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

TL;DR

This paper proposes a feasible cold-atom quantum simulator for 3+1D U(1) lattice gauge theory with dynamical matter, demonstrating its accuracy and robustness through tensor network simulations and error mitigation techniques.

Contribution

It introduces a scalable experimental design for simulating 3+1D lattice gauge theories, including gauge protection and error mitigation methods, advancing quantum simulation of high-energy physics.

Findings

Excellent agreement with ideal gauge theory in simulations

Effective analog quantum error mitigation developed

Paves way for realistic 3+1D lattice gauge theory simulators

Abstract

The stated overarching goal of the highly active field of quantum simulation of high-energy physics (HEP) is to achieve the capability to study \textit{ab-initio} real-time microscopic dynamics of $3+1$D 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 \textit{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 \textit{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 $3+1$D lattice gauge theories that can probe regimes well beyond classical simulability.