dq.spre

spre(x: QArrayLike) -> QArray

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 (qarray-like of shape (..., n, n)) –

  Operator.

Returns

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

Examples

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