Witness Algebra and Anyon Braiding

TL;DR

This paper introduces a simpler algebraic framework for understanding anyon braiding in topological quantum computation, reducing reliance on complex category theory.

Contribution

It presents a new algebraic approach to modeling anyon braiding, simplifying the mathematical foundation of topological quantum computation.

Findings

Simplifies the mathematical framework for anyon braiding

Reduces reliance on complex category theory

Provides a more accessible algebraic model

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.