TensorFlow Solver for Quantum PageRank in Large-Scale Networks

Abstract

Google PageRank is a prevalent and useful algorithm for ranking the significance of nodes or websites in a network, and a recent quantum counterpart for PageRank algorithm has been raised to suggest a higher accuracy of ranking comparing to Google PageRank. The quantum PageRank algorithm is essentially based on quantum stochastic walks and can be expressed using Lindblad master equation, which, however, needs to solve the Kronecker products of an O(N 4 ) dimension and requires severely large memory and time when the number of nodes N in a network increases above 150. Here, we present an efficient solver for quantum PageRank by using the Runge-Kutta method to reduce the matrix dimension to O(N 2 ) and employing TensorFlow to conduct GPU parallel computing. We demonstrate its performance in solving quantum PageRank for the USA major airline network with up to 922 nodes. Compared with the previous quantum PageRank solver, our solver dramatically reduces the required memory and time to only 1% and 0.2%, respectively, making it practical to work in a normal computer with a memory of 4-8 GB in no more than 100 seconds. This efficient solver for large-scale quantum PageRank and quantum stochastic walks would greatly facilitate studies of quantum information in real-life applications.

Classical and quantum random-walk centrality measures in multilayer networks

“…Third, we provided a mathematical framework that is applicable to both monolayer and multilayer networks. Our results complement earlier studies that focused on quantum occupation [44,42,19,55] and PageRank [27,51] centrality measures on monolayer networks.…”

“…[36] and CTQW and quantum-stochastic-walk (QSW) versions of PageRank were proposed in Refs. [27,51].…”

Large-scale Sustainable Search on Unconventional Computing Hardware

“…For the numerical calculations of the XYRank, the numerical parameters in Eqs. (14,15) are fixed to be ρ th = 10, = 60, dt = 0.005, across datasets 'harvard', 'california', and 'facebook', while for the 'wiki-topcats' dataset ρ th = 1, = 15, dt = 0.0005. The presented rankings in Table I and Table II are consistent across different choices of parameters with gain-dissipative networks converging to the similar steady state under the fixed tolerance, although the required number of iterations for convergence greatly depends on a particular choice.…”

“…The XYRank is calculated by minimising the XY Hamiltonian for the Google matrices with Eqs. (14)(15). The difference between the XYRank and PageRank distributions is indicated by green (red) arrows showing the shift in the PageRank towards a higher (lower) rating by a certain number of positions with respect to the XYRank.…”

“…Albeit enough computing resources may be available today, the future demand for prodigious amounts of processing power is beyond traditional hardware. The adiabatic quantum algorithm [13] and quantum stochastic walks [14,15] are considered as potential quantum analogues of the PageRank algorithm. Classical physical systems, such as crosspoint resistive memory arrays [16], are proposed for emulating the original PageRank algorithm based on the power method.…”