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 zeta function for multi-particle models with probabilistic or quantum interactions, called the interacting particle system (IPS). We compute the zeta function for some tensor-type IPSs.

arXiv:2105.04056Quantum Information and ComputationFeb 1, 20223 citations

arXiv:2402.17183 · Quantum Studies Mathematics and Foundations

QW-search/zeta correspondence

Taisuke Hosaka, Norio Konno, Etsuo Segawa

Published Mar 11, 2025• 0 citations

arXiv HTML PDF

DOI: 10.1007/s40509-025-00361-y

Related papers

Walk/Zeta Correspondence

Takashi Komatsu, Norio Konno, Iwao Sato

arXiv:2104.10287Journal of Statistical PhysicsDec 19, 20229 citations

Mahler/Zeta Correspondence

Takashi Komatsu, Norio Konno, Iwao Sato +1 more

arXiv:2202.05966Quantum Information ProcessingAug 20, 20223 citations

Grover/Zeta Correspondence based on the Konno–Sato theorem

Takashi Komatsu, Norio Konno, Iwao Sato

arXiv:2103.12971Quantum Information ProcessingAug 1, 202112 citations

Absolute Zeta functions and periodicity of quantum walks on cycles

Jirô Akahori, Norio Konno, Iwao Sato +1 more

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 $\mathbf{F}_1$ . This study presents a connection between quantum walks and absolute zeta functions. In this paper, we focus on Hadamard walks and $3$ -state Grover walks on cycle graphs. The Hadamard walks and the Grover walks are typical models of the quantum walks. We consider the periods and zeta functions of such quantum walks. Moreover, we derive the explicit forms of the absolute zeta functions of corresponding zeta functions. Also, it is shown that our zeta functions of quantum walks are absolute automorphic forms.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 $\mathbf{F}_1$. This study presents a connection between quantum walks and absolute zeta functions. In this paper, we focus on Hadamard walks and $3$-state Grover walks on cycle graphs. The Hadamard walks and the Grover walks are typical models of the quantum walks. We consider the periods and zeta functions of such quantum walks. Moreover, we derive the explicit forms of the absolute zeta functions of corresponding zeta functions. Also, it is shown that our zeta functions of quantum walks are absolute automorphic forms.

arXiv:2405.05995Quantum Information and ComputationOct 1, 20240 citations

Implementation and Viusalization of Quantum Walks

Addie Jordon, Austin Hawkins-Seagram, Ulrike Stege

Quantum walks (QWs) are the quantum analogue to classical random walks. We explore various implementations of QWs and create visualizations for each, with the goal of increasing educational accessibility. A new QW, called sticky walk, is introduced, where the walker sticks to targets once found. Corresponding pseudocode and Qiskit implementations are provided. Sticky walk helps bridge the gap between non-searching QWs and Quantum Walk Search (which may be an unintuitive search algorithm for those new to QWs).Quantum walks (QWs) are the quantum analogue to classical random walks. We explore various implementations of QWs and create visualizations for each, with the goal of increasing educational accessibility. A new QW, called sticky walk, is introduced, where the walker sticks to targets once found. Corresponding pseudocode and Qiskit implementations are provided. Sticky walk helps bridge the gap between non-searching QWs and Quantum Walk Search (which may be an unintuitive search algorithm for those new to QWs).

IEEE International Conference on Quantum Computing and Engineering (QCE)Sep 1, 20223 citations

IPS/Zeta correspondence

Takashi Komatsu, Norio Konno, Iwao Sato

arXiv:2105.04056Quantum Information and ComputationFeb 1, 20223 citations

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

\mathbf{F}_1

. This study presents a connection between quantum walks and absolute zeta functions. In this paper, we focus on Hadamard walks and

3

-state Grover walks on cycle graphs. The Hadamard walks and the Grover walks are typical models of the quantum walks. We consider the periods and zeta functions of such quantum walks. Moreover, we derive the explicit forms of the absolute zeta functions of corresponding zeta functions. Also, it is shown that our zeta functions of quantum walks are absolute automorphic forms.