Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data in the form of pairs of input and output quantum states associated with the vertices of a graph, together with edges encoding correlations between the vertices. We explain how to systematically exploit this additional graph structure to improve quantum learning algorithms. These algorithms are numerically simulated and exhibit excellent learning behavior. Scalable quantum implementations of the learning procedures are likely feasible on the next generation of quantum computing devices.

Graph structures are ubiquitous throughout the natural sciences. Here we develop an approach that exploits the quantum source's graph structure to improve learning via an arbitrary quantum neural network (QNN) ansatz.In particular, we devise and optimize a self-supervised objective to capture the information-theoretic closeness of the quantum states in the training of a QNN. Numerical simulations show that our approach improves the learning efficiency and the generalization behavior of the base QNN. On a practical note, scalable quantum implementations of the learning procedure described in this paper are likely feasible on the next generation of quantum computing devices.