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.
 Quantum information technologies, and intelligent learning systems, are both emergent technologies that will likely have a transforming impact on our society. The respective underlying fields of research -- quantum information (QI) versus machine learning (ML) and artificial intelligence (AI) -- have their own specific challenges, which have hitherto been investigated largely independently. However, in a growing body of recent work, researchers have been probing the question to what extent these fields can learn and benefit from each other. QML explores the interaction between quantum computing and ML, investigating how results and techniques from one field can be used to solve the problems of the other. Recently, we have witnessed breakthroughs in both directions of influence. For instance, quantum computing is finding a vital application in providing speed-ups in ML, critical in our "big data" world. Conversely, ML already permeates cutting-edge technologies, and may become instrumental in advanced quantum technologies. Aside from quantum speed-up in data analysis, or classical ML optimization used in quantum experiments, quantum enhancements have also been demonstrated for interactive learning, highlighting the potential of quantum-enhanced learning agents. Finally, works exploring the use of AI for the very design of quantum experiments, and for performing parts of genuine research autonomously, have reported their first successes. Beyond the topics of mutual enhancement, researchers have also broached the fundamental issue of quantum generalizations of ML AI concepts. This deals with questions of the very meaning of learning and intelligence in a world that is described by quantum mechanics. In this review, we describe the main ideas, recent developments, and progress in a broad spectrum of research investigating machine learning and artificial intelligence in the quantum domain.  In several applications the information is naturally represented by graphs. Traditional approaches cope with graphical data structures using a preprocessing phase which transforms the graphs into a set of flat vectors. However, in this way, important topological information may be lost and the achieved results may heavily depend on the preprocessing stage. This paper presents a new neural model, called graph neural network (GNN), capable of directly processing graphs. GNNs extends recursive neural networks and can be applied on most of the practically useful kinds of graphs, including directed, undirected, labelled and cyclic graphs. A learning algorithm for GNNs is proposed and some experiments are discussed which assess the properties of the model. This paper initiates the study of quantum computing within the constraints of using a polylogarithmic (O(logkn), k?1) number of qubits and a polylogarithmic number of computation steps. The current research in the literature has focussed on using a polynomial number of qubits. A new mathematical model of computation called Quantum Neural Networks (QNNs) is defined, building on Deutsch's model of quantum computational network. The model introduces a nonlinear and irreversible gate, similar to the speculative operator defined by Abrams and Lloyd. The precise dynamics of this operator are defined and while giving examples in which nonlinear Schrodinger's equations are applied, we speculate on its possible implementation. The many practical problems associated with the current model of quantum computing are alleviated in the new model. It is shown that QNNs of logarithmic size and constant depth have the same computational power as threshold circuits, which are used for modeling neural networks. QNNs of polylogarithmic size and polylogarithmic depth can solve the problems in NC, the class of problems with theoretically fast parallel solutions. Thus, the new model may indeed provide an approach for building scalable parallel computers. A digital computer is generally believed to be an efficient universal computing device; that is, it is believed to be able to simulate any physical computing device with an increase in computation time by at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. This paper considers factoring integers and finding discrete logarithms, two problems that are generally thought to be hard on classical computers and that have been used as the basis of several proposed cryptosystems. Efficient randomized algorithms are given for these two problems on a hypothetical quantum computer. These algorithms take a number of steps polynomial in the input size, for example, the number of digits of the integer to be factored. Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with a number of parameters independent of the input size, resulting in efficient deep architectures. Recent progress implies that a crossover between machine learning and quantum information processing benefits both fields. Traditional machine learning has dramatically improved the benchmarking an ...