Quantum computing has the potential to revolutionize the way hard computational problems are solved in terms of speed and accuracy. Quantum hardware is an active area of research and different hardware platforms are being developed. Quantum algorithms target each hardware implementation and bring advantages to specific applications. The focus of this paper is to compare how well quantum annealing techniques and the QAOA models constrained optimization problems. As a use case, a constrained optimization problem called mission covering optimization is used. Quantum annealing is implemented in adiabatic hardware such as D-Wave, and QAOA is implemented in gate-based hardware such as IBM. This effort provides results in terms of cost, timing, constraints held, and qubits used.
Quantum computing has the potential to revolutionize the way hard computational problems are solved in terms of speed and accuracy. Quantum hardware is an active area of research and different hardware platforms are being developed. Quantum algorithms target each hardware implementation and bring advantages to specific applications. The focus of this paper is to compare how well quantum annealing techniques and the QAOA models constrained optimization problems. As a use case, a constrained optimization problem called mission covering optimization is used. Quantum annealing is implemented in adiabatic hardware such as D-Wave, and QAOA is implemented in gate-based hardware such as IBM. This effort provides results in terms of cost, timing, constraints held, and qubits used.
Quantum computing has emerged as a transformative paradigm with the potential to revolutionize computational tasks previously deemed intractable for classical computers. This paper explores the application of quantum computing algorithms in solving optimization problems, a cornerstone of numerous fields including logistics, finance, machine learning, and operations research. Quantum computers harness quantum mechanical phenomena such as superposition and entanglement to perform computations in ways fundamentally different from classical computers. This enables quantum algorithms to explore vast solution spaces simultaneously, offering potential exponential speedups over classical algorithms for certain optimization tasks. The abstract focuses on reviewing prominent quantum algorithms tailored for optimization, such as Grover's algorithm and quantum annealing approaches like those developed by D-Wave Systems. These algorithms target diverse optimization challenges including combinatorial optimization, portfolio optimization, and scheduling problems. We discuss their theoretical underpinnings, computational complexities, and practical implementations on current and near-term quantum hardware.
BACKGROUND: Quantum computing (QC) is emerging as a transformative tool for solving complex optimization problems across various fields, including biomedical applications. While classical optimization methods are well-established, they frequently face limitations when applied to complex and large-scale problems in radiotherapy planning. PURPOSE: This study aims to explore the implementation and evaluate the effectiveness of quantum optimization methods, specifically quantum annealing and the quantum approximate optimization algorithm (QAOA), in radiotherapy planning. In particular, we employ an Ising Hamiltonian formulation of the cost function, empirically implementing it on annealing-based quantum hardware and for the first time on circuit-based one. METHODS: We formulated a simplified radiotherapy optimization problem and solved it using quantum annealing on a D-Wave quantum annealer. Subsequently, we adapted this optimization problem for the QAOA framework and implemented it on IBM Quantum circuit-model hardware. Comparative analyses were conducted between classical and quantum methods and implementations, highlighting QC's potential advantages and limitations in specific optimization contexts. To demonstrate that the Hamiltonian formulation is valid and practically usable, we first tested it in simplified proof-of-principle examples and then extended it to a more clinically relevant bilateral prostate proton plan. In this new example, dose parameters were extracted directly from a commercial treatment planning system (RayStation) and incorporated into the Hamiltonian optimization workflow. Both one-qubit-per-voxel and two-qubits-per-voxel encodings were evaluated to illustrate scalability. Additionally, we discussed scalability considerations, practical challenges, and future research directions necessary for integrating quantum algorithms into routine clinical radiation therapy practices. RESULTS: To our knowledge, this study presents the first demonstration of using QC circuit-model hardware for radiotherapy planning optimization. The quantum annealing approach successfully determined the optimal solution. Convergence was achieved after 20 iterations on a quantum simulator (noise free) and after 100 iterations on actual quantum hardware (due to inherent hardware noise). In the bilateral prostate proton plan derived from realistic data, the Hamiltonian-based optimization assigned higher dose to the prostate relative to surrounding organs-at-risk, confirming the feasibility of applying QC optimization directly to clinically sourced parameters. CONCLUSIONS: Quantum optimization techniques demonstrate potential advantages over classical methods, particularly in complex optimization scenarios relevant to radiation therapy. The formulation of a Hamiltonian cost function, its validation on real quantum hardware, and its application to realistic data collectively represent a first concrete step toward QC-based treatment planning optimization in medical physics. Future research should focus on addressing scalability, overcoming practical implementation challenges, and advancing the development of scalable, fault-tolerant quantum systems suitable for clinical integration.
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, leveraging quantum mechanics, promises to enhance optimization processes in artificial intelligence (AI) by addressing challenges faced by classical computing in solving complex problems. This study investigates the role of quantum computing in optimizing AI tasks, focusing on algorithms such as Quantum Approximate Optimization Algorithm (QAOA) and Quantum Annealing (QA) for improved efficiency in optimization. A hybrid quantum-classical approach was used to evaluate the performance of quantum algorithms in optimization tasks, including combinatorial optimization and machine learning model tuning. QAOA and QA were applied to benchmark problems, such as Max-Cut and Traveling Salesman Problem (TSP). The study involved a comparative analysis between quantum algorithms and classical optimization techniques using performance metrics like solution quality, computational time, and scalability. Data were gathered through simulation on a quantum computing platform, and results were analyzed using statistical methods to assess improvements. The results showed that quantum computing significantly outperformed classical methods in solving large-scale optimization problems. QAOA demonstrated a 30% improvement in solution quality for Max-Cut problems, and QA showed a 25% faster convergence in TSP compared to classical algorithms. Quantum algorithms demonstrated scalability advantages as the problem size increased, with quantum methods achieving up to a 40% reduction in computational time for large instances. Furthermore, 70% of the tested cases showed significant improvements in solution accuracy, confirming the potential of quantum computing in real-world AI applications. Quantum computing, through QAOA and QA, offers substantial improvements in solving complex optimization problems in AI, presenting a transformative opportunity for the future of optimization algorithms.
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.