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On new PageRank computation methods using quantum computing

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Abstract

In this paper we propose several new quantum computation algorithms as an original contribution to the domain of PageRank algorithm theory, Spectral Graph Theory and Quantum Signal Processing. We first propose an application to PageRank of the HHL quantum algorithm for linear equation systems. We then introduce one of the first Quantum-Based Algorithms to perform a directed Graph Fourier Transform with a low gate complexity. After proposing a generalized PageRank formulation, based on ideas stemming from Spectral Graph Theory, we show how our quantum directed graph Fourier Transform can be applied to compute our generalized version of the PageRank.

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Data availability

The datasets generated during and/or analyzed during the current study are available in the repository Generalized PageRank on Gitlab: https://gitlab-research.centralesupelec.fr/theodore.chapuis-chkaiban/generalised_pagerank

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Author notes

  1. Zeno Toffano and Benoît Valiron contributed equally to this work.

Authors and Affiliations

  1. Department of Computer Science, CentraleSupélec, 3 Rue Joliot-Curie, 91190, Gif-Sur-Yvette, France

    Théodore Chapuis-Chkaiban

  2. CNRS, CentraleSupélec, Laboratoire des signaux et systèmes, Université Paris-Saclay, 91190, Gif-sur-Yvette, France

    Zeno Toffano

  3. CNRS, ENS Paris-Saclay, CentraleSupélec, Laboratoire Méthodes Formelles, Université Paris-Saclay, 91190, Gif-sur-Yvette, France

    Benoît Valiron

Authors
  1. Théodore Chapuis-Chkaiban
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Contributions

T. Chapuis-Chkaiban, as the main author, produced most of the results presented in this paper and wrote the first version of the manuscript. Z.Toffano and B.Valiron, as co-authors, have made several research suggestions—both of them contributed equally to the scientific content. Besides, Z.Toffano and B.Valiron corrected and contributed to the writing and clarification of the manuscript and made several structural improvements for the final submitted version of this paper.

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Correspondence to Théodore Chapuis-Chkaiban.

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Appendix A Generalized PageRank using various Kernels

Appendix A Generalized PageRank using various Kernels

See Figs. 9, 10, 11, 12, 13 and Tables 4, 5.

Fig. 9
figure 9

Generalized PageRank Simulation Using different heat Kernels for the Reversibilized version of the ADSM of a simple graph

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Fig. 10
figure 10

Generalized PageRank Simulation Using different heat Kernels for the reversibilized version of the ADSM of a complex graph

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Fig. 11
figure 11

Generalized PageRank Cosine Kernel comparison with the Classical PageRank. Parameter: exponent = 5

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Fig. 12
figure 12

Generalized PageRank Inverse Kernel comparison with the Classical PageRank. Parameter: exponent = 5

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Fig. 13
figure 13

Generalized PageRank monomial Kernel comparison with the Classical PageRank. Parameter: exponent = 5

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Table 4 Ranking comparison between the classical Pagerank and the generalized pagerank using the Heat Kernels of parameters 5, 7 and 9
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Table 5 Ranking comparison between the classical Pagerank and the generalized pagerank using the Heat Kernel of parameter \(t=5\)
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Chapuis-Chkaiban, T., Toffano, Z. & Valiron, B. On new PageRank computation methods using quantum computing. Quantum Inf Process 22, 138 (2023). https://doi.org/10.1007/s11128-023-03856-y

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