Application of Kernel Methods for Quantum Machine Learning

Quantum machine learning (QML) is an emerging field that combines quantum computing with classical machine learning techniques. This work presents a hybrid quantum-classical algorithm for the classification and clustering of quantum states. The quantum component estimates overlaps between quantum states using a SWAP-test analogue, which are used to construct a kernel matrix. This kernel is then employed by a classical Support Vector Machine (SVM) for learning tasks. A key advantage of this approach is that the complexity of the classical part scales polynomially with the number of samples, independent of the quantum state dimension. The quantum complexity depends solely on the state preparation circuit depth, making it suitable for Noisy Intermediate-Scale Quantum (NISQ) devices. This method provides a promising path for efficiently analyzing quantum data where classical methods fail due to the exponential growth of the state space.