def test_spectral_decomposition(self, tol):
"""Test that the correct spectral decomposition is returned."""
a, P = spectral_decomposition(H)
# verify that H = \sum_k a_k P_k
assert np.allclose(H, np.einsum("i,ijk->jk", a, P), atol=tol, rtol=0)
def test_spectral_decomposition(self):
"""Test that the correct spectral decomposition is returned."""
self.logTestName()
a, P = spectral_decomposition(H)
# verify that H = \sum_k a_k P_k
self.assertAllAlmostEqual(H, np.einsum("i,ijk->jk", a, P), delta=self.tol)
def sample(self, observable, wires, par):
if not isinstance(observable, list):
observable, wires, par = [observable], [wires], [par]
matrices = [
self._get_operator_matrix(o, p) for o, p in zip(observable, par)
]
decompositions = [spectral_decomposition(A) for A in matrices]
eigenvalues, projector_groups = list(zip(*decompositions))
eigenvalues = list(eigenvalues)
# Matching each projector with the wires it acts on
# while preserving the groupings
projectors_with_wires = [[
(proj, wires[idx]) for proj in proj_group
] for idx, proj_group in enumerate(projector_groups)]
# The eigenvalue - projector maps are preserved as product() preserves
# the previous ordering by creating a lexicographic ordering
joint_outcomes = list(product(*eigenvalues))
projector_tensor_products = list(product(*projectors_with_wires))
joint_probabilities = []
for projs in projector_tensor_products:
obs_nodes = []
obs_wires = []
for proj, proj_wires in projs:
tensor = proj.reshape([2] * len(proj_wires) * 2)
obs_nodes.append(self._add_node(tensor, proj_wires))
obs_wires.append(proj_wires)
joint_probabilities.append(self.ev(obs_nodes, obs_wires))
outcomes = np.array([np.prod(p) for p in joint_outcomes])
return np.random.choice(outcomes, self.shots, p=joint_probabilities)