Nonstabilizerness in U(1) lattice gauge theory

TL;DR

This paper investigates nonstabilizerness, a quantum resource measuring state complexity, in a 1D U(1) lattice gauge theory, revealing its extensive nature and sensitivity to critical points, with implications for quantum simulation costs.

Contribution

It provides the first detailed analysis of nonstabilizerness in lattice gauge theories, highlighting its volume dependence and criticality sensitivity, distinct from entanglement.

Findings

Nonstabilizerness is extensive with volume.

It shows discontinuities at critical points.

Provides bounds on quantum resources for lattice gauge simulations.

Abstract

We present a thorough investigation of nonstabilizerness - a fundamental quantum resource that quantifies state complexity within the framework of quantum computing - in a one-dimensional U(1) lattice gauge theory. We show how nonstabilizerness is always extensive with volume, and has no direct relation to the presence of critical points. However, its derivatives typically display discontinuities across the latter: This indicates that nonstabilizerness is strongly sensitive to criticality, but in a manner that is very different from entanglement (that, typically, is maximal at the critical point). Our results indicate that error-corrected simulations of lattice gauge theories close to the continuum limit have similar computational costs to those at finite correlation length and provide rigorous lower bounds for quantum resources of such quantum computations.