10 papers
Walk/Zeta correspondence for quantum walks on path graphs: a pre-geometric structure implied by a generalized reflection principle
Jiro Akahori, Riki Kitano, Norio Konno +1
We establish a local Konno-Sato correspondence for reflected random and Szegedy walks on a finite path graph. A generalized reflection principle, using explicit involutions rather…
Spectral analysis of hierarchical continuous-time quantum walks
Jirô Akahori, Yusuke Ide, Tomoki Kato +3
In this paper, we introduce hierarchical random walks at first. In this model, we use two types of random walkers, {global and local} walkers. The global walker chooses a local wal…
Grover algorithm and absolute zeta functions
Jirô Akahori, Kazuki Horita, Norio Konno +3
The Grover algorithm is one of the most famous quantum algorithms. On the other hand, the absolute zeta function can be regarded as a zeta function over defined by…
Periodicity and absolute zeta functions of multi-state Grover walks on cycles
Jirô Akahori, Norio Konno, Iwao Sato +1
Quantum walks, the quantum counterpart of classical random walks, are extensively studied for their applications in mathematics, quantum physics, and quantum information science. T…
Absolute zeta functions for zeta functions of quantum walks
Jirô Akahori, Norio Konno, Rikuki Okamoto +1
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 w…
Multi-dimensional continuous time quantum walks related to the birth and death chains
Yusuke Ide, Norio Konno, Akihiro Narimatsu
In this paper, we consider multi-dimensional birth and death chains and continuous time quantum walks (CTQW) related to them. For CTQW related to our forms of multi-dimensional bir…
Absolute zeta functions and periodicity of quantum walks on cycles
Jirô Akahori, Norio Konno, Iwao Sato +1
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 . This stu…
A quantization of interacting particle systems
Jirô Akahori, Norio Konno, Rikuki Okamoto +1
Interacting particle systems studied in this paper are probabilistic cellular automata with nearest-neighbor interaction including the Domany-Kinzel model. A special case of the Do…
Spectral analysis of three-state quantum walks with general coin matrices
Chusei Kiumi, Jirô Akahori, Takuya Watanabe +1
Mathematical analysis of the spectral properties of the time evolution operator in quantum walks is essential for understanding key dynamical behaviors such as localization and lon…
Metzler/Zeta Correspondence
Yusuke Ide, Takashi Komatsu, Norio Konno +1
We present an explicit formula for the determinant on the Metzler matrix of a digraph . Furthermore, we introduce a walk-type zeta function with respect to this Metzler matrix o…