Sociedad Colombiana de Matemáticas:Publicaciones
Revista Colombiana de Matemáticas
Volumen 50 [2] (2016)Páginas 273-294

Solutions of the hexagon equation for abelian anyons

César Galindo,Nicolás Jaramillo
Universidad de los Andes, Bogota, Colombia

Abstract. We provide an elementary introduction to topological quantum computation based on the Jones representation of the braid group. We first cover the Burau representation and Alexander polynomial. Then we discuss the Jones representation and Jones polynomial and their application to anyonic quantum computation. Finally we outline the approximation of the Jones polynomial by a quantum computer and explicit localizations of braid group representations.

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