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arXiv:2610.41788

Query-Efficient Quantum Multi-Objective Optimization for Materials Configuration Search via Bayesian Weight Selection

Onur Boyar, Seiji Takeda, Akihiro Kosugi, Indra Priyadarsini S, Lisa Hamada, Sina Klampt

physics.comp-phquant-phSubmitted Oct 30, 2026• Announced Nov 2, 2026
arXivHTMLPDF

Abstract

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 $m\in\{3,4\}$ objectives and $n\in\{10,11,12\}$ 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.

AI Summary

The paper asks whether adaptive selection of scalarization weights can reduce the number of QAOA solves needed to approximate a multi-objective Pareto front. QAMOO solves weighted sums of Ising objectives using randomly sampled weights; BW-QAMOO replaces this sampling with Bayesian optimization over the weight simplex, leaving the quantum solver unchanged. The method fits an independent Matérn-$5/2$ Gaussian process for each objective, initialized with solves at the simplex corners. It selects subsequent weights from fresh Dirichlet candidate pools by maximizing predicted hypervolume improvement. Although framed in terms of expected hypervolume improvement, the implemented acquisition evaluates a single optimistic objective vector, $\boldsymbol{\mu}-1.5\boldsymbol{\sigma}$, rather than integrating over the posterior. Experiments use synthetic frustrated Ising instances with $n\in\{10,11,12\}$ sites and $m\in\{3,4\}$ objectives, with ten instances per setting. Each solve uses simulated depth-$2$ QAOA, COBYLA angle optimization, and 4,096 final measurement shots. Performance is measured by solves required to reach 90% or 95% of the exactly enumerated Pareto hypervolume. BW-QAMOO reduces this count by a median 33% relative to random weights, with lower means in all 12 settings. Paired Wilcoxon tests pooled across sizes report significance. Savings against an ordered uniform-grid baseline are 61–74% for four objectives. The stated limitations are small synthetic instances, no hardware execution or device-noise model, and no fitted materials interactions. Weighted-sum scalarization cannot recover unsupported non-convex front regions. Larger instances, real materials data, nonlinear scalarizations, and multicomponent-alloy encodings remain future directions.

Likely largely AI-generatedIncrementalSmall numerics onlyMissing comparisonOverclaims

Error found: The implemented acquisition uses hypervolume improvement at μ−1.5σ rather than the posterior expected hypervolume improvement claimed in the abstract and Eq. (2). The abstract's 60–74% saving against the grid applies only to the four-objective benchmarks; the three-objective savings in Table 1 are approximately 32–60%. Table 1 reports a mean of 32.3 solves for a baseline described as traversing a 28-weight grid, without explaining repetitions or how unreached targets are scored. Because only BW-QAMOO receives simplex-corner initialization, the reported comparison does not isolate the benefit of adaptation from the benefit of initialization.

Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.

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11 pages, 2 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.
The paper asks whether adaptive selection of scalarization weights can reduce the number of QAOA solves needed to approximate a multi-objective Pareto front. QAMOO solves weighted sums of Ising objectives using randomly sampled weights; BW-QAMOO replaces this sampling with Bayesian optimization over the weight simplex, leaving the quantum solver unchanged.
The method fits an independent Matérn-5/25/25/2 Gaussian process for each objective, initialized with solves at the simplex corners. It selects subsequent weights from fresh Dirichlet candidate pools by maximizing predicted hypervolume improvement. Although framed in terms of expected hypervolume improvement, the implemented acquisition evaluates a single optimistic objective vector, μ−1.5σ\boldsymbol{\mu}-1.5\boldsymbol{\sigma}μ−1.5σ, rather than integrating over the posterior.
Experiments use synthetic frustrated Ising instances with n∈{10,11,12}n\in\{10,11,12\}n∈{10,11,12} sites and m∈{3,4}m\in\{3,4\}m∈{3,4} objectives, with ten instances per setting. Each solve uses simulated depth-222 QAOA, COBYLA angle optimization, and 4,096 final measurement shots. Performance is measured by solves required to reach 90% or 95% of the exactly enumerated Pareto hypervolume. BW-QAMOO reduces this count by a median 33% relative to random weights, with lower means in all 12 settings. Paired Wilcoxon tests pooled across sizes report significance. Savings against an ordered uniform-grid baseline are 61–74% for four objectives.
The stated limitations are small synthetic instances, no hardware execution or device-noise model, and no fitted materials interactions. Weighted-sum scalarization cannot recover unsupported non-convex front regions. Larger instances, real materials data, nonlinear scalarizations, and multicomponent-alloy encodings remain future directions.
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.
We present QAMOO, a novel quantum computing framework for multi-objective portfolio optimization that simultaneously optimizes four distinct financial objectives—expected return, portfolio volatility, transaction costs, and entropy-based diversification—within a unified quantum Hamiltonian formulation. Unlike prior quantum finance approaches that treat diversification as a post-hoc penalty or encode transaction fees as scalarized weights, QAMOO embeds a Shannon entropy term directly into the quantum cost function through amplitude encoding of the portfolio weight vector. This formulation enables joint optimization over a non-convex objective landscape that cannot be faithfully reduced to a classical convex program without exponential complexity growth. The framework employs the Quantum Approximate Optimization Algorithm (QAOA) with pre-trained parameter transfer, executed on IBM Quantum hardware featuring heavy-hex topology processors with up to 156 qubits. A custom Pareto engine discovers the complete frontier of non-dominated portfolio solutions, enabling investors to select allocations matching their individual risk preferences. Empirical evaluation on a multi-asset portfolio demonstrates a 0.21% hypervolume improvement over the state-of-the-art classical multi-objective evolutionary algorithm (NSGA-III), while requiring approximately 30% fewer optimization cycles. The quantum-derived portfolios exhibit 23% lower turnover-adjusted volatility after accounting for realistic transaction fees. QAMOO establishes a new research direction at the intersection of quantum computing and quantitative finance, providing a hardware-aware optimization paradigm that integrates entropy-driven diversification directly into quantum annealing and gate-model formulations.
In quantum optimization approaches, such as Quantum Approximate Optimization Algorithms (QAOA) and quantum annealing, the optimal solution is obtained by minimizing an energy function that encapsulates the optimization problem. In the case of multi-objective optimization problems, the trade-offs between competing objective functions are managed by adjusting a set of weight parameters. This paper investigates two parameter-tuning techniques, a grid search and Bayesian optimization, applied to a computational resource allocation problem with multiple objective functions. We compare the performance of these methods by evaluating the efficiency, diversity, and uniformity of the Pareto solutions derived from the optimization results.
The quantum approximate optimization algorithm (QAOA) is a leading variational approach to combinatorial optimization, but its practical performance depends strongly on objective design, parameter search, and shot allocation. We present a resource-efficient QAOA framework that uses the cut value of the most probable measured bitstring as the optimization objective, combines it with Bayesian optimization, and adaptively allocates shots using dual criteria based on mode confidence and normalized cut-value variance. Numerical experiments on 3-regular MaxCut show that, for both unweighted and weighted instances, the proposed scheme achieves discrete-solution quality comparable to that of the conventional expectation-based objective while typically requiring fewer total shots to reach the same final mode accuracy. These results indicate that reorganizing QAOA around the maximum-probability bitstring provides an effective route to improving practical performance under limited measurement budgets.
The goal of multi-objective optimization is to understand optimal trade-offs between competing objective functions by finding the Pareto front, that is, the set of all Pareto-optimal solutions, where no objective can be improved without degrading another one. Multi-objective optimization can be challenging classically, even if the corresponding single-objective optimization problems are efficiently solvable. Thus, multi-objective optimization represents a compelling problem class to analyze with quantum computers. Here we use a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of certain multi-objective weighted maximum-cut problems. We demonstrate its performance on an IBM Quantum computer, as well as with matrix product state numerical simulation, and show its potential to outperform classical approaches. This study explores the use of quantum computing to address multi-objective optimization challenges. By using a low-depth quantum approximate optimization algorithm to approximate the optimal Pareto front of multi-objective weighted max-cut problems, the authors demonstrate promising results—both in simulation and on IBM Quantum hardware—surpassing classical approaches.
An important task in multi-objective optimization is generating the Pareto front -- the set of all Pareto-optimal compromises among multiple objective functions applied to the same set of variables. Since this task can be computationally intensive even for small problems, it is a natural target for quantum optimization. Indeed, this problem was recently approached using the quantum approximate optimization algorithm (QAOA) on an IBM gate-model processor. Here we compare these QAOA results with quantum annealing on the same two input problems, using the same methodology. We find that quantum annealing vastly outperforms not just QAOA run on the IBM processor, but all classical and quantum methods analyzed in the previous study. On the harder problem, quantum annealing improves upon the best known Pareto front. This small study reinforces the promise of quantum annealing in multi-objective optimization.