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arXiv:2112.04768

Quantum Link Prediction in Complex Networks

João P. Moutinho, André Melo, Bruno Coelho Coutinho, István A. Kovács, Yasser Omar

Published Dec 9, 2021• 3 citations
arXivHTMLPDF

Abstract

Predicting new links in physical, biological, social, or technological networks has a significant scientific and societal impact. Path-based link prediction methods utilize explicit counting of even and odd-length paths between nodes to quantify a score function and infer new or unobserved links. Here, we propose a quantum algorithm for path-based link prediction, QLP, using a controlled continuous-time quantum walk to encode even and odd path-based prediction scores. Through classical simulations on a few real networks, we confirm that the quantum walk scoring function performs similarly to other path-based link predictors. In a brief complexity analysis we identify the potential of our approach in uncovering a quantum speedup for path-based link prediction.

DOI
10.48550/arxiv.2112.04768

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Predicting new links in physical, biological, social, or technological networks has a significant scientific and societal impact. Path-based link prediction methods utilize explicit counting of even and odd-length paths between nodes to quantify a score function and infer new or unobserved links. Here, we propose a quantum algorithm for path-based link prediction, QLP, using a controlled continuous-time quantum walk to encode even and odd path-based prediction scores. Through classical simulations on a few real networks, we confirm that the quantum walk scoring function performs similarly to other path-based link predictors. In a brief complexity analysis we identify the potential of our approach in uncovering a quantum speedup for path-based link prediction.
Predicting new links in physical, biological, social, or technological networks has a significant scientific and societal impact. Path-based link prediction methods utilize the explicit counting of even- and odd-length paths between nodes to quantify a score function and infer new or unobserved links. Here, we propose a quantum algorithm for path-based link prediction using a controlled continuous-time quantum walk to encode even and odd path-based prediction scores. Through classical simulations on a few real networks, we confirm that the quantum walk scoring function performs similarly to other path-based link predictors. In a brief complexity analysis we identify the potential of our approach in uncovering a quantum speedup for path-based link prediction.
Prediction of missing links is an important part of many applications, such as friends' recommendations on social media, reduction of economic cost of protein functional modular mining, and implementation of accurate recommendations in the shopping platform. However, the existing algorithms for predicting missing links fall short in the accuracy and the efficiency. To ameliorate these, we propose a simplified quantum walk model whose Hilbert space dimension is only twice the number of nodes in a complex network. This property facilitates simultaneous consideration of the self-loop of each node and the common neighbour information between arbitrary pair of nodes. These effects decrease the negative effect generated by the interference effect in quantum walks while also recording the similarity between nodes and its neighbours. Consequently, the observed probability after the two-step walk is utilised to represent the score of each link as a missing link, by which extensive computations are omitted. Using the AUC index as a performance metric, the proposed model records the highest average accuracy in the prediction of missing links compared to 14 competing algorithms in nine real complex networks. Furthermore, experiments using the precision index show that our proposed model ranks in the first echelon in predicting missing links. These performances indicate the potential of our simplified quantum walk model for applications in network alignment and functional modular mining of protein-protein networks.
Link prediction methods use patterns in known network data to infer which connections may be missing. Previous work has shown that continuous-time quantum walks can be used to represent path-based link prediction, which we further study here to develop a more optimized quantum algorithm. Using a sampling framework for link prediction, we analyze the query access to the input network required to produce a certain number of prediction samples. Considering both well-known classical path-based algorithms using powers of the adjacency matrix as well as our proposed quantum algorithm for path-based link prediction, we argue that there is a polynomial quantum advantage on the dependence on N, the number of nodes in the network. We further argue that the complexity of our algorithm, although sub-linear in N, is limited by the complexity of performing a quantum simulation of the network's adjacency matrix, which may prove to be an important problem in the development of quantum algorithms for network science in general.
Original scientific paperLink prediction is one of the key issues of complex networks, which attracts much research interest currently.Many link prediction methods have been proposed so far.The classical random walk as an effective tool has been widely used to study the link prediction problems.Quantum walk is the quantum analogue of classical random walk.Numerous research results show that quantum algorithms using quantum walk outperform their classical counterparts in many applications, such as graph matching and searching.But there have been few studies of the link prediction based on quantum walk, especially on discrete-time quantum walk.This paper proposes a new link prediction method based on discrete-time quantum walk.Experiment results show that prediction accuracy of our method is better than the typical methods.The time complexity of our method running on classical computers, compared with the methods based on classical random walk, is slightly higher.But our method can be greatly accelerated by executing on quantum computers.
Compared with the classical random walk, the quantum walk has the advantages of less time to find the target node and less time scattered from the source node to all nodes. Therefore, in order to further improve the accuracy of link prediction algorithms, a link prediction algorithm based on discrete-time quantum walk (DTQW) on weighted graphs is proposed by integrating node attributes and introducing the idea of assigning weights to edges in network dynamics. In this algorithm, a weighted graph is first constructed based on the attribute information of nodes in the graph, and then a DTQW model is constructed based on the weighted graph. Then, under the control of the evolution operator, the walker performs a DTQW on the weighted graph; Finally, the link prediction algorithm is implemented by defining the similarity between nodes based on the average probability of the walker reaching each node. The experimental results show that in three real social networks, Douban, Weibo and Zhihu, this algorithm has different degrees of improvement in prediction accuracy and the algorithm stability is among the top in comparison with the optimal benchmark prediction algorithm.
Quantum walks provide a natural framework to approach graph problems with quantum computers, exhibiting speedups over their classical counterparts for tasks such as the search for marked nodes or the prediction of missing links. Continuous-time quantum walk algorithms assume that we can simulate the dynamics of quantum systems where the Hamiltonian is given by the adjacency matrix of the graph. It is known that such can be simulated efficiently if the underlying graph is row-sparse and efficiently row-computable. While this is sufficient for many applications, it limits the applicability for this class of algorithms to study real world complex networks, which, among other properties, are characterized by the existence of a few densely connected nodes, called hubs. In other words, complex networks are typically not row-sparse, even though the average connectivity over all nodes can be very small. In this work, we extend the state-of-the-art results on quantum simulation to graphs that contain a small number of hubs, but that are otherwise sparse. Hopefully, our results may lead to new applications of quantum computing to network science.