dq.spre

spre(x: ArrayLike) -> Array

Returns the superoperator formed from pre-multiplication by an operator.

Pre-multiplication by matrix \(A\) is defined by the superoperator \(I_n \otimes A\) in vectorized form: $$ AX \to (I_n \otimes A) \kett{X}. $$

Parameters

• x (array_like of shape (..., n, n)) –

  Operator.

Returns

(array of shape (..., n^2, n^2)) Pre-multiplication superoperator.

Examples

>>> dq.spre(dq.destroy(3)).shape
(9, 9)