A primary challenge of computational science is solving NP-hard optimization problems since they are too complicated and cannot be effectively solved deterministically in large instances. Even though quantum computing can solve these problems with the help of its key properties quantum parallelism and tunneling, the modern hardware is yet not sufficiently developed. In this case, QICAs are considered as a new method in which the key aspects of quantum mechanics, such as superposition, entanglement, interference and tunneling are replicated in classical, non-quantum computers. It aims to attain rapid optimization of NP-hard problems through a hybrid approach that combines cartography-based exploration, variable state reduction with tensor networks as well as an inclusion of a variant-based approach inspired by QAOA. A number of standard problems are used to test the model, e.g., the Traveling Salesman Problem (TSP), the 0/1 Knapsack Problem and Max-Cut Problem. Genetic Algorithms, Simulated Annealing and Ant Colony Optimization trials all concur that QICA converges to superior solutions much faster and it can nonetheless handle bigger-sized problems. More precisely, the algorithm provides better approximation results as well as lesser computing power requirements, thus demonstrating the effectiveness of quantum-inspired methods in the case of classical systems. They establish the fact that QICAs have the potential to solve challenging optimization problems, particularly in the cases where quantum machines are absent or inaccessible. The way of solving the problem represented in the study is quite innovative and serves as a bridge between the theory of quantum and practical implementation in the optimization field.
A primary challenge of computational science is solving NP-hard optimization problems since they are too complicated and cannot be effectively solved deterministically in large instances. Even though quantum computing can solve these problems with the help of its key properties quantum parallelism and tunneling, the modern hardware is yet not sufficiently developed. In this case, QICAs are considered as a new method in which the key aspects of quantum mechanics, such as superposition, entanglement, interference and tunneling are replicated in classical, non-quantum computers. It aims to attain rapid optimization of NP-hard problems through a hybrid approach that combines cartography-based exploration, variable state reduction with tensor networks as well as an inclusion of a variant-based approach inspired by QAOA. A number of standard problems are used to test the model, e.g., the Traveling Salesman Problem (TSP), the 0/1 Knapsack Problem and Max-Cut Problem. Genetic Algorithms, Simulated Annealing and Ant Colony Optimization trials all concur that QICA converges to superior solutions much faster and it can nonetheless handle bigger-sized problems. More precisely, the algorithm provides better approximation results as well as lesser computing power requirements, thus demonstrating the effectiveness of quantum-inspired methods in the case of classical systems. They establish the fact that QICAs have the potential to solve challenging optimization problems, particularly in the cases where quantum machines are absent or inaccessible. The way of solving the problem represented in the study is quite innovative and serves as a bridge between the theory of quantum and practical implementation in the optimization field.
NP-hard problems are one of the most computationally intensive challenges in computer science, appearing in many domains such as logistics, cybersecurity, drug design, and financial modelling. Classical algorithms become impractical as problem size increases due to combinatorial explosion. This paper presents a structured framework for analysing quantum algorithms targeting NP-hard optimization problems, like the Traveling Salesman Problem (TSP), Max-Cut, and Boolean Satisfiability (SAT). We have developed a taxonomy which categorizes quantum approaches—quantum annealing, variational algorithms (QAOA/VQE), and Grover-based search—based on problem encoding strategies, resource requirements, and theoretical guarantees. From the comparative analysis of existing literature, we: 1) Map algorithm classes to problem domains (e.g., QAOA for Max-Cut, annealing for TSP) 2) Identify performance trade-offs between solution quality, qubit counts, and circuit depth 3) Analyse hardware compatibility constraints across NISQ platforms 4) Reveal fundamental scalability barriers including noise susceptibility and embedding overhead The framework establishes implementation guidelines for near- term quantum hardware and proposes hybrid quantum-classical pathways to bridge theoretical potential and practical deployment. This systematic analysis prioritizes research directions for achieving quantum advantage in combinatorial optimization.
Quantum computing is a promising technology that may provide breakthrough solutions to today’s difficult problems such as breaking encryption and solving large-scale combinatorial optimization problems. A class of algorithms referred to as Quantum Approximate Optimization Algorithm (QAOA) have been recently proposed. QAOA attempts to approximately solve hard problems using a protocol know as bang-bang. The technique is based on the unitary evolution using a Hamiltonian encoding of the objective function of the combinatorial optimization problem. QAOA has been explored in the context of several optimization problems such as Max-Cut problem, variational Eigenvalue problem etc. Recently, attempts have been made to create QAOA for the Traveling Salesman Problem (TSP). Due to small node size and limited solution capability of the currently available Quantum computers and/or simulators, we develop a hybrid approach where subgraphs of a TSP tour are executed on a Quantum computer and the results from the quantum optimization are combined in further optimization of the whole tour. Since the local optimization of a subgraph is prone to getting stuck in a local minima, we overcome this problem by using a parallel Ant Colony Optimization Algorithm with periodic pheromone exchange between colonies. Our results are encouraging and yield optimum results for benchmarks with less than 50 nodes, and usually within 1% of the optimal solution for benchmarks with around 200 nodes.
Quantum computing is a promising technology that may provide breakthrough solutions to today’s difficult problems such as breaking encryption and solving large-scale combinatorial optimization problems. An algorithm referred to as Quantum Approximate Optimization Algorithm (QAOA) has been recently proposed to approximately solve hard problems using a protocol know as bang–bang. The technique is based on unitary evolution using a Hamiltonian encoding of the objective function of the combinatorial optimization problem. The QAOA was explored in the context of several optimization problems such as the Max-Cut problem and the Traveling Salesman Problem (TSP). Due to the relatively small node-size solution capability of the available quantum computers and simulators, we developed a hybrid approach where sub-graphs of a TSP tour can be executed on a quantum computer, and the results from the quantum optimization are combined for a further optimization of the whole tour. Since the local optimization of a sub-graph is prone to becoming trapped in a local minimum, we overcame this problem by using a parallel Ant Colony Optimization (ACO) algorithm with periodic pheromone exchange between colonies. Our method exceeds existing approaches which have attempted partitioning a graph for small problems (less than 48 nodes) with sub-optimal results. We obtained optimum results for benchmarks with less than 150 nodes and results usually within 1% of the known optimal solution for benchmarks with around 2000 nodes.
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 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.
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.