Scalable cold-atom quantum simulator of a 3+1D U(1) lattice gauge theory with dynamical matter

The stated overarching goal of the highly active field of quantum simulation of high-energy physics (HEP) is to achieve the capability to study ab-initio real-time microscopic dynamics of 3+1D quantum chromodynamics (QCD). However, existing experimental realizations and theoretical proposals for future ones have remained restricted to one or two spatial dimensions. Here, we take a big step towards this goal by proposing a concrete experimentally feasible scalable cold-atom quantum simulator of a U(1) quantum link model of quantum electrodynamics (QED) in three spatial dimensions, employing linear gauge protection to stabilize gauge invariance. Using tree tensor network simulations, we benchmark the performance of this quantum simulator through near- and far-from-equilibrium observables, showing excellent agreement with the ideal gauge theory. Additionally, we introduce a method for analog quantum error mitigation that accounts for unwanted first-order tunneling processes, vastly improving agreement between quantum-simulator and ideal-gauge-theory results. Our findings pave the way towards realistic quantum simulators of 3+1D lattice gauge theories that can probe regimes well beyond classical simulability.