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

Simion Stoilow Institute of Mathematics of the Romanian Academy, 21 Calea Grivitei Street, Bucharest 010702, Romania
Asesoft International SA, Mihai Bravu Street, Nr. 10, 100550 Ploiesti, Prahova 100550, Romania
Author to whom correspondence should be addressed.
Academic Editor: Angel Garrido
Axioms 2014, 3(4), 360-368;
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)
PDF [216 KB, uploaded 14 November 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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