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

TL;DR

This paper introduces minimal non-Abelian lattice gauge theories by extending Abelian models like the Jaynes-Cummings model, demonstrating their potential for quantum simulation with current technology.

Contribution

It provides a formalism to map non-Abelian gauge theories to multi-level systems and discusses their feasible implementation on digital quantum computers.

Findings

Minimal non-Abelian gauge theories can be mapped to three or four level systems.

Upper bounds for Hilbert space dimensions of SU(2) lattice gauge theories are established.

Implementation with current digital quantum computers appears feasible.

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.