Quantum computing has shown great potential and advantages in solving integer factorization and disordered database search. However, it is not easy to solve specific problems with quantum computing device efficiently and widely, because a lot of professional background knowledge is required. In order to solve this problem, we propose an optimization problem’s automatic hybird quantum framework (OpAQ) for solving user-specified problems on a hybrid computing architecture including both quantum and classical computing resources. Such a solver can allow nonprofessionals who are not familiar with quantum physics and quantum computing to use quantum computing device to solve some classically difficult problems easily. Combinatorial optimization problem is one of the most important problems in both academic and industry. In this paper, we mainly focus on these problems and solve them with OpAQ, which is based on quantum approximation optimization algorithm (QAOA). We evaluate the performance of our approach in solving Graph Coloring, Max-cut, Traveling Salesman and Knapsack Problem. The experimental results show that quantum solver can achieve almost the same optimal solutions with the classical.
Quantum computing has shown great potential and advantages in solving integer factorization and disordered database search. However, it is not easy to solve specific problems with quantum computing device efficiently and widely, because a lot of professional background knowledge is required. In order to solve this problem, we propose an optimization problem’s automatic hybird quantum framework (OpAQ) for solving user-specified problems on a hybrid computing architecture including both quantum and classical computing resources. Such a solver can allow nonprofessionals who are not familiar with quantum physics and quantum computing to use quantum computing device to solve some classically difficult problems easily. Combinatorial optimization problem is one of the most important problems in both academic and industry. In this paper, we mainly focus on these problems and solve them with OpAQ, which is based on quantum approximation optimization algorithm (QAOA). We evaluate the performance of our approach in solving Graph Coloring, Max-cut, Traveling Salesman and Knapsack Problem. The experimental results show that quantum solver can achieve almost the same optimal solutions with the classical.
The design of a good algorithm to solve NP-hard combinatorial approximation problems requires specific domain knowledge about the problems and often needs a trial-and-error problem solving approach. Graph coloring is one of the essential fields to provide an efficient solution for combinatorial applications such as flight scheduling, frequency allocation in networking, and register allocation. In particular, some optimization algorithms have been proposed to solve the multi-coloring graph problems but most of the cases a simple searching method would be the best approach to find an optimal solution for graph coloring problems. However, this naive approach can increase the computation cost exponentially as the graph size and the number of colors increase. To mitigate such intolerable overhead, we investigate the methods to take the advantages of quantum computing properties to find a solution for multi-coloring graph problems in polynomial time. We utilize the variational quantum eigensolver (VQE) technique and quantum approximate optimization algorithm (QAOA) to find solutions for three combinatorial applications by both transferring each problem model to the corresponding Ising model and by using the calculated Hamiltonian matrices. Our results demonstrate that VQE and QAOA algorithms can find one of the best solutions for each application. Therefore, our modeling approach with hybrid quantum algorithms can be applicable for combinatorial problems in various fields to find an optimal solution in polynomial time.
Combinatorial optimization problems play a vital role in computer science and engineering, with applications in logistics, network design, finance, and resource allocation. However, many of these problems are NP-hard, making them computationally expensive to solve using classical optimization techniques, especially for large-scale instances. In recent years, quantum computing has emerged as a promising paradigm capable of addressing these limitations by leveraging quantum mechanical principles such as superposition and entanglement. This study investigates the application of quantum computing for solving combinatorial optimization problems, with a focus on algorithm design, complexity analysis, and real-world applicability. The research primarily employs the Quantum Approximate Optimization Algorithm (QAOA) and Grover's search algorithm to solve representative problems such as Max-Cut and the Knapsack problem. The performance of these algorithms is evaluated using key metrics including accuracy, execution time, and approximation ratio, and is compared with classical optimization techniques. The results demonstrate that QAOA is capable of generating near-optimal solutions, achieving accuracy levels of up to 93% for small problem instances. However, the study also highlights the challenges associated with current quantum systems, including noise, limited qubit availability, and increased execution time. Comparative analysis reveals that while classical methods remain more efficient for small-scale problems, quantum algorithms show significant potential for scalability and handling complex optimization tasks. The findings suggest that hybrid quantum-classical approaches offer a practical solution in the current Noisy Intermediate-Scale Quantum (NISQ) era. The study concludes that although quantum computing is still evolving, it holds strong potential for transforming combinatorial optimization in the future.
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.
This study presents a rigorous empirical evaluation of the Quantum Approximate Optimization Algorithm (QAOA) within a hybrid quantum-classical framework for solving the NP-hard Max-Cut problem. Using Python and Qiskit Aer statevector simulations, we benchmark QAOA (depths p = 2 and p = 3) against established classical algorithms, including simulated annealing, the Goemans–Williamson algorithm, and greedy heuristics, across Erdős–Rényi and regular graphs with 4 to 20 nodes (100 instances per size). Results demonstrate that low-depth QAOA suffers from significant performance degradation, achieving a 0.467 approximation ratio at 20 nodes compared to 0.856 for Goemans–Williamson, alongside a 210× runtime overhead. Convergence analysis further reveals low optimality probabilities and high iteration costs, highlighting limitations of variational optimization in NISQ-era devices. This work provides a reproducible benchmarking framework and contributes to a realistic assessment of near-term quantum advantage.
This research explores the integration of the Quantum Approximate Optimization Algorithm (QAOA) into Hybrid Quantum-HPC systems for solving the Max-Cut problem, comparing its performance with classical algorithms like brute-force search and greedy heuristics. We develop a theoretical model to analyze the time complexity, scalability, and communication overhead in hybrid systems. Using simulations, we evaluate QAOA's performance on small-scale Max-Cut instances, benchmarking its runtime, solution accuracy, and resource utilization. The study also investigates the scalability of QAOA with increasing problem size, offering insights into its potential advantages over classical methods for large-scale combinatorial optimization problems, with implications for future Quantum computing applications in HPC environments.
Quantum Computing is revolutionary paradigm that harnesses the principles of quantum mechanics such as superposition and entanglement to process the information in fundamentally new ways. It has shown potential across various fields, including Cryptography, Materials Science, Machine Learning, Optimization and many others. Among its many applications, Combinatorial Optimization problems stand out as a critical area where Quantum Computing can address problems that are often intractable for classical methods. This paper surveys current quantum approaches including Quantum Annealing, Variational Algorithms, Quantum Approximation Optimization Algorithm (QAOA) and asses their effectiveness in solving Classical Intractable Combinatorial Optimization (CICO) problems such as Max Cut Problem, Traveling Salesman Problem, Graph Coloring and Knapsack Problems. The paper explores the QAOA, approach to solve the CICO problems. Practical applications of quantum optimization approaches are highlighted in the fields such as finance, material science, communication networks. Additionally, the case studies demonstrate the algorithm's efficacy in real world scenarios. However, the paper also discusses the challenges that remain including issues related to noise, scalability and complexity of the algorithms. Finally, the survey discusses the future directions for research, emphasizing the potential of hybrid-quantum classical frameworks and the development of new quantum algorithms, aiming to enhance the practical applications in complex optimization scenarios. This survey provides valuable insights for researchers and practitioners interested in leveraging quantum advantages to solve combinatorial optimization problems effectively.