dq.parity

parity(dim: int, *, layout: Layout | None = None) -> QArray

Returns the parity operator of a bosonic mode.

It is defined by \(P = e^{i\pi a^\dag a}\), where \(a\) and \(a^\dag\) are the annihilation and creation operators, respectively.

Parameters:

• dim –

  Dimension of the Hilbert space.

• layout –

  Matrix layout (dq.dense, dq.dia or None).

Returns:

• (qarray of shape (dim, dim)) –

  Parity operator.

Examples:

>>> dq.parity(4)
QArray: shape=(4, 4), dims=(4,), dtype=complex64, layout=dia, ndiags=1
[[ 1.+0.j    ⋅       ⋅       ⋅   ]
 [   ⋅    -1.+0.j    ⋅       ⋅   ]
 [   ⋅       ⋅     1.+0.j    ⋅   ]
 [   ⋅       ⋅       ⋅    -1.+0.j]]