  Quantum machine learning (QML) models based on parameterized quantum circuits
are often highlighted as candidates for quantum computing's near-term ``killer
application''. However, the understanding of the empirical and generalization
performance of these models is still in its infancy. In this paper we study how
to balance between training accuracy and generalization performance (also
called structural risk minimization) for two prominent QML models introduced by
Havl\'{i}\v{c}ek et al. (Nature, 2019), and Schuld and Killoran (PRL, 2019).
Firstly, using relationships to well understood classical models, we prove that
two model parameters -- i.e., the dimension of the sum of the images and the
Frobenius norm of the observables used by the model -- closely control the
models' complexity and therefore its generalization performance. Secondly,
using ideas inspired by process tomography, we prove that these model
parameters also closely control the models' ability to capture correlations in
sets of training examples. In summary, our results give rise to new options for
structural risk minimization for QML models.

Quantum Physics;Machine Learning