  Classification, the computational process of categorizing an input into
pre-existing classes, is now a cornerstone in modern computation in the era of
machine learning. Here we propose a new type of quantum classifier, based on
quantum transport of particles in a trained quantum network. The classifier is
based on sending a quantum particle into a network and measuring the particle's
exit point, which serves as a "class" and can be determined by changing the
network parameters. Using this scheme, we demonstrate three examples of
classification; in the first, wave functions are classified according to their
overlap with predetermined (random) groups. In the second, we classify
wave-functions according to their level of localization. Both examples use
small training sets and achieve over 90\% precision and recall. The third
classification scheme is a "real-world problem", concerning classification of
catalytic aromatic-aldehyde substrates according to their reactivity. Using
experimental data, the quantum classifier reaches an average 86\%
classification accuracy. We show that the quantum classifier outperforms its
classical counterpart for these examples, thus demonstrating quantum advantage,
especially in the regime of "small data". These results pave the way for a
novel classification scheme, which can be implemented as an algorithm, and
potentially realized experimentally on quantum hardware such as photonic
networks.
