论文标题
与Anyons的量子计算：$ f $ -matrix和辫子计算器
Quantum computing with anyons: an $F$-matrix and braid calculator
论文作者
论文摘要
我们引入了五角大方方程求解器，作为SageMath的一部分，并使用它来构建与某些Anyon系统相关的编织组表示。我们回想起拓扑量子计算的类别理论框架，以解释这些表示方式如何描述可用于信息处理的任何量子计算机可用的逻辑门集。在这样做的过程中，我们避免冒险进入拓扑或保形量子场理论。取而代之的是，我们抽象地将Anyons作为标签集以及满足许多公理的数据集合，包括五角大楼和六边形方程，并解释这些数据如何表征功能融合类别（RFC）。在RFC的语言中，我们的求解器可以为任何与与简单的lie代数相关的量子群的表示理论产生的$ f $ amatrices，该系统与与统一的词根相关的量子群的表示理论而产生。
We introduce a pentagon equation solver, available as part of SageMath, and use it to construct braid group representations associated to certain anyon systems. We recall the category-theoretic framework for topological quantum computation to explain how these representations describe the sets of logical gates available to an anyonic quantum computer for information processing. In doing so, we avoid venturing deep into topological or conformal quantum field theory. Instead, we present anyons abstractly as sets of labels together with a collection of data satisfying a number of axioms, including the pentagon and hexagon equations, and explain how these data characterize ribbon fusion categories (RFCs). In the language of RFCs, our solver can produce $F$-matrices for anyon systems corresponding to multiplicity-free fusion rings arising in connection with the representation theory of quantum groups associated to simple Lie algebras with deformation parameter a root of unity.
