In recent years, along with the overwhelming advances in the field of neural information processing, quantum information processing (QIP) has shown significant progress in solving problems that are intractable on classical computers. Quantum machine learning (QML) explores the ways in which these fields can learn from one another. We propose quantum walk neural networks (QWNN), a new graph neural network architecture based on quantum random walks, the quantum parallel to classical random walks. A QWNN learns a quantum walk on a graph to construct a diffusion operator which can be applied to a signal on a graph. We demonstrate the use of the network for prediction tasks for graph structured signals.
The second approach of interest due to Kipf and Welling @cite_15 , was proposed to tackle semi-supervised learning using a CNN architecture built via a localized approximation of spectral graph convolutions. The proposed Graph Convolutional Neural Network (GCNN) works in a similar fashion as DCNN described above. Here the augmented adjacency matrix @math and degree matrix @math replace @math and @math . @math can be equivalently thought of as the adjacency matrix of @math with a self-loop on every node. The GCNN uses a doubly normalized version of @math to diffuse the input with respect to the local neighborhood as follows, [ Y =h( D ^ -1 2 A D ^ -1 2 XW ), ] where, again, @math are learning weights and @math is an activation function.
@cite_15
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We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions. Our model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes. In a number of experiments on citation networks and on a knowledge graph dataset we demonstrate that our approach outperforms related methods by a significant margin.