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International Journal of Mathematical Engineering and Management Sciences

A Comprehensive Review on Quantum-inspired Metaheuristic Algorithms: Basics to Recent Advancements

Sunita Salunke, Anuj Kumar, Sangeeta Pant, Manoj Kumar Singh

Published Jul 29, 2026• 0 citations
Publisher

Abstract

Quantum-inspired metaheuristic approaches, often called QIMAs, basically try to mix quantum computing ideas with the usual metaheuristic search routines. In practice, they make it easier to go through tangled search spaces, and they also help maintain a broader population variety, thanks to probabilistic qubit style encodings. Because of that, these methods have drawn a lot of attention across multiple academic directions, like materials science and engineering optimization, plus areas such as drug development and cryptography. QIMAs deliver a decent alternative by stitching Quantum-inspired mechanisms into algorithms that can run on ordinary classical machines, even if actually building full universal quantum computers is still hard, because quantum states are fragile and need heavy error correction, also the hardware is just plain complicated. Theoretical underpinnings, algorithmic progress and real-world applications of QIMAs are all looked at in depth in this article, sort of in a grounded way. The literature covering primarily 2015 to 2025 is reviewed carefully, then organized by the kind of inspiration it uses, like evolutionary algorithms, swarm intelligence approaches, and also genetic algorithms that are inspired by quantum mechanics in a more direct sense. The studies we examine show quite clearly how QIMAs can be used effectively for things like structural design, image processing, flight control, feature selection, and predictive modeling. The intention behind this review is to offer scholars and practitioners a complete, operationally efficient resource on Quantum-inspired optimization methods, for tackling tricky optimization problems.

DOI
10.33889/ijmems.2026.11.4.075

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Quantum-inspired metaheuristic approaches, often called QIMAs, basically try to mix quantum computing ideas with the usual metaheuristic search routines. In practice, they make it easier to go through tangled search spaces, and they also help maintain a broader population variety, thanks to probabilistic qubit style encodings. Because of that, these methods have drawn a lot of attention across multiple academic directions, like materials science and engineering optimization, plus areas such as drug development and cryptography. QIMAs deliver a decent alternative by stitching Quantum-inspired mechanisms into algorithms that can run on ordinary classical machines, even if actually building full universal quantum computers is still hard, because quantum states are fragile and need heavy error correction, also the hardware is just plain complicated. Theoretical underpinnings, algorithmic progress and real-world applications of QIMAs are all looked at in depth in this article, sort of in a grounded way. The literature covering primarily 2015 to 2025 is reviewed carefully, then organized by the kind of inspiration it uses, like evolutionary algorithms, swarm intelligence approaches, and also genetic algorithms that are inspired by quantum mechanics in a more direct sense. The studies we examine show quite clearly how QIMAs can be used effectively for things like structural design, image processing, flight control, feature selection, and predictive modeling. The intention behind this review is to offer scholars and practitioners a complete, operationally efficient resource on Quantum-inspired optimization methods, for tackling tricky optimization problems.
By violating the extended Church-Turing thesis, the quantum computing (QC) paradigm has emerged as a serious contender to classical computing. We now know that certain classical exponential problems (NP (nondeterministic polynomial time)-complete) can be solved in polynomial time by QC. Shor’s integer factorization and Grover’s method for unstructured search are perhaps the most well-known quantum algorithms. QC has been successfully applied to a variety of domains including optimization problems. Optimization can be solved by using deterministic/numerical as well as stochastic methods. Genetic algorithms (GA) belong to the latter category. Incorporating quantum mechanical properties such as superposition, entanglement, interference into the structure of GA has resulted in a more efficient evolutionary computing method called the quantum-inspired genetic algorithm. This method has been successfully applied to image processing, signal processing, economic load dispatch, coalition formation, task scheduling, etc. This chapter presents an overview of the current trends and developments in the domain of quantum-inspired genetic algorithms with the aim of investigating areas of further research in this sphere.
The increasing complexity of artificial intelligence (AI) has created a need for effective optimisation of highdimensional, nonlinear, and computationally expensive problems. Quantum-inspired optimisation provides an alternative approach by employing quantum-inspired representations and search mechanisms within classical computing systems. This review examines major approaches, including Quantum-Inspired Evolutionary Algorithms (QIEA), Quantum-Inspired Genetic Algorithms (QIGA), Quantum-Inspired Particle Swarm Optimisation (QIPSO), quantum annealing-related approaches, and hybrid methods. Their applications in machine learning, feature selection, hyperparameter optimisation, reinforcement learning, healthcare, finance, cybersecurity, robotics, and smart manufacturing are reviewed. Particular emphasis is placed on solution quality, convergence behaviour, computational cost, scalability, robustness, and reproducibility. The review identifies inconsistent benchmarking, parameter sensitivity, computational overhead, and limited reproducibility as major challenges. The findings indicate that quantum-inspired optimisation should not be considered universally superior to classical optimisation, as its effectiveness depends on problem structure and evaluation conditions. Future research should focus on scalable, hybrid, explainable, and reproducible optimisation frameworks for realistic large-scale AI applications.
Quantum-inspired metaheuristics are solvers that incorporate principles inspired from quantum mechanics into classical-approximate algorithms using non-quantum machines. Due to the uniqueness of quantum principles, the inspiration of quantum phenomena and the way it is done in fundamentally different non-quantum systems rather than real or simulated quantum computers raise important questions about these algorithms’ design and the reproducibility of their results in real or simulated quantum devices. Thus, this work’s contribution stands in a first step towards answering those questions as an attempt to identify key findings in the existing literature that should be considered or adapted in order to build hybrid or fully-quantum algorithms that can be used in quantum machines. This is done by proposing and studying four inspired, simulated and real quantum cellular genetic algorithms that, as far as the authors’ knowledge, are the first quantum structured metaheuristics studied in the three quantum realms using a quantum simulator with 32 quantum bits and a real quantum machine employing 15 superconducting quantum bits. The users’ mobility management in cellular networks is taken as a validation problem using 13 real-world instances. The comparisons have been made against 6 diverse algorithms using 9 comparison metrics. Thorough statistical tests and parameters’ sensitivity analysis have been also conducted. The experiments allowed answering several questions, including how quantum hardware influences the studied-algorithms’ search process. They also enabled opening new perspectives in quantum metaheuristics’ design.
A groundbreaking advancement in computing theory, quantum search algorithms leverage quantum mechanics to outperform their classical counterparts in solving search issues. With a focus on their theoretical underpinnings, practical applications, and performance in a variety of computational contexts, this systematic review carefully investigates the evolution, progress, and current state of quantum search algorithms. We present a thorough analysis of significant algorithms, such as Grover’s search algorithm, together with recent developments in quantum optimization and quantum-enhanced search techniques. We also go over the challenges with quantum error correction, scalability, and hardware constraints that prevent the broad application of quantum search techniques.
Quantum computers have made significant progress in the last two decades showing great potential in tackling some of the most challenging problems in computing. This ongoing progress creates an opportunity to implement and evaluate quantum-inspired metaheuristics on real quantum devices, with the aim of uncovering potential computational advantages. Additionally, the practical constraints associated with current quantum computers have highlighted a critical need for classical heuristic methods to optimize the tunable parameters of quantum circuits. Nature-inspired metaheuristics have emerged as promising candidates for fulfilling this optimization role. In this paper, we discuss both of these potential directions at the intersection of evolutionary computing and quantum computing while surveying some of the most promising advancements in these directions. We start with the review of quantum-inspired metaheuristics and then explore implementations of some of these quantum-inspired algorithms on physical quantum devices, capitalizing on the progress in quantum computing technology. Furthermore, we investigate the role of nature-inspired metaheuristics in enhancing the performance of noisy intermediate-scale quantum computers by fine-tuning their parameters. Finally, we discuss some of the recent progress at the intersection of both computing frameworks to highlight the current status and potential of the currently available quantum computing hardware. Synergies between these two computing frameworks demonstrate the potential of a strongly symbiotic relation that can contribute to the simultaneous advancements in both of these computing paradigms.
This article comprehensively reviews the recently developed quantum mechanics-based optimization techniques. The quantum theory has been employed to speed up the evolutionary method and enhance the possibility of finding the optimal solution of conventional optimization techniques. Current developments in quantum computing have demonstrated that quantum theory can offer significant benefits over conventional theory for certain optimization techniques. The future prospective and benefits and drawbacks of this fresh category of quantum optimization techniques have been presented in this review. It also enables new researchers and algorithm developers to use these simple but extremely effective algorithms for problem-solving. This paper aims to give readers an overview of the fundamental elements and recent advances in optimization techniques so that they can develop and implement these for various applications. Finally, a few findings are reached, and future study on quantum-based optimization techniques is discussed.