Quantum walks and discrete gauge theories

Pablo Arnault and Fabrice Debbasch
Phys. Rev. A 93, 052301 – Published 2 May 2016

Abstract

A particular example is produced to prove that quantum walks can be used to simulate full-fledged discrete gauge theories. A family of two-dimensional walks is introduced and its continuous limit is shown to coincide with the dynamics of a Dirac fermion coupled to arbitrary electromagnetic fields. The electromagnetic interpretation is extended beyond the continuous limit by proving that these discrete-time quantum walks (DTQWs) exhibit an exact discrete local U(1) gauge invariance and possess a discrete gauge-invariant conserved current. A discrete gauge-invariant electromagnetic field is also constructed and that field is coupled to the conserved current by a discrete generalization of Maxwell equations. The dynamics of the DTQWs under crossed electric and magnetic fields is finally explored outside the continuous limit by numerical simulations. Bloch oscillations and the so-called E×B drift are recovered in the weak-field limit. Localization is observed for some values of the gauge fields.

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  • Received 28 July 2015
  • Revised 16 October 2015

DOI:https://doi.org/10.1103/PhysRevA.93.052301

©2016 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & Technology

Authors & Affiliations

Pablo Arnault* and Fabrice Debbasch

  • LERMA, UMR 8112, UPMC and Observatoire de Paris, 61 Avenue de l'Observatoire, 75014 Paris, France

  • *pablo-arnault@hotmail.fr
  • fabrice.debbasch@gmail.com

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Issue

Vol. 93, Iss. 5 — May 2016

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