def test_unitary_size(self, tol):
"""test n=2 unitaries are not decomposed"""
U = random_interferometer(2)
with pytest.raises(
ValueError,
match="Input matrix for decomposition must be at least 3x3."):
dec.sun_compact(U, tol)
def test_interferometer_reconstruction(self, n, tol):
"""test numerical reconstruction of Unitary matrix equals the original matrix"""
U = random_interferometer(n)
factorization_params, phase = dec.sun_compact(U, tol)
det = np.exp(1j * phase)**(1 / n)
SU_reconstructed = self._sun_reconstruction(n, factorization_params)
U_reconstructed = det * SU_reconstructed
assert np.allclose(U_reconstructed, U)
def test_SU_reconstruction(self, n, tol):
"""test numerical reconstruction of Special Unitary matrix equals the original matrix"""
# Generate a random SU(n) matrix.
U = random_interferometer(n)
SU_expected = U / np.linalg.det(U)**(1 / n)
# get result from factorization
factorization_params, global_phase = dec.sun_compact(SU_expected, tol)
SU_reconstructed = self._sun_reconstruction(n, factorization_params)
assert global_phase is None
assert np.allclose(SU_expected, SU_reconstructed, atol=tol, rtol=0)
def test_embeded_unitary(self, n, permutation, phase, tol):
"""test factorization of U(n-1) transformations embeded on U(n) transformation"""
# Embed U(4) on n=5 matrix
U = np.zeros((n, n), dtype=complex)
U[0, 0] = np.exp(1j * phase)
U4 = random_interferometer(n - 1)
U[1:, 1:] = U4
# permute rows
U = U[permutation, :]
factorization_params, _ = dec.sun_compact(U, tol)
_, first_params = factorization_params[0]
assert first_params == [0.0, 0.0, 0.0]
def test_global_phase(self, SU_matrix, tol):
"""test factorized phase from unitary matrix"""
n = 3
# Generate a random SU(n) matrix.
U = random_interferometer(n)
det = np.linalg.det(U)
if SU_matrix:
U /= det**(1 / n)
# get result from factorization
_, global_phase = dec.sun_compact(U, tol)
if SU_matrix:
assert global_phase is None
else:
expected_phase = np.angle(det)
assert np.allclose(global_phase, expected_phase, atol=tol)
def test_unitary_validation(self, tol):
"""Test that an exception is raised if not unitary"""
A = np.random.random([5, 5]) + 1j * np.random.random([5, 5])
with pytest.raises(ValueError,
match="The input matrix is not unitary."):
dec.sun_compact(A, tol)