  Classical machine learning has succeeded in the prediction of both classical
and quantum phases of matter. Notably, kernel methods stand out for their
ability to provide interpretable results, relating the learning process with
the physical order parameter explicitly. Here, we exploit quantum kernels
instead. They are naturally related to the \emph{fidelity} and thus it is
possible to interpret the learning process with the help of quantum information
tools. In particular, we use a support vector machine (with a quantum kernel)
to predict and characterize second order quantum phase transitions. We explain
and understand the process of learning when the fidelity per site (rather than
the fidelity) is used. The general theory is tested in the Ising chain in
transverse field. We show that for small-sized systems, the algorithm gives
accurate results, even when trained away from criticality. Besides, for larger
sizes we confirm the success of the technique by extracting the correct
critical exponent $\nu$. Finally, we present two algorithms, one based on
fidelity and one based on the fidelity per site, to classify the phases of
matter in a quantum processor.
