Analysis of the confinement string in (2+1)-dimensional Quantum Electrodynamics with a trapped-ion quantum computer

Abstract Understanding strongly interacting quantum field theories is a central challenge in theoretical physics, with direct relevance to nuclear, high-energy and condensed matter systems. Here we present a quantum algorithm for compact lattice Quantum Electrodynamics in 2+1 dimensions with dynamical fermionic matter. Using a variational quantum approach, we extract the static potential between charges across Coulomb, confinement, and string-breaking regimes. Our method employs a symmetry-preserving, resource-efficient circuit to prepare ground states, enabling accurate calculations on the Quantinuum H1-1 trapped-ion device and emulator, in agreement with noiseless simulations. Moreover, we visualize the electric field flux configurations that mainly contribute to the wave function of the quantum ground state, giving insights into the mechanisms of confinement and string-breaking. These results are a promising step forward in the grand challenge of solving higher dimensional lattice gauge theory problems with quantum computing algorithms.