def test_fidelity_known_values():
vec1 = np.array([1, 1j, -1, -1j]) * 0.5
vec2 = np.array([1, -1, 1, -1], dtype=np.complex128) * 0.5
vec3 = np.array([1, 0, 0, 0], dtype=np.complex128)
tensor1 = np.reshape(vec1, (2, 2))
mat1 = cirq.density_matrix(np.outer(vec1, vec1.conj()))
mat2 = cirq.density_matrix(np.outer(vec2, vec2.conj()))
mat3 = 0.3 * mat1.density_matrix() + 0.7 * mat2.density_matrix()
np.testing.assert_allclose(cirq.fidelity(vec1, vec1, qid_shape=(4, )), 1)
np.testing.assert_allclose(cirq.fidelity(vec2, vec2, qid_shape=(4, )), 1)
np.testing.assert_allclose(cirq.fidelity(vec1, vec3, qid_shape=(4, )),
0.25)
np.testing.assert_allclose(cirq.fidelity(vec1, tensor1, qid_shape=(4, )),
1)
np.testing.assert_allclose(cirq.fidelity(tensor1, vec1, qid_shape=(2, 2)),
1)
np.testing.assert_allclose(cirq.fidelity(mat1, mat1, qid_shape=(2, 2)), 1)
np.testing.assert_allclose(cirq.fidelity(mat2, mat2, qid_shape=(2, 2)), 1)
np.testing.assert_allclose(cirq.fidelity(vec1, mat1, qid_shape=(2, 2)), 1)
np.testing.assert_allclose(cirq.fidelity(mat2, vec2, qid_shape=(2, 2)), 1)
np.testing.assert_allclose(cirq.fidelity(vec1, vec2, qid_shape=(4, )), 0)
np.testing.assert_allclose(cirq.fidelity(vec1, mat2, qid_shape=(2, 2)), 0)
np.testing.assert_allclose(cirq.fidelity(mat1, vec2, qid_shape=(2, 2)), 0)
np.testing.assert_allclose(cirq.fidelity(vec1, mat3, qid_shape=(2, 2)),
0.3)
np.testing.assert_allclose(cirq.fidelity(tensor1, mat3, qid_shape=(2, 2)),
0.3)
np.testing.assert_allclose(cirq.fidelity(mat3, tensor1, qid_shape=(2, 2)),
0.3)
np.testing.assert_allclose(cirq.fidelity(mat3, vec2, qid_shape=(2, 2)),
0.7)
def test_fidelity_invariant_under_unitary_transformation():
np.testing.assert_allclose(
cirq.fidelity(cirq.density_matrix(MAT1), MAT2, qid_shape=(15, )),
cirq.fidelity(cirq.density_matrix(U @ MAT1 @ U.T.conj()),
U @ MAT2 @ U.T.conj(),
qid_shape=(15, )),
)
def test_fidelity_symmetric():
np.testing.assert_allclose(cirq.fidelity(VEC1, VEC2), cirq.fidelity(VEC2, VEC1))
np.testing.assert_allclose(cirq.fidelity(VEC1, MAT1), cirq.fidelity(MAT1, VEC1))
np.testing.assert_allclose(
cirq.fidelity(cirq.density_matrix(MAT1), MAT2),
cirq.fidelity(cirq.density_matrix(MAT2), MAT1),
)
def test_density_matrix():
density_matrix_1 = np.eye(4, dtype=np.complex64) / 4
state_vector_1 = cirq.one_hot(shape=(4,), dtype=np.complex64)
state = cirq.density_matrix(density_matrix_1)
assert state.data is density_matrix_1
assert state.qid_shape == (2, 2)
assert state.dtype == np.complex64
with pytest.raises(ValueError, match='square'):
_ = cirq.density_matrix(state_vector_1)
def test_fidelity_commuting_matrices():
d1 = np.random.uniform(size=N)
d1 /= np.sum(d1)
d2 = np.random.uniform(size=N)
d2 /= np.sum(d2)
mat1 = cirq.density_matrix(U @ np.diag(d1) @ U.T.conj())
mat2 = U @ np.diag(d2) @ U.T.conj()
np.testing.assert_allclose(cirq.fidelity(mat1, mat2, qid_shape=(15, )),
np.sum(np.sqrt(d1 * d2))**2)
def test_fidelity_between_zero_and_one():
assert 0 <= cirq.fidelity(VEC1, VEC2, qid_shape=(15, )) <= 1
assert 0 <= cirq.fidelity(VEC1, MAT1, qid_shape=(15, )) <= 1
assert 0 <= cirq.fidelity(
cirq.density_matrix(MAT1), MAT2, qid_shape=(15, )) <= 1
def test_fidelity_between_zero_and_one():
assert 0 <= cirq.fidelity(VEC1, VEC2) <= 1
assert 0 <= cirq.fidelity(VEC1, MAT1) <= 1
assert 0 <= cirq.fidelity(cirq.density_matrix(MAT1), MAT2) <= 1
