Related papers: CTM/Zeta Correspondence
In this paper, following the recent paper on Walk/Zeta Correspondence by the first author and his coworkers, we compute the zeta function for the three- and four-state quantum walk and correlated random walk, and the multi-state random walk…
We consider the connection between this zeta function and quantum search via quantum walk. First, we give an explicit expression of the zeta function on the one-dimensional torus in the general case of the number and position of marked…
Our previous work presented explicit formulas for the generalized zeta function and the generalized Ihara zeta function corresponding to the Grover walk and the positive-support version of the Grover walk on the regular graph via the…
We present an explicit formula for the characteristic polynomial of the transition matrix of the discrete-time quantum walk on a graph via the second weighted zeta function. As applications, we obtain new proofs for the results on spectra…
Recently, quantized versions of random walks have been explored as effective elements for quantum algorithms. In the simplest case of one dimension, the theory has remained divided into the discrete-time quantum walk and the continuous-time…
The Ronkin function was defined by Ronkin in the consideration of the zeros of almost periodic function. Recently, this function has been used in various research fields in mathematics, physics and so on. Especially in mathematics, it has a…
The quantum walk is a quantum counterpart of the classical random walk. On the other hand, the absolute zeta function can be considered as a zeta function over F_1. This paper presents a connection between the quantum walk and the absolute…
The quantum walk is a quantum counterpart of the classical random walk. On the other hand, absolute zeta functions can be considered as zeta functions over $\mathbb{F}_1$. This study presents a connection between quantum walks and absolute…
The Mahler measure was introduced by Mahler in the study of number theory. It is known that the Mahler measure appears in different areas of mathematics and physics. On the other hand, we have been investigated a new class of zeta functions…
Quantum walks, the quantum mechanical counterpart of classical random walks, is an advanced tool for building quantum algorithms that has been recently shown to constitute a universal model of quantum computation. Quantum walks is now a…
Quantum walk is one of the main tools for quantum algorithms. Defined by analogy to classical random walk, a quantum walk is a time-homogeneous quantum process on a graph. Both random and quantum walks can be defined either in continuous or…
This paper presents a connection between the quantum walk and the absolute mathematics. The quantum walk is a quantum counterpart of the classical random walk. We especially deal with the Grover walk on a graph. The Grover walk is a typical…
We present the structure theorem for the positive support of the cube of the Grover transition matrix of the discrete-time quantum walk (the Grover walk) on a general graph $G$ under same condition. Thus, we introduce a zeta function on the…
Quantum walks, the quantum counterpart of classical random walks, are extensively studied for their applications in mathematics, quantum physics, and quantum information science. This study explores the periods and absolute zeta functions…
This tutorial article showcases the many varieties and uses of quantum walks. Discrete time quantum walks are introduced as counterparts of classical random walks. The emphasis is on the connections and differences between the two types of…
We consider the alternating zeta function and the alternating $L$-function of a graph $G$, and express them by using the Ihara zeta function of $G$. Next, we define a generalized alternating zeta function of a graph, and express the…
Our previous works presented zeta functions by the Konno-Sato theorem or the Fourier analysis for one-particle models including random walks, correlated random walks, quantum walks, and open quantum random walks. This paper introduces a new…
We present an explicit formula for the determinant on the Metzler matrix of a digraph $D$. Furthermore, we introduce a walk-type zeta function with respect to this Metzler matrix of the symmetric digraph of a finite torus, and express its…
This work deals with both instantaneous uniform mixing property and temporal standard deviation for continuous-time quantum random walks on circles in order to study their fluctuations comparing with discrete-time quantum random walks, and…
This paper reviews recent advances in continuous-time quantum walks (CTQW) and their application to transport in various systems. The introduction gives a brief survey of the historical background of CTQW. After a short outline of the…