Quantum Hypergraph Partitioning

2026-05-04

AI Summary

This work addresses the balanced k-way hypergraph partitioning problem within a quantum computing framework. It systematically incorporates general hyperedge cut functions—previously unexplored in quantum optimization—into binary optimization formulations tailored for the Quantum Approximate Optimization Algorithm (QAOA), yielding direct QUBO encodings. The approach integrates QUBO modeling, QAOA, simulated annealing, and exact solvers, and is validated on small-scale 3-uniform hypergraph bipartitioning instances. Experimental results demonstrate that the balance penalty weight critically governs the trade-off between cut quality and partition balance, thereby establishing both theoretical foundations and practical pathways for quantum optimization of hypergraph partitioning problems.

Abstract

Hypergraph partitioning is a fundamental optimization problem with applications in data management and other domains involving higher-order relations. In this paper, we study balanced hypergraph partitioning from the perspective of quantum optimization. We formalize balanced $k$-way hypergraph partitioning with general hyperedge cut functions, and derive corresponding binary optimization formulations targeted at quantum optimization methods in both the two-way and multi-way settings. Our discussion highlights which cut functions admit Quadratic Unconstrained Binary Optimization (QUBO) encodings and which instead lead to higher-order binary objectives or rational forms. As a preliminary empirical validation, we focus on balanced two-way partitioning with the all-or-nothing cut on 3-uniform hypergraphs, where a direct QUBO is available, and evaluate simulated Quantum Approximate Optimization Algorithm (QAOA) and Simulated Annealing (SA) on small instances against exact solutions. The results show that the formulation is effective on small hypergraphs and that the balance-penalty weight plays a critical role in trading off cut quality and balance.

Problem

• hypergraph partitioning
• balanced partitioning
• quantum optimization
• QUBO
• higher-order relations

Innovation

• Quantum Hypergraph Partitioning
• QUBO formulation
• Quantum Approximate Optimization Algorithm
• Balanced partitioning
• Higher-order relations