Abstract Complete exploration of design spaces is often computationally prohibitive. Classical search methods offer a solution but are limited by challenges like local optima and an inability to traverse dislocated design spaces. Quantum computing (QC) offers a potential solution by leveraging quantum phenomena to achieve computational speed-ups. However, the practical capability of current QC platforms to deliver these advantages remains unclear. To investigate this, we apply and compare two quantum approaches – the Gate-Based Grover’s algorithm and quantum annealing (QA) – to a generic tile placement problem. We benchmark their performance on real quantum hardware (IBM and D-Wave, respectively) against a classical brute-force search. QA on D-Wave’s hardware successfully produced usable results, significantly outperforming a classical brute-force approach (0.137 s vs 14.8 s) at the largest scale tested. Conversely, Grover’s algorithm on IBM’s gate-based hardware was dominated by noise and failed to yield solutions. While successful, the QA results exhibited a hardware-induced bias, where equally optimal solutions were not returned with the same probability (coefficient of variation: 0.248–0.463). These findings suggest that for near-term engineering applications, QA shows more immediate promise than current gate-based systems. This study’s contribution is a direct comparison of two physically implemented quantum approaches, offering practical insights, reformulation examples and clear recommendations on the utilisation of QC in engineering design.
Abstract Complete exploration of design spaces is often computationally prohibitive. Classical search methods offer a solution but are limited by challenges like local optima and an inability to traverse dislocated design spaces. Quantum computing (QC) offers a potential solution by leveraging quantum phenomena to achieve computational speed-ups. However, the practical capability of current QC platforms to deliver these advantages remains unclear. To investigate this, we apply and compare two quantum approaches – the Gate-Based Grover’s algorithm and quantum annealing (QA) – to a generic tile placement problem. We benchmark their performance on real quantum hardware (IBM and D-Wave, respectively) against a classical brute-force search. QA on D-Wave’s hardware successfully produced usable results, significantly outperforming a classical brute-force approach (0.137 s vs 14.8 s) at the largest scale tested. Conversely, Grover’s algorithm on IBM’s gate-based hardware was dominated by noise and failed to yield solutions. While successful, the QA results exhibited a hardware-induced bias, where equally optimal solutions were not returned with the same probability (coefficient of variation: 0.248–0.463). These findings suggest that for near-term engineering applications, QA shows more immediate promise than current gate-based systems. This study’s contribution is a direct comparison of two physically implemented quantum approaches, offering practical insights, reformulation examples and clear recommendations on the utilisation of QC in engineering design.
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.
Quantum computing has the potential to revolutionize the way we solve problems that are computationally infeasible for classical computers. This paper explores the application of quantum computing to NP-complete problems, and by focusing on the Graph Coloring Problem (GCP) we benchmark the performance of two prominent quantum computing devices: D-Wave's quantum annealer and IBM's gatebased quantum processors. After mapping instances of the GCP native formulation, we evaluate the effectiveness and limitations of quantum annealing and gate-based approaches in tackling such combinatorial problems. For annealers, the problem is cast into Quadratic Unconstrained Binary Optimization (QUBO) forms, while gate-based quantum devices employ variational algorithms like the Quantum Approximate Optimization Algorithm (QAOA). The research includes a comparative analysis, highlighting the scalability, accuracy, and practical challenges faced by current quantum hardware.
This study explores how well Grover's Algorithm performs in solving the Boolean Satisfiability Problem (SAT) using quantum circuits. The algorithm is implemented with IBM's Qiskit framework and compared to classical brute-force methods. Experiments focus on 3-SAT, 4-SAT, and 5-SAT problems, using quantum simulators and IBM quantum hardware. The results show that Grover's Algorithm is more efficient, offering a theoretical quadratic speedup over classical methods. However, practical issues like limited qubit availability, hardware noise, and optimization challenges impact its current performance. The data highlights the potential for quantum computing to scale and solve NP-complete problems. This research shows how quantum computing can improve problem-solving and lays the groundwork for future studies on more complex SAT problems and advanced quantum hardware.
Quantum computing offers the potential to address complex computational challenges, particularly in areas such as simulation and optimisation. Despite this promise, current gate-based quantum devices remain limited in scale and reliability, constraining their practical use. In this context, quantum annealing (QA) emerges as a viable and currently accessible alternative for solving optimisation problems, as it employs adiabatic quantum evolution to efficiently explore large and complex search spaces. This makes it a natural candidate for search-based software testing in the Cyber-Physical Systems (CPS) domain, which demands effective test cases due to their complexity and combination of continuous and discrete domains. This work explores the use of quantum annealing to enhance test case generation for CPS through a mutation-based approach. We employ quantum annealing to identify areas on test cases that can be improved and apply mutations to those areas. We encode test case mutation as a binary optimisation problem, and use quantum annealing to identify and target critical regions of the test cases for improvement. Our approach mechanises this process into an algorithm that uses D-Wave's quantum annealer to find the solution. As a main contribution, we offer insights into how quantum annealing can advance testing methodologies by empirically evaluating the correlation between problem size, hardware limitations, and the effectiveness of the results. Moreover, we compare the proposed method against state-of-the-art classical optimisation algorithms, targeting efficiency (time to generate test cases) and effectiveness (fault detection rates). Our results indicate that quantum annealing may enable faster test case generation (when problem decomposition, sampling and scheduling strategies are applied) while achieving comparable fault detection performance to state-of-the-art alternatives.
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.
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.