def test_kronecker_prod(self):
matrix = torch.tensor([[[1, 2], [3, 4]], [[5, 6], [7, 8]]],
dtype=torch.double)
expect = torch.tensor(
[
[
[-24, -28, -28, -32],
[-32, -36, -36, -40],
[-32, -36, -36, -40],
[-40, -44, -44, -48],
],
[
[10, 16, 16, 24],
[22, 28, 32, 40],
[22, 32, 28, 40],
[42, 52, 52, 64],
],
],
dtype=torch.double,
)
self.assertTensorsEqual(cplx.kronecker_prod(matrix, matrix),
expect,
msg="Kronecker product failed!")
def rotate_rho(self, basis, space, Z, unitaries, rho=None):
r"""Computes the density matrix rotated into some basis
:param basis: The basis into which to rotate the density matrix
:type basis: numpy.ndarray
:param space: The Hilbert space of the system
:type space: torch.Tensor
:param unitaries: A dictionary of unitary matrices associated with
rotation into each basis
:type unitaries: dict[str, torch.Tensor]
:returns: The rotated density matrix
:rtype: torch.Tensor
"""
rho = self.rhoRBM(space, space) if rho is None else rho
unitaries = {k: v for k, v in unitaries.items()}
us = [unitaries[b] for b in basis]
if len(us) == 0:
return rho
# After ensuring there is more than one measurement, compute the
# composite unitary by repeated Kronecker products
U = us[0]
for index in range(len(us) - 1):
U = cplx.kronecker_prod(U, us[index + 1])
U = U.to(rho)
U_dag = cplx.conjugate(U)
rot_rho = cplx.matmul(rho, U_dag)
rot_rho_ = cplx.matmul(U, rot_rho)
return rot_rho_
def test_kronecker_prod_error_large(self):
# take KronProd of 2 rank 4 tensors, instead of rank 3
tensor = torch.arange(16, dtype=torch.double).reshape(2, 2, 2, 2)
with self.assertRaises(ValueError):
cplx.kronecker_prod(tensor, tensor)
def test_kronecker_prod_error_small(self):
# take KronProd of 2 rank 2 tensors, instead of rank 3
tensor = torch.tensor([[1, 2], [3, 4]], dtype=torch.double)
with self.assertRaises(ValueError):
cplx.kronecker_prod(tensor, tensor)