About Unitary States and Commutative Gates in a Two-Qubit Quantum System

Mars Gabbassov; Bakytzhan Oralbekov; Batyrzhan Daulet

doi:10.20944/preprints202311.1280.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 17 November 2023 / Approved: 20 November 2023 / Online: 21 November 2023 (10:27:08 CET)

This work is devoted to the construction and study of commutative gates for a two-qubit quantum system. Using four-dimensional algebra developed by the Kazakh mathematician Abenov M.M. all groups of commutative gates have been constructed, and among all states of a two-qubit quantum system, unitary states with which a specific gate is connected have been identified. An explicit type of gate is described that transfers a quantum system from one unitary state to another unitary state. The proposed approach opens up new possibilities for the design of quantum algorithms not only for two-qubit quantum systems, but also for $n$-qubit quantum systems.

Quantum computing; quantum algorithm; gate; unitary operator; four-dimensional mathematics; Abelian group

Computer Science and Mathematics, Applied Mathematics

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About Unitary States and Commutative Gates in a Two-Qubit Quantum System

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