def test_incorrect_heisenberg_size(self, monkeypatch):
"""The number of dimensions of a CV observable Heisenberg representation does
not match the ev_order attribute."""
monkeypatch.setattr(qml.P, "ev_order", 2)
with pytest.raises(ValueError, match="Mismatch between the polynomial order"):
CVParamShiftTape._transform_observable(qml.P(0), np.identity(3), device_wires=[0])
def test_first_order_transform(self, tol):
"""Test that a first order observable is transformed correctly"""
# create a symmetric transformation
Z = np.arange(3 ** 2).reshape(3, 3)
Z = Z.T + Z
obs = qml.X(0)
res = CVParamShiftTape._transform_observable(obs, Z, device_wires=[0])
# The Heisenberg representation of the X
# operator is simply... X
expected = np.array([0, 1, 0]) @ Z
assert isinstance(res, qml.PolyXP)
assert res.wires.labels == (0,)
assert np.allclose(res.data[0], expected, atol=tol, rtol=0)
def test_second_order_transform(self, tol):
"""Test that a second order observable is transformed correctly"""
# create a symmetric transformation
Z = np.arange(3 ** 2).reshape(3, 3)
Z = Z.T + Z
obs = qml.NumberOperator(0)
res = CVParamShiftTape._transform_observable(obs, Z, device_wires=[0])
# The Heisenberg representation of the number operator
# is (X^2 + P^2) / (2*hbar) - 1/2
A = np.array([[-0.5, 0, 0], [0, 0.25, 0], [0, 0, 0.25]])
expected = A @ Z + Z @ A
assert isinstance(res, qml.PolyXP)
assert res.wires.labels == (0,)
assert np.allclose(res.data[0], expected, atol=tol, rtol=0)
def test_device_wire_expansion(self, tol):
"""Test that the transformation works correctly
for the case where the transformation applies to more wires
than the observable."""
# create a 3-mode symmetric transformation
wires = qml.wires.Wires([0, "a", 2])
ndim = 1 + 2 * len(wires)
Z = np.arange(ndim ** 2).reshape(ndim, ndim)
Z = Z.T + Z
obs = qml.NumberOperator(0)
res = CVParamShiftTape._transform_observable(obs, Z, device_wires=wires)
# The Heisenberg representation of the number operator
# is (X^2 + P^2) / (2*hbar) - 1/2. We use the ordering
# I, X0, Xa, X2, P0, Pa, P2.
A = np.diag([-0.5, 0.25, 0.25, 0, 0, 0, 0])
expected = A @ Z + Z @ A
assert isinstance(res, qml.PolyXP)
assert res.wires == wires
assert np.allclose(res.data[0], expected, atol=tol, rtol=0)
def test_higher_order_observable(self, monkeypatch):
"""An exception should be raised if the observable is higher than 2nd order."""
monkeypatch.setattr(qml.P, "ev_order", 3)
with pytest.raises(NotImplementedError, match="order > 2 not implemented"):
CVParamShiftTape._transform_observable(qml.P(0), np.identity(3), device_wires=[0])