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Improved QUBO Formulation of the Graph Isomorphism Problem

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Abstract

In this paper, we provide a practically efficient QUBO formulation for the Graph Isomorphism Problem that is suitable for quantum annealers such as those produced by D-Wave. After proving the correctness of our new method, based on exploiting vertex degree classes, we did some experimental work on a D-Wave 2X computer. We observe that for all “hard” graphs of 6 vertices, we save around 50–95% of the number of required physical qubits over the standard QUBO formulation that was given earlier by Calude et al. (Theor Comput Sci 701:54–69, 2017). We also provide some theoretical analysis showing that, for two random graphs with the same degree sequence, our new method substantially improves in qubit savings as the number of vertices increases beyond 6.

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Notes

  1. Note that this publication refers to map size as ‘chain length’ which could be somewhat misleading since the set of physical qubits is not necessarily a path.

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Acknowledgements

This project was supported in part by the Quantum Computing Research Initiatives at Lockheed Martin. We thank Cris Calude and the anonymous referee for useful comments on an earlier draft.

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  1. School of Computer Science, University of Auckland, Auckland, New Zealand

    Richard Hua & Michael J. Dinneen

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  1. Richard Hua
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  2. Michael J. Dinneen
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Correspondence to Michael J. Dinneen.

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Appendix: Drawing of Test Graphs

Appendix: Drawing of Test Graphs

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Hua, R., Dinneen, M.J. Improved QUBO Formulation of the Graph Isomorphism Problem. SN COMPUT. SCI. 1, 19 (2020). https://doi.org/10.1007/s42979-019-0020-1

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