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Finding the chromatic sums of graphs using a D-Wave quantum computer

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Abstract

In this paper we demonstrate how to solve the chromatic sum problem using a D-Wave quantum computer. Starting from a BIP (binary integer programming) formulation, we develop a QUBO (quadratic unconstrained binary optimization) formulation of the chromatic sum problem, which is acceptable to a D-Wave quantum computer. Our construction requires nk qubits for a graph of n vertices and upper bound of k colors. Further, we present the experimental results obtained by running several QUBOs on a D-Wave quantum computer.

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Acknowledgements

This work was supported in part by the Quantum Computing Research Initiatives at Lockheed Martin. AM would like to thank André Nies for helpful discussions and also for the funds received through the Department of Computer Science of the University of Auckland and Marsden Grant.

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Authors and Affiliations

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

    Michael J. Dinneen, Anuradha Mahasinghe & Kai Liu

  2. Department of Mathematics, University of Colombo, Colombo, Sri Lanka

    Anuradha Mahasinghe

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  1. Michael J. Dinneen
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  2. Anuradha Mahasinghe
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  3. Kai Liu
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Correspondence to Michael J. Dinneen.

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Dinneen, M.J., Mahasinghe, A. & Liu, K. Finding the chromatic sums of graphs using a D-Wave quantum computer. J Supercomput 75, 4811–4828 (2019). https://doi.org/10.1007/s11227-019-02761-5

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