Experimental Machine Learning with Classical and Quantum Data via NMR Quantum Kernels

TL;DR

This paper demonstrates the implementation of quantum kernel methods on an NMR platform, showing their potential for classical and quantum machine learning tasks through experimental encoding and classification of data.

Contribution

It introduces a novel experimental approach to quantum kernels using NMR, including a double-layered register for handling complex inputs and validating the method both numerically and experimentally.

Findings

Quantum kernels can be effectively implemented on NMR systems.

The extended kernel handles non-parametrized operator inputs.

Experimental results show good generalization to unseen data.

Abstract

Kernel methods map data into high-dimensional spaces, enabling linear algorithms to learn nonlinear functions without explicitly storing the feature vectors. Quantum kernel methods promise efficient learning by encoding feature maps into exponentially large Hilbert spaces inherent in quantum systems. In this work, we implement quantum kernels on a 10-qubit star-topology register in a nuclear magnetic resonance (NMR) platform. We experimentally encode classical data in the evolution of multiple quantum coherence orders using data-dependent unitary transformations and then demonstrate one-dimensional regression and two-dimensional classification tasks. By extending the register to a double-layered star configuration, we propose an extended quantum kernel to handle non-parametrized operator inputs. Specifically, we set up a kernel for the classification of entangling and non-entangling operations and then validate this kernel first numerically by computing it on a double-layered star register and then experimentally by computing it on a three-qubit NMR register. Our results show that this kernel exhibits an ability to generalize well over unseen data. These results confirm that quantum kernels possess strong capabilities in classical as well as quantum machine learning tasks.