Experimental quantum kernel trick with nuclear spins in a solid

We employ so-called quantum kernel estimation to exploit complex dynamics of solid-state nuclear magnetic resonance for machine learning. propose map an input a feature space by input-dependent Hamiltonian evolution, and the is estimated interference evolution. Simple learning tasks, namely one-dimensional regression tasks two-dimensional classification are performed using proton spins which exhibit correlation over 10 spins. also numerical simulations evaluate performance without noise inevitable in actual experiments. The trained model tends increase with longer evolution time, or equivalently, larger number involved certain tasks. This work presents experiment one largest systems date.