{"title":"Konno–Sato theorem for a covering of a graph","authors":"Iwao Sato, Takashi Komatsu, Norio Konno, Hideo Mitsuhashi","doi":"10.1007/s11005-025-01960-x","DOIUrl":null,"url":null,"abstract":"<div><p>The Grover matrix of a graph <i>G</i> is a typical time evolution matrix of a discrete-time quantum walk on <i>G</i>. We treat the Grover matrix of a finite covering of <i>G</i> and present a decomposition formula for the determinant of it. Furthermore, we define an <i>L</i>-function of a graph with respect to the Grover matrix and present its determinant expression. As a corollary, we express the determinant of the Grover matrix of a covering of <i>G</i> as a product of its <i>L</i>-functions.\n</p></div>","PeriodicalId":685,"journal":{"name":"Letters in Mathematical Physics","volume":"115 4","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Letters in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s11005-025-01960-x","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
The Grover matrix of a graph G is a typical time evolution matrix of a discrete-time quantum walk on G. We treat the Grover matrix of a finite covering of G and present a decomposition formula for the determinant of it. Furthermore, we define an L-function of a graph with respect to the Grover matrix and present its determinant expression. As a corollary, we express the determinant of the Grover matrix of a covering of G as a product of its L-functions.
期刊介绍:
The aim of Letters in Mathematical Physics is to attract the community''s attention on important and original developments in the area of mathematical physics and contemporary theoretical physics. The journal publishes letters and longer research articles, occasionally also articles containing topical reviews. We are committed to both fast publication and careful refereeing. In addition, the journal offers important contributions to modern mathematics in fields which have a potential physical application, and important developments in theoretical physics which have potential mathematical impact.