论文标题
由关联方案引起的常规图的子因子
Subfactors from regular graphs induced by association schemes
论文作者
论文摘要
我们阐明了在常规图上及其在任何核心系统中的实现的数学结构之间的关系。我们的主角是可以从具有规范构造亚比例构造的II型矩阵中合成的关联方案。这样，我们就通过相互作用的Fock空间引起的结合方案引起的距离规则图的增长，并将其与亚基因子所描述的任何系统相关联。我们详细讨论了可能在这种方法中处理的大型图。协会方案和可实现的Anyon系统的分类是复杂的组合问题，我们通过基于量子的步行应用方法来解决其中的一部分。
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.
