From the Jaynes-Cummings model to non-abelian gauge theories: A guided tour for the quantum engineer

Valentin Kasper*, Gediminas Juzeliūnas, Maciej Lewenstein, Fred Jendrzejewski, Erez Zohar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


The design of quantum many body systems, which have to fulfill an extensive number of constraints, appears as a formidable challenge within the field of quantum simulation. Lattice gauge theories are a particular important class of quantum systems with an extensive number of local constraints and play a central role in high energy physics, condensed matter and quantum information. Whereas recent experimental progress points towards the feasibility of large-scale quantum simulation of abelian gauge theories, the quantum simulation of non-abelian gauge theories appears still elusive. In this paper we present minimal non-abelian lattice gauge theories, whereby we introduce the necessary formalism in well-known abelian gauge theories, such as the Jaynes-Cumming model. In particular, we show that certain minimal non-abelian lattice gauge theories can be mapped to three or four level systems, for which the design of a quantum simulator is standard with current technologies. Further we give an upper bound for the Hilbert space dimension of a one dimensional SU(2) lattice gauge theory, and argue that the implementation with current digital quantum computer appears feasible.

Original languageAmerican English
Article number103027
JournalNew Journal of Physics
Issue number10
StatePublished - Oct 2020

Bibliographical note

Publisher Copyright:
© 2020 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.


  • lattice gauge theory
  • quantum optics
  • quantum simulation


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