Generate the Kraus operators corresponding to a pauli channel.

Params probabilities:

The 4^num_qubits list of probabilities specifying the desired pauli channel. There should be either 4 or 16 probabilities specified in the order I, X, Y, Z for 1 qubit or II, IX, IY, IZ, XI, XX, XY, etc for 2 qubits.

For example:

The d-dimensional depolarizing channel \Delta parameterized as
\Delta(\rho) = p \rho + [(1-p)/d] I
is specified by the list of probabilities
[p + (1-p)/d, (1-p)/d,  (1-p)/d), ... , (1-p)/d)]
Return type:



A list of the 4^num_qubits Kraus operators that parametrize the map.