ginibre_state_matrix

forest.benchmarking.operator_tools.random_operators.ginibre_state_matrix(dim: int, rank: int) → numpy.ndarray

Given a Hilbert space dimension dim and a desired rank K, returns a dim by dim positive semidefinite matrix of rank K drawn from the Ginibre ensemble.

For dim = K these are states drawn from the Hilbert-Schmidt measure.

See reference [IM] for more details.

Parameters:
  • dim – Hilbert space dimension.
  • rank – The rank of a state.
Returns:

Returns a dim by rank matrix, drawn from the Ginibre ensemble.