Work

Quantum Hypergraph Partitioning

Year: 2026

Type: conference-paper

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.

DOI: 10.1145/3811628.3811836

Authors: Yiran Li, Y. Batuhan Yilmaz, Michael Silver, Zachary Vernec, Hans-Arno Jacobsen

Institution: University of Toronto

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Funders: Canada Research Chairs, Natural Sciences and Engineering Research Council of Canada

Awards: G1650159453, G8932819803

OpenAlex ID: W7160442012

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