Quantum annealing has the potential to provide practical quantum advantage for complex optimization tasks. Here, we present a systematic assessment of an integrated factorization-machine and quantum-annealing workflow (FM+QA) for a technologically relevant application: multi-objective Pareto optimization in metal up-cycling through alloy design. To address the non-convex nature of the Pareto front, we employ the recently proposed data-driven Tchebycheff scalarization (DDTS) scheme. Our results show that FM+QA extends the applicability of QUBO-based optimization to data-driven materials discovery problems with multiple competing objectives. In particular, we analyze the scaling behavior of the approach and compare quantum annealing with classical simulated annealing using both regular binary encoding and one-hot encoding. Finally, we provide a critical perspective on the problem sizes and encoding strategies for which quantum-annealing-based optimization may become practically beneficial in the near future.
Quantum annealing has the potential to provide practical quantum advantage for complex optimization tasks. Here, we present a systematic assessment of an integrated factorization-machine and quantum-annealing workflow (FM+QA) for a technologically relevant application: multi-objective Pareto optimization in metal up-cycling through alloy design. To address the non-convex nature of the Pareto front, we employ the recently proposed data-driven Tchebycheff scalarization (DDTS) scheme. Our results show that FM+QA extends the applicability of QUBO-based optimization to data-driven materials discovery problems with multiple competing objectives. In particular, we analyze the scaling behavior of the approach and compare quantum annealing with classical simulated annealing using both regular binary encoding and one-hot encoding. Finally, we provide a critical perspective on the problem sizes and encoding strategies for which quantum-annealing-based optimization may become practically beneficial in the near future.
Here, we present two complementary approaches that advance quadratic unconstrained binary optimization (QUBO) toward practical use in data-driven materials design and other real-valued black-box optimization tasks. First, we introduce a simple yet powerful preprocessing scheme that, when applied to a machine-learned QUBO model, entirely removes system-level equality constraints by construction. This makes cumbersome soft-penalty terms obsolete, simplifies QUBO formulation, and substantially accelerates solution search. Second, we develop a multi-objective optimization strategy inspired by Tchebycheff scalarization that is compatible with non-convex objective landscapes and outperforms existing QUBO-based Pareto front methods. We demonstrate the effectiveness of both approaches using a simplified model of a multi-phase aluminum alloy design problem, highlighting significant gains in efficiency and solution quality. Together, these methods broaden the applicability of QUBO-based optimization and provide practical tools for data-driven materials discovery and beyond.
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.
Data scarcity remains a central challenge in materials discovery, where finding meaningful descriptors and tuning models for generalization is critical but inherently a discrete optimization problem prone to multiple local minima confounding the true optimal state. Classical methods often get trapped in these minima, while quantum annealing can escape them via quantum fluctuations, including tunneling, that overcome narrow energy barriers. We present a quantum-assisted machine-learning (QaML) framework that employs quantum annealing to address these combinatorial optimization challenges through feature selection, support-vector training formulated in QUBO form for classification and regression, and a new QUBO-based neural-network pruning formulation. Recursive batching enables quantum annealing to handle large feature spaces beyond current qubit limits, while quantum-pruned networks exhibit superior generalization over classical methods, suggesting that quantum annealing preferentially samples flatter, more stable regions of the loss landscape. Applied to high-entropy alloys (HEAs), a data-limited but compositionally complex testbed, the framework integrates models for fracture-strain classification and yield-strength regression under physics-based constraints. The framework identified and experimentally validated Al8Cr38Fe50Mn2Ti2 (at.%), a single-phase BCC alloy exhibiting a 0.2 % yield strength of 568 MPa, greater than 40 % compressive strain without fracture, and a critical current density in reducing acid nearly an order of magnitude lower than 304 stainless steel. These results establish QA as a practical route to overcome classical optimization limits and accelerate materials discovery.
With an increase in the complexity of society, solving multi-objective optimization problems (MOPs) has become crucial. In this study, we introduced a novel method called “quadratic unconstrained binary optimization based on the weighted normal” for solving MOPs using Ising machines, such as quantum annealing and digital annealer (DA), in the field of combinatorial optimization. The proposed method applies the penalty-based boundary intersection method to Ising machines under a setting limited to linear objective functions and maximizes the speed and performance of the DA, which is a quadratic unconstrained binary optimization-specific solver. We demonstrated the effectiveness of the proposed method by solving a real-world problem with a nonconvex shaped Pareto front (component combination problem). The results suggested that the proposed method could handle both convex- and nonconvex-shaped Pareto fronts, expanding the potential applications of Ising machines to solving complex MOPs. This development could significantly enhance decision-making processes, particularly in achieving sustainable development goals.
Artificial intelligence (AI) has greatly expanded the generative capacity of drug discovery, yet the ability to translate large candidate pools into structured, resource-aware decisions remains limited. This review addresses this emerging optimization bottleneck by examining quantum annealing as a potential decision-optimization layer within hybrid computational workflows. We focus on discrete, constraint-dominated tasks-such as compound subset selection, combinatorial design, and multi-objective prioritization-that can be formulated as quadratic unconstrained binary optimization (QUBO) problems. Rather than positioning quantum annealing as a predictive tool, we analyze its role as a complementary optimization interface integrated with AI-generated scores. We further discuss practical implementation considerations, including embedding overhead, noise, scalability, and benchmarking challenges. By emphasizing workflow-level design and rigorous evaluation, this review provides a pragmatic framework for assessing annealing-based optimization in drug discovery and related data-intensive scientific domains.
Abstract : We propose a hybrid quantum–classical framework that integrates variational quantum machine learning (QML) for molecular binding affinity prediction with quantum annealing for Pareto-optimal drug formulation design. Leveraging a four-qubit variational circuit, our QML model achieves superior predictive performance compared to state-of-the-art classical baselines, effectively capturing complex molecular interactions. In parallel, we formulate drug formulation optimization as a Quadratic Unconstrained Binary Optimization (QUBO) problem and solve it using D-Wave’s quantum annealer, enabling efficient identification of Pareto-optimal solutions that balance bioavailability, toxicity, and stability. By unifying predictive modeling and combinatorial optimization within a single pipeline, our framework demonstrates the potential of near-term quantum devices to accelerate and enhance critical stages of drug discovery. These findings underscore the transformative role of NISQ-era algorithms in bridging molecular informatics and formulation design, paving the way for scalable, data-driven pharmaceutical innovation.