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

2026-04-22

AI Summary

This work addresses the challenge of efficiently solving large-scale higher-order unconstrained binary optimization (HUBO) problems by proposing a Distributed Quantum Optimization Framework (DQOF). DQOF directly models high-order variable interactions using quantum circuits, circumventing the need to reduce the problem to quadratic form as required by conventional approaches. By clustering variables to construct wide yet shallow quantum circuits and integrating high-performance computing for large-scale parallelization and coordinated scheduling, the framework substantially scales up solvable problem sizes without increasing circuit depth. The method solves a 500-variable HUBO instance with high quality in 170 seconds, significantly outperforming classical algorithms, and demonstrates its practical relevance through successful application to optical metamaterial design, thereby validating the critical role of high-order interactions in real-world optimization.

Technology Category

• Search and Optimization: Distributed Search
• Machine Learning: Quantum Machine Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

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.

Problem

• higher-order optimization
• dense interactions
• large-scale problems
• quantum optimization
• HUBO

Innovation

• distributed quantum optimization
• higher-order optimization
• dense interactions
• quantum circuit clustering
• large-scale HUBO