def aschannel(self) -> 'Channel':
"""Converts a Gate into a Channel"""
N = self.qubit_nb
R = 4
tensor = bk.outer(self.tensor, self.H.tensor)
tensor = bk.reshape(tensor, [2**N] * R)
tensor = bk.transpose(tensor, [0, 3, 1, 2])
return Channel(tensor, self.qubits)
def test_trace():
tensor = bk.astensor(np.asarray([[1, 0, 0, 0],
[0, -1, 0, 0],
[0, 0, 2.7, 1],
[0, 0, 1, 0.3j]]))
tensor = bk.reshape(tensor, (4, 4)) # FIXME astensor should not reshape
tr = bk.evaluate(bk.trace(tensor))
print(tr)
assert tr - (2.7+0.3j) == ALMOST_ZERO
def sharp(self) -> 'Channel':
r"""Return the 'sharp' transpose of the superoperator.
The transpose :math:`S^\#` switches the two covariant (bra)
indices of the superoperator. (Which in our representation
are the 2nd and 3rd super-indices)
If :math:`S^\#` is Hermitian, then :math:`S` is a Hermitian-map
(i.e. transforms Hermitian operators to hJrmitian operators)
Flattening the :math:`S^\#` superoperator to a matrix gives
the Choi matrix representation. (See channel.choi())
"""
N = self.qubit_nb
tensor = self.tensor
tensor = bk.reshape(tensor, [2**N] * 4)
tensor = bk.transpose(tensor, (0, 2, 1, 3))
tensor = bk.reshape(tensor, [2] * 4 * N)
return Channel(tensor, self.qubits)
def chi(self) -> bk.BKTensor:
"""Return the chi (or process) matrix representation of this
superoperator"""
N = self.qubit_nb
return bk.reshape(self.sharp.tensor, [2**(N * 2)] * 2)
def choi(self) -> bk.BKTensor:
"""Return the Choi matrix representation of this super
operator"""
# Put superop axes in [ok, ib, ob, ik] and reshape to matrix
N = self.qubit_nb
return bk.reshape(self.sharp.tensor, [2**(N * 2)] * 2)