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

• URL: http://arxiv.org/abs/2006.01258v2
• Date: Thu, 5 Nov 2020 10:01:33 GMT
• Title: From the Jaynes-Cummings model to non-Abelian gauge theories: a guided tour for the quantum engineer
• Authors: Valentin Kasper, Gediminas Juzeliunas, Maciej Lewenstein, Fred Jendrzejewski, Erez Zohar
• Abstract summary: Non-Abelian lattice gauge theories play a central role in high energy physics, condensed matter and quantum information. We introduce the necessary formalism in well-known Abelian gauge theories, such as the Jaynes-Cumming model. We show that certain minimal non-Abelian lattice gauge theories can be mapped to three or four level systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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