A unifying primary framework for quantum graph neural networks from quantum graph states

Graph states are used to represent mathematical graphs as quantum states on quantum computers. They can be formulated through stabilizer codes or directly quantum gates and quantum states. In this paper we show that a quantum graph neural network model can be understood and realized based on graph states. We show that they can be used either as a parameterized quantum circuits to represent neural networks or as an underlying structure to construct graph neural networks on quantum computers.Comment: short version 6 pages, a few important typos are correcte

Graph Transformer: Learning Better Representations for Graph Neural Networks

Graph classifications are significant tasks for many real-world applications. Recently, Graph Neural Networks (GNNs) have achieved excellent performance on many graph classification tasks. However, most state-of-the-art GNNs face the challenge of the over-smoothing problem and cannot learn latent relations between distant vertices well. To overcome this problem, we develop a novel Graph Transformer (GT) unit to learn latent relations timely. In addition, we propose a mixed network to combine different methods of graph learning. We elucidate that the proposed GT unit can both learn distant latent connections well and form better representations for graphs. Moreover, the proposed Graph Transformer with Mixed Network (GTMN) can learn both local and global information simultaneously. Experiments on standard graph classification benchmarks demonstrate that our proposed approach performs better when compared with other competing methods

Learning Backtrackless Aligned-Spatial Graph Convolutional Networks for Graph Classification.

In this paper, we develop a novel Backtrackless Aligned-Spatial Graph Convolutional Network (BASGCN) model to learn effective features for graph classification. Our idea is to transform arbitrary-sized graphs into fixed-sized backtrackless aligned grid structures and define a new spatial graph convolution operation associated with the grid structures. We show that the proposed BASGCN model not only reduces the problems of information loss and imprecise information representation arising in existing spatially-based Graph Convolutional Network (GCN) models, but also bridges the theoretical gap between traditional Convolutional Neural Network (CNN) models and spatially-based GCN models. Furthermore, the proposed BASGCN model can both adaptively discriminate the importance between specified vertices during the convolution process and reduce the notorious tottering problem of existing spatially-based GCNs related to the Weisfeiler-Lehman algorithm, explaining the effectiveness of the proposed model. Experiments on standard graph datasets demonstrate the effectiveness of the proposed model