Machine learning with solid-state NMR using quantum kernel

We employ so-called quantum kernel estimation to exploit complex quantum dynamics of solid-state NMR for machine learning. Kernel method is a popular branch in machine learning algorithms where only the inner products among feature vectors each representing an input datum are required to construct a prediction model. We propose to map an input to a feature space by input-dependent Hamiltonian evolution, and the kernel is estimated by the interference of the evolution. Simple machine learning tasks, namely one-dimensional fitting tasks and two-dimensional classification tasks, are performed as demonstrations. The performance of the trained model tends to increase with the longer evolution time, or equivalently, with a larger number of spins involved in the dynamics. This work can be regarded as one of the baselines for this emerging field.