Quantum machine learning beyond kernel methods

With noisy intermediate-scale quantum computers showing great promise for near-term applications, a number of machine learning algorithms based on parametrized quantum circuits have been suggested as possible means to achieve learning advantages. Yet, our understanding of how these quantum machine learning models compare, both to existing classical models and to each other, remains limited. A big step in this direction has been made by relating them to so-called kernel methods from classical machine learning. By building on this connection, previous works have shown that a systematic reformulation of many quantum machine learning models as kernel models was guaranteed to improve their training performance. In this work, we first extend the applicability of this result to a more general family of parametrized quantum circuit models called data re-uploading circuits. Secondly, we show, through simple constructions and numerical simulations, that models defined and trained variationally can exhibit a critically better generalization performance than their kernel formulations, which is the true figure of merit of machine learning tasks. Our results constitute another step towards a more comprehensive theory of quantum machine learning models next to kernel formulations.