Learning magic in the Schwinger model

Abstract: We demonstrate the use of variational neural network quantum states to study non-stabilizerness in qubit-regularised quantum field theory. Applying the methodology recently introduced by Sinibaldi et al., we numerically compute the stabilizer R\'enyi entropy of ground states of the Schwinger model with a topological term. We examine how the magic content of these states depends on the separation between external probe charges, providing insight into the classical hardness of simulating gauge theories with non-trivial infrared structure.