Magic of discrete lattice gauge theories

TL;DR

The paper investigates non-stabilizerness as a quantum-resource for simulating lattice gauge theories with discrete gauge groups. By formalizing Stabilizer Entropy (SE) and its linear variant (LSE) and introducing the SE gap, it analyzes the resource cost of projecting onto the gauge-invariant subspace. Analytic results for abelian cases show zero SE gap for $Z_2$ and general $Z_l$ lattices, while a non-abelian $SU(2)$ example yields a nonzero gap ($\Delta M=8/45$ on a single site), highlighting a fundamental difference in simulability between abelian and non-abelian gauge theories. The findings suggest a deep connection between non-commutativity and computational resource demands, with implications for resource-aware quantum simulations of gauge theories on near-term hardware.

Abstract

Simulation of quantum field theories and fundamental interactions are one of the most challenging tasks in modern particle physics. Classical computers generally fail to reproduce accurate results when it comes to strongly coupled theories such as QCD. Recent developments in quantum technologies open up the possibility of simulating such physical regimes by using quantum computers. In this paper, we study the quantum resource related to the simulability of a quantum theory, i.e. non-stabilizerness for Lattice Gauge Theory (LGT) with discrete symmetry gauge groups. We show that enforcing gauge constraints for $\mathbb{Z}_l$ LGTs has no cost in terms of this resource and discuss the relation between non-abelianity of the gauge group with the average non-stabilizerness of the gauge invariant Hilbert space.