dq.excited_dm

excited_dm() -> QArray

Returns the projector on the eigenvector with eigenvalue \(+1\) of the Pauli \(\sigma_z\) operator.

It is defined by \(\ket{e}\bra{e} = \begin{pmatrix}1 & 0\\0 & 0\end{pmatrix}\).

Note

This function is named excited_dm because \(\ket{e}\) is the higher energy state of a two-level-system with Hamiltonian \(H=\omega \sigma_z\).

Returns

(qarray of shape (2, 2)) Density matrix \(\ket{e}\bra{e}\).

Examples

>>> dq.excited_dm()
QArray: shape=(2, 2), dims=(2,), dtype=complex64, layout=dense
[[1.+0.j 0.+0.j]
 [0.+0.j 0.+0.j]]