dq.dissipator

dissipator(L: QArrayLike, rho: QArrayLike) -> QArray

Applies the Lindblad dissipation superoperator to a density matrix.

The dissipation superoperator \(\mathcal{D}[L]\) is defined by: $$ \mathcal{D}[L] (\rho) = L\rho L^\dag - \frac{1}{2}L^\dag L \rho - \frac{1}{2}\rho L^\dag L. $$

Parameters

• L (qarray-like of shape (..., n, n)) –

  Jump operator.

• rho (qarray-like of shape (..., n, n)) –

  Density matrix.

Returns

(qarray of shape (..., n, n)) Resulting operator (it is not a density matrix).

See also

• dq.sdissipator(): returns the dissipation superoperator in matrix form (vectorized).

Examples

>>> L = dq.destroy(4)
>>> rho = dq.fock_dm(4, 2)
>>> dq.dissipator(L, rho)
QArray: shape=(4, 4), dims=(4,), dtype=complex64, layout=dense
[[ 0.+0.j  0.+0.j  0.+0.j  0.+0.j]
 [ 0.+0.j  2.+0.j  0.+0.j  0.+0.j]
 [ 0.+0.j  0.+0.j -2.+0.j  0.+0.j]
 [ 0.+0.j  0.+0.j  0.+0.j  0.+0.j]]