论文标题
拓扑量子计算的功能区类别框架
The ribbon category framework for topological quantum computing
论文作者
论文摘要
此说明性文章提供了基于Arxiv中引入的编织表示计算器的数学背景：2212.00831;这些表示形式描述了可用于处理编码Qubits的拓扑量子计算机可用的逻辑门集。假设几乎没有类别理论的背景，我们首先回想起色带融合类别（RFC）的概念，收集了大多数必要的定义。然后，我们讨论某些RFC是如何来自量子群的表示理论。我们详细探讨了这些类别中的编织，因为它对于量子计算应用至关重要。
This expository article supplies the mathematical background underpinning the braid representation calculator introduced in arXiv:2212.00831; those representations describe the sets of logic gates available to a topological quantum computer for processing encoded qubits. Assuming little background in category theory, we first recall the notion of a ribbon fusion category (RFC), collecting most of the necessary definitions. Then we discuss how certain RFCs arise from the representation theory of quantum groups. We explore the braiding in these categories in detail, since it is essential for the quantum computing application.
