Background Quantum support vector machines and quantum kernel methods have emerged as promising approaches within quantum machine learning, with the goal of leveraging quantum computing to enhance classification performance and computational efficiency. This review systematically surveys recent advances in QSVM and kernel‐based quantum classifiers, and analyzes their algorithmic frameworks, experimental implementations, and practical challenges. Methods We systematically examine QSVM approaches, including three schemes based on HHL algorithm, Hadamard test, and variational optimization, alongside multi‐class extension and quantum feature mapping. Result Findings indicate that QSVM can offer theoretical speed‐ups in specific settings, particularly when combined with quantum feature mappings that encode data into high‐dimensional Hilbert spaces. However, current implementations remain constrained by hardware limitations, and a lack of large‐scale general validation. Most studies focus on proof‐of‐principle experiments with limited real‐world applicability. Conclusion While promising, QSVM requires further work on scalability, noise resilience, and real‐world integration. Future research should focus on robust algorithms and empirical studies.
Background Quantum support vector machines and quantum kernel methods have emerged as promising approaches within quantum machine learning, with the goal of leveraging quantum computing to enhance classification performance and computational efficiency. This review systematically surveys recent advances in QSVM and kernel‐based quantum classifiers, and analyzes their algorithmic frameworks, experimental implementations, and practical challenges. Methods We systematically examine QSVM approaches, including three schemes based on HHL algorithm, Hadamard test, and variational optimization, alongside multi‐class extension and quantum feature mapping. Result Findings indicate that QSVM can offer theoretical speed‐ups in specific settings, particularly when combined with quantum feature mappings that encode data into high‐dimensional Hilbert spaces. However, current implementations remain constrained by hardware limitations, and a lack of large‐scale general validation. Most studies focus on proof‐of‐principle experiments with limited real‐world applicability. Conclusion While promising, QSVM requires further work on scalability, noise resilience, and real‐world integration. Future research should focus on robust algorithms and empirical studies.
Quantum Machine Learning (QML) has emerged as a paradigm that combines the computational advantages of quantum computing with the predictive capabilities of machine learning to address complex data classification problems. As data dimensionality increases rapidly and classical learning algorithms face scalability constraints, QML leverages quantum parallelism, entanglement, and high-dimensional Hilbert space representations to enhance learning performance. This paper reviews and analyses advanced QML algorithms, including Quantum Support Vector Machines (QSVM), Variational Quantum Circuits (VQC), Quantum Neural Networks (QNN), and Quantum Kernel Estimation, for optimizing both binary and multi-class classification tasks under high-complexity conditions. The proposed QML framework is evaluated on benchmark datasets like MNIST, the Breast Cancer Wisconsin (BCW) dataset, and synthetic nonlinear datasets, and is compared against classical machine learning baselines, including Support Vector Machines (SVM), Random Forests (RF), and Deep Neural Networks (DNN). The results demonstrate notable improvements in classification accuracy (up to 96.8%), decision margins, and computational efficiency in quantum-suitable data regimes, while also highlighting current limitations related to noise, circuit depth, and hardware constraints. Overall, the study presents a unified QML framework, theoretical formulations, and experimental evaluations that illustrate the potential of quantum algorithms for next-generation classification tasks.
The quantum support vector machines (QSVMs) offer a paradigm change that may leverage quantum mechanical processes to outperform traditional support vector machines (SVMs) in high-dimensional and nonlinear classification tasks. These machines are located at the crossroads of supervised machine learning and quantum computing. The purpose of this chapter is to provide a comprehensive technical analysis of QSVMs, with a particular emphasis on the use of variation quantum circuits for implicit feature space transformations and the development of these circuits within the context of quantum kernel estimation. Through the use of quantum state preparation and interference, we provide a comprehensive explanation of the possible fabrication of quantum kernels that are based on inner product evaluations in exponentially huge Hilbert spaces. When it comes to boosting model expressivity beyond classical limits, the importance that entanglement and quantum feature mapping play is specifically stressed. In addition to this, we investigate algorithmic implementations on noisy intermediate-scale quantum (NISQ) hardware, focusing on problems associated with quantum decoherence, gate fidelity, and loop depth optimization. Several fields, including quantum-enhanced drug discovery, anomaly detection in quantum sensor networks, fault classification in quantum error correction, and portfolio optimization, are now the focus of research that is being conducted in order to develop real-world applications. This chapter comes to a close with an analysis of the existing theoretical limits, resource needs, and future perspectives for the use of QSVMs in machine learning applications in order to achieve a quantum advantage. In order to facilitate the development of scalable quantum machine learning models that are founded on strong mathematical and computational notions, this synthesis is geared at academics and practitioners.
Quantum machine learning (QML) has emerged as a promising interdisciplinary field that integrates principles of quantum computing with machine learning techniques to address complex computational challenges. By leveraging quantum phenomena such as superposition and entanglement, QML aims to enhance learning efficiency, improve model performance, and enable the exploration of high-dimensional feature spaces that are intractable for classical methods. This paper presents a comprehensive review of recent developments in QML, covering fundamental concepts, algorithmic taxonomies, data encoding techniques, implementation challenges, and real-world applications. Key approaches, including quantum support vector machines (QSVM), variational quantum circuits (VQC), and quantum neural networks (QNN), are systematically analyzed. Furthermore, critical challenges, including noisy intermediate-scale quantum (NISQ) limitations, barren plateaus, data encoding bottlenecks, and the lack of demonstrated quantum advantage, are discussed in detail. The review also highlights emerging applications in material informatics, energy systems, healthcare, and optimization problems. Finally, future research directions are outlined, emphasizing the need for advancements in quantum hardware, scalable algorithms, hybrid frameworks, and standardized benchmarking. This work aims to provide a structured perspective on the current state of QML and to identify opportunities in deploy it effectively in solve real-world problems.
Abstract Support vector machines (SVMs) are widely used for classification, but become computationally expensive as datasets grow and data become high-dimensional or nonlinearly separable. Quantum support vector machines (QSVMs) enhance the traditional SVMs by replacing conventional feature mappings with quantum-implemented embeddings that project data into high-dimensional Hilbert spaces, potentially improving expressive power and efficiency. However, training QSVMs on current noisy intermediate-scale quantum (NISQ) devices remains challenging, as constructing the quantum kernel matrix requires repeated circuit executions and scales quadratically with dataset size. We propose NQ-SVM , a hybrid quantum-classical method that incorporates the Nystr\"om approximation to enhance the scalability of QSVMs. By selecting a small set of landmark points, the Nystr\"om method yields a low-rank kernel approximation, reducing complexity from (O(n2)) to (O(nm)), while preserving the quantum advantages in handling high-dimensional, non-linear data. Extensive simulations demonstrate that NQ-SVM achieves comparable classification accuracy to classical SVMs and full QSVMs, while substantially reducing training time and kernel evaluation costs. These results underscore the potential of NQ-SVM as a scalable and practical hybrid framework for near-term quantum machine learning (QML).
The current development of Support Vector Machines (SVM) has reached a bottleneck, with issues such as long training times and weak interpretability when dealing with large-scale, multi-dimensional data. This paper introduces the concept of Quantum Support Vector Machines (QSVM) and achieves efficient solutions through quantum algorithms such as the HHL algorithm. The research designs a computational architecture that combines classical and quantum computing, utilizing the Pauli decomposition of Hermitian matrices to simulate the quantum simulation of Hamiltonian quantities and implementing the quantum simulation of unitary operators. Based on the conclusions, a complete quantum linear solver circuit is designed, achieving exponential growth in computational complexity. Experiments using the Iris dataset demonstrate the excellent classification performance of QSVM, which outperform classical SVM in classification accuracy, computational time complexity, and memory requirements. More efficient quantum mapping algorithms and quantum circuit optimization methods are implemented, providing new ideas and methods for the application of SVM to large-scale datasets.
As the limits of classical machine learning (ML) become increasingly evident—especially in terms of computational scalability and data processing—quantum computing emerges as a promising frontier capable of addressing these challenges. Quantum Machine Learning (QML) represents the intersection of quantum computing and traditional ML, aiming to leverage quantum phenomena such as superposition, entanglement, and quantum parallelism to enhance learning capabilities, accelerate training, and solve complex problems that are intractable for classical algorithms. This paper provides a comprehensive overview of the evolving field of QML, beginning with the theoretical foundations of quantum computing and its synergy with classical machine learning principles. We explore key QML algorithms, including quantum support vector machines (QSVM), variational quantum classifiers (VQC), quantum neural networks (QNN), and hybrid quantum-classical approaches that exemplify the practical integration of both paradigms. We further examine real-world applications of QML across domains such as drug discovery, finance, climate modeling, and optimization, where quantum enhancements have begun to show early but promising results. Despite its theoretical potential, QML faces substantial limitations, including quantum hardware instability, limited qubit scalability, noise sensitivity, and unresolved challenges in quantum data encoding and interpretability. In synthesizing recent advancements and persistent obstacles, this paper highlights the importance of continued interdisciplinary research, algorithmic refinement, and hardware evolution. We also outline future directions that could lead QML from experimental promise to practical utility, including developments in quantum error correction, benchmarking standards, and application-specific quantum architectures