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A note on the discrete-time evolutions of quantum walk on a graph

By Yusuke Higuchi, Norio Konno, Iwao Sato, Etsuo Segawa, 雄介 樋口, 紀雄 今野, 巖 佐藤 and 悦生 瀬川


MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス・フォア・インダストリ教育研究拠点」For a quantum walk on a graph, there exist many kinds of operators for the discrete-time evolution. We give a general relation between the characteristic polynomial of the evolution matrix of a quantum walk on edges and that of a kind of transition matrix of a classical random walk on vertices. Furthermore we determine the structure of the positive support of the cube of some evolution matrix, which is said to be useful for isospectral problem in graphs, under a certain condition

Topics: quantum walk, evolution matrix, characteristic polynomial, isospectral problem
Publisher: 九州大学大学院数理学研究院
Year: 2013
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