Quantum walks induced by Dirichlet random walks on infinite trees

Yusuke Higuchi; Etsuo Segawa

doi:10.1088/1751-8121/aa8fba

Quantum walks induced by Dirichlet random walks on infinite trees

Yusuke Higuchi, Etsuo Segawa

Information Sciences

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

We consider the Grover walk on infinite trees from the viewpoint of spectral analysis. From the previous work, infinite regular trees provide localization. In this paper, we give the complete characterization of the eigenspace of this Grover walk, which involves localization of its behavior and recovers the previous work. Our result suggests that the Grover walk on infinite trees may be regarded as a limit of the quantum walk induced by the isotropic random walk with the Dirichlet boundary condition at the n-th depth rather than one with the Neumann boundary condition.

Original language	English
Article number	075303
Journal	Journal of Physics A: Mathematical and Theoretical
Volume	51
Issue number	7
DOIs	https://doi.org/10.1088/1751-8121/aa8fba
Publication status	Published - 2018 Jan 19

Keywords

Dirichlet condition
eigenspace
flow
infinite tree
quantum walk

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Modelling and Simulation
Mathematical Physics
Physics and Astronomy(all)

Access to Document

10.1088/1751-8121/aa8fba

Fingerprint Dive into the research topics of 'Quantum walks induced by Dirichlet random walks on infinite trees'. Together they form a unique fingerprint.

Cite this

@article{773a4343e93248e9ba801d051f9ba6bb,

title = "Quantum walks induced by Dirichlet random walks on infinite trees",

abstract = "We consider the Grover walk on infinite trees from the viewpoint of spectral analysis. From the previous work, infinite regular trees provide localization. In this paper, we give the complete characterization of the eigenspace of this Grover walk, which involves localization of its behavior and recovers the previous work. Our result suggests that the Grover walk on infinite trees may be regarded as a limit of the quantum walk induced by the isotropic random walk with the Dirichlet boundary condition at the n-th depth rather than one with the Neumann boundary condition.",

keywords = "Dirichlet condition, eigenspace, flow, infinite tree, quantum walk",

author = "Yusuke Higuchi and Etsuo Segawa",

note = "Funding Information: YuH{\textquoteright}s work was supported in part by the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (C) 25400208, (B) 24340031 and (A) 15K02055 for Challenging Exploratory Research 26610025. ES acknowledges financial support from the Grant-in-Aid for Young Scientists (B) and of the Scientific Research (B) Japan Society for the Promotion of Science (Grant Nos. 16K17637, No. 16K03939). Publisher Copyright: {\textcopyright} 2018 IOP Publishing Ltd.",

year = "2018",

month = jan,

day = "19",

doi = "10.1088/1751-8121/aa8fba",

language = "English",

volume = "51",

journal = "Journal of Physics A: Mathematical and Theoretical",

issn = "1751-8113",

publisher = "IOP Publishing Ltd.",

number = "7",

}

TY - JOUR

T1 - Quantum walks induced by Dirichlet random walks on infinite trees

AU - Higuchi, Yusuke

AU - Segawa, Etsuo

N1 - Funding Information: YuH’s work was supported in part by the Japan Society for the Promotion of Science Grant-in-Aid for Scientific Research (C) 25400208, (B) 24340031 and (A) 15K02055 for Challenging Exploratory Research 26610025. ES acknowledges financial support from the Grant-in-Aid for Young Scientists (B) and of the Scientific Research (B) Japan Society for the Promotion of Science (Grant Nos. 16K17637, No. 16K03939). Publisher Copyright: © 2018 IOP Publishing Ltd.

PY - 2018/1/19

Y1 - 2018/1/19

N2 - We consider the Grover walk on infinite trees from the viewpoint of spectral analysis. From the previous work, infinite regular trees provide localization. In this paper, we give the complete characterization of the eigenspace of this Grover walk, which involves localization of its behavior and recovers the previous work. Our result suggests that the Grover walk on infinite trees may be regarded as a limit of the quantum walk induced by the isotropic random walk with the Dirichlet boundary condition at the n-th depth rather than one with the Neumann boundary condition.

AB - We consider the Grover walk on infinite trees from the viewpoint of spectral analysis. From the previous work, infinite regular trees provide localization. In this paper, we give the complete characterization of the eigenspace of this Grover walk, which involves localization of its behavior and recovers the previous work. Our result suggests that the Grover walk on infinite trees may be regarded as a limit of the quantum walk induced by the isotropic random walk with the Dirichlet boundary condition at the n-th depth rather than one with the Neumann boundary condition.

KW - Dirichlet condition

KW - eigenspace

KW - flow

KW - infinite tree

KW - quantum walk

UR - http://www.scopus.com/inward/record.url?scp=85040929519&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85040929519&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/aa8fba

DO - 10.1088/1751-8121/aa8fba

M3 - Article

AN - SCOPUS:85040929519

VL - 51

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 7

M1 - 075303

ER -

Quantum walks induced by Dirichlet random walks on infinite trees

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Cite this