Quantum Walk Neural Networks for Graph-Structured Data

Stefan Dernbach, Arman Mohseni-Kabir, Siddharth Pal, Don Towsley

Abstract: In recent years, neural network architectures designed to operate on graph-structured data have pushed the state-of-the-art in the field. A large set of these architectures utilize a form of classical random walks to diffuse information throughout the graph. We propose quantum walk neural networks (QWNN), a novel 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 then be applied to graph-structured data. We demonstrate the use of this model on a variety of prediction tasks on graphs involving temperature, biological, and molecular datasets.