Exploring the impact of graph locality for the resolution of MIS with neutral atom devices

TL;DR

This paper investigates how the spatial locality of graphs affects solving the Maximum Independent Set problem using neutral atom quantum devices, advancing the encoding of complex graphs beyond 2D limitations.

Contribution

It introduces 3D atom arrangements to encode more complex graph classes, surpassing previous 2D limitations and enabling quantum solutions for problems without classical approximation schemes.

Findings

Experimental results demonstrate feasibility of 3D embeddings.

Theoretical analysis shows potential for tackling complex graph classes.

Progress towards quantum solutions for classically hard combinatorial problems.

Abstract

In the past years, many quantum algorithms have been proposed to tackle hard combinatorial problems. In particular, the Maximum Independent Set (MIS) is a known NP-hard problem that can be naturally encoded in Rydberg atom arrays. By representing a graph with an ensemble of neutral atoms one can leverage Rydberg dynamics to naturally encode the constraints and the solution to MIS. However, the classes of graphs that can be directly mapped ``vertex-to-atom" on standard devices with 2D capabilities are currently limited to Unit-Disk graphs. In this setting, the inherent spatial locality of the graphs can be leveraged by classical polynomial-time approximation schemes (PTAS) that guarantee an $\epsilon$-approximate solution. In this work, we build upon recent progress made for using 3D arrangements of atoms to embed more complex classes of graphs. We report experimental and theoretical results which represent important steps towards tackling combinatorial tasks on quantum computers for which no classical efficient $\varepsilon$-approximation scheme exists.