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

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...

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Bibliographic Details
Published inQuantum information processing Vol. 16; no. 12; pp. 1 - 16
Main Authors Komatsu, Takashi, Konno, Norio
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2017
Springer Nature B.V
Subjects
Data Structures and Information Theory
Eigenvalues
Mathematical Physics
Physics
Physics and Astronomy
Quantum Computing
Quantum Information Technology
Quantum Physics
Spintronics
Stationary measure
Higher-dimensional integer lattice
Discrete time quantum walk
Stationary amplitude
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Summary: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.
ISSN:1570-0755
1573-1332
DOI:10.1007/s11128-017-1737-1