Quantum computing is a new form of computational technology, which can potentially be used to solve certain problems faster than is possible using classical computers. For this reason, there is an industry drive to develop early quantum computing applications. In this thesis, an overview of quantum computing technologies is provided, along with a practical discussion of the Traveling Salesman Problem, making use of the D-Wave quantum annealer. Subsequently, the main objective of the thesis can be investigated, which is to explore how quantum computing can be used to aid in solving structural optimization problems. Two methods are developed with which simple 2-dimensional truss systems can be optimized using the D-Wave quantum annealer. The methods aim to find the most lightweight choices for the truss cross-sectional areas while complying with material limit stress constraints. The first method directly casts such an optimization problem into a QUBO format. However, due to difficulties with formulating the stress constraint, this method was found to produce a trivial optimization problem. The second method attempts to symbolically solve a truss finite-element problem, using the resulting symbolic expressions to set up an optimization objective function. Although these objective functions are confirmed to work via classical brute-force analysis, the quantum annealer is shown to have difficulty finding the global optimum solution for truss systems with three or more elements. These results indicate that it is not currently beneficial to use quantum annealing for these structural optimization problems. Nevertheless, some improvements to the method for setting up the objective functions are suggested. The next generation of quantum annealers is expected to perform better for these practical applications, potentially becoming a useful tool in the engineering toolbox.
Quantum computing is a new form of computational technology, which can potentially be used to solve certain problems faster than is possible using classical computers. For this reason, there is an industry drive to develop early quantum computing applications. In this thesis, an overview of quantum computing technologies is provided, along with a practical discussion of the Traveling Salesman Problem, making use of the D-Wave quantum annealer. Subsequently, the main objective of the thesis can be investigated, which is to explore how quantum computing can be used to aid in solving structural optimization problems. Two methods are developed with which simple 2-dimensional truss systems can be optimized using the D-Wave quantum annealer. The methods aim to find the most lightweight choices for the truss cross-sectional areas while complying with material limit stress constraints. The first method directly casts such an optimization problem into a QUBO format. However, due to difficulties with formulating the stress constraint, this method was found to produce a trivial optimization problem. The second method attempts to symbolically solve a truss finite-element problem, using the resulting symbolic expressions to set up an optimization objective function. Although these objective functions are confirmed to work via classical brute-force analysis, the quantum annealer is shown to have difficulty finding the global optimum solution for truss systems with three or more elements. These results indicate that it is not currently beneficial to use quantum annealing for these structural optimization problems. Nevertheless, some improvements to the method for setting up the objective functions are suggested. The next generation of quantum annealers is expected to perform better for these practical applications, potentially becoming a useful tool in the engineering toolbox.
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.
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.
Quantum computing has emerged as a promising computational paradigm with the potential to solve problems that are intractable for classical computers. This paper provides an overview of the current state of quantum computing, including its historical development, hardware advancements, applications, and challenges. Special attention is given to combinatorial optimization, which is considered one of the most promising application domains. The limitations of current quantum systems and future research directions are also discussed. This paper presents a comparative study between a conventional D-Wave-based simulated annealing approach and a proposed hybrid optimization model for solving largescale combinatorial optimization problems. The study focuses on benchmark problems, including AES, TSP gr24, and a real-world load balancing problem, all formulated as QUBO models. The D-Wave approach employs the dwave-neal simulated annealing engine with various parameter settings, while the proposed model introduces a decomposition-based framework combined with adaptive parameter control and iterative refinement. The experimental results demonstrate that the proposed model consistently outperforms the conventional approach in terms of solution quality, achieving significantly lower energy values across all problem instances. In particular, for the TSP gr24 problem, the proposed model achieves near-optimal solutions with substantially reduced computation time. For large-scale problems such as AES and load balancing, the proposed model maintains scalability and robustness, whereas the conventional approach suffers from increased computational cost and performance degradation. Although the proposed method introduces additional computational steps, its hybrid structure effectively mitigates limitations related to local minima, parameter sensitivity, and scalability. These findings indicate that integrating classical optimization techniques with quantum-inspired methods is essential for practical applications. The proposed model provides a promising framework for solving complex real-world optimization problems and highlights the importance of hybrid approaches in advancing quantum annealing technologies.
Quantum algorithms offer promising advancements in solving complex optimization problems that are critical in various fields, including logistics, finance, and machine learning. Classical optimization techniques, while effective, often struggle with large-scale and high-dimensional data sets, leading to inefficiencies and long processing times.Quantum algorithms, leveraging the principles of superposition, entanglement, and quantum parallelism, provide a potential solution by exponentially speeding up certain computational tasks. This paper explores key quantum algorithms for optimization, including Grover's algorithm, the Quantum Approximate Optimization Algorithm (QAOA), and the Quantum Annealing method. We analyze their theoretical foundations, implementation challenges, and practical applications. Special attention is given to the performance comparisons between quantum and classical approaches in solving combinatorial optimization problems, such as the traveling salesman problem and portfolio optimization. We also discuss the limitations of current quantum hardware and the prospects for future improvements that could make quantum optimization algorithms more practical for real-world use.Our findings suggest that, while quantum algorithms are still in their early stages, they hold immense potential for transforming optimization in a variety of domains, offering new pathways toward more efficient problem-solving in both theoretical and applied contexts. we explore how hybrid quantum-classical approaches can enhance optimization results by combining the strengths of both paradigms. Future research directions are highlighted, focusing on improving quantum error correction, scaling quantum systems, and developing more robust quantum algorithms to tackle increasingly complex optimization problems.
This thesis studies several aspects of the quantum annealing (QA) computing approach. Quantum annealers' primary objective is to solve hard computational optimization problems. Because these optimization problems are in the NP-Hard complexity class, they are of great interest in several fields. One of the leading open questions concerning quantum annealers asks whether they will outperform other classical methods for solving these problems; Some aspects of this question are addressed in this thesis. The first part of the thesis investigates whether quantum annealing provides improved performance for solving a particular family of NP problems, called the Quadratic Knapsack Problem (QKP), using the D-Wave Quantum Annealer. The performance metrics used to assess QKP solving are the solution quality and the total runtime, and are benchmarked against other classical solvers. \n \nFurthermore, we extend our research on quantum annealers to propose two use cases for such systems. One is for Blockchain technology, and the second is in the area of quantum chaos. For the first use case of QA, an application for Blockchain's Proof of Work (PoW) is proposed, based on having hard optimization problems as an alternative to PoW hashing challenge, and using quantum annealers as solvers. For the second use case of QA, we propose simulating quantum chaos on the D-Wave Quantum Annealer to study the transition between the deep quantum realm and the classical limit in a chaotic system, and obtain insights into the “quantumness" of quantum annealers.
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.