2018/02/06 by Hayato Saigo, Saigo, Hayato, Hiroki Sako +1
Computer Science · #46L99 #60F05 #81Q99 #Blockchain Technology Applications and Security #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Quantum Computing Algorithms and Architecture
paper · pdf · doi:10.48550/arxiv.1802.01837
openalex publication_date 2018/02/06 · openalex created_date 2018/02/23 · openalex updated_date 2026/07/28
The subject of this paper is quantum walks, which are expected to simulate several kinds of quantum dynamical systems. In this paper, we define analyticity for quantum walks on Z. Almost all the quantum walks on ℤ which have been already studied are analytic. In the framework of analytic quantum walks, we can enlarge the theory of quantum walks. We obtain not only several generalizations of known results, but also new types of theorems. It is proved that every analytic space-homogeneous quantum walk on Z is essentially a composite of shift operators and continuous-time analytic space-homogeneous quantum walks. We also prove existence of the weak limit distribution for analytic space-homogeneous quantum walks on Z.