Spectral analysis for a multi-dimensional split-step quantum walk with a defect

被引：2

作者：

Fuda, Toru ^{[1
]}

Narimatsu, Akihiro ^{[2
]}

Saito, Kei ^{[3
]}

Suzuki, Akito ^{[4
]}

机构：

[1] Kokushikan Univ, Sch Sci & Engn, Setagaya Ku, Tokyo 1548515, Japan

[2] Yokohama Natl Univ, Grad Sch Sci & Engn, Yokohama, Kanagawa 2408501, Japan

[3] Kanagawa Univ, Fac Engn, Yokohama, Kanagawa 2218686, Japan

[4] Shinshu Univ, Fac Engn, Wakasato, Nagano 3808553, Japan

来源：

QUANTUM STUDIES-MATHEMATICS AND FOUNDATIONS | 2022年 / 9卷 / 01期

关键词：

Quantum walks; Spectral analysis; Localization; Time-averaged limit measure;

D O I：

10.1007/s40509-021-00258-6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper studies the spectrum of a multi-dimensional split-step quantum walk with a defect that cannot be analyzed in previous papers by Fuda et al. (Quantum Inf Process 18:203-226, 2017; J Math Phys 59:082201, 2018). To this end, we have developed a new technique which allow us to use a spectral mapping theorem for the one-defect model. We also derive the time-averaged limit measure for one-dimensional case as an application of the spectral analysis.

引用

页码：93 / 112

页数：20

共 23 条

[11]

Hiroshima F., 2012, J MATH FOR IND, V4, P105

[12] Time averaged distribution of a discrete-time quantum walk on the path [J].

Ide, Yusuke ;

Konno, Norio ;

Segawa, Etsuo .

QUANTUM INFORMATION PROCESSING, 2012, 11 (05) :1207-1218

[13] One-dimensional three-state quantum walk [J].

Inui, N ;

Konno, N ;

Segawa, E .

PHYSICAL REVIEW E, 2005, 72 (05)

[14] Topological phenomena in quantum walks: elementary introduction to the physics of topological phases [J].

Kitagawa, Takuya .

QUANTUM INFORMATION PROCESSING, 2012, 11 (05) :1107-1148

[15] Exploring topological phases with quantum walks [J].

Kitagawa, Takuya ;

Rudner, Mark S. ;

Berg, Erez ;

Demler, Eugene .

PHYSICAL REVIEW A, 2010, 82 (03)

[16] Complete classification of trapping coins for quantum walks on the two-dimensional square lattice [J].

Kollar, B. ;

Gilyen, A. ;

Tkacova, I ;

Kiss, T. ;

Jex, I ;

Stefanak, M. .

PHYSICAL REVIEW A, 2020, 102 (01)

[17] Localization of an inhomogeneous discrete-time quantum walk on the line [J].

Konno, Norio .

QUANTUM INFORMATION PROCESSING, 2010, 9 (03) :405-418

[18]

Matsue K., 2017, Interdiscip. Inf. Sci., V23, P105

[19] Numerical Study on Quantum Walks Implemented on Cascade Rotational Transitions in a Diatomic Molecule [J].

Matsuoka, Leo ;

Kasajima, Tatsuya ;

Hashimoto, Masashi ;

Yokoyama, Keiichi .

JOURNAL OF THE KOREAN PHYSICAL SOCIETY, 2011, 59 (04) :2897-2900

[20]

Portugal R., 2018, Quantum Walks and Search Algorithms, P175, DOI [10.1007/978-3-319-97813-0, DOI 10.1007/978-3-319-97813-0]

← 1 2 3 →