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The Yang-Baxter Equation, (Quantum) Computers and Unifying Theories

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Simion Stoilow Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, Bucharest 010702, Romania
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Asesoft International SA, Mihai Bravu Street, Nr. 10, 100550 Ploiesti, Prahova 100550, Romania
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Author to whom correspondence should be addressed.
Academic Editor: Angel Garrido
Axioms 2014, 3(4), 360-368; https://doi.org/10.3390/axioms3040360
Received: 22 September 2014 / Revised: 25 October 2014 / Accepted: 4 November 2014 / Published: 14 November 2014
(This article belongs to the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations 2014)
Quantum mechanics has had an important influence on building computers;nowadays, quantum mechanics principles are used for the processing and transmission ofinformation. The Yang-Baxter equation is related to the universal gates from quantumcomputing and it realizes a unification of certain non-associative structures. Unifyingstructures could be seen as structures which comprise the information contained in other(algebraic) structures. Recently, we gave the axioms of a structure which unifies associativealgebras, Lie algebras and Jordan algebras. Our paper is a review and a continuation of thatapproach. It also contains several geometric considerations. View Full-Text
Keywords: universal gate; quantum computer; Yang-Baxter equation; Jordan algebras; Lie algebras; associative algebras universal gate; quantum computer; Yang-Baxter equation; Jordan algebras; Lie algebras; associative algebras
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Iordanescu, R.; Nichita, F.F.; Nichita, I.M. The Yang-Baxter Equation, (Quantum) Computers and Unifying Theories. Axioms 2014, 3, 360-368.

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