Corpus ID: 237532641

Walk/Zeta Correspondence for quantum and correlated random walks

  title={Walk/Zeta Correspondence for quantum and correlated random walks},
  author={Norio Konno and Shunya Tamura},
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 threeand fourstate quantum walk and correlated random walk, and the multi-state random walk on the one-dimensional torus by using the Fourier analysis. We deal with also the four-state quantum walk and correlated random walk on the two-dimensional torus. In addition, we introduce a new class of models determined by the generalized Grover matrix… Expand


Limit theorems of a 3-state quantum walk and its application for discrete uniform measures
  • T. Machida
  • Mathematics, Physics
  • Quantum Inf. Comput.
  • 2015
Two long-time limit theorems of a 3-state quantum walk on the line when the walker starts from the origin are presented and discrete uniform limit measures are obtained from the 3- state walk with a delocalized initial state. Expand
Localization of multi-state quantum walk in one dimension
Particle trapping in multi-state quantum walk on a circle is studied. The time-averaged probability distribution of a particle which moves four different lattice sites according to four internalExpand
On the relation between quantum walks and zeta functions
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, weExpand
The Ihara Zeta Function of the Infinite Grid
  • Bryan Clair
  • Mathematics, Computer Science
  • Electron. J. Comb.
  • 2014
The Ihara zeta function for the infinite grid is computed using elliptic integrals and theta functions, which is the first computed example which is non-elementary, and which takes infinitely many values at each point of its domain. Expand
Grover/Zeta Correspondence based on the Konno-Sato theorem
The relation between the Grover walk and the zeta function based on the Konno-Sato theorem is called “Grover/Zeta Correspondence” here. Expand
Limit distributions of twodimensional quantum walks
  • Phys. Rev. A, 77
  • 2008