Parallel Multi-Qubit Evolution in the Quantum Non-Demolition Interaction Protocol

To date, two-qubit quantum logic gates have become an essential part of quantum computing. The study of methods for their implementation is an important practical problem for various quantum optical and information applications. In this paper, we have considered a protocol for multimode quantum non-demolition interaction between an atomic ensemble and multimode light with orbital angular momentum in order to analyze the applicability of this protocol in discrete variables computing. We have developed a multimode interaction Hamiltonian and analyzed the dynamics of field and atomic variables depending on the structure of the driving field. We discuss in detail the procedure for separating qubit noninteracting subsystems on a set of atomic and field modes for various values of the orbital angular momentum of the driving field. Such a procedure helps to reduce the considered protocol to the parallel evolution of two-qubit closed systems.