We present a novel formulation of structural design optimization problems specifically tailored to be solved by qa. Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is qa. This approach requires the optimization problem to be present, e.g., as a qubo model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a qubo problem that can be immediately solved by qa. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware. Remarkably, for small-scale problems, our approach showcases functionality on today’s hardware such that this study can lay the groundwork for continued exploration of qa’s impact on engineering design optimization problems.
We present a novel formulation of structural design optimization problems specifically tailored to be solved by qa. Structural design optimization aims to find the best, i.e., material-efficient yet high-performance, configuration of a structure. To this end, computational optimization strategies can be employed, where a recently evolving strategy based on quantum mechanical effects is qa. This approach requires the optimization problem to be present, e.g., as a qubo model. Thus, we develop a novel formulation of the optimization problem. The latter typically involves an analysis model for the component. Here, we use energy minimization principles that govern the behavior of structures under applied loads. This allows us to state the optimization problem as one overall minimization problem. Next, we map this to a qubo problem that can be immediately solved by qa. We validate the proposed approach using a size optimization problem of a compound rod under self-weight loading. To this end, we develop strategies to account for the limitations of currently available hardware. Remarkably, for small-scale problems, our approach showcases functionality on today’s hardware such that this study can lay the groundwork for continued exploration of qa’s impact on engineering design optimization problems.
This paper explores the application of Quantum Annealing (QA) to the field of combinatorial optimization. The core idea is to leverage the principles of quantum mechanics, specifically quantum tunneling, to efficiently solve complex optimization problems. We present a framework for utilizing QA to tackle problems represented as quadratic unconstrained binary optimization (QUBO) models. The methodology focuses on mapping the problem's constraints and objective function into a form suitable for QA hardware. We discuss the challenges involved in this mapping process, including the limitations of current QA devices and the need for careful problem formulation. Furthermore, we analyze the potential advantages of QA over classical optimization techniques, particularly concerning the exploration of a wider solution space. The research highlights the promise of QACO as a viable approach for tackling computationally demanding combinatorial optimization tasks, offering a novel method to enhance optimization efficiency.
The welded beam design problem represents a real-world engineering challenge in structural optimization. The objective is to determine the optimal dimensions of a steel beam and weld length to minimize cost while satisfying constraints related to shear stress (τ), bending stress (σ), critical buckling load (Pc), end deflection (δ), and side constraints. The structural analysis of this problem involves the following four design variables: weld height (x1), weld length (x2), beam thickness (x3), and beam width (x4), which are commonly denoted in structural engineering as h,l,t,b respectively. The structural formulation of this problem leads to a nonlinear objective function, which is subject to five nonlinear and two linear inequality constraints. The optimal solution lies on the boundary of the feasible region, with a very small feasible-to-search-space ratio, making it a highly challenging problem for classical optimization algorithms. This paper explores the application of quantum computing to solve the welded beam optimization problem, utilizing the unique properties of quantum computers for constrained optimization in engineering problems. Specifically, we employ the D-Wave quantum computing system, which utilizes quantum annealing and is particularly well-suited for solving constrained optimization problems. The study presents a detailed formulation of the problem in a format compatible with the D-Wave system, ensuring the efficient encoding of constraints and objective functions. Furthermore, we analyze the performance of quantum computing in solving this problem and compare the obtained results with classical optimization methods. The effectiveness of quantum computing is evaluated in terms of computational efficiency, accuracy, and its ability to navigate complex, constrained search spaces. This research highlights the potential of quantum algorithms in tackling real-world engineering optimization problems and discusses the challenges and limitations of current quantum hardware in solving practical industrial application issues.
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum computing, quantum annealing (QA), has been proposed to solve these problems by encoding optimization problems into physical energy landscapes and solving them by quantum tunnelling systematically through exploration of solution space. This is a critical review that summarizes the current applications of quantum annealing to combinatorial optimization and includes a theoretical background, hardware designs, algorithm implementation strategies, encoding and embedding schemes, protocols to benchmark quantum annealing, areas of implementation, and links with the quantum algorithms implementation with gate-based hardware and classical solvers. We develop a unified framework, relating adiabatic quantum dynamics, Ising and QUBO models, stoquastic and non-stoquastic Hamiltonians, and diabatic transitions to modern flux-qubit annealers (Chimera, Pegasus, Zephyr topologies), and emergent architectures (Lechner-Hauke-Zoller systems, Rydberg atom platforms), and hybrids of quantum and classical computation. Through our analysis, we find that overhead in embedding and encoding is the largest determinant of the scalability and performance (this is not just the number of qubits). Minor embeddings also usually have a physical qubit count per logical variable of between 5 and 12 qubits, which limits effective problem capacity by 80-92% and, due to chain-breaking errors, compromises the quality of solutions.
We present a quantum annealing-based solution method for topology optimization (TO). In particular, we consider TO in a more general setting, i.e., applied to structures of continuum domains where designs are represented as distributed functions, referred to as continuum TO problems. According to the problem's properties and structure, we formulate appropriate sub-problems that can be solved on an annealing-based quantum computer. The methodology established can effectively tackle continuum TO problems formulated as mixed-integer nonlinear programs. To maintain the resulting sub-problems small enough to be solved on quantum computers currently accessible with small numbers of qubits and limited connectivity, we further develop a splitting approach that splits the problem into two parts: the first part can be efficiently solved on classical computers, and the second part with a reduced number of variables is solved on a quantum computer. By such, a practical continuum TO problem of varying scales can be handled on the D-Wave quantum annealer. More specifically, we concern the minimum compliance, a canonical TO problem that seeks an optimal distribution of materials to minimize the compliance with desired material usage. The superior performance of the developed methodology is assessed and compared with the stateof-the-art heuristic classical methods, in terms of both solution quality and computational efficiency. The present work hence provides a promising new avenue of applying quantum computing to practical designs of topology for various applications.
With the advent of novel quantum computing technologies and the new possibilities thereby offered, a prime opportunity has presented itself to investigate the practical application of quantum computing. This work investigates the feasibility of using quantum annealing for structural optimization. The target problem is the discrete truss sizing problem—the goal is to select the best size for each truss member so as to minimize a stress-based objective function. To make the problem compatible with quantum annealing devices, the objective function must be translated into a quadratic unconstrained binary optimization (QUBO) form. This work focuses on exploring the feasibility of making this translation. The practicality of using a quantum annealer for such optimization problems is also assessed. A method is eventually established to translate the objective function into a QUBO form and have it solved by a quantum annealer. However, scaling the method to larger problems faces some challenges that would require further research to address.
Quantum computing has emerged as a transformative paradigm, leveraging principles of quantum mechanics to tackle computationally intractable problems. This manuscript explores the potential of quantum computing for solving complex engineering problems—specifically optimization, simulation, and data analysis tasks—using technologies and methodologies available up to 2022. We examine both gate-based and quantum annealing approaches, outline experimental frameworks, and compare performance against classical counterparts. Results from simulated benchmark problems demonstrate promising speedups in select cases, though practical adoption is constrained by hardware limitations such as qubit coherence times and noise. The study concludes by highlighting avenues for integrating hybrid quantum-classical workflows in engineering, along with a discussion of current constraints and future directions. Over the past decade, research efforts have focused on understanding how quantum phenomena like superposition and entanglement can be harnessed to realize computational advantages for specific problem classes. In particular, combinatorial optimization problems—ubiquitous in engineering design and logistics—offer fertile ground for quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) and quantum annealing. Additionally, quantum simulation techniques, including the Variational Quantum Eigensolver (VQE), promise to accelerate the modeling of physical systems at the molecular and materials level, potentially informing the design of next-generation structural and functional materials. Beyond raw algorithmic performance, this paper carefully assesses the end‑to‑end workflow, accounting for overheads in problem encoding, error mitigation, and classical post‑processing. We also present a detailed analysis of resource utilization—quantified by qubit counts, circuit depths, and annealing schedules—highlighting trade‑offs between solution quality and execution time. Ultimately, our findings underscore that, while pure quantum speedups remain rare in 2022, hybrid approaches harnessing both quantum and classical resources can yield practical benefits for small‑to‑medium scale engineering tasks. This expanded evaluation provides a roadmap for researchers and practitioners interested in applying quantum computing to real‑world engineering challenges.