Quantum walks in low dimension

研究成果: Conference contribution

抄録

Discrete-time quantum walks are defined as a non-commutative analogue of the usual random walks on standard lattices and have been formulated in computer sciences. They are new objects in mathematics and are investigated in various areas, such as computer sciences, quantum physics, probability theory, and discrete geometric analysis. In this article, recent works on point-wise asymptotic behavior and an effective formula for nth power of the discrete-time quantum walks in one dimension are surveyed. The idea to obtain the formula for the nth power in one dimension is applied in this paper to compute the nth power of certain two-dimensional quantum walk, called the Grover walk to obtain a new formula for the two-dimensional Grover walk. The formula for nth power in one dimension has been used to prove a weak limit theorem. In this paper, the large deviation asymptotics, in one dimension, is deduced by using this formula which is a new proof of a previously obtained result.

本文言語English
ホスト出版物のタイトルGeometric Methods in Physics - 34th Workshop
編集者Piotr Kielanowski, S. Twareque Ali, Pierre Bieliavsky, Anatol Odzijewicz, Martin Schlichenmaier, Theodore Voronov
出版社Springer International Publishing
ページ261-278
ページ数18
ISBN(印刷版)9783319317557
DOI
出版ステータスPublished - 2016
イベント34th Workshop on Geometric Methods in Physics, 2015 - >Białowieża, Poland
継続期間: 2015 6 282015 7 4

出版物シリーズ

名前Trends in Mathematics
0
ISSN(印刷版)2297-0215
ISSN(電子版)2297-024X

Other

Other34th Workshop on Geometric Methods in Physics, 2015
国/地域Poland
City>Białowieża
Period15/6/2815/7/4

ASJC Scopus subject areas

  • 数学 (全般)

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