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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2021
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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) |
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spatial search quantum walks Dirac equation electric field Science Q Astrophysics QB460-466 Physics QC1-999 |
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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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1718412286347968512 |