Application of Kernel Methods for Quantum Machine Learning

Quantum Machine Learning (QML) aims to harness the power of quantum computing to enhance classical data analysis and pattern recognition techniques. In this work, we propose a hybrid quantum–classical framework for the classification and clustering of quantum states. The quantum subroutine estimates pairwise similarities between states through a SWAP-test–based procedure, forming a kernel matrix that serves as input to a classical Support Vector Machine (SVM). This hybrid construction combines quantum feature extraction with efficient classical optimization. The overall computational cost of the classical stage scales polynomially with the number of samples and remains independent of the Hilbert-space dimension, while the quantum part depends only on the depth of the state-preparation circuit. As a result, the proposed method is well suited for implementation on Noisy Intermediate-Scale Quantum (NISQ) devices. The approach offers a scalable tool for analyzing quantum data and distinguishing complex quantum states where classical methods become intractable.