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.

该研究提出了一种名为量子扩散卷积（QDC）算子的新卷积核，该算子通过基于顶点之间的占据相关性交换的泛化扩散范例，对图进行有效地重连。此外，该研究还引入了一种多尺度变种，将 QDC 算子和传统组合型拉普拉斯算子的信息相结合。通过对谱相关性和量子动力学的研究，以及在各种数据集上的实验证明，与类似方法相比，QDC 算子在广泛使用的基准数据集上改进了预测性能。