Distributed Quantum Optimization for Large-Scale Higher-Order Problems with Dense Interactions

TL;DR

The paper introduces a distributed quantum optimization framework (DQOF) that efficiently solves large-scale higher-order problems with dense interactions, demonstrating superior performance and scalability on real-world applications.

Contribution

Develops a novel distributed quantum optimization framework that captures higher-order interactions directly and scales to large problems using a clustering strategy and near-term quantum hardware.

Findings

Successfully solved HUBOs with up to 500 variables in 170 seconds.

Outperformed conventional methods in solution quality and scalability.

Applied to optical metamaterial design, discovering high-performance structures.

Abstract

Many real-world problems are naturally formulated as higher-order optimization (HUBO) tasks involving dense, multi-variable interactions, which are challenging to solve with classical methods. Quantum optimization offers a promising route, but hardware constraints and limitations to quadratic formulations have hampered their practicality. Here, we develop a distributed quantum optimization framework (DQOF) for dense, large-scale HUBO problems. DQOF assigns quantum circuits a central role in directly capturing higher-order interactions, while high-performance computing orchestrates large-scale parallelism and coordination. A clustering strategy enables wide quantum circuits without increasing depth, allowing efficient execution on near-term quantum hardware. We demonstrate high-quality solutions for HUBOs up to 500 variables within 170 seconds, significantly outperforming conventional approaches in solution quality and scalability. Applied to optical metamaterial design, DQOF efficiently discovers high-performance structures and shows that higher-order interactions are important for practical optimization problems. These results establish DQOF as a practical and scalable computational paradigm for large-scale scientific optimization.