Non-Abelian $SU(2)$ Lattice Gauge Theories in Superconducting Circuits

TL;DR

This paper proposes a minimal, resource-efficient superconducting circuit-based digital quantum simulator for non-Abelian $SU(2)$ gauge theories, enabling experimental exploration of complex gauge dynamics.

Contribution

It introduces a novel minimal implementation of non-Abelian gauge models using quantum link models and superconducting circuits, reducing resource demands.

Findings

Designs two superconducting architectures for simulation

Estimates experimental requirements for realization

Establishes a pathway for non-Abelian physics simulation

Abstract

We propose a digital quantum simulator of non-Abelian pure-gauge models with a superconducting circuit setup. Within the framework of quantum link models, we build a minimal instance of a pure $SU(2)$ gauge theory, using triangular plaquettes involving geometric frustration. This realization is the least demanding, in terms of quantum simulation resources, of a non-Abelian gauge dynamics. We present two superconducting architectures that can host the quantum simulation, estimating the requirements needed to run possible experiments. The proposal establishes a path to the experimental simulation of non-Abelian physics with solid-state quantum platforms.