论文标题
一维整数晶格的Grover Walk和广义的Ihara Zeta功能的注释
A note on the Grover walk and the generalized Ihara zeta function of the one-dimensional integer lattice
论文作者
论文摘要
Chinta，Jorgenson和Karlsson引入了与有限或无限常规图相关的Ihara Zeta函数的确定性公式的广义版本。另一方面，Konno和Sato通过使用有限图的第二个加权Zeta函数来获得Grover矩阵的特征多项式的公式。在本文中，我们专注于Grover Walk和广义Ihara Zeta功能之间的关系。也就是说，我们将一维整数晶格的广义ihara zeta函数视为循环图的ihara zeta函数的限制。
Chinta, Jorgenson and Karlsson introduced a generalized version of the determinant formula for the Ihara zeta function associated to finite or infinite regular graphs. On the other hand, Konno and Sato obtained a formula of the characteristic polynomial of the Grover matrix by using the determinant expression for the second weighted zeta function of a finite graph. In this paper, we focus on a relationship between the Grover walk and the generalized Ihara zeta function. That is to say, we treat the generalized Ihara zeta function of the one-dimensional integer lattice as a limit of the Ihara zeta function of the cycle graph.
