Learning magic in the Schwinger model

TL;DR

This paper uses variational neural network quantum states to analyze the non-stabilizerness, or 'magic', in the ground states of the Schwinger model, revealing how it varies with external charge separation.

Contribution

It applies a novel neural network approach to quantify quantum 'magic' in a gauge theory, advancing understanding of classical simulation complexity.

Findings

Magic content depends on charge separation.

Provides numerical estimates of stabilizer Rényi entropy.

Insights into simulation hardness of gauge theories.

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.