  Nowadays quantum SWAP gate has become an integral part of quantum computing,
so investigation of methods of its realization seems to be an important
practical problem for various quantum-optical and information applications. In
the present paper we propose a scheme for performing a SWAP logic operation in
discrete variables in the framework of quantum non-demolition interaction
between an atomic ensemble and a multimode light with orbital angular momentum.
We discuss in detail the procedure for revealing two-qubit closed subsystems on
a set of atomic and field states for different values of the driving field
orbital momentum. We also demonstrate the possibility of implementing a
parallel multi-two-qubit quantum SWAP gate.
