Related papers: Discrete-Time Open Quantum Walks for Vertex Rankin…
Quantum random walks have been shown to be powerful quantum algorithms for certain tasks on graphs like database searching, quantum simulations etc. In this work we focus on its applications for the graph isomorphism problem. In particular…
The staggered quantum walk model allows to establish an unprecedented connection between discrete-time quantum walks and graph theory. We call attention to the fact that a large subclass of the coined model is included in Szegedy's model,…
A randomly walking quantum particle evolving by Schr\"odinger's equation searches on $d$-dimensional cubic lattices in $O(\sqrt{N})$ time when $d \ge 5$, and with progressively slower runtime as $d$ decreases. This suggests that graph…
Recently bipartite graphs have been widely used to represent the relationship two sets of items for information retrieval applications. The Web offers a wide range of data which can be represented by bipartite graphs, such us movies and…
The aim of this work is to develop a framework for realising quantum network algorithms with the use of prior knowledge about the structure of the network. We seek to obtain computational methods that allows us to locally determine network…
Fast computational algorithms are in constant demand, and their development has been driven by advances such as quantum speedup and classical acceleration. This paper intends to study search algorithms based on quantum walks in quantum…
Biomolecular networks, such as protein-protein interactions, gene-gene associations, and cell-cell interactions, offer valuable insights into the complex organization of biological systems. These networks are key to understanding cellular…
We consider the problem of finding a marked vertex in a graph from an arbitrary starting distribution, using a quantum walk based algorithm. We work in the framework introduced by Belovs which showed how to detect the existence of a marked…
De novo DNA sequence assembly is based on finding paths in overlap graphs, which is a NP-hard problem. We developed a quantum algorithm for de novo assembly based on quantum walks in graphs. The overlap graph is partitioned repeatedly to…
We define the discrete-time quantum walk on complex networks and utilize it for community detection. We numerically show that the quantum walk with the Fourier coin is localized in a community to which the initial node belongs. Meanwhile,…
In recent years, new 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…
We study the quantum query algorithms for simplex finding, a generalization of triangle finding to hypergraphs. This problem satisfies a rank-reduction property: a quantum query algorithm for finding simplices in rank-$r$ hypergraphs can be…
We investigate the behavior of coherence in scattering quantum walk search on complete graph under the condition that the total number of vertices of the graph is greatly larger than the marked number of vertices we are searching, $N \gg…
PageRank is a popular centrality metric that assigns importance to the vertices of a graph based on its neighbors and their score. Efficient parallel algorithms for updating PageRank on dynamic graphs is crucial for various applications,…
We study scattering quantum walks on highly symmetric graphs and use the walks to solve search problems on these graphs. The particle making the walk resides on the edges of the graph, and at each time step scatters at the vertices. All of…
We study quantum transport on finite discrete structures and we model the process by means of continuous-time quantum walks. A direct and effective comparison between quantum and classical walks can be attained based on the average…
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computational complexity of spatial search by continuous-time…
Processing large complex networks recently attracted considerable interest. Complex graphs are useful in a wide range of applications from technological networks to biological systems like the human brain. Sometimes these networks are…
We analyze continuous-time quantum and classical random walk on spidernet lattices. In the framework of Stieltjes transform, we obtain density of states, which is an efficiency measure for the performance of classical and quantum mechanical…
Comparative analyses of protein-protein interaction networks play important roles in the understanding of biological processes. However, the growing enormity of available data on the networks becomes a computational challenge for the…