perms.swap_operator

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

Functions

swap_operator(dim[, is_sparse])

Produce a unitary operator that swaps two subsystems.

Module Contents

perms.swap_operator.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.

Examples

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

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

Using 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 \(3\)-dimensional operator may be obtained using 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.]])

Parameters:

• dim (list[int] | int) – The dimensions of the subsystems.

• is_sparse (bool) – Sparse if True and non-sparse if False.

Returns:

The swap operator of dimension dim.

Return type:

numpy.ndarray