QDC: Quantum Diffusion Convolution Kernels on Graphs
This work addresses graph learning tasks, offering a novel method for enhancing GCNs, though it appears incremental as it builds on existing diffusion paradigms.
The authors tackled the problem of improving graph convolutional neural networks (GCNs) by proposing a Quantum Diffusion Convolution (QDC) kernel that rewires graphs based on quantum particle propagation, and they observed improved predictive performance on benchmark datasets compared to similar methods.
Graph convolutional neural networks (GCNs) operate by aggregating messages over local neighborhoods given the prediction task under interest. Many GCNs can be understood as a form of generalized diffusion of input features on the graph, and significant work has been dedicated to improving predictive accuracy by altering the ways of message passing. In this work, we propose a new convolution kernel that effectively rewires the graph according to the occupation correlations of the vertices by trading on the generalized diffusion paradigm for the propagation of a quantum particle over the graph. We term this new convolution kernel the Quantum Diffusion Convolution (QDC) operator. In addition, we introduce a multiscale variant that combines messages from the QDC operator and the traditional combinatorial Laplacian. To understand our method, we explore the spectral dependence of homophily and the importance of quantum dynamics in the construction of a bandpass filter. Through these studies, as well as experiments on a range of datasets, we observe that QDC improves predictive performance on the widely used benchmark datasets when compared to similar methods.