Konno–Sato theorem for a covering of a graph

IF 1.4 3区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Iwao Sato, Takashi Komatsu, Norio Konno, Hideo Mitsuhashi
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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.

图的覆盖的Konno-Sato定理
图G的Grover矩阵是G上离散时间量子行走的典型时间演化矩阵,本文讨论了G的有限覆盖的Grover矩阵,并给出了其行列式的分解公式。进一步,我们定义了一个关于格罗弗矩阵的图的l函数,并给出了它的行列式。作为推论,我们将G的一个覆盖的格罗弗矩阵的行列式表示为它的l函数的乘积。
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来源期刊
Letters in Mathematical Physics
Letters in Mathematical Physics 物理-物理:数学物理
CiteScore
2.40
自引率
8.30%
发文量
111
审稿时长
3 months
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.
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