Overcoming the sign-problem with variational Monte-Carlo methods: a study of (2+1)-dimensional compact quantum electrodynamics

Studying lattice gauge theories with Monte-Carlo simulations based upon importance sampling has been a major success over several decades. Unfortunately, some theories of interest are affected by the sign problem which prevents the use of the aforementioned method so that certain questions cannot be addressed (e.g. finite chemical potential scenarios or real-time dynamics). Based on the Hamiltonian formulation of lattice gauge theory we develope a variational ansatz that is evaluated with Monte-Carlo methods but inherently sign problem free and study as a first step towards higher-dimensional gauge theories (2+1)-dimensional compact QED. First, we investigate real-time dynamics after various global quenches, with a focus on confinement and the equilibration of expectation values. To verify the ansatz, we benchmark for small system sizes against exact diagonalization. Secondly, we study (2+1)-dimensional compact QED with multiple flavors of massless fermions. We benchmark against standard Monte-Carlo simulations at an even number of fermion flavors where the sign problem is absent and then study the theory at an odd number of fermion flavors. We also discuss how these results can help in the design of future quantum simulators for gauge theories.