toqito.perms.swap_operator

toqito.perms.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)
[[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)
[[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 – The dimensions of the subsystems.

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

Returns:

The swap operator of dimension dim.