  The rapid development of reliable Quantum Processing Units (QPU) opens up
novel computational opportunities for machine learning. Here, we introduce a
procedure for measuring the similarity between graph-structured data, based on
the time-evolution of a quantum system. By encoding the topology of the input
graph in the Hamiltonian of the system, the evolution produces measurement
samples that retain key features of the data. We study analytically the
procedure and illustrate its versatility in providing links to standard
classical approaches. We then show numerically that this scheme performs well
compared to standard graph kernels on typical benchmark datasets. Finally, we
study the possibility of a concrete implementation on a realistic neutral-atom
quantum processor.
