def test_hermitian_basis(dim, result):
"""
Test the method for creating the basis of Hermitian matrices.
"""
for basis_vector, result_vector in zip(hermitian_basis(dim), result):
assert basis_vector == result_vector
assert hermitian_basis(dim) == result
[1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
[0, 0, 0, -1, 0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, -1, 0],
[0, 0, 0, 0, 1, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0, -1, 0, 0, 0],
[0, 0, 0, 0, 0, 0, 0, 0, 0, 1],
])),
(matrix_to_expr_operator([[0, 1, 0], [1, 0, 0], [0, 0, -1]
]), monomial_basis(*range(2)), expr_to_vector,
sp.Matrix([[1, 0, 0, 0], [0, 0, 1, 0], [0, 1, 0, 0], [0, 0, 0, -1]])),
(repr_to_matrix_operator(sp.Matrix(
[[0, 1], [1, 0]])), hermitian_basis(2), hermitian_to_vector,
sp.Matrix([
[0, 1, 0, 0],
[1, 0, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, -1],
])),
(repr_to_matrix_operator(
sp.Matrix([[0, 1], [1, 0]]),
complex_conjugate=True), hermitian_basis(2), hermitian_to_vector,
sp.Matrix([
[0, 1, 0, 0],
[1, 0, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1],
])),
sp.Matrix([[1, 0, 0], [0, 0, 0], [0, 0, 0]]),
sp.Matrix([[0, 0, 0], [0, 1, 0], [0, 0, 0]]),
sp.Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 1]]),
sp.Matrix([[0, 1, 0], [1, 0, 0], [0, 0, 0]]),
sp.Matrix([[0, -sp.I, 0], [sp.I, 0, 0], [0, 0, 0]]),
sp.Matrix([[0, 0, 1], [0, 0, 0], [1, 0, 0]]),
sp.Matrix([[0, 0, -sp.I], [0, 0, 0], [sp.I, 0, 0]]),
sp.Matrix([[0, 0, 0], [0, 0, 1], [0, 1, 0]]),
sp.Matrix([[0, 0, 0], [0, 0, -sp.I], [0, sp.I, 0]]),
])])
def test_hermitian_basis(dim, result):
"""
Test the method for creating the basis of Hermitian matrices.
"""
for basis_vector, result_vector in zip(hermitian_basis(dim), result):
assert basis_vector == result_vector
assert hermitian_basis(dim) == result
@pytest.mark.parametrize(
'mat,vec,basis',
[(sp.Matrix([[0, 1 + sp.I], [1 - sp.I, 0]]),
(0, 0, 1, -1), hermitian_basis(2)),
(sp.Matrix([[2, sp.sqrt(2) + sp.I], [sp.sqrt(2) - sp.I, -3]]),
(2, -3, sp.sqrt(2), -1), hermitian_basis(2))])
def test_hermitian_to_vector(mat, vec, basis):
"""
Test that a Hermitian matrix is correctly converted to a vector.
"""
assert hermitian_to_vector(mat, basis) == vec
def test_hermitian_basis(dim, result):
for basis_vector, result_vector in zip(hermitian_basis(dim), result):
assert basis_vector == result_vector
assert hermitian_basis(dim) == result