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arXiv:2607.18848

Quantum-Enhanced Multi-Objective Optimization

Maolin Luo, Jiapei Zhuang, Zuoheng Zou, Man-Hong Yung

quant-phSubmitted Jul 21, 2026• Announced Jul 22, 2026• 0 citations• Revised Sep 2, 2026 (v2)
v1 · Jul 21, 2026v2 · Sep 2, 2026
arXivHTMLPDF

Abstract

Multi-objective combinatorial optimization requires identifying Pareto-optimal trade-off solutions among conflicting objectives, often making it more demanding than its single-objective counterpart. Although quantum multi-objective optimization methods have begun to emerge, most existing quantum optimization workflows are still built around single-objective or fixed-scalarization settings. Building on existing weighted-sum QAOA approaches to quantum multi-objective optimization, we propose QEMOO, a quantum-enhanced multi-objective optimization framework that combines Pareto-based selection and warm-started QAOA sampling in a multi-round protocol under the same total shot budget. We further introduce a PBI-inspired adaptive direction-update scheme to improve coverage in strongly conflicting benchmark regimes. Across three benchmark stages, QEMOO improves Pareto-front hypervolume over the single-pass weighted-sum QAOA baseline under matched shot budgets, suggesting a practical route toward shot-efficient quantum-assisted multi-objective optimization and its future applications.

Comments
20 pages, 13 figures

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Materials design is a multi-objective problem, and recent advances in quantum optimization make it possible to bring quantum solvers to bear on such problems. The realistic near-term win, though, is not raw quantum advantage but making an expensive, noisy quantum solver usable by spending its calls wisely. Quantum Approximate Multi-Objective Optimization (QAMOO) traces a Pareto front by solving a family of scalarized Ising problems, one per objective-weight vector, with QAOA --- but chooses those weights \emph{non-adaptively}, sampling them at random, blind to what it has already found. We recast weight selection as \emph{multi-objective Bayesian optimization}: our method, BW-QAMOO (Bayes-Weighted QAMOO), picks each next weight by expected hypervolume improvement (EHVI) under a Gaussian-process (GP) surrogate over the weight-to-objective map. On a frustrated alloy-configuration benchmark across m∈{3,4}m\in\{3,4\}m∈{3,4} objectives and n∈{10,11,12}n\in\{10,11,12\}n∈{10,11,12} sites, BW-QAMOO reaches the same Pareto hypervolume as QAMOO's random sampling with a median 33% fewer scalarized solves across the 90/95\% targets and 60--74\% fewer than a uniform-grid baseline), on a genuine (simulated) QAOA solver; a paired Wilcoxon test confirms the saving is significant, and the advantage grows with the objective count m as the weight simplex expands and blind sampling wastes more of the budget. This is a \emph{query-efficiency} result, and we close with the open challenges on the path to real alloy data and hardware.
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