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

Parallel multi-two-qubit SWAP gate via QND interaction of OAM light and atomic ensemble