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

Gauge theories are the most successful theories for describing nature, but obtaining numerical solutions is challenging. We propose a quantum simulation to study properties in two-dimensional quantum electro-dynamics (2D QED). Our protocols allow in principle scaling up to large lattices and offer the perspective to connect the lattice simulation to low energy observable quantities in the continuum theory. By including both dynamical matter and a non-minimal gauge field truncation, we provide the opportunity to observe 2D effects on present day quantum hardware. More specifically, we present two Variational Quantum Eigensolver (VQE) based protocols for the study of magnetic field effects, and for taking an important first step towards computing the running coupling of QED. For both instances, we include variational quantum circuits, which we apply to trapped ion quantum computers. We simulate the proposed VQE experiments to calculate the required measurement budget. While this feasibility analysis is done for trapped ions, our approach can be adapted to other platforms. The techniques presented here pave the way for reaching beyond the capabilities of classical simulations by extending our framework to include fermionic potentials or topological terms.