matrices.gen_pauli_x

Produces a generalized Pauli-X operator matrix.

Functions

gen_pauli_x(dim)

Produce a dim-by-dim gen_pauli_x matrix [1].

Module Contents

matrices.gen_pauli_x.gen_pauli_x(dim)

Produce a dim-by-dim gen_pauli_x matrix [1].

Returns the gen_pauli_x matrix of dimension dim described in [1]. The gen_pauli_x matrix generates the following dim-by-dim matrix:

\[\begin{split}\Sigma_{1, d} = \begin{pmatrix} 0 & 0 & 0 & \ldots & 0 & 1 \\ 1 & 0 & 0 & \ldots & 0 & 0 \\ 0 & 1 & 0 & \ldots & 0 & 0 \\ 0 & 0 & 1 & \ldots & 0 & 0 \\ \vdots & \vdots & \vdots & \ddots & \vdots & \vdots \\ 0 & 0 & 0 & \ldots & 1 & 0 \end{pmatrix}\end{split}\]

The gen_pauli_x matrix is primarily used in the construction of the generalized Pauli operators.

Examples

The gen_pauli_x matrix generated from \(d = 3\) yields the following matrix:

\[\begin{split}\Sigma_{1, 3} = \begin{pmatrix} 0 & 0 & 1 \\ 1 & 0 & 0 \\ 0 & 1 & 0 \end{pmatrix}\end{split}\]

>>> from toqito.matrices import gen_pauli_x
>>> gen_pauli_x(3)
array([[0., 0., 1.],
       [1., 0., 0.],
       [0., 1., 0.]])

References

[1] (1,2,3)

Wikipedia. Generalizations of Pauli matrices. URL: https://en.wikipedia.org/wiki/Generalizations_of_Pauli_matrices.

Parameters:

dim (int) – Dimension of the matrix.

Returns:

dim-by-dim gen_pauli_x matrix.

Return type:

numpy.ndarray