Noise robustness and threshold of many-body quantum magic

TL;DR

This paper studies how noise impacts the stability of quantum magic in many-body systems, revealing that certain entangled states are fragile while others exhibit robust global magic properties.

Contribution

It introduces a quantitative analysis of magic decay under noise in hypergraph states, identifying states with stable global magic despite local fragility.

Findings

High-degree gate interactions are noise-sensitive.

C^{n-1}Z states have a magic threshold decreasing with system size.

Some hypergraph states maintain non-vanishing global magic thresholds.

Abstract

Understanding quantum magic (i.e., nonstabilizerness) in many-body quantum systems is challenging but essential to the study of quantum computation and many-body physics. We investigate how noise affects magic properties in entangled many-body quantum states by quantitatively examining the magic decay under noise, with a primary aim being to understand the stability of magic associated with different kinds of entanglement structures. As a standard model, we study hypergraph states, a representative class of many-body magic states, subject to depolarizing noise. First, we show that interactions facilitated by high-degree gates are fragile to noise. In particular, the $\mathrm{C}^{n-1}Z$ state family exhibits a vanishing magic threshold of $\Theta(1/n)$. Furthermore, we demonstrate efficiently preparable families of hypergraph states without local magic but with a non-vanishing magic threshold which signifies robust magic that is entirely embedded in global entanglement. We also discuss the qudit case based on the discrete Wigner formalism.