Quantum Support Vector Machines and Quantum Kernel Methods

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.