toqito.perms.swap_operator
==========================

.. py:module:: toqito.perms.swap_operator

.. autoapi-nested-parse::

   Swap operator. is used to generate a unitary operator that can swap two subsystems.





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

.. py:function:: swap_operator(dim, is_sparse = False)

   Produce a unitary operator that swaps two subsystems.

   Provides the unitary operator that swaps two copies of `dim`-dimensional space. If the two subsystems are not
   of the same dimension, `dim` should be a 1-by-2 vector containing the dimension of the subsystems.

   .. rubric:: Examples

   The \(2\)-dimensional swap operator is given by the following matrix

   \[
       X_2 =
       \begin{pmatrix}
           1 & 0 & 0 & 0 \\
           0 & 0 & 1 & 0 \\
           0 & 1 & 0 & 0 \\
           0 & 0 & 0 & 1
       \end{pmatrix}
   \]

   Using `|toqito⟩` we can obtain this matrix as follows.

   ```python exec="1" source="above"
   from toqito.perms import swap_operator

   print(swap_operator(2))
   ```

   The \(3\)-dimensional operator may be obtained using `|toqito⟩` as follows.

   ```python exec="1" source="above"
   from toqito.perms import swap_operator

   print(swap_operator(3))
   ```

   :param dim: The dimensions of the subsystems.
   :param is_sparse: Sparse if `True` and non-sparse if `False`.

   :returns: The swap operator of dimension `dim`.