Magic of discrete lattice gauge theories

TL;DR

This paper explores the quantum resources needed for simulating lattice gauge theories with discrete symmetry groups, highlighting how gauge constraints affect non-stabilizerness and the role of non-abelian gauge groups.

Contribution

It analyzes the non-stabilizerness in lattice gauge theories, showing gauge constraints do not increase quantum resource costs and relating non-abelianity to non-stabilizerness.

Findings

Gauge constraints do not increase non-stabilizerness costs.

Non-abelian gauge groups are linked to higher non-stabilizerness.

Insights into quantum simulation resource requirements for LGTs.

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.