Local unitary representations of the braid group and their applications to quantum computing

2016/04/21 by Colleen Delaney, Eric C. Rowell, Delaney, Colleen +3 · 1 voice · 3 citations
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paper · pdf · doi:10.48550/arxiv.1604.06429

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 and explicit localizations of braid group representations.

Cited by

• Fusion Trees and Homological Representations
• Eventually periodic resolutions with applications to integral group rings
• On the irreducibility of singular braid group representations

Discussions

• Theoretician explains experimentalist how to construct a universal quantum computer. arxiv.org/abs/1604.06429 [bsky, 21 points, 2 comments]

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