubit.range(4)
circuit = cirq.Circuit.from_ops(
cirq.pauli_string_expectation(
cirq.PauliString({qubits[3]: cirq.Z}),
key='z3'
),
cirq.X(qubits[1]),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[0]: cirq.Z,
qubits[1]: cirq.Z}),
key='z0z1'
),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[0]: cirq.Z,
qubits[1]: cirq.X}),
key='z0x1'
),
cirq.H(qubits[2]),
cirq.X(qubits[3]),
cirq.H(qubits[3]),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[1]: cirq.Z,
qubits[2]: cirq.X}),
key='z1x2'
),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[0]: cirq.X,
qubits[1]: cirq.Z}),
key='x0z1'
),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[3]: cirq.X}),
key='x3'
),
cirq.pauli_string_expectation(
cirq.PauliString({qubits[1]: cirq.Z,
qubits[2]: cirq.X}),
num_samples=1,
key='approx_z1x2'
),
)
simulator = cirq.Simulator(dtype=dtype)
result = simulator.compute_displays(circuit)
np.testing.assert_allclose(result.display_values['z3'], 1, atol=1e-7)
np.testing.assert_allclose(result.display_values['z0z1'], -1, atol=1e-7)
np.testing.assert_allclose(result.display_values['z0x1'], 0, atol=1e-7)
np.testing.assert_allclose(result.display_values['z1x2'], -1, atol=1e-7)
np.testing.assert_allclose(result.display_values['x0z1'], 0, atol=1e-7)
np.testing.assert_allclose(result.display_values['x3'], -1, atol=1e-7)
np.testing.assert_allclose(result.display_values['approx_z1x2'], -1,
atol=1e-7)
def test_approx_pauli_string_expectation_measurement_basis_change(paulis):
qubits = cirq.LineQubit.range(2)
display = cirq.pauli_string_expectation(cirq.PauliString({
qubits[0]:
paulis[0],
qubits[1]:
paulis[1]
}),
num_samples=1)
matrix = np.kron(cirq.unitary(paulis[0]), cirq.unitary(paulis[1]))
circuit = cirq.Circuit.from_ops(display.measurement_basis_change())
unitary = circuit.to_unitary_matrix(qubit_order=qubits)
ZZ = np.diag([1, -1, -1, 1])
np.testing.assert_allclose(
np.dot(unitary, np.dot(matrix, unitary.T.conj())), ZZ)
def test_pauli_string_expectation_value_pure_state():
qubits = cirq.LineQubit.range(4)
qubit_index_map = {q: i for i, q in enumerate(qubits)}
circuit = cirq.Circuit.from_ops(
cirq.X(qubits[1]),
cirq.H(qubits[2]),
cirq.X(qubits[3]),
cirq.H(qubits[3]),
)
wavefunction = circuit.apply_unitary_effect_to_state(qubit_order=qubits)
density_matrix = np.outer(wavefunction, np.conj(wavefunction))
z0z1 = cirq.pauli_string_expectation(
cirq.PauliString({
qubits[0]: cirq.Z,
qubits[1]: cirq.Z
}))
z0z2 = cirq.pauli_string_expectation(
cirq.PauliString({
qubits[0]: cirq.Z,
qubits[2]: cirq.Z
}))
z0z3 = cirq.pauli_string_expectation(
cirq.PauliString({
qubits[0]: cirq.Z,
qubits[3]: cirq.Z
}))
z0x1 = cirq.pauli_string_expectation(
cirq.PauliString({
qubits[0]: cirq.Z,
qubits[1]: cirq.X
}))
z1x2 = cirq.pauli_string_expectation(
cirq.PauliString({
qubits[1]: cirq.Z,
qubits[2]: cirq.X
}))
x0z1 = cirq.pauli_string_expectation(
cirq.PauliString({
qubits[0]: cirq.X,
qubits[1]: cirq.Z
}))
x3 = cirq.pauli_string_expectation(cirq.PauliString({qubits[3]: cirq.X}))
np.testing.assert_allclose(
z0z1.value_derived_from_wavefunction(wavefunction, qubit_index_map),
-1)
np.testing.assert_allclose(
z0z2.value_derived_from_wavefunction(wavefunction, qubit_index_map), 0)
np.testing.assert_allclose(
z0z3.value_derived_from_wavefunction(wavefunction, qubit_index_map), 0)
np.testing.assert_allclose(
z0x1.value_derived_from_wavefunction(wavefunction, qubit_index_map), 0)
np.testing.assert_allclose(
z1x2.value_derived_from_wavefunction(wavefunction, qubit_index_map),
-1)
np.testing.assert_allclose(
x0z1.value_derived_from_wavefunction(wavefunction, qubit_index_map), 0)
np.testing.assert_allclose(
x3.value_derived_from_wavefunction(wavefunction, qubit_index_map), -1)
np.testing.assert_allclose(
z0z1.value_derived_from_density_matrix(density_matrix,
qubit_index_map), -1)
np.testing.assert_allclose(
z0z2.value_derived_from_density_matrix(density_matrix,
qubit_index_map), 0)
np.testing.assert_allclose(
z0z3.value_derived_from_density_matrix(density_matrix,
qubit_index_map), 0)
np.testing.assert_allclose(
z0x1.value_derived_from_density_matrix(density_matrix,
qubit_index_map), 0)
np.testing.assert_allclose(
z1x2.value_derived_from_density_matrix(density_matrix,
qubit_index_map), -1)
np.testing.assert_allclose(
x0z1.value_derived_from_density_matrix(density_matrix,
qubit_index_map), 0)
np.testing.assert_allclose(
x3.value_derived_from_density_matrix(density_matrix, qubit_index_map),
-1)
def test_approx_pauli_string_expectation_value(measurements, value):
display = cirq.pauli_string_expectation(cirq.PauliString({}),
num_samples=1)
assert display.value_derived_from_samples(measurements) == value
