Comparing classical and quantum PageRanks

Loke, T.; Tang, Jiangshan; Rodriguez, J. P. J.; Small, Michael; Wang, J. B.

doi:10.48550/arxiv.1511.04823

Cited by 4 publications

(5 citation statements)

References 2 publications

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“…As an interesting application of QSWs to directed graphs, we now briefly discuss the recent continuous-time quantum page rank algorithm (QPR) introduced by Sánchez-Burillo et al [20,45], based on the well-known (classical) Page Rank algorithm (CPR) [46] which is a key component of the Google search engine. The basic idea of CPR is to represent the world wide web as a directed graph, with each webpage representing a vertex and the links on each page representing outward edges to the pages linked to; the algorithm then carries out a CRW on this graph to determine the centrality, or "rank", of each page.…”

Section: Quantum Page Rankmentioning

confidence: 99%

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QSWalk: A Mathematica package for quantum stochastic walks on arbitrary graphs

Falloon

Rodriguez

Wang

2017

Computer Physics Communications

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We present a Mathematica package, QSWalk, to simulate the time evaluation of Quantum Stochastic Walks (QSWs) on arbitrary directed and weighted graphs. QSWs are a generalization of continuous time quantum walks that incorporate both coherent and incoherent dynamics and as such, include both quantum walks and classical random walks as special cases. The incoherent component allows for quantum walks along directed graph edges. The dynamics of QSWs are expressed using the Lindblad formalism, originally developed for open quantum systems, which frames the problem in the language of density matrices. For a QSW on a graph of N vertices, we have a sparse superoperator in an N 2 -dimensional space, which can be solved efficiently using the built-in MatrixExp function in Mathematica. We illustrate the use of the QSWalk package through several example case studies. Nature of problem:The QSWalk package provides a method for simulating quantum stochastic walks on arbitrary (directed/undirected, weighted/unweighted) graphs. Solution method:For an N -vertex graph, the solution of a quantum stochastic walk can be expressed as an N 2 ×N 2 sparse matrix exponential. The QSWalk package makes use of Mathematica's sparse linear algebra routines to solve this efficiently. Restrictions:The size of graphs that can be treated is constrained by available memory. Running time:Running time depends on the size of the graph and the propagation time of the walk.

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Section: Quantum Page Rankmentioning

confidence: 99%

“…A detailed discussion of the QPR and CPR algorithms can be found in Refs. [20,45]; here we just describe the main features. We begin with a directed graph G having N vertices and adjacency matrix A.…”

Section: Quantum Page Rankmentioning

confidence: 99%

QSWalk: A Mathematica package for quantum stochastic walks on arbitrary graphs

Falloon

Rodriguez

Wang

2017

Computer Physics Communications

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“…They have also been explored as a basis for quantum algorithms. A QSW-based variant of the PageRank search engine algorithm exhibited final distributions which broke undesirable degeneracies present in the classical version, while also speeding up the rate of convergence [6,7].…”

Section: Introductionmentioning

confidence: 99%

QSW_MPI: a framework for parallel simulation of quantum stochastic walks

Matwiejew,

Wang

2020

Preprint

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QSW MPI is a python package developed for the modeling of quantum stochastic walks, a generalization of the classical random walk and continuous-time quantum walk in the Lindblad formalism. This model allows for the study of a wide range of Markovian open quantum systems subject to varying degrees of incoherent scattering. Consisting of a python interface built on parallelized Fortran libraries utilizing sparse data structures; QSW MPI is scalable to massively parallel computers, making possible the simulation of walks on graphs with many thousands of vertices. QSW MPI also provides explicit support for an extension of the standard quantum stochastic walk model to the study of non-Hermitian absorption and emission processes.

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“…In the last two decades, quantum walks have produced a wide variety of quantum algorithms to address different problems, such as the graph isomorphism problem [1][2][3], ranking nodes in a network [4][5][6], and quantum simulation [7][8][9][10][11]. There are two main types of quantum walks, the discrete-time quantum walk [12,13] and the continuous-time quantum walk [14,15].…”

Section: Introductionmentioning

confidence: 99%

Efficient quantum circuits for Szegedy quantum walks

Loke

Wang

2017

Annals of Physics

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A major advantage in using Szegedy's formalism over discrete-time and continuous-time quantum walks lies in its ability to define a unitary quantum walk on directed and weighted graphs. In this paper, we present a general scheme to construct efficient quantum circuits for Szegedy quantum walks that correspond to classical Markov chains possessing transformational symmetry in the columns of the transition matrix. In particular, the transformational symmetry criteria do not necessarily depend on the sparsity of the transition matrix, so this scheme can be applied to non-sparse Markov chains. Two classes of Markov chains that are amenable to this construction are cyclic permutations and complete bipartite graphs, for which we provide explicit efficient quantum circuit implementations. We also prove that our scheme can be applied to Markov chains formed by a tensor product. We also briefly discuss the implementation of Markov chains based on weighted interdependent networks. In addition, we apply this scheme to construct efficient quantum circuits simulating the Szegedy walks used in the quantum Pagerank algorithm for some classes of non-trivial graphs, providing a necessary tool for experimental demonstration of the quantum Pagerank algorithm.

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Comparing classical and quantum PageRanks

Cited by 4 publications

References 2 publications

QSWalk: A Mathematica package for quantum stochastic walks on arbitrary graphs

QSWalk: A Mathematica package for quantum stochastic walks on arbitrary graphs

QSW_MPI: a framework for parallel simulation of quantum stochastic walks

Efficient quantum circuits for Szegedy quantum walks

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