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Quantum Information Processing
Erschienen in: Quantum Information Processing 12/2020

01.11.2020

A systematic method to building Dirac quantum walks coupled to electromagnetic fields

verfasst von: Gareth Jay, Fabrice Debbasch, Jingbo Wang

Erschienen in: Quantum Information Processing | Ausgabe 12/2020

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Abstract

A quantum walk whose continuous limit coincides with Dirac equation is usually called a Dirac quantum walk (DQW). A new systematic method to build DQWs coupled to electromagnetic (EM) fields is introduced and put to test on several examples of increasing difficulty. It is first used to derive the EM coupling of a 3D walk on the cubic lattice. Recently introduced DQWs on the triangular lattice are then re-derived, showing for the first time that these are the only DQWs that can be defined with spinors living on the vertices of these lattices. As a third example of the method’s effectiveness, a new 3D walk on a parallelepiped lattice is derived. As a fourth, negative example, it is shown that certain lattices like the rhombohedral lattice cannot be used to build DQWs. The effect of changing representation in the Dirac equation is also discussed. Furthermore, we show the simulation of the established DQWs can be efficiently implemented on a quantum computer.
Vorheriger Artikel Fast preparation of Bell state and W state with Rydberg superatom
Nächster Artikel N-qudit SLOCC equivalent W states are determined by their bipartite reduced density matrices with tree form

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Fußnoten
1
Our third direction across this lattice will still be the same as the x-direction in the square lattice.
 
2
This works similarly for b and d.
 
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Metadaten
Titel
A systematic method to building Dirac quantum walks coupled to electromagnetic fields
verfasst von
Gareth Jay
Fabrice Debbasch
Jingbo Wang
Publikationsdatum
01.11.2020
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 12/2020
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-020-02933-w

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