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.

中文翻译：

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见证代数和任意子编织

拓扑量子计算采用称为任意子的二维准粒子。任意子理论普遍接受的数学基础是模张量范畴的框架。该框架涉及大量类别理论，因此被认为相当难以理解。当前框架的复杂性是否必要？关联性和编织矩阵的计算可以基于一个更简单的框架，它看起来不像范畴论，而更像熟悉的代数。我们在这里介绍该框架。