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Quantum walk inspired algorithm for graph similarity and isomorphism

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Abstract

Large-scale complex systems, such as social networks, electrical power grid, database structure, consumption pattern or brain connectivity, are often modelled using network graphs. Valuable insight can be gained by measuring similarity between network graphs in order to make quantitative comparisons. Since these networks can be very large, scalability and efficiency of the algorithm are key concerns. More importantly, for graphs with unknown labelling, this graph similarity problem requires exponential time to solve using existing algorithms. In this paper, we propose a quantum walk inspired algorithm, which provides a solution to the graph similarity problem without prior knowledge on graph labelling. This algorithm is capable of distinguishing between minor structural differences, such as between strongly regular graphs with the same parameters. The algorithm has a polynomial complexity, scaling with \(O(n^9)\).

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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. YL acknowledges funding from the National Sciences and Engineering Research Council of Canada.

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Authors and Affiliations

  1. Department of Physics, The University of Western Australia, Perth, Australia

    Callum Schofield & Jingbo B. Wang

  2. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

    Yuying Li

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  1. Callum Schofield
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  2. Jingbo B. Wang
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  3. Yuying Li
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Correspondence to Jingbo B. Wang.

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Schofield, C., Wang, J.B. & Li, Y. Quantum walk inspired algorithm for graph similarity and isomorphism. Quantum Inf Process 19, 281 (2020). https://doi.org/10.1007/s11128-020-02758-7

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