由关联方案诱导的正则图导出的子因子
Subfactors from regular graphs induced by association schemes
AI总结：
本文阐明了正则图量子行走与任意子系统间的数学结构关系，利用II型矩阵合成的关联方案及其子因子典范构造，通过相互作用Fock空间在距离正则图上建立量子行走并联系任意子系统，同时探讨了图族及分类问题。
摘要：
我们阐明了能够在正则图上构建量子行走及其在任意子系统中实现的数学结构之间的关系。我们的核心是关联方案，它可由II型矩阵合成，这些矩阵具有子因子的典范构造。通过这种方式，我们利用相互作用Fock空间在由关联方案诱导的距离正则图上建立量子行走，并将其与由子因子描述的任意子系统联系起来。我们详细讨论了可在此方法内处理的一大类图。关联方案和可实现的任意子系统的分类是复杂的组合问题，我们基于量子行走应用的方法解决了其中一部分。
英文摘要：
We clarify the relations between the mathematical structures that enable fashioning quantum walks on regular graphs and their realizations in anyonic systems. Our protagonist is association schemes that may be synthesized from type-II matrices which have a canonical construction of subfactors. This way we set up quantum walks on growing distance-regular graphs induced by association schemes via interacting Fock spaces and relate them to anyon systems described by subfactors. We discuss in detail a large family of graphs that may be treated within this approach. Classification of association schemes and realizable anyon systems are complex combinatorial problems and we tackle a part of it with a quantum walk application based approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
