computational2pauli_basis_matrix

forest.benchmarking.operator_tools.superoperator_transformations.computational2pauli_basis_matrix(dim) → numpy.ndarray

Produces a basis transform matrix that converts from a computational basis to the unnormalized pauli basis.

This is the conjugate transpose of pauli2computational_basis_matrix with an extra dimensional factor.

\[\rm{c2p\_transform(dim)} = \frac{1}{dim} sum_{k=1}^{dim^2} | k > << \sigma_k |\]

For example

\[vec(\sigma_z) = | \sigma_z >> = [1, 0, 0, -1].T\]

in the computational basis, so

\[c2p * | \sigma_z >> = [0, 0, 0, 1].T\]

Parameters:dim – dimension of the hilbert space on which the operators act. Returns:A dim**2 by dim**2 basis transform matrix