Study on structural analysis of networks by quantum walks

2015 Fiscal Year Final Research Report

• Project/Area Number: 25800088
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tohoku University
• Principal Investigator: Etsuo Segawa 東北大学, 情報科学研究科, 准教授 (30634547)
• Research Collaborator: Konno Norio 横浜国立大学, 工学研究院, 教授 ; Sato Iwao 小山高等専門学校, 数学科, 教授 ; Higuchi Yusuke 昭和大学, 富士吉田教育部, 講師 ; Fukuizumi Reika 東北大学, 情報科学研究科, 准教授 ; Adami Riccardo Politecnico di Torino, Dipartimento di Scienze Matematiche, Associate professor
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 量子ウォーク / 極限定理 / 固有値写像 / グラフゼータ

Outline of Final Research Achievements

In this research, we studied a mathematical model named quantum walk, which is investigated as quantum speed up quantum search algorithm and also a nice model accomplishing a topological insulator. In particular, by many time iterations of quantum walks on a network, we attempted to extract some structures of the network. By measuring a quantum walk on infinite graph after sufficiently large time, then we can know the existence of cycles and edges of the network as localization phenomena. We also observe its opposite property named linear spreading simultaneously. This phenomena provides which takes a quantum walker to quadratically further place comparing with random walker with respect to time iterations.

Free Research Field

量子ウォーク