toqito.matrices.gen_pauli_x
===========================

.. py:module:: toqito.matrices.gen_pauli_x

.. autoapi-nested-parse::

   Produces a generalized Pauli-X operator matrix.





Module Contents
---------------

.. py:function:: gen_pauli_x(dim)

   Produce a `dim`-by-`dim` gen_pauli_x matrix [@WikiPauliGen].

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

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

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

   .. rubric:: Examples

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

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

   ```python exec="1" source="above"
   from toqito.matrices import gen_pauli_x

   print(gen_pauli_x(3))
   ```

   :param dim: Dimension of the matrix.

   :returns: `dim`-by-`dim` gen_pauli_x matrix.