Related papers: Discrete-time quantum walk algorithm for ranking n…
Hitting the exit node from the entrance node faster on a graph is one of the properties that quantum walk algorithms can take advantage of to outperform classical random walk algorithms. Especially, continuous-time quantum walks on…
The theory of random walks on finite graphs is well developed with numerous applications. In quantum walks, the propagation is governed by quantum mechanical rules; generalizing random walks to the quantum setting. They have been…
Testing graph completeness is a critical problem in computer science and network theory. Leveraging quantum computation, we present an efficient algorithm using the Szegedy quantum walk and quantum phase estimation (QPE). Our algorithm,…
We consider the problem of selecting important nodes in a random network, where the nodes connect to each other randomly with certain transition probabilities. The node importance is characterized by the stationary probabilities of the…
Random Walk is a basic algorithm to explore the structure of networks, which can be used in many tasks, such as local community detection and network embedding. Existing random walk methods are based on single networks that contain limited…
This work examines the time complexity of quantum search algorithms on combinatorial $t$-designs with multiple marked elements using the continuous-time quantum walk. Through a detailed exploration of $t$-designs and their incidence…
Various quantum-walk based algorithms have been proposed to analyse and rank the centrality of graph vertices. However, issues arise when working with directed graphs --- the resulting non-Hermitian Hamiltonian leads to non-unitary…
Empirical networks possess considerable heterogeneity of node connections, resulting in a small portion of nodes playing crucial roles in network structure and function. Yet, how to characterize nodes' influence and identify vital nodes is…
Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states.…
Comparative analyses of graph structured datasets underly diverse problems. Examples of these problems include identification of conserved functional components (biochemical interactions) across species, structural similarity of large…
Interplay between quantum interference and classical randomness can enhance performance of various quantum information tasks. In the present paper we analyze recurrence phenomena in the discrete-time quantum stochastic walk on a line, which…
The PageRank algorithm enables to rank the nodes of a network through a specific eigenvector of the Google matrix, using a damping parameter $\alpha \in ]0,1[$. Using extensive numerical simulations of large web networks, with a special…
In the study of dynamical processes on networks, there has been intense focus on network structure -- i.e., the arrangement of edges and their associated weights -- but the effects of the temporal patterns of edges remains poorly…
Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an…
Designing an operational architecture for the Quantum Internet is challenging in light of both fundamental limits imposed by physics laws and technological constraints. Here, we propose a method to abstract away most of the quantum-specific…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
We study the biased random walk process in random uncorrelated networks with arbitrary degree distributions. In our model, the bias is defined by the preferential transition probability, which, in recent years, has been commonly used to…
The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts - including ranking websites - and can be interpreted as the average portion of time spent at…
Many complex systems exhibit a natural hierarchy in which elements can be ranked according to a notion of "influence". While the complete and accurate knowledge of the interactions between constituents is ordinarily required for the…
We propose an algorithm to locate the most critical nodes to network robustness. Such critical nodes may be thought of as those most related to the notion of network centrality. Our proposal relies only on a localized spectral analysis of a…