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<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.</p>

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Konno–Sato theorem for a covering of a graph

  • 期刊论文

  • 发表日期：

    2025年7月12日

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  • Iwao Sato,
  • Takashi Komatsu,
  • Norio Konno,
  • Hideo Mitsuhashi

摘要

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.