def _convert_to_su4(U):
r"""Check unitarity of a 4x4 matrix and convert it to :math:`SU(4)` if the determinant is not 1.
Args:
U (array[complex]): A matrix, presumed to be :math:`4 \times 4` and unitary.
Returns:
array[complex]: A :math:`4 \times 4` matrix in :math:`SU(4)` that is
equivalent to U up to a global phase.
"""
# Check unitarity
if not math.allclose(
math.dot(U, math.T(math.conj(U))), math.eye(4), atol=1e-7):
raise ValueError("Operator must be unitary.")
# Compute the determinant
det = math.linalg.det(U)
# Convert to SU(4) if it's not close to 1
if not math.allclose(det, 1.0):
exp_angle = -1j * math.cast_like(math.angle(det), 1j) / 4
U = math.cast_like(U, det) * math.exp(exp_angle)
return U
def _convert_to_su2(U):
r"""Check unitarity of a matrix and convert it to :math:`SU(2)` if possible.
Args:
U (array[complex]): A matrix, presumed to be :math:`2 \times 2` and unitary.
Returns:
array[complex]: A :math:`2 \times 2` matrix in :math:`SU(2)` that is
equivalent to U up to a global phase.
"""
# Check unitarity
if not math.allclose(
math.dot(U, math.T(math.conj(U))), math.eye(2), atol=1e-7):
raise ValueError("Operator must be unitary.")
# Compute the determinant
det = U[0, 0] * U[1, 1] - U[0, 1] * U[1, 0]
# Convert to SU(2) if it's not close to 1
if not math.allclose(det, [1.0]):
exp_angle = -1j * math.cast_like(math.angle(det), 1j) / 2
U = math.cast_like(U, exp_angle) * math.exp(exp_angle)
return U