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About Unitary States and Commutative Gates in a Two-Qubit Quantum System
Version 1
: Received: 17 November 2023 / Approved: 20 November 2023 / Online: 21 November 2023 (10:27:08 CET)
How to cite: Gabbassov, M.; Oralbekov, B.; Daulet, B. About Unitary States and Commutative Gates in a Two-Qubit Quantum System. Preprints 2023, 2023111280. https://doi.org/10.20944/preprints202311.1280.v1 Gabbassov, M.; Oralbekov, B.; Daulet, B. About Unitary States and Commutative Gates in a Two-Qubit Quantum System. Preprints 2023, 2023111280. https://doi.org/10.20944/preprints202311.1280.v1
Abstract
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.
Keywords
Quantum computing; quantum algorithm; gate; unitary operator; four-dimensional mathematics; Abelian group
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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