def test_matrix_from_basis_coefficients(expansion):
m = cirq.matrix_from_basis_coefficients(expansion, PAULI_BASIS)
for name, coefficient in expansion.items():
element = PAULI_BASIS[name]
expected_coefficient = cirq.hilbert_schmidt_inner_product(
m, element) / cirq.hilbert_schmidt_inner_product(element, element)
assert np.isclose(coefficient, expected_coefficient)
def test_hilbert_schmidt_inner_product_is_conjugate_symmetric(m1, m2, expect_real):
v1 = cirq.hilbert_schmidt_inner_product(m1, m2)
v2 = cirq.hilbert_schmidt_inner_product(m2, m1)
assert v1 == v2.conjugate()
assert np.isreal(v1) == expect_real
if not expect_real:
assert v1 != v2
def test_kron_bases_repeat_sanity_checks(basis, repeat):
product_basis = cirq.kron_bases(basis, repeat=repeat)
assert len(product_basis) == 4**repeat
for name1, matrix1 in product_basis.items():
for name2, matrix2 in product_basis.items():
p = cirq.hilbert_schmidt_inner_product(matrix1, matrix2)
if name1 != name2:
assert p == 0
else:
assert abs(p) >= 1
def test_hilbert_schmidt_inner_product_values(m1, m2, expected_value):
v = cirq.hilbert_schmidt_inner_product(m1, m2)
assert np.isclose(v, expected_value)
def test_hilbert_schmidt_inner_product_is_positive_definite(m):
v = cirq.hilbert_schmidt_inner_product(m, m)
assert np.isreal(v)
assert v.real > 0
def test_hilbert_schmidt_inner_product_is_linear(a, m1, b, m2):
v1 = cirq.hilbert_schmidt_inner_product(H, (a * m1 + b * m2))
v2 = (a * cirq.hilbert_schmidt_inner_product(H, m1) +
b * cirq.hilbert_schmidt_inner_product(H, m2))
assert v1 == v2
def test_hilbert_schmidt_inner_product_is_positive_definite(m):
v = cirq.hilbert_schmidt_inner_product(m, m)
# Cannot check using np.is_real due to bug in aarch64.
# See https://github.com/quantumlib/Cirq/issues/4379
assert np.isclose(np.imag(v), 1e-16)
assert v.real > 0
