Quantum machine learning beyond kernel methods. (arXiv:2110.13162v1 [quant-ph])

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.