Learnability of a hybrid quantum-classical neural network for graph-structured quantum data

Classical data with graph structure always exists when dealing with many real-world problems. In parallel, quantum data with graph structure also need to be investigated since they are always produced by structured quantum data sources.In this paper, we make use of a hybrid quantum-classical neural network with deep residual learning (Res-HQCNN) to learn graph-structured quantum data. Specifically, based on the special definition of graph-structured quantum data, we first find suitable cost functions so that Res-HQCNN can learn both semisupervised quantum data with or without graphs. Moreover, the training algorithm of Res-HQCNN for graph-structured training data is given in detail. Next, in order to show the learning ability of Res-HQCNN,we perform extensive experiments to show that the using of information about graph structures for quantum data can lead to better learning efficiency compared with the state of the arts. At the same time, we also design comparable experiments to explain that the using of residual learning can also bring better performance when training for deep quantum neural networks.