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

Axioms

Radu Iordanescu¹  Florin F. Nichita¹  Ion M. Nichita² 

[1] 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;

关键词: universal gate;    quantum computer;    Yang-Baxter equation;    Jordan algebras;    Lie algebras;    associative algebras;   

DOI  :  10.3390/axioms3040360

来源: mdpi

【 摘 要 】

Quantum mechanics has had an important influence on building computers; nowadays, quantum mechanics principles are used for the processing and transmission of information. The Yang-Baxter equation is related to the universal gates from quantum computing and it realizes a unification of certain non-associative structures. Unifying structures could be seen as structures which comprise the information contained in other (algebraic) structures. Recently, we gave the axioms of a structure which unifies associative algebras, Lie algebras and Jordan algebras. Our paper is a review and a continuation of that approach. It also contains several geometric considerations.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland.