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Teoreticheskaya i Matematicheskaya Fizika, 2024, Volume 219, Number 1, Pages 17–31
DOI: https://doi.org/10.4213/tmf10618 (Mi tmf10618) 		 
Yang–Baxter equation in all dimensions and universal qudit gates

A. Pourkia

College of Engineering and Technology, American University of the Middle East, Kuwait
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DOI: https://doi.org/10.4213/tmf10618
Abstract: We construct solutions of the Yang–Baxter equation in any dimension $d\geqslant 2$ by directly generalizing the previously found solutions for $d=2$. We equip those solutions with unitarity and entangling properties. Being unitary, they can be turned into $2$-qudit quantum logic gates for qudit-based systems. The entangling property enables each of those solutions, together with all $1$-qudit gates, to form a universal set of quantum logic gates.
Keywords: Yang–Baxter equation, qudit, quantum logic gate, universal gate.
Received: 29.09.2023
Revised: 05.11.2023
English version:
Theoretical and Mathematical Physics, 2024, Volume 219, Issue 1, Pages 544–556
DOI: https://doi.org/10.1134/S0040577924040032
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. Pourkia, “Yang–Baxter equation in all dimensions and universal qudit gates”, TMF, 219:1 (2024), 17–31; Theoret. and Math. Phys., 219:1 (2024), 544–556
Citation in format AMSBIB
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\by A.~Pourkia
\paper Yang--Baxter equation in all dimensions and universal qudit
gates
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\vol 219
\issue 1
\pages 17--31
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\crossref{https://doi.org/10.4213/tmf10618}
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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2024TMP...219..544P}
\transl
\jour Theoret. and Math. Phys.
\yr 2024
\vol 219
\issue 1
\pages 544--556
\crossref{https://doi.org/10.1134/S0040577924040032}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85191399517}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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