dq.excited

excited() -> Array

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

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

Note

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

Returns

(array of shape (2, 1)) Ket \(\ket{e}\).

Examples

>>> dq.excited()
Array([[1.+0.j],
       [0.+0.j]], dtype=complex64)