189 citations · 1.9k across the 148 of their papers we have counts for
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Absolute zeta functions for zeta functions of quantum cellular automata
Jirô Akahori, Norio Konno, Iwao Sato
Our previous work dealt with the zeta function for the interacting particle system (IPS) including quantum cellular automaton (QCA) as a typical model in the study of ``IPS/Zeta Co…
On the relation between quantum walks and absolute zeta functions
Norio Konno
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 pres…
Parrondo's game of quantum search based on quantum walk
Taisuke Hosaka, Norio Konno
The Parrondo game, devised by Parrondo, means that winning strategy is constructed a combination of losing strategy. This situation is called the Parrondo paradox. The Parrondo gam…
An analogue of the Riemann Hypothesis via quantum walks
Norio Konno
We consider an analogue of the well-known Riemann Hypothesis based on quantum walks on graphs with the help of the Konno-Sato theorem. Furthermore, we give some examples for comple…
Comfortable place for quantum walkers on finite path
Yoshihiro Anahara, Norio Konno, Hisashi Morioka +1
We consider the stationary state of a quantum walk on the finite path, where the sink and source are set at the left and right boundaries. The quantum coin is uniformly placed at e…
Mahler/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato +1
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 h…
Walk/Zeta Correspondence for quantum and correlated random walks
Norio Konno, 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 three- and four-state quantum walk…
CTM/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato
In our previous work, we investigated the relation between zeta functions and discrete-time models including random and quantum walks. In this paper, we introduce a zeta function f…
IPS/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato
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…
Walk/Zeta Correspondence
Takashi Komatsu, Norio Konno, Iwao Sato
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 ve…
Grover/Zeta Correspondence based on the Konno-Sato theorem
Takashi Komatsu, Norio Konno, Iwao Sato
Recently the Ihara zeta function for the finite graph was extended to infinite one by Clair and Chinta et al. In this paper, we obtain the same expressions by a different approach…
General condition of quantum teleportation by one-dimensional quantum walks
Tomoki Yamagami, Etsuo Segawa, Norio Konno
We extend the scheme of quantum teleportation by quantum walks introduced by Wang et al. (2017). First, we introduce the mathematical definition of the accomplishment of quantum te…
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…
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 ,…
Explicit expression of scattering operator of some quantum walks on impurities
Takashi Komatsu, Norio Konno, Hisashi Morioka +1
In this paper, we consider the scattering theory for a one-dimensional quantum walk with impurities which make reflections and transmissions. We focus on an explicit expression of…
Periodicity for the 3-state quantum walk on cycles
Takeshi Kajiwara, Norio Konno, Shohei Koyama +1
Dukes (2014) and Konno, Shimizu, and Takei (2017) studied the periodicity for 2-state quantum walks whose coin operator is the Hadamard matrix on cycle graph C_N with N vertices. T…
Stationary measure induced by the eigenvalue problem of the one-dimensional Hadamard walk
Takashi Komatsu, Norio Konno
In this paper, we consider the stationary measure of the Hadamard walk on the one-dimensional integer lattice. Here all the stationary measures given by solving the eigenvalue prob…
Eigenvalues of quantum walk induced by recurrence properties of the underlying birth and death process: application to computation of an edge state
Yusuke Ide, Norio Konno, Etsuo Segawa
In this paper, we consider an extended coined Szegedy model and discuss the existence of the point spectrum of induced quantum walks in terms of recurrence properties of the underl…
The Fourier and Grover walks on the two-dimensional lattice and torus
Masahiro Asano, Takashi Komatsu, Norio Konno +1
In this paper, we consider discrete-time quantum walks with moving shift (MS) and flip-flop shift (FF) on two-dimensional lattice and torus .…
Uniform stationary measure of space-inhomogeneous quantum walks in one dimension
Yusuke Ide, Norio Konno, Daichi Nakayama
The discrete-time quantum walk (QW) is a quantum version of the random walk (RW) and has been widely investigated for the last two decades. Some remarkable properties of QW are wel…
A new time-series model based on quantum walk
Norio Konno
The quantum walk (QW) was introduced as a quantum counterpart of the classical random walk. A number of non-classical properties of the QW have been shown, e.g., ballistic spreadin…
How does Grover walk recognize the shape of crystal lattice?
Chul Ki Ko, Norio Konno, Etsuo Segawa +1
We consider the support of the limit distribution of the Grover walk on crystal lattices with the linear scaling. The orbit of the Grover walk is denoted by the parametric plot of…
Stationary measure for two-state space-inhomogeneous quantum walk in one dimension
Hikari Kawai, Takashi Komatsu, Norio Konno
We consider the two-state space-inhomogeneous coined quantum walk (QW) in one dimension. For a general setting, we obtain the stationary measure of the QW by solving the eigenvalue…
A spectral analysis of discrete-time quantum walks related to the birth and death chains
Choon-Lin Ho, Yusuke Ide, Norio Konno +2
In this paper, we consider a spectral analysis of discrete time quantum walks on the path. For isospectral coin cases, we show that the time averaged distribution and stationary di…