toqito.perms.permutation_operator
=================================

.. py:module:: toqito.perms.permutation_operator

.. autoapi-nested-parse::

   Permutation operator is a unitary operator that permutes subsystems.





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

.. py:function:: permutation_operator(dim, perm, inv_perm = False, is_sparse = False)

   Produce a unitary operator that permutes subsystems.

   Generates a unitary operator that permutes the order of subsystems according to the permutation vector `perm`,
   where the \(i^{th}\) subsystem has dimension `dim[i]`.

   If `inv_perm` = True, it implements the inverse permutation of `perm`. The permutation operator return
   is full is `is_sparse` is `False` and sparse if `is_sparse` is `True`.

   .. rubric:: Examples

   The permutation operator obtained with dimension \(d = 2\) is equivalent to the standard swap operator on two
   qubits

   \[
       P_{2, [1, 0]} =
       \begin{pmatrix}
           1 & 0 & 0 & 0 \\
           0 & 0 & 1 & 0 \\
           0 & 1 & 0 & 0 \\
           0 & 0 & 0 & 1
       \end{pmatrix}
   \]

   Using `|toqito⟩`, this can be achieved in the following manner.

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

   print(permutation_operator(2, [1, 0]))
   ```

   :param dim: The dimensions of the subsystems to be permuted.
   :param perm: A permutation vector.
   :param inv_perm: Boolean dictating if `perm` is inverse or not.
   :param is_sparse: Boolean indicating if return is sparse or not.

   :returns: Permutation operator of dimension `dim`.