Dirac Spatial Search with Electric Fields

Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle to perform a spatial search on a 2D grid of <i&g...

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Autores principales: Julien Zylberman, Fabrice Debbasch
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Lenguaje:EN
Publicado: MDPI AG 2021
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spelling oai:doaj.org-article:5ef49fb5b7634d6b9020d97e725fbc732021-11-25T17:29:41ZDirac Spatial Search with Electric Fields10.3390/e231114411099-4300https://doaj.org/article/5ef49fb5b7634d6b9020d97e725fbc732021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1441https://doaj.org/toc/1099-4300Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle to perform a spatial search on a 2D grid of <i>N</i> points. As other quantum walks proposed for spatial search, these walks localise partially on the charge after a finite period of time. However, contrary to other walks, this localisation time scales as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula> for small values of <i>N</i> and tends asymptotically to a constant for larger <i>N</i>s, thus offering a speed-up over conventional methods.Julien ZylbermanFabrice DebbaschMDPI AGarticlespatial searchquantum walksDirac equationelectric fieldScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1441, p 1441 (2021)
institution DOAJ
collection DOAJ
language EN
topic spatial search
quantum walks
Dirac equation
electric field
Science
Q
Astrophysics
QB460-466
Physics
QC1-999
spellingShingle spatial search
quantum walks
Dirac equation
electric field
Science
Q
Astrophysics
QB460-466
Physics
QC1-999
Julien Zylberman
Fabrice Debbasch
Dirac Spatial Search with Electric Fields
description Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle to perform a spatial search on a 2D grid of <i>N</i> points. As other quantum walks proposed for spatial search, these walks localise partially on the charge after a finite period of time. However, contrary to other walks, this localisation time scales as <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msqrt><mi>N</mi></msqrt></semantics></math></inline-formula> for small values of <i>N</i> and tends asymptotically to a constant for larger <i>N</i>s, thus offering a speed-up over conventional methods.
format article
author Julien Zylberman
Fabrice Debbasch
author_facet Julien Zylberman
Fabrice Debbasch
author_sort Julien Zylberman
title Dirac Spatial Search with Electric Fields
title_short Dirac Spatial Search with Electric Fields
title_full Dirac Spatial Search with Electric Fields
title_fullStr Dirac Spatial Search with Electric Fields
title_full_unstemmed Dirac Spatial Search with Electric Fields
title_sort dirac spatial search with electric fields
publisher MDPI AG
publishDate 2021
url https://doaj.org/article/5ef49fb5b7634d6b9020d97e725fbc73
work_keys_str_mv AT julienzylberman diracspatialsearchwithelectricfields
AT fabricedebbasch diracspatialsearchwithelectricfields
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