Iterative Optimization with Partial Convergence Guarantees on Neutral Atom Quantum Computers

TL;DR

This paper presents Lp-Quts, a hybrid quantum-classical algorithm that leverages neutral atom quantum computers within a cutting-plane framework to solve large MWIS problems with performance guarantees.

Contribution

It introduces a novel hybrid approach integrating quantum sampling into classical optimization, providing convergence guarantees for certain graph classes.

Findings

Lp-Quts achieves solutions within 5-10% of optimality on 300-vertex instances.

The method outperforms direct quantum protocols and greedy algorithms under equal sampling budgets.

Simulated annealing remains the best sample-based solver at this scale.

Abstract

Neutral atom quantum computers (NAQCs) have emerged as a promising platform for solving the maximum weighted independent set (MWIS) problem. However, analog quantum approaches face two key limitations: constraints of the atomic layout on realizable graph geometries and the absence of performance guarantees. We introduce Lp-Quts, a hybrid quantum-classical framework that integrates an NAQC sampler into a classical cutting-plane algorithm. At each iteration, a relaxed linear program (RLP) bounds the MWIS and induces a reduced graph from which independent sets are sampled using an analog quantum sampler. A novel sample-informed separation problem guides odd-cycle cut selection and accelerates convergence. For t-perfect graphs, Lp-Quts inherits polynomial-time convergence guarantees from the classical theory of cutting planes. We evaluate our approach on instances with up to 300 vertices -- a scale that exceeds the capabilities of current NAQC hardware. In this regime, Lp-Quts reaches solutions within 5--10\% of optimality, outperforming direct analog quantum protocols and greedy baselines under equal sampling budgets. As expected, simulated annealing remains the strongest sample-based solver at this scale. These results demonstrate how quantum samplers can be effectively embedded within classical optimization frameworks to deliver near-optimal solutions with reduced quantum resources while preserving formal guarantees.