Stationary amplitudes of quantum walks on the higher-dimensional integer lattice

被引：0
|
作者：
Takashi Komatsu
Norio Konno
机构：
[1] Yokohama National University,Department of Applied Mathematics, Faculty of Engineering
来源：
Quantum Information Processing | 2017年 / 16卷
关键词：
Discrete time quantum walk; Stationary amplitude; Higher-dimensional integer lattice; Stationary measure;
D O I：
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学科分类号：
摘要：
Stationary measures of quantum walks on the one-dimensional integer lattice are well studied. However, the stationary measure for the higher-dimensional case has not been clarified. In this paper, we give the stationary amplitude for quantum walks on the d-dimensional integer lattice with a finite support by solving the corresponding eigenvalue problem. As a corollary, we can obtain the stationary measures of the Grover walks. In fact, the amplitude for the stationary measure is an eigenfunction with eigenvalue 1.
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