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Comparing classical and quantum PageRanks

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Abstract

Following recent developments in quantum PageRanking, we present a comparative analysis of discrete-time and continuous-time quantum-walk-based PageRank algorithms. Relative to classical PageRank and to different extents, the quantum measures better highlight secondary hubs and resolve ranking degeneracy among peripheral nodes for all networks we studied in this paper. For the discrete-time case, we investigated the periodic nature of the walker’s probability distribution for a wide range of networks and found that the dominant period does not grow with the size of these networks. Based on this observation, we introduce a new quantum measure using the maximum probabilities of the associated walker during the first couple of periods. This is particularly important, since it leads to a quantum PageRanking scheme that is scalable with respect to network size.

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Acknowledgements

This work was supported by resources provided by the Pawsey Supercomputing Centre with funding from the Australian Government and the Government of Western Australia. TL thanks the Okinawa Institute of Science and Technology as much background learning was done there under the research internship programme, supervised by Thomas Busch and Chandrashekar Madaiah.

Author contributions TL made the most significant contribution to this work, including the development of methodology, detailed simulation and analysis especially for DTQW, as well as preparation of the manuscript. JT and JR worked on the open-system CTQW formulation, simulation, and analysis; MS provided very helpful feedback on network analysis in general; and JW provided direction and guidance.

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Authors and Affiliations

  1. School of Physics, The University of Western Australia, Crawley, WA, 6009, Australia

    T. Loke, J. W. Tang, J. Rodriguez & J. B. Wang

  2. School of Physics, Nanjing University, Nanjing, Jiangsu, China

    J. W. Tang

  3. School of Mathematics and Statistics, The University of Western Australia, Crawley, WA, 6009, Australia

    M. Small

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  1. T. Loke
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  2. J. W. Tang
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  3. J. Rodriguez
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  4. M. Small
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  5. J. B. Wang
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Correspondence to J. B. Wang.

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Loke, T., Tang, J.W., Rodriguez, J. et al. Comparing classical and quantum PageRanks. Quantum Inf Process 16, 25 (2017). https://doi.org/10.1007/s11128-016-1456-z

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