- 著者
- Yusuke HIGUCHI Norio KONNO Iwao SATO Etsuo SEGAWA
- 出版者
- 東北大学大学院情報科学研究科ジャーナル編集委員会
- 雑誌
- Interdisciplinary Information Sciences (ISSN:13409050)
- 巻号頁・発行日
- vol.23, no.1, pp.75-86, 2017 (Released:2017-03-31)
- 参考文献数
- 23
- 被引用文献数
- 1
In this paper we discuss the periodicity of the evolution matrix of Szegedy walk, which is a special type of quantum walk induced by the classical simple random walk, on a finite graph. We completely characterize the periods of Szegedy walks for complete graphs, compete bipartite graphs and strongly regular graphs. In addition, we discuss the periods of Szegedy walk induced by a non-reversible random walk on a cycle.
- 著者
- Shimpei ENDO Takako ENDO Norio KONNO Etsuo SEGAWA Masato TAKEI
- 出版者
- 東北大学大学院情報科学研究科ジャーナル編集委員会
- 雑誌
- Interdisciplinary Information Sciences (ISSN:13409050)
- 巻号頁・発行日
- pp.2016.R.01, (Released:2016-03-25)
- 参考文献数
- 24
- 被引用文献数
- 6
We attempt to analyze a one-dimensional space-inhomogeneous quantum walk (QW) with one defect at the origin, which has two different quantum coins in positive and negative parts. We call the QW ``the two-phase QW with one defect'', which we treated concerning localization theorems. The two-phase QW with one defect has been expected to be a mathematical model of topological insulator which is an intense issue both theoretically and experimentally. In this paper, we derive the weak limit theorem describing the ballistic spreading, and as a result, we obtain the mathematical expression of the whole picture of the asymptotic behavior. Our approach is based mainly on the generating function of the weight of the passages. We emphasize that the time-averaged limit measure is symmetric for the origin , however, the weak limit measure is asymmetric, which implies that the weak limit theorem represents the asymmetry of the probability distribution.