Return probability of one-dimensional discrete-time quantum walks with final-time dependence

Authors:
Yusuke Ide;Norio Konno;Takuya Machida;Etsuo Segawa
Affiliations:
Department of Information Systems Creation, Kanagawa University, Kanagawa, Yokohama, Japan;Department of Applied Mathematics, Yokohama National University, Hodogaya, Yokohama, Japan;Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Tama, Kawasaki, Japan;Department of Mathematical Informatics, The University of Tokyo, Bunkyo, Tokyo, Japan
Venue:
Quantum Information & Computation
Year:
2011

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Abstract

We analyze final-time dependent discrete-time quantum walks in one dimension. We compute asymptotics of the return probability of the quantum walk by a path counting approach. Moreover, we discuss a relation between the quantum walk and the corresponding final-time dependent classical random walk.