Experimental demonstration of quantum-enhanced machine learning in a nitrogen-vacancy-center system

We demonstrate the quantum-enhanced supervised classification of vectors in a nitrogen-vacancy ($NV$)--center system using the algorithm of Lloyd, Mohseni, and Rebentrost (arXiv:1307.0411). A $^{13}\mathrm{C}$ nuclear spin is employed to encode the vectors with the spin-triplet state of the $NV$ center as an ancilla. We design efficient methods to prepare the initial electron-nuclear entangled state within the coherence time ${T}_{2}^{*}$ of the electron spin, and then compute the distance between the test vector and the center of each class by measuring the level population through maximum likelihood estimation. Our experiment allows more than one reference vector in each class, thus forming an important enabling step toward quantum-enhanced machine learning.