Quantum simulation of fermionic, non-Abelian lattice gauge theories in (2 + 1)D with intrinsic gauge protection

Understanding and simulating non-Abelian quantum spin-liquids and dimer models is an open challenge in the condensed matter and high energy physics landscape. Recent advancements in the field of quantum simulations have significantly expanded its potential for applications, particularly in the context of lattice gauge theories (LGTs). Maintaining gauge invariance throughout a simulation remains a critical challenge, especially for large-scale non-Abelian LGTs.

We propose a novel approach to simulate non-Abelian U(N) LGTs with dynamical fermionic matter in (2+1) dimensions. Our method enhances the reliability of the simulation by embedding the target states within a robust energy subspace, where rishon-number violating terms are energetically suppressed, and gauge protection is maintained through spin-independent interactions present in SU(N) Hubbard models. We present a comprehensive framework detailing the required interactions and lattice initialization and we study a minimal setup that allows one to simulate dynamics ubiquitous to the non-Abelian gauge structure. Additionally, we propose two experimental platforms -- utilizing ultracold alkaline-earth-like atoms and Rydberg-atoms -- to implement these models, enabling the quantum simulation of large-scale non-Abelian gauge theories in near-term experiments.