Abstract

DELANEY, Colleen; ROWELL, Eric C  and  WANG, Zhenghan. Local unitary representations of the braid group and their applications to quantum computing. Rev.colomb.mat. [online]. 2016, vol.50, n.2, pp.211-276. ISSN 0034-7426.  https://doi.org/10.15446/recolma.v50n2.62211.

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.

Keywords : topological quantum computation; braid group representations; localizations; quantum algebra.

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