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.

翻译：许多实际问题天然地适合用高阶优化（HUBO）任务来建模，其中涉及稠密的多变量交互，这对经典方法而言极具挑战性。量子优化提供了一条有前景的路径，但硬件限制以及局限于二次型表达的问题阻碍了其实用性。本文针对稠密的大规模HUBO问题，提出了一种分布式量子优化框架（DQOF）。该框架赋予量子电路在直接捕获高阶交互中的核心角色，同时由高性能计算负责大规模并行与协调。一种聚类策略使得量子电路宽度可扩展而深度不增加，从而能在近期量子硬件上高效执行。我们展示了在170秒内求解最多含500个变量的HUBO问题的高质量解，在解质量和可扩展性上显著优于传统方法。应用于光学超构材料设计时，DQOF高效发现了高性能结构，并表明高阶交互对实际优化问题至关重要。这些结果确立了DQOF作为大规模科学优化的实用且可扩展的计算范式。