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Quantum simulation of fermionic non-Abelian lattice gauge theories in (2+1) dimensions with built-in gauge protection

Gaia De Paciani1,2,*, Lukas Homeier3,4,1,2, Jad C. Halimeh5,1,2, Monika Aidelsburger5,1,2, and Fabian Grusdt1,2

  • *Contact author: gaia.paciani@lmu.de
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Phys. Rev. A 113, 063327 – Published 25 June, 2026

DOI: https://doi.org/10.1103/ngk1-9zy3

Abstract

Recent advancements in the field of quantum simulation have significantly expanded the potential for applications, particularly in the context of lattice gauge theories (LGTs). Maintaining gauge invariance throughout a simulation remains a central challenge, especially for large-scale non-Abelian LGTs with dynamical matter, which are particularly complex in terms of engineering for experiments. Gauge-symmetry breaking is inevitable in established rishon-based schemes for alkaline-earth-like atoms (AELAs) and controlling the magnitude of its effect is an open challenge. Here we first construct a minimal model to quantum simulate non-Abelian LGTs ensuring that the gauge constraints are met and explicitly derive their unambiguous non-Abelian nature. Second, we present a proposal for a gauge protection scheme using native interactions in AELAs enabling the simulation of toy models of non-Abelian U(2) LGTs with dynamical fermionic matter in (2+1) dimensions on large scales. Due to the simplicity of the gauge protection mechanism, based on a Zeeman shift in combination with superexchange interactions, our scheme can be naturally included in other rishon-based quantum simulation protocols. Third, we extend our approach to a fully scalable, hybrid digital-analog simulator for U(N) LGTs based on Rydberg AELA with variable rishon number. The proposed general mechanism for gauge protection provides a promising path towards the simulation of non-Abelian LGTs relevant to particle physics.

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Phys. Rev. A 113, 063327– Published 25 June, 2026
  • Received 30 June 2025
  • Revised 8 April 2026
  • Accepted 5 June 2026
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