From the Jaynes–Cummings model to non-abelian gauge theories: a guided tour for the quantum engineer. (13th October 2020)

• Record Type: Journal Article
• Authors: Kasper, Valentin; Juzeliūnas, Gediminas; Lewenstein, Maciej; Jendrzejewski, Fred; Zohar, Erez
• Is Part Of: New journal of physics. Volume 22:Number 10(2020:Oct.)
• Publication Date: 2020-10-13
• Subjects: lattice gauge theory -- quantum simulation -- quantum optics; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/abb961
• Languages: English
• ISSNs: 1367-2630

Abstract

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.