189 citations · 1.9k across the 148 of their papers we have counts for
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A Characteristic Polynomial for The Transition Probability Matrix of A Correlated Random Walk on A Graph
Takashi Komatsu, Norio Konno, Iwao Sato
We define a correlated random walk (CRW) induced from the time evolution matrix (the Grover matrix) of the Grover walk on a graph , and present a formula for the characteristic…
A note on the Grover walk and the generalized Ihara zeta function of the one-dimensional integer lattice
Takashi Komatsu, Norio Konno, Iwao Sato
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…
Return probability and self-similarity of the Riesz walk
Ryota Hanaoka, Norio Konno
The quantum walk is a counterpart of the random walk. The 2-state quantum walk in one dimension can be determined by a measure on the unit circle in the complex plane. As for the s…
Generalized eigenfunctions for quantum walks via path counting approach
Takashi Komatsu, Norio Konno, Hisashi Morioka +1
We consider the time-independent scattering theory for time evolution operators of one-dimensional two-state quantum walks. The scattering matrix associated with the position-depen…
A crossover between open quantum random walks to quantum walks
Norio Konno, Kaname Matsue, Etsuo Segawa
We propose an intermediate walk continuously connecting an open quantum random walk and a quantum walk with parameters controlling a decoherence effect; if ,…
The limit theorem with respect to the matrices on non-backtracking paths of a graph
Takehiro Hasegawa, Takashi Komatsu, Norio Konno +4
We give a limit theorem with respect to the matrices related to non-backtracking paths of a regular graph. The limit obtained closely resembles the th moments of the arcsine law…
On the support of the Grover walk on higher-dimensional lattices
Norio Konno, Sarato Takahashi
This paper presents the minimum supports of states for stationary measures of the Grover walk on the d-dimensional lattice by solving the corresponding eigenvalue problem. The numb…