TensorFlow solver for quantum PageRank in large-scale networks

Hao Tang; Ruoxi Shi; Tian-Shen He; Yan-Yan Zhu; Tian-Yu Wang; Marcus Lee; Xian-Min Jin

doi:10.1016/j.scib.2020.09.009

TensorFlow solver for quantum PageRank in large-scale networks

Sci Bull (Beijing). 2021 Jan 30;66(2):120-126. doi: 10.1016/j.scib.2020.09.009. Epub 2020 Sep 8.

Authors

Hao Tang¹, Ruoxi Shi², Tian-Shen He², Yan-Yan Zhu³, Tian-Yu Wang², Marcus Lee⁴, Xian-Min Jin⁵

Affiliations

¹ Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China; CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China.
² Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China.
³ School of Physical Science, University of Chinese Academy of Sciences, Beijing 100049, China.
⁴ Department of Physics, Cambridge University, Cambridge CB3 0HE, UK.
⁵ Center for Integrated Quantum Information Technologies (IQIT), School of Physics and Astronomy and State Key Laboratory of Advanced Optical Communication Systems and Networks, Shanghai Jiao Tong University, Shanghai 200240, China; CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China. Electronic address: xianmin.jin@sjtu.edu.cn.

PMID: 36654218
DOI: 10.1016/j.scib.2020.09.009

Abstract

Google PageRank is a prevalent 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(N⁴) 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(N²) and employing TensorFlow to conduct GPU parallel computing. We demonstrate its performance in solving quantum stochastic walks on Erdös-Rényi graphs using an RTX 2060 GPU. The test on the graph of 6000 nodes requires a memory of 5.5 GB and time of 223 s, and that on the graph of 1000 nodes requires 226 MB and 3.6 s. Compared with QSWalk, a currently prevalent Mathematica solver, our solver for the same graph of 1000 nodes reduces the required memory and time to only 0.2% and 0.05%. We apply the solver to quantum PageRank for the USA major airline network with up to 922 nodes, and to quantum stochastic walk on a glued tree of 2186 nodes. This efficient solver for large-scale quantum PageRank and quantum stochastic walks would greatly facilitate studies of quantum information in real-life applications.

Keywords: Lindblad master equation; Quantum PageRank; Quantum stochastic walk; Runge-Kutta method; TensorFlow GPU parallel computing.