  Quantum machine learning has seen considerable theoretical and practical
developments in recent years and has become a promising area for finding real
world applications of quantum computers. In pursuit of this goal, here we
combine state-of-the-art algorithms and quantum hardware to provide an
experimental demonstration of a quantum machine learning application with
provable guarantees for its performance and efficiency. In particular, we
design a quantum Nearest Centroid classifier, using techniques for efficiently
loading classical data into quantum states and performing distance estimations,
and experimentally demonstrate it on a 11-qubit trapped-ion quantum machine,
matching the accuracy of classical nearest centroid classifiers for the MNIST
handwritten digits dataset and achieving up to 100% accuracy for 8-dimensional
synthetic data.
