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arXiv · 1807.10414

Witness Algebra and Anyon Braiding

Andreas Blass·Yuri Gurevich
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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.

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Andreas Blass, Yuri Gurevich. 2018-08-02. Witness Algebra and Anyon Braiding. https://doi.org/10.1017/s0960129520000055

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