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Witness algebra and anyon braiding

Published online by Cambridge University Press:  16 March 2020

Andreas Blass  and
Yuri Gurevich Open the ORCID record for Yuri Gurevich [Opens in a new window]
Andreas Blass
Affiliation:
Mathematics Department, University of Michigan, Ann Arbor, MI48109-1043, USA
Yuri Gurevich*
Affiliation:
Computer Science and Engineering, University of Michigan, Ann Arbor, MI48109-2121, USA
*
*Corresponding author. Email: gurevich@umich.edu
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Abstract

Topological quantum computation employs two-dimensional quasiparticles called anyons. The generally accepted mathematical basis for the theory of anyons is the framework of modular tensor categories. That framework involves a substantial amount of category theory and is, as a result, considered rather difficult to understand. Is the complexity of the present framework necessary? The computations of associativity and braiding matrices can be based on a much simpler framework, which looks less like category theory and more like familiar algebra. We introduce that framework here.

Keywords

Anyonsbraidingmodular tensor categoriestopological quantum computingwitness algebra
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 30 , Issue 3 , March 2020 , pp. 234 - 270
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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