Quantum algorithms have evolved from initial proofs-of-concept to hundreds of specialized methods promising speed-ups in chemistry, cryptography, optimization, and machine learning. We conduct a Systematic Mapping Review (SMR) of 262 algorithms published between 2000 and April 2024, following PRISMA guidelines. Using searches across Scopus, IEEE Xplore, Web of Science, and arXiv, we screen 1,245 candidate papers and extract metadata for qualifying algorithms. We propose a taxonomy organizing algorithms by problem class and application domain. Bibliometric analyses show that simulation and variational optimization dominate, quantum machine learning (QML) exhibits the fastest growth, and gaps persist in quantum control, error correction, and domain-specific optimization. We discuss trends and recommend hardware-aware design and exploration of untapped problem structures.
Quantum algorithms have evolved from initial proofs-of-concept to hundreds of specialized methods promising speed-ups in chemistry, cryptography, optimization, and machine learning. We conduct a Systematic Mapping Review (SMR) of 262 algorithms published between 2000 and April 2024, following PRISMA guidelines. Using searches across Scopus, IEEE Xplore, Web of Science, and arXiv, we screen 1,245 candidate papers and extract metadata for qualifying algorithms. We propose a taxonomy organizing algorithms by problem class and application domain. Bibliometric analyses show that simulation and variational optimization dominate, quantum machine learning (QML) exhibits the fastest growth, and gaps persist in quantum control, error correction, and domain-specific optimization. We discuss trends and recommend hardware-aware design and exploration of untapped problem structures.
Quantum algorithms have evolved from early proofs-of-concept to hundreds of specialized methods promising computational speed-ups in fields such as chemistry, cryptography, optimization, and machine learning. This Systematic Mapping Review (SMR) analyzes 262 algorithms published between 2000 and April 2024, adhering to PRISMA guidelines. We searched Scopus, IEEE Xplore, Web of Science, and arXiv, screened 1,245 candidate papers, and extracted detailed metadata for qualifying algorithms. A two-dimensional taxonomy organizes algorithms by problem class and application domain. Bibliometric analyses reveal that simulation and variational optimization dominate, quantum machine learning (QML) shows the fastest growth, and significant gaps exist in quantum control, error correction, and domain-specific optimization. We discuss these trends and propose research directions emphasizing hardware-aware design and exploration of novel problem structures.
Quantum computing is a high-powered computational model that possess the capability to solve problems that are non-detectable by traditional algorithms. These algorithms primarily exploit well-known rules and principles of quantum mechanics i.e., superposition and entanglement to implement and deploy solutions for sophisticated tasks. Its applications have revolutionized various domains like optimization, cryptography, machine learning, and simulation. With the increasing research in this significant computational field, it is becoming more essential to critically assess that how quantum algorithms are being employed in real-world problem-solving contexts. The comprehensive literature review that has been conducted in this study is primarily based upon the critical assessment of four key quantum algorithms, which are 1) Shor's Algorithm, 2) Grover's Algorithm, 3) the Quantum Approximate Optimization Algorithm (QAOA), and the 4) Quantum Fourier Transform (QFT). We have primarily focused upon their uses in secure communication, machine learning, chemistry, cryptography, and optimization. 30 excellent studies published between 2015 and 2024 were found through a systematic search of IEEE Xplore, SpringerLink, ScienceDirect, arXiv, and Google Scholar. Our results identify major patterns in the usage of algorithms like Grover's, Shor's, QAOA, and VQE and elucidate their applications in tackling theoretical and pragmatic problems. Unlike previous reviews that concentrate narrowly on algorithm design or on particular areas, this SLR presents a wide but organized synthesis that highlights problem-driven applications. Moreover, we have also highlighted the primary research gaps in this area and also suggested possible future directions for further investigation. This review provides a basis for researchers who would like to apply quantum algorithms to new or interdisciplinary problems.
Abstract Quantum Machine Learning (QML) is an emerging interdisciplinary field that merges quantum computing with classical machine learning (ML) to enhance computational efficiency, scalability, and accuracy in data-driven tasks. By leveraging quantum properties such as superposition, entanglement, and quantum parallelism, QML has the potential to solve complex problems that are intractable for classical models. This survey provides a comprehensive, systematic review of recent advancements in QML, conducted following the PRISMA 2020 guidelines and covering fundamental encoding techniques that enable quantum computers to process classical data, as well as essential tools, datasets, and evaluation metrics used in quantum model development. Furthermore, it explores various QML approaches, including supervised, semi-supervised, unsupervised, and reinforcement learning, alongside quantum deep learning (QDL) models such as Quantum Neural Networks (QNNs) and Variational Quantum Circuits (VQCs). The paper also discusses the challenges in QML, including hardware limitations, scalability issues, and the need for improved quantum error correction. A dual-axis taxonomy simultaneously classifies algorithms by learning paradigm and quantum-classical integration level – a structure not found in prior surveys. The survey also covers Quantum Transfer Learning, Quantum Graph Neural Networks, and hardware-aware encoding selection, and introduces the first structured adversarial robustness taxonomy and Explainable QML treatment in a comprehensive QML survey. Together, these contributions position this work as both a reference and a methodological guide for advancing QML research and applications.
The rapid advancement of artificial intelligence has positioned Machine Learning (ML) as a cornerstone technology across scientific and industrial domains. In parallel, the emergence of quantum computing has catalyzed a new interdisciplinary field—Quantum Machine Learning (QML)—which promises to transcend the computational barriers faced by classical algorithms. This review paper systematically examines the evolution of ML from foundational statistical models to contemporary transformer architectures, and provides a structured analysis of QML paradigms including variational quantum circuits (VQCs), quantum kernel methods, and quantum neural networks (QNNs). Drawing from 95+ peer-reviewed publications indexed in Scopus and Science Citation Index (SCI) journals—with particular emphasis on 2025–2026 publications in IEEE Access, Nature Communications, Nature Computational Science, and Physical Review Letters—we analyze performance benchmarks, identify hardware constraints, and outline algorithmic innovations shaping the near-term quantum advantage landscape. Our findings indicate that while classical ML retains superiority in large-scale perception tasks, QML demonstrates significant advantages in combinatorial optimization and quantum chemistry simulation. Recent 2025 advances in error mitigation on superconducting qubits and improved VQC barren-plateau mitigation are narrowing this gap rapidly. The paper concludes with a forward-looking research agenda covering fault-tolerant QML, hybrid architectures, and quantum NLP.
This research project presents a PRISMA-guided systematic literature review exploring the application of quantum machine learning (QML) in oncology, a rapidly growing field with fragmented evidence. The study synthesizes peer-reviewed studies from six databases (ACM, IEEE, MDPI, Scopus, Wiley, and PubMed) published between 2020 and 2026, screening 212 records and selecting 49 studies for analysis. The review examines clinical tasks, cancer domains, QML architectures, challenges, and future directions, revealing that current research mainly focuses on classification and detection, particularly in breast cancer and brain tumors, using hybrid quantum-classical models. Despite promising results, progress is limited by hardware constraints, simulator dependence, and insufficient clinical validation. The findings provide a clear overview of current QML trends and highlight future priorities, including real quantum hardware testing, diverse clinical datasets, standardized benchmarking, and stronger collaboration between computing and oncology communities.
This paper presents a comprehensive systematic and bibliometric review of the rapidly expanding literature on quantum computing. The study addresses six research questions concerning prominent themes, temporal evolution, types of key findings, frequently reported research gaps, higher-order gap typologies, and future research directions. Utilizing a researcher-curated database, the final corpus comprises 153 studies compiled from non-Scopus, Scopus and Web of Science. The results demonstrate that quantum hardware and architecture, algorithms, and theoretical foundations dominate the current literature. Furthermore, publication output has risen significantly between 2018 and 2025. Among the reported findings, algorithmic innovations, performance claims, and hardware advancements are the most common. Despite this progress, the field faces substantial barriers; technical, scalability, fault-tolerance, and methodological-standardization gaps are the most frequently reported. Based on these identified gaps, eight actionable future research directions emerge to guide the scientific community. Ultimately, this review concludes that quantum computing is actively transitioning from a purely physics-driven domain into a multidisciplinary, engineering- and application-oriented science. However, its continued advancement is presently constrained by a hardware-methodology-application triad, wherein reporting practices often outpace empirical verification and standardized benchmarking.