ABSTRACT This study examines the fragmented and rapidly evolving body of knowledge on the application of quantum computing to NP‐hard decision problems in Operations Management (OM) and Operations Research (OR). It aims to systematically map how quantum optimization approaches are formulated and applied across core OM/OR problem classes, highlighting current advances and unresolved challenges for research and practice. A systematic mapping review was conducted using peer‐reviewed studies indexed in Scopus and Web of Science from 2014 to 2026. The literature was classified by problem type, mathematical formulation, quantum technique, and application domain, with attention to the alignment between quantum models and established OM/OR decision frameworks. The review reveals a strong predominance of QUBO‐based formulations and annealing‐oriented approaches, mainly applied to logistics, manufacturing, and financial optimization problems. Applications remain largely exploratory, with limited empirical validation, weak theoretical integration with OM/OR decision‐making models, and persistent challenges related to scalability and hybrid quantum‐classical performance. Only a small subset of studies demonstrates how quantum formulations can support real‐world scheduling and resource coordination problems. This study proposes an analytical framework linking quantum optimization paradigms to canonical OM/OR NP‐hard problem classes, identifying key research gaps and methodological tensions to support more theory‐driven and empirically grounded future applications, especially in complex decision environments.
ABSTRACT This study examines the fragmented and rapidly evolving body of knowledge on the application of quantum computing to NP‐hard decision problems in Operations Management (OM) and Operations Research (OR). It aims to systematically map how quantum optimization approaches are formulated and applied across core OM/OR problem classes, highlighting current advances and unresolved challenges for research and practice. A systematic mapping review was conducted using peer‐reviewed studies indexed in Scopus and Web of Science from 2014 to 2026. The literature was classified by problem type, mathematical formulation, quantum technique, and application domain, with attention to the alignment between quantum models and established OM/OR decision frameworks. The review reveals a strong predominance of QUBO‐based formulations and annealing‐oriented approaches, mainly applied to logistics, manufacturing, and financial optimization problems. Applications remain largely exploratory, with limited empirical validation, weak theoretical integration with OM/OR decision‐making models, and persistent challenges related to scalability and hybrid quantum‐classical performance. Only a small subset of studies demonstrates how quantum formulations can support real‐world scheduling and resource coordination problems. This study proposes an analytical framework linking quantum optimization paradigms to canonical OM/OR NP‐hard problem classes, identifying key research gaps and methodological tensions to support more theory‐driven and empirically grounded future applications, especially in complex decision environments.
The growing intersection of quantum computing and operations research (OR) has opened new avenues for solving high-dimensional optimization problems that remain computationally intractable under classical paradigms. This study presents a systematic mapping and critical evaluation of both quantum and quantum-inspired optimization algorithms, with a particular focus on their scalability, convergence efficiency, and applicability to large-scale operations research challenges. Through a structured review of contemporary literature and empirical implementations, the research categorizes existing algorithms into key families—such as quantum annealing, variational quantum algorithms (VQAs), and hybrid quantum–classical frameworks—while identifying trends in algorithmic performance across industrial logistics, network design, and resource allocation models. The systematic mapping process was conducted collaboratively, emphasizing transparent data collection, inclusion–exclusion criteria, and reproducible methodology following evidence-based review standards. Critical evaluation highlighted the need for unified performance metrics, improved hybridization strategies, and enhanced interpretability in quantum-inspired heuristics. The research also provided valuable insight into refining methodological rigor, including bibliometric analysis, coding frameworks, and academic presentation of findings. Ultimately, this work contributes to the ongoing dialogue between quantum computation and operations research, demonstrating how quantum-enhanced optimization can accelerate decision-making processes in complex, data-intensive environments.
In recent years, quantum computing has emerged as a rapidly advancing interdisciplinary field, attracting growing attention from both academia and industry owing to its fundamentally novel approach to information processing and its potential to achieve computational capabilities beyond the reach of classical systems. This paper presents a structured review of quantum computing approaches applied to scheduling problems, which are among the most challenging NP-hard optimization problems. We first introduce fundamental principles of quantum computing, including gate-based models, quantum annealing, and hybrid frameworks. We then explore how various scheduling problems such as job-shop, flow-shop, and project scheduling-are encoded into quantum models, particularly using QUBO formulations suitable for current quantum devices. Finally, we discuss key limitations such as hardware constraints and model scalability, and we identify research directions to advance quantumenhanced scheduling methods. By grounding theory in empirical case studies and highlighting near-term deployable solutions, this study bridges the gap between quantum algorithm development and practical scheduling demands, offering a roadmap for researchers and practitioners in quantum optimization.
Industrial engineering increasingly depends on solving large-scale optimization problems involving scheduling, routing, resource allocation, inventory control, energy management, and supply-chain coordination. Classical exact methods often become computationally expensive when problem size, uncertainty, and combinatorial complexity grow rapidly. Although practical quantum computers are still developing, quantum-inspired computing approaches have emerged as powerful alternatives that adapt principles from quantum mechanics to run on classical hardware. This paper investigates quantum-inspired computing approaches for complex optimization problems in industrial engineering. It examines methodologies including simulated annealing, tensor-network optimization, Ising formulations, quantum- inspired evolutionary algorithms, digital annealers, and hybrid classical-intelligent heuristics. Applications in production scheduling, facility layout, vehicle routing, maintenance planning, portfolio optimization, warehouse operations, and smart manufacturing are analyzed. Particular attention is given to solution quality, scalability, stochastic decision-making, real-time adaptability, and integration with Industry 4.0 data systems. Benefits include faster near-optimal solutions, improved operational efficiency, reduced energy consumption, and better responsiveness under uncertainty. Major challenges include formulation difficulty, parameter tuning, benchmarking inconsistency, interpretability, and transition barriers within traditional industrial workflows. A future roadmap is proposed involving hybrid quantum-classical ecosystems, AI- guided optimization engines, digital twins, and autonomous decision platforms. The paper concludes that quantum-inspired computing can deliver practical industrial value today by bridging the gap between conventional optimization and future quantum advantage, especially in environments where speed, flexibility, and complexity management are essential.
Optimization problems across domains such as logistics, finance, and artificial intelligence often involve complex and NP-hard formulations that are computationally challenging for classical algorithms due to scalability and efficiency limitations. The study aims to systematically investigate the role of Quantum Machine Learning (QML) in addressing complex optimization problems and to analyze its advantages over traditional optimization techniques. A comprehensive survey and comparative analysis of key QML algorithms, including Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), Quantum Neural Networks (QNNs), and Quantum Support Vector Machines (QSVMs), is conducted by examining their working principles, optimization capabilities, and real-world applications. The findings indicate that QML algorithms demonstrate significant potential in exploring large solutions spaces efficiently, achieving faster convergence, and providing improved optimization performance compared to classical approaches, although challenges such as quantum noise, scalability, and hardware limitations remain. The novelty of this study lies in providing a unified and critical comparative framework that integrates multiple QML optimization algorithms, highlights their practical feasibility, and identifies key research gaps hindering their real-world deployment. The implications of this research provide valuable insights for researchers and practitioners in selecting appropriate QML techniques and emphasize the need for advancements in hybrid quantum -classical systems, algorithms design, and quantum hardware to enable practical large-scale optimization.
Abstract Quantum computing has emerged as a promising field with the potential to revolutionize information processing and storage. Understanding its current state and research trajectory is crucial. This study aims to map the current literature on quantum computing, to identify how quantum computing is being used in solving quantum software problems and improving quantum algorithms. Moreover, it examines evaluation parameters and the challenges faced in this field. A systematic mapping study was conducted using the SCOPUS database, including all papers up to December 2024. Relevant articles were selected based on inclusion criteria, and a content analysis was performed to categorize and synthesize the findings. Information was gathered from 33 primary studies. Findings show that quantum computing is mainly applied in machine learning and optimization, though classical methods still outperform it. IBM Quantum is the most used platform. Research focuses on algorithm efficiency, verification over validation, and resource optimization, but lacks standardized evaluation methods. Key limitations include hardware constraints, noise, and scalability, while challenges involve integration, error correction, and problem formulation. Quantum computing continues to face significant technological challenges, but current research lays the groundwork for future advances. More practical studies on real hardware and strategies to improve the implementation and performance of quantum algorithms are needed. Effective evaluation, verification, and validation of quantum solutions must be further investigated.
Quantum computing offers transformative potential to solve complex optimisation problems in transportation and logistics, particularly those that involve large combinatorial decision spaces such as vehicle routing, traffic control, and supply chain design. Despite theoretical promise and growing empirical interest, its adoption remains limited. This systematic literature review synthesises fifteen peer-reviewed studies published between 2015 and 2025, examining the application of quantum and quantum-inspired methods to transport optimisation. The review identifies five key problem domains (vehicle routing, factory scheduling, network design, traffic operations, and energy management) and categorises the quantum techniques used, including quantum annealing, variational circuits, and digital annealers. Although several studies demonstrate performance gains over classical heuristics, most rely on synthetic datasets, lack statistical robustness, and omit critical operational metrics such as energy consumption and queue latency. Four cross-cutting barriers are identified: hardware limitations, data availability, energy inefficiency, and organisational readiness. The review identifies limited real-world deployment, a lack of standardised benchmarks, and scarce cost–benefit evaluations, highlighting key areas where further empirical work is needed. It concludes with a structured research agenda aimed at bridging the gap between laboratory demonstrations and practical implementation, emphasising the need for pilot trials, open datasets, robust experimental protocols, and interdisciplinary collaboration.