:py:mod:`perms.swap_operator`
=============================

.. py:module:: perms.swap_operator

.. autoapi-nested-parse::

   Swap operator.



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


Functions
~~~~~~~~~

.. autoapisummary::

   perms.swap_operator.swap_operator



.. 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 :code:`dim`-dimensional space. If the two subsystems are not
   of the same dimension, :code:`dim` should be a 1-by-2 vector containing the dimension of the subsystems.

   .. rubric:: Examples

   The :math:`2`-dimensional swap operator is given by the following matrix

   .. math::
       X_2 =
       \begin{pmatrix}
           1 & 0 & 0 & 0 \\
           0 & 0 & 1 & 0 \\
           0 & 1 & 0 & 0 \\
           0 & 0 & 0 & 1
       \end{pmatrix}

   Using :code:`toqito` we can obtain this matrix as follows.

   >>> from toqito.perms import swap_operator
   >>> swap_operator(2)
   array([[1., 0., 0., 0.],
          [0., 0., 1., 0.],
          [0., 1., 0., 0.],
          [0., 0., 0., 1.]])

   The :math:`3`-dimensional operator may be obtained using :code:`toqito` as follows.

   >>> from toqito.perms import swap_operator
   >>> swap_operator(3)
   array([[1., 0., 0., 0., 0., 0., 0., 0., 0.],
          [0., 0., 0., 1., 0., 0., 0., 0., 0.],
          [0., 0., 0., 0., 0., 0., 1., 0., 0.],
          [0., 1., 0., 0., 0., 0., 0., 0., 0.],
          [0., 0., 0., 0., 1., 0., 0., 0., 0.],
          [0., 0., 0., 0., 0., 0., 0., 1., 0.],
          [0., 0., 1., 0., 0., 0., 0., 0., 0.],
          [0., 0., 0., 0., 0., 1., 0., 0., 0.],
          [0., 0., 0., 0., 0., 0., 0., 0., 1.]])

   :param dim: The dimensions of the subsystems.
   :param is_sparse: Sparse if :code:`True` and non-sparse if :code:`False`.
   :return: The swap operator of dimension :code:`dim`.