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: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/5ef49fb5b7634d6b9020d97e725fbc73 |
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| Sumario: | 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. |
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