Full revivals in 2D quantum walks

M. Štefaňák, B. Kollár, T. Kiss, I. Jex

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Citations (Scopus)

Abstract

Recurrence of a random walk is described by the Pólya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full revival of its quantum state. Localization for two-dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show, on the example of the 2D Grover walk, that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference, which has no counterpart in classical random walks.

Original languageEnglish
Title of host publicationPhysica Scripta T
VolumeT140
DOIs
Publication statusPublished - 2010
Event16th Central European Workshop on Quantum Optics, CEWQO2009 - Turku, Finland
Duration: May 23 2009May 27 2009

Other

Other16th Central European Workshop on Quantum Optics, CEWQO2009
CountryFinland
CityTurku
Period5/23/095/27/09

Fingerprint

random walk
interference
cycles

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Štefaňák, M., Kollár, B., Kiss, T., & Jex, I. (2010). Full revivals in 2D quantum walks. In Physica Scripta T (Vol. T140). [014035] https://doi.org/10.1088/0031-8949/2010/T140/014035

Full revivals in 2D quantum walks. / Štefaňák, M.; Kollár, B.; Kiss, T.; Jex, I.

Physica Scripta T. Vol. T140 2010. 014035.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Štefaňák, M, Kollár, B, Kiss, T & Jex, I 2010, Full revivals in 2D quantum walks. in Physica Scripta T. vol. T140, 014035, 16th Central European Workshop on Quantum Optics, CEWQO2009, Turku, Finland, 5/23/09. https://doi.org/10.1088/0031-8949/2010/T140/014035
Štefaňák M, Kollár B, Kiss T, Jex I. Full revivals in 2D quantum walks. In Physica Scripta T. Vol. T140. 2010. 014035 https://doi.org/10.1088/0031-8949/2010/T140/014035
Štefaňák, M. ; Kollár, B. ; Kiss, T. ; Jex, I. / Full revivals in 2D quantum walks. Physica Scripta T. Vol. T140 2010.
@inproceedings{1a4c40c6572948d9bbd815fd73f56167,
title = "Full revivals in 2D quantum walks",
abstract = "Recurrence of a random walk is described by the P{\'o}lya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full revival of its quantum state. Localization for two-dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show, on the example of the 2D Grover walk, that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference, which has no counterpart in classical random walks.",
author = "M. Štefaň{\'a}k and B. Koll{\'a}r and T. Kiss and I. Jex",
year = "2010",
doi = "10.1088/0031-8949/2010/T140/014035",
language = "English",
volume = "T140",
booktitle = "Physica Scripta T",

}

TY - GEN

T1 - Full revivals in 2D quantum walks

AU - Štefaňák, M.

AU - Kollár, B.

AU - Kiss, T.

AU - Jex, I.

PY - 2010

Y1 - 2010

N2 - Recurrence of a random walk is described by the Pólya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full revival of its quantum state. Localization for two-dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show, on the example of the 2D Grover walk, that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference, which has no counterpart in classical random walks.

AB - Recurrence of a random walk is described by the Pólya number. For quantum walks, recurrence is understood as the return of the walker to the origin, rather than the full revival of its quantum state. Localization for two-dimensional quantum walks is known to exist in the sense of non-vanishing probability distribution in the asymptotic limit. We show, on the example of the 2D Grover walk, that one can exploit the effect of localization to construct stationary solutions. Moreover, we find full revivals of a quantum state with a period of two steps. We prove that there cannot be longer cycles for a four-state quantum walk. Stationary states and revivals result from interference, which has no counterpart in classical random walks.

UR - http://www.scopus.com/inward/record.url?scp=78650900347&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650900347&partnerID=8YFLogxK

U2 - 10.1088/0031-8949/2010/T140/014035

DO - 10.1088/0031-8949/2010/T140/014035

M3 - Conference contribution

AN - SCOPUS:78650900347

VL - T140

BT - Physica Scripta T

ER -