dq.ground_dm

ground_dm() -> QArray

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

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

Note

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

Returns

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

Examples

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