Related papers: Discrete-Time Open Quantum Walks for Vertex Rankin…
In this paper we isolate the combinatorial property responsible (at least in part) for the computational speedups recently observed in some quantum walk algorithms. We find that continuous-time quantum walks can exploit the covering space…
In a network, the vertices with similar characteristics construct communities. The vertices in a community are well-connected. Detecting the communities in a network is a challenging and important problem in the theory of complex networks.…
There are presently two models for quantum walks on graphs. The "coined" walk uses discrete time steps, and contains, besides the particle making the walk, a second quantum system, the coin, that determines the direction in which the…
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.…
We study the typical behavior of a generalized version of Google's PageRank algorithm on a large family of inhomogeneous random digraphs. This family includes as special cases directed versions of classical models such as the…
This paper proposes a computational procedure that applies a quantum algorithm to train classical artificial neural networks. The goal of the procedure is to apply quantum walk as a search algorithm in a complete graph to find all synaptic…
Quantum walks play an important role in the area of quantum algorithms. Many interesting problems can be reduced to searching marked states in a quantum Markov chain. In this context, the notion of quantum hitting time is very important,…
The "abstract search algorithm" is a well known quantum method to find a marked vertex in a graph. It has been applied with success to searching algorithms for the hypercube and the two-dimensional grid. In this work we provide an example…
Quantum walks on graphs are ubiquitous in quantum computing finding a myriad of applications. Likewise, random walks on graphs are a fundamental building block for a large number of algorithms with diverse applications. While the…
We define a discrete-time, coined quantum walk on weighted graphs that is inspired by Szegedy's quantum walk. Using this, we prove that many lackadaisical quantum walks, where each vertex has $l$ integer self-loops, can be generalized to a…
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…
An important method for search engine result ranking works by finding the principal eigenvector of the "Google matrix." Recently, a quantum algorithm for preparing this eigenvector and evidence of an exponential speedup for some scale-free…
In this work, we generalize the recently-introduced graph composition framework to the non-boolean setting. A quantum algorithm in this framework is represented by a hypergraph, where each hyperedge is adjacent to multiple vertices. The…
This work introduces a graph-phased Szegedy's quantum walk, which incorporates link phases and local arbitrary phase rotations (APR), unlocking new possibilities for quantum algorithm efficiency. We demonstrate how to adapt quantum circuits…
This paper shows that pairwise PageRank orders emerge from two-hop walks. The main tool used here refers to a specially designed sign-mirror function and a parameter curve, whose low-order derivative information implies pairwise PageRank…
In the search engine of Google, the PageRank algorithm plays a crucial role in ranking the search results. The algorithm quantifies the importance of each web page based on the link structure of the web. We first provide an overview of the…
Google employs PageRank to rank web pages, determining the order in which search results are presented to users based on their queries. PageRank is primarily utilized for directed networks, although there are instances where it is also…
We propose a new method for designing quantum search algorithms for finding a "marked" element in the state space of a classical Markov chain. The algorithm is based on a quantum walk \'a la Szegedy (2004) that is defined in terms of the…
Random walks simulate the randomness of objects, and are key instruments in various fields such as computer science, biology and physics. The counter part of classical random walks in quantum mechanics are the quantum walks. Quantum walk…
PageRank (PR) is a fundamental tool for assessing the relative importance of the nodes in a network. In this paper, we propose a measure, weighted PageRank (WPR), extended from the classical PR for weighted, directed networks with possible…