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arXiv:2603.10518

Airfoil shape optimization via coherent Ising machine

Hao Ni, Qi Gao, Zhen Lu, Yue Yang

quant-phSubmitted Mar 11, 2026• Announced Mar 12, 2026• 0 citations
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Abstract

Airfoil shape optimization presents a challenge where classical solvers frequently struggle with computational efficiency and local minima. In the promising paradigm of quantum computing, the coherent Ising machine (CIM), a specialized physical solver, offers acceleration capabilities. However, its native discrete binary architecture restricts the application in aerodynamic design. To bridge this gap, we propose a comprehensive framework that translates airfoil shape optimization into hardware-compliant quadratic unconstrained binary optimization formulations. We integrate high-order response surface models via the Rosenberg order reduction, enabling the CIM to capture strong nonlinearities in the aerodynamic performance response. Furthermore, we introduce a block-diagonal scalarization strategy that compose trade-off scenarios into a single optimization. Validated on the NACA 4-digit airfoil series using CIM hardware with 615 spins, the framework successfully locates the global optimum with a computational speedup of three orders of magnitude compared to the classical simulated annealing. The parallel embedding capacity allows for the extraction of an entire optimal Pareto front in a single hardware execution. This work demonstrates a viable, quantum-enhanced paradigm for engineering optimization.

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Airfoil shape optimization presents a challenge where classical solvers frequently struggle with computational efficiency and local minima. In the promising paradigm of quantum computing, the coherent Ising machine (CIM), a specialized physical solver, offers acceleration capabilities. However, its native discrete binary architecture restricts the application in aerodynamic design. To bridge this gap, we propose a comprehensive framework that translates airfoil shape optimization into hardware-compliant quadratic unconstrained binary optimization formulations. We integrate high-order response surface models via the Rosenberg order reduction, enabling the CIM to capture strong nonlinearities in the aerodynamic performance response. Furthermore, we introduce a block-diagonal scalarization strategy that compose trade-off scenarios into a single optimization. Validated on the NACA 4-digit airfoil series using CIM hardware with 615 spins, the framework successfully locates the global optimum with a computational speedup of three orders of magnitude compared to the classical simulated annealing. The parallel embedding capacity allows for the extraction of an entire optimal Pareto front in a single hardware execution. This work demonstrates a viable, quantum-enhanced paradigm for engineering optimization.
Optimization problems, which involve finding the best solution from a set of possible solutions, are ubiquitous in various fields, from finance to engineering. Traditional algorithms sometimes struggle with these problems, especially when the solution space is vast, or the landscape is filled with numerous local minima. Quantum-inspired computing, which emulates quantum mechanical principles on classical hardware, emerges as a promising paradigm to address these challenges. This paper delves into two notable approaches: coherent Ising machines (CIM) and graphics processing unit (GPU)-accelerated simulated annealing. In essence, both methods offer innovative strategies to navigate the solution landscape, potentially bypassing the pitfalls of local optima and ensuring more efficient convergence to solutions. By harnessing the strengths of these quantum-inspired techniques, we can pave the way for enhanced computational capabilities in tackling complex optimization problems, even without a fault-tolerant quantum computer.
Public transport systems play a crucial role in the development of large cities. Bus network design to optimize passenger flow coverage in a global metropolis is a challenging task. As an essential part of bus travel planning, considering the bus transfer factor in the existing extremely complex and extensive public bus network usually leads to a optimization problem characterized by high-dimensionality and non-linearity. While classical computers struggle to deal with this kind of problems, quantum computers shed new light into this field. The coherent Ising machine (CIM), a specialized optical quantum computer using a photonic dissipative architecture, has shown its remarkable computational power in combinatorial optimization problems. We construct the classical model and the quadratic unconstrained binary optimization (QUBO) model of the bus route optimization problem, and solve it using a classical computer and CIM, respectively. Our experimental results demonstrate the significant acceleration capability of CIM over classical computers in finding the optimal or near-optimal solutions, albeit subject to the hardware limitations of the 100-qubit CIM.
Constructing realistic digital twins for applications such as training autonomous driving models requires the efficient allocation of real-world data, yet data sovereignty regulations present a major challenge. To address this, we tackle the optimization problem faced by metaverse service providers (MSPs) responsible for allocating geographically constrained data resources. We propose a two-stage stochastic integer programming (SIP) model that incorporates reservation and on-demand planning, enabling MSPs to efficiently subscribe and allocate data from specific regions to clients for training their models on local road conditions. The SIP model is transformed into a quadratic unconstrained binary optimization (QUBO) formulation and implemented for the first time at a practical scale on a 550-qubit coherent Ising machine (CIM), representing an exploratory step toward future quantum computing paradigms. Our approach introduces an MSP-centric framework for compliant data collection under sovereignty constraints, a hybrid cost model combining deterministic fees with probabilistic penalties, and a practical implementation on quantum hardware. Experimental results demonstrate that CIM-based optimization finds high-quality solutions with millisecond-scale (10310^3103 second) computation times, significantly outperforming quantum-inspired solvers like PyQUBO. Although classical solvers such as Gurobi can achieve marginally better solution quality, CIM is orders of magnitude faster, establishing a practical paradigm for quantum-enhanced resource management.
Optimization is a crucial challenge across various domains, including finance, resource allocation, and mobility. Quantum computing has the potential to redefine the way we handle complex problems by reducing computational complexity and enhancing solution quality. Optimization, particularly of objective functions, stands to benefit significantly from quantum solvers, which leverage principles of quantum mechanics like superposition, entanglement, and tunneling. The Ising and Quadratic Unconstrained Binary Optimization (QUBO) models are the most suitable formulations for these solvers, involving binary variables and constraints treated as penalties within the overall objective function. To harness quantum approaches for optimization, two primary strategies are employed: exploiting quantum annealers—special-purpose optimization devices—and designing algorithms based on quantum circuits. This review provides a comprehensive overview of quantum optimization methods, examining their advantages, challenges, and limitations. It demonstrates their application to real-world scenarios and outlines the steps to convert generic optimization problems into quantum-compliant models. Lastly, it discusses available tools and frameworks that facilitate the exploration of quantum solutions for optimization tasks.
Coherent Ising machines (CIMs) have emerged as specialized quantum hardware for large-scale combinatorial optimization. However, for large instances that remain challenging for classical methods, some platforms support only finite-precision inputs, and the required scaling and quantization can degrade solution quality. Dynamic portfolio optimization (DPO) can be formulated as a quadratic unconstrained binary optimization (QUBO) problem, but large instances are especially vulnerable to precision loss under global scaling. We propose a block coordinate descent method that decomposes the DPO model along the time dimension and iteratively solves compact time-block subproblems on the device. Experiments on finite-precision CIM hardware show that the method enables these instances to be solved under hardware precision limits, yields portfolios competitive with classical benchmark solvers, and reduces runtime through fast CIM solution of the resulting subproblems. These results demonstrate the promise of finite-precision CIMs as a practical and scalable approach to structured large-scale combinatorial optimization.
Quantum computing promises to have a tremendous advantage over its classical counterpart for solving computationally hard problems, yet remains in a relatively early stage for practical applications owing to the limited capabilities of today’s quantum computers. The approach to the special purposes of quantum computers by exploiting the special-purpose physics-inspired or quantum-inspired computers is emerging as a novel alternative to its quantum counterpart in tackling hard problems in high-performance computing. Inspired by physics, the Ising machine — a type of special-purpose computer that implements or emulates physics or quantum effects of the Ising model to speed up finding solutions to optimization problems — has recently become an active research area in the field of combinatorial optimization. This paper is to address the key enabling software and hardware technology underlying physics-inspired optimization using Ising machines in the unified quadratic unconstrained binary optimization (QUBO) framework for modeling and solving computationally hard combinatorial optimization problems, and with an aim to shed some light on the challenges and opportunities associated with the ever-growing landscape of this novel high-performance computing.