def circuit(w, x, y, z):
"""Test QNode"""
qml.BasisState(np.array([0, 1]), wires=[0, 1])
qml.Hadamard(wires=1)
plf.CPHASE(w, 1, wires=[0, 1])
qml.Rot(x, y, z, wires=0)
plf.CPHASE(w, 3, wires=[0, 1])
plf.CPHASE(w, 0, wires=[0, 1])
return qml.expval(qml.PauliY(1))
class TestQVMBasic(BaseTest):
"""Unit tests for the QVM simulator."""
# pylint: disable=protected-access
def test_identity_expectation(self, shots, qvm, compiler):
"""Test that identity expectation value (i.e. the trace) is 1"""
theta = 0.432
phi = 0.123
dev = plf.QVMDevice(device="2q-qvm", shots=shots)
with qml.tape.QuantumTape() as tape:
qml.RX(theta, wires=[0])
qml.RX(phi, wires=[1])
qml.CNOT(wires=[0, 1])
O1 = qml.expval(qml.Identity(wires=[0]))
O2 = qml.expval(qml.Identity(wires=[1]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
res = np.array([dev.expval(O1.obs), dev.expval(O2.obs)])
# below are the analytic expectation values for this circuit (trace should always be 1)
self.assertAllAlmostEqual(res,
np.array([1, 1]),
delta=3 / np.sqrt(shots))
def test_pauliz_expectation(self, shots, qvm, compiler):
"""Test that PauliZ expectation value is correct"""
theta = 0.432
phi = 0.123
dev = plf.QVMDevice(device="2q-qvm", shots=shots)
with qml.tape.QuantumTape() as tape:
qml.RX(theta, wires=[0])
qml.RX(phi, wires=[1])
qml.CNOT(wires=[0, 1])
O1 = qml.expval(qml.PauliZ(wires=[0]))
O2 = qml.expval(qml.PauliZ(wires=[1]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
res = np.array([dev.expval(O1.obs), dev.expval(O2.obs)])
# below are the analytic expectation values for this circuit
self.assertAllAlmostEqual(
res,
np.array([np.cos(theta),
np.cos(theta) * np.cos(phi)]),
delta=3 / np.sqrt(shots))
def test_paulix_expectation(self, shots, qvm, compiler):
"""Test that PauliX expectation value is correct"""
theta = 0.432
phi = 0.123
dev = plf.QVMDevice(device="2q-qvm", shots=shots)
with qml.tape.QuantumTape() as tape:
qml.RY(theta, wires=[0])
qml.RY(phi, wires=[1])
qml.CNOT(wires=[0, 1])
O1 = qml.expval(qml.PauliX(wires=[0]))
O2 = qml.expval(qml.PauliX(wires=[1]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
res = np.array([dev.expval(O1.obs), dev.expval(O2.obs)])
# below are the analytic expectation values for this circuit
self.assertAllAlmostEqual(
res,
np.array([np.sin(theta) * np.sin(phi),
np.sin(phi)]),
delta=3 / np.sqrt(shots))
def test_pauliy_expectation(self, shots, qvm, compiler):
"""Test that PauliY expectation value is correct"""
theta = 0.432
phi = 0.123
dev = plf.QVMDevice(device="2q-qvm", shots=shots)
with qml.tape.QuantumTape() as tape:
qml.RX(theta, wires=[0])
qml.RX(phi, wires=[1])
qml.CNOT(wires=[0, 1])
O1 = qml.expval(qml.PauliY(wires=[0]))
O2 = qml.expval(qml.PauliY(wires=[1]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
res = np.array([dev.expval(O1.obs), dev.expval(O2.obs)])
# below are the analytic expectation values for this circuit
self.assertAllAlmostEqual(res,
np.array([0, -np.cos(theta) * np.sin(phi)]),
delta=3 / np.sqrt(shots))
def test_hadamard_expectation(self, shots, qvm, compiler):
"""Test that Hadamard expectation value is correct"""
theta = 0.432
phi = 0.123
dev = plf.QVMDevice(device="2q-qvm", shots=shots)
with qml.tape.QuantumTape() as tape:
qml.RY(theta, wires=[0])
qml.RY(phi, wires=[1])
qml.CNOT(wires=[0, 1])
O1 = qml.expval(qml.Hadamard(wires=[0]))
O2 = qml.expval(qml.Hadamard(wires=[1]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
res = np.array([dev.expval(O1.obs), dev.expval(O2.obs)])
# below are the analytic expectation values for this circuit
expected = np.array([
np.sin(theta) * np.sin(phi) + np.cos(theta),
np.cos(theta) * np.cos(phi) + np.sin(phi)
]) / np.sqrt(2)
self.assertAllAlmostEqual(res, expected, delta=3 / np.sqrt(shots))
@flaky(max_runs=10, min_passes=3)
def test_hermitian_expectation(self, shots, qvm, compiler):
"""Test that arbitrary Hermitian expectation values are correct.
As the results coming from the qvm are stochastic, a constraint of 3 out of 5 runs was added.
"""
theta = 0.432
phi = 0.123
dev = plf.QVMDevice(device="2q-qvm", shots=shots)
with qml.tape.QuantumTape() as tape:
qml.RY(theta, wires=[0])
qml.RY(phi, wires=[1])
qml.CNOT(wires=[0, 1])
O1 = qml.expval(qml.Hermitian(H, wires=[0]))
O2 = qml.expval(qml.Hermitian(H, wires=[1]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
res = np.array([dev.expval(O1.obs), dev.expval(O2.obs)])
# below are the analytic expectation values for this circuit with arbitrary
# Hermitian observable H
a = H[0, 0]
re_b = H[0, 1].real
d = H[1, 1]
ev1 = ((a - d) * np.cos(theta) +
2 * re_b * np.sin(theta) * np.sin(phi) + a + d) / 2
ev2 = ((a - d) * np.cos(theta) * np.cos(phi) + 2 * re_b * np.sin(phi) +
a + d) / 2
expected = np.array([ev1, ev2])
self.assertAllAlmostEqual(res, expected, delta=4 / np.sqrt(shots))
def test_multi_qubit_hermitian_expectation(self, shots, qvm, compiler):
"""Test that arbitrary multi-qubit Hermitian expectation values are correct"""
theta = 0.432
phi = 0.123
A = np.array([
[-6, 2 + 1j, -3, -5 + 2j],
[2 - 1j, 0, 2 - 1j, -5 + 4j],
[-3, 2 + 1j, 0, -4 + 3j],
[-5 - 2j, -5 - 4j, -4 - 3j, -6],
])
dev = plf.QVMDevice(device="2q-qvm", shots=10 * shots)
with qml.tape.QuantumTape() as tape:
qml.RY(theta, wires=[0])
qml.RY(phi, wires=[1])
qml.CNOT(wires=[0, 1])
O1 = qml.expval(qml.Hermitian(A, wires=[0, 1]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
res = np.array([dev.expval(O1.obs)])
# below is the analytic expectation value for this circuit with arbitrary
# Hermitian observable A
expected = 0.5 * (6 * np.cos(theta) * np.sin(phi) - np.sin(theta) *
(8 * np.sin(phi) + 7 * np.cos(phi) + 3) -
2 * np.sin(phi) - 6 * np.cos(phi) - 6)
self.assertAllAlmostEqual(res, expected, delta=5 / np.sqrt(shots))
def test_var(self, shots, qvm, compiler):
"""Tests for variance calculation"""
dev = plf.QVMDevice(device="2q-qvm", shots=shots)
phi = 0.543
theta = 0.6543
with qml.tape.QuantumTape() as tape:
qml.RX(phi, wires=[0])
qml.RY(theta, wires=[0])
O1 = qml.var(qml.PauliZ(wires=[0]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
var = np.array([dev.var(O1.obs)])
expected = 0.25 * (3 - np.cos(2 * theta) -
2 * np.cos(theta)**2 * np.cos(2 * phi))
self.assertAlmostEqual(var, expected, delta=3 / np.sqrt(shots))
def test_var_hermitian(self, shots, qvm, compiler):
"""Tests for variance calculation using an arbitrary Hermitian observable"""
dev = plf.QVMDevice(device="2q-qvm", shots=100 * shots)
phi = 0.543
theta = 0.6543
A = np.array([[4, -1 + 6j], [-1 - 6j, 2]])
with qml.tape.QuantumTape() as tape:
qml.RX(phi, wires=[0])
qml.RY(theta, wires=[0])
O1 = qml.var(qml.Hermitian(A, wires=[0]))
# test correct variance for <A> of a rotated state
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
var = np.array([dev.var(O1.obs)])
expected = 0.5 * (2 * np.sin(2 * theta) * np.cos(phi)**2 +
24 * np.sin(phi) * np.cos(phi) *
(np.sin(theta) - np.cos(theta)) +
35 * np.cos(2 * phi) + 39)
self.assertAlmostEqual(var, expected, delta=0.3)
@pytest.mark.parametrize(
"op",
[
qml.QubitUnitary(np.array(U), wires=0),
qml.BasisState(np.array([1, 1, 1]), wires=list(range(3))),
qml.PauliX(wires=0),
qml.PauliY(wires=0),
qml.PauliZ(wires=0),
qml.S(wires=0),
qml.T(wires=0),
qml.RX(0.432, wires=0),
qml.RY(0.432, wires=0),
qml.RZ(0.432, wires=0),
qml.Hadamard(wires=0),
qml.Rot(0.432, 2, 0.324, wires=0),
qml.Toffoli(wires=[0, 1, 2]),
qml.SWAP(wires=[0, 1]),
qml.CSWAP(wires=[0, 1, 2]),
qml.CZ(wires=[0, 1]),
qml.CNOT(wires=[0, 1]),
qml.PhaseShift(0.432, wires=0),
qml.CSWAP(wires=[0, 1, 2]),
plf.CPHASE(0.432, 2, wires=[0, 1]),
plf.ISWAP(wires=[0, 1]),
plf.PSWAP(0.432, wires=[0, 1]),
],
)
def test_apply(self, op, apply_unitary, shots, qvm, compiler):
"""Test the application of gates to a state"""
dev = plf.QVMDevice(device="3q-qvm",
shots=shots,
parametric_compilation=False)
obs = qml.expval(qml.PauliZ(0))
if op.name == "QubitUnitary":
state = apply_unitary(U, 3)
elif op.name == "BasisState":
state = np.array([0, 0, 0, 0, 0, 0, 0, 1])
elif op.name == "CPHASE":
state = apply_unitary(test_operation_map["CPHASE"](0.432, 2), 3)
elif op.name == "ISWAP":
state = apply_unitary(test_operation_map["ISWAP"], 3)
elif op.name == "PSWAP":
state = apply_unitary(test_operation_map["PSWAP"](0.432), 3)
else:
state = apply_unitary(op.matrix, 3)
with qml.tape.QuantumTape() as tape:
qml.apply(op)
obs
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
res = dev.expval(obs.obs)
expected = np.vdot(state, np.kron(np.kron(Z, I), I) @ state)
# verify the device is now in the expected state
# Note we have increased the tolerance here, since we are only
# performing 1024 shots.
self.assertAllAlmostEqual(res, expected, delta=3 / np.sqrt(shots))
def test_sample_values(self, qvm, tol):
"""Tests if the samples returned by sample have
the correct values
"""
dev = plf.QVMDevice(device="1q-qvm", shots=10)
with qml.tape.QuantumTape() as tape:
qml.RX(1.5708, wires=[0])
O1 = qml.expval(qml.PauliZ(wires=[0]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
s1 = dev.sample(O1.obs)
# s1 should only contain 1 and -1
self.assertAllAlmostEqual(s1**2, 1, delta=tol)
self.assertAllAlmostEqual(s1, 1 - 2 * dev._samples[:, 0], delta=tol)
def test_sample_values_hermitian(self, qvm, tol):
"""Tests if the samples of a Hermitian observable returned by sample have
the correct values
"""
theta = 0.543
shots = 1_000_000
A = np.array([[1, 2j], [-2j, 0]])
dev = plf.QVMDevice(device="1q-qvm", shots=shots)
with qml.tape.QuantumTape() as tape:
qml.RX(theta, wires=[0])
O1 = qml.sample(qml.Hermitian(A, wires=[0]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
s1 = dev.sample(O1.obs)
# s1 should only contain the eigenvalues of
# the hermitian matrix
eigvals = np.linalg.eigvalsh(A)
assert np.allclose(sorted(list(set(s1))),
sorted(eigvals),
atol=tol,
rtol=0)
# the analytic mean is 2*sin(theta)+0.5*cos(theta)+0.5
assert np.allclose(np.mean(s1),
2 * np.sin(theta) + 0.5 * np.cos(theta) + 0.5,
atol=0.1,
rtol=0)
# the analytic variance is 0.25*(sin(theta)-4*cos(theta))^2
assert np.allclose(np.var(s1),
0.25 * (np.sin(theta) - 4 * np.cos(theta))**2,
atol=0.1,
rtol=0)
def test_sample_values_hermitian_multi_qubit(self, qvm, tol):
"""Tests if the samples of a multi-qubit Hermitian observable returned by sample have
the correct values
"""
theta = 0.543
shots = 100_000
A = np.array([
[1, 2j, 1 - 2j, 0.5j],
[-2j, 0, 3 + 4j, 1],
[1 + 2j, 3 - 4j, 0.75, 1.5 - 2j],
[-0.5j, 1, 1.5 + 2j, -1],
])
dev = plf.QVMDevice(device="2q-qvm", shots=shots)
with qml.tape.QuantumTape() as tape:
qml.RX(theta, wires=[0])
qml.RY(2 * theta, wires=[1])
qml.CNOT(wires=[0, 1])
O1 = qml.sample(qml.Hermitian(A, wires=[0, 1]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
s1 = dev.sample(O1.obs)
# s1 should only contain the eigenvalues of
# the hermitian matrix
eigvals = np.linalg.eigvalsh(A)
assert np.allclose(sorted(list(set(s1))),
sorted(eigvals),
atol=tol,
rtol=0)
# make sure the mean matches the analytic mean
expected = (88 * np.sin(theta) + 24 * np.sin(2 * theta) -
40 * np.sin(3 * theta) + 5 * np.cos(theta) -
6 * np.cos(2 * theta) + 27 * np.cos(3 * theta) + 6) / 32
assert np.allclose(np.mean(s1), expected, atol=0.1, rtol=0)
def test_wires_argument(self):
"""Test that the wires argument gets processed correctly."""
dev_no_wires = plf.QVMDevice(device="2q-qvm", shots=5)
assert dev_no_wires.wires == Wires(range(2))
with pytest.raises(ValueError, match="Device has a fixed number of"):
plf.QVMDevice(device="2q-qvm", shots=5, wires=1000)
dev_iterable_wires = plf.QVMDevice(device="2q-qvm",
shots=5,
wires=range(2))
assert dev_iterable_wires.wires == Wires(range(2))
with pytest.raises(ValueError, match="Device has a fixed number of"):
plf.QVMDevice(device="2q-qvm", shots=5, wires=range(1000))
@pytest.mark.parametrize("shots", list(range(0, -10, -1)))
def test_raise_error_if_shots_is_not_positive(self, shots):
"""Test that instantiating a QVMDevice if the number of shots is not a postivie
integer raises an error"""
with pytest.raises(
ValueError,
match="Number of shots must be a positive integer."):
dev = plf.QVMDevice(device="2q-qvm", shots=shots)
def test_raise_error_if_shots_is_none(self, shots):
"""Test that instantiating a QVMDevice to be used for analytic computations raises an error"""
with pytest.raises(
ValueError,
match="QVM device cannot be used for analytic computations."):
dev = plf.QVMDevice(device="2q-qvm", shots=None)
@pytest.mark.parametrize(
"device", ["2q-qvm", np.random.choice(TEST_QPU_LATTICES)])
def test_timeout_set_correctly(self, shots, device):
"""Test that the timeout attrbiute for the QuantumComputer stored by the QVMDevice
is set correctly when passing a value as keyword argument"""
dev = plf.QVMDevice(device=device, shots=shots, timeout=100)
assert dev.qc.compiler.client.timeout == 100
@pytest.mark.parametrize(
"device", ["2q-qvm", np.random.choice(TEST_QPU_LATTICES)])
def test_timeout_default(self, shots, device):
"""Test that the timeout attrbiute for the QuantumComputer stored by the QVMDevice
is set correctly when passing a value as keyword argument"""
dev = plf.QVMDevice(device=device, shots=shots)
qc = pyquil.get_qc(device, as_qvm=True)
# Check that the timeouts are equal (it has not been changed as a side effect of
# instantiation
assert dev.qc.compiler.client.timeout == qc.compiler.client.timeout
def test_compiled_program_stored(self, qvm, monkeypatch):
"""Test that QVM device stores the latest compiled program."""
dev = qml.device("forest.qvm", device="2q-qvm")
dev.compiled_program is None
theta = 0.432
phi = 0.123
with qml.tape.QuantumTape() as tape:
qml.RX(theta, wires=[0])
qml.RX(phi, wires=[1])
qml.CNOT(wires=[0, 1])
O1 = qml.expval(qml.Identity(wires=[0]))
O2 = qml.expval(qml.Identity(wires=[1]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev.generate_samples()
dev.compiled_program is not None
def test_stored_compiled_program_correct(self, qvm, monkeypatch):
"""Test that QVM device stores the latest compiled program."""
dev = qml.device("forest.qvm", device="2q-qvm")
dev.compiled_program is None
theta = 0.432
with qml.tape.QuantumTape() as tape:
qml.RZ(theta, wires=[0])
qml.CZ(wires=[0, 1])
O1 = qml.expval(qml.PauliZ(wires=[0]))
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev.generate_samples()
dev.compiled_program.program == compiled_program
class TestWavefunctionBasic(BaseTest):
"""Unit tests for the NumPy wavefunction simulator."""
def test_var(self, tol):
"""Tests for variance calculation"""
dev = plf.NumpyWavefunctionDevice(wires=2)
phi = 0.543
theta = 0.6543
with qml.tape.QuantumTape() as tape:
qml.RX(phi, wires=[0])
qml.RY(theta, wires=[0])
O = qml.var(qml.PauliZ(wires=[0]))
# test correct variance for <Z> of a rotated state
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
var = dev.var(O)
expected = 0.25 * (3 - np.cos(2 * theta) -
2 * np.cos(theta)**2 * np.cos(2 * phi))
self.assertAlmostEqual(var, expected, delta=tol)
def test_var_hermitian(self, tol):
"""Tests for variance calculation using an arbitrary Hermitian observable"""
dev = plf.NumpyWavefunctionDevice(wires=2)
phi = 0.543
theta = 0.6543
H = np.array([[4, -1 + 6j], [-1 - 6j, 2]])
with qml.tape.QuantumTape() as tape:
qml.RX(phi, wires=[0])
qml.RY(theta, wires=[0])
O = qml.var(qml.Hermitian(H, wires=[0]))
# test correct variance for <Z> of a rotated state
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
var = dev.var(O)
# test correct variance for <H> of a rotated state
expected = 0.5 * (2 * np.sin(2 * theta) * np.cos(phi)**2 +
24 * np.sin(phi) * np.cos(phi) *
(np.sin(theta) - np.cos(theta)) +
35 * np.cos(2 * phi) + 39)
self.assertAlmostEqual(var, expected, delta=tol)
@pytest.mark.parametrize(
"op",
[
qml.QubitUnitary(np.array(U), wires=0),
qml.BasisState(np.array([1, 1, 1]), wires=list(range(3))),
qml.PauliX(wires=0),
qml.PauliY(wires=0),
qml.PauliZ(wires=0),
qml.S(wires=0),
qml.T(wires=0),
qml.RX(0.432, wires=0),
qml.RY(0.432, wires=0),
qml.RZ(0.432, wires=0),
qml.Hadamard(wires=0),
qml.Rot(0.432, 2, 0.324, wires=0),
qml.Toffoli(wires=[0, 1, 2]),
qml.SWAP(wires=[0, 1]),
qml.CSWAP(wires=[0, 1, 2]),
qml.CZ(wires=[0, 1]),
qml.CNOT(wires=[0, 1]),
qml.PhaseShift(0.432, wires=0),
qml.CSWAP(wires=[0, 1, 2]),
plf.CPHASE(0.432, 2, wires=[0, 1]),
plf.ISWAP(wires=[0, 1]),
plf.PSWAP(0.432, wires=[0, 1]),
],
)
def test_apply(self, op, apply_unitary, tol):
"""Test the application of gates to a state"""
dev = plf.NumpyWavefunctionDevice(wires=3)
obs = qml.expval(qml.PauliZ(0))
if op.name == "QubitUnitary":
state = apply_unitary(U, 3)
elif op.name == "BasisState":
state = np.array([0, 0, 0, 0, 0, 0, 0, 1])
elif op.name == "CPHASE":
state = apply_unitary(test_operation_map["CPHASE"](0.432, 2), 3)
elif op.name == "ISWAP":
state = apply_unitary(test_operation_map["ISWAP"], 3)
elif op.name == "PSWAP":
state = apply_unitary(test_operation_map["PSWAP"](0.432), 3)
else:
state = apply_unitary(op.matrix, 3)
with qml.tape.QuantumTape() as tape:
qml.apply(op)
obs
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
# verify the device is now in the expected state
self.assertAllAlmostEqual(dev._state, state, delta=tol)
def test_sample_values(self, tol):
"""Tests if the samples returned by sample have
the correct values
"""
dev = plf.NumpyWavefunctionDevice(wires=1, shots=10)
theta = 1.5708
O = qml.sample(qml.PauliZ(0))
with qml.tape.QuantumTape() as tape:
qml.RX(theta, wires=[0])
qml.sample(qml.PauliZ(0))
dev.apply(tape._ops, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
s1 = dev.sample(O.obs)
# s1 should only contain 1 and -1
self.assertAllAlmostEqual(s1**2, 1, delta=tol)
def test_sample_values_hermitian(self, tol):
"""Tests if the samples of a Hermitian observable returned by sample have
the correct values
"""
dev = plf.NumpyWavefunctionDevice(wires=1, shots=1_000_000)
theta = 0.543
A = np.array([[1, 2j], [-2j, 0]])
circuit_operations = [qml.RX(theta, wires=[0])]
O = qml.sample(qml.Hermitian(A, wires=[0]))
with qml.tape.QuantumTape() as tape:
qml.RX(theta, wires=[0])
O = qml.sample(qml.Hermitian(A, wires=[0]))
# test correct variance for <Z> of a rotated state
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
s1 = dev.sample(O.obs)
# s1 should only contain the eigenvalues of
# the hermitian matrix
eigvals = np.linalg.eigvalsh(A)
assert np.allclose(sorted(list(set(s1))),
sorted(eigvals),
atol=tol,
rtol=0)
# the analytic mean is 2*sin(theta)+0.5*cos(theta)+0.5
assert np.allclose(np.mean(s1),
2 * np.sin(theta) + 0.5 * np.cos(theta) + 0.5,
atol=0.1,
rtol=0)
# the analytic variance is 0.25*(sin(theta)-4*cos(theta))^2
assert np.allclose(np.var(s1),
0.25 * (np.sin(theta) - 4 * np.cos(theta))**2,
atol=0.1,
rtol=0)
def test_sample_values_hermitian_multi_qubit(self, tol):
"""Tests if the samples of a multi-qubit Hermitian observable returned by sample have
the correct values
"""
shots = 1_000_000
dev = plf.NumpyWavefunctionDevice(wires=2, shots=shots)
theta = 0.543
A = np.array([
[1, 2j, 1 - 2j, 0.5j],
[-2j, 0, 3 + 4j, 1],
[1 + 2j, 3 - 4j, 0.75, 1.5 - 2j],
[-0.5j, 1, 1.5 + 2j, -1],
])
with qml.tape.QuantumTape() as tape:
qml.RX(theta, wires=[0]),
qml.RY(2 * theta, wires=[1]),
qml.CNOT(wires=[0, 1]),
O = qml.sample(qml.Hermitian(A, wires=[0, 1]))
# test correct variance for <Z> of a rotated state
dev.apply(tape.operations, rotations=tape.diagonalizing_gates)
dev._samples = dev.generate_samples()
s1 = dev.sample(O.obs)
# s1 should only contain the eigenvalues of
# the hermitian matrix
eigvals = np.linalg.eigvalsh(A)
assert np.allclose(sorted(list(set(s1))),
sorted(eigvals),
atol=tol,
rtol=0)
# make sure the mean matches the analytic mean
expected = (88 * np.sin(theta) + 24 * np.sin(2 * theta) -
40 * np.sin(3 * theta) + 5 * np.cos(theta) -
6 * np.cos(2 * theta) + 27 * np.cos(3 * theta) + 6) / 32
assert np.allclose(np.mean(s1), expected, atol=0.1, rtol=0)