Towards simulating 2D effects in lattice gauge theories on a quantum computer

Abstract

Quantum Field Theories (QFTs) are the most successful theories for describing nature at its most fundamental level. Despite the fact that QFTs are capable of predicting a wide range of phenomena, obtaining solutions to QFTs in parameter regimes where perturbation theory cannot be applied remains a challenge. We propose an experimental scheme to perform quantum simulations of two-dimensional Abelian lattice gauge theories using contemporary quantum devices, paving the way to reach beyond the capabilities of classical simulations. We consider quantum electrodynamics and examine the basic building block of the two-dimensional lattice to study non-trivial magnetic field effects, which are absent in one-dimensional systems. By imposing periodic boundary conditions, we extend the scope of our work to include an infinite 2D structure. Our protocol uses a variational quantum-classical approach to relax the hardware requirements for capturing the intricate many-body interactions that naturally arise in the formulation of gauge-invariant effective field theories. Although we remain platform-independent, we also provide a detailed example of implementation on state-of-the-art trapped ion quantum devices, which can be generalized to other platforms. The techniques for simulating QFTs presented here, combined with advancements in quantum hardware, pose the potential to address longstanding questions in high energy physics.