Experimental Quantum Kernels in NMR Applied to Machine Learning with Classical and Quantum Data

Abstract

Kernel methods enable the learning of nonlinear functions by mapping data into high-dimensional spaces, where linear techniques can then be applied effectively. In quantum kernel methods, classical data is encoded into quantum states, thereby leveraging the exponentially large Hilbert space available in quantum systems. This thesis implements quantum kernel methods using nuclear magnetic resonance (NMR) as a platform to control and measure nuclear spin systems. In this work, classical data is encoded through tailored pulse sequences that generate multiple quantum coherences, first in solid-state, followed by liquid-state NMR setups. We demonstrate the effectiveness of the resulting quantum kernels by applying them to standard machine learning tasks such as one-dimensional regression using a kernel ridge regression model and two-dimensional classification using Support Vector Machines (SVMs). In addition, we extend the method to process quantum data directly. For this, we develop a protocol to compute quantum kernels for unparameterized operator inputs and present experimental results for the classification of quantum operators based on their entangling properties. Overall, our results confirm that quantum kernels derived from NMR quantum systems can be successfully used for machine learning tasks involving both classical and quantum data.