Abstract
A major limitation of current generations of quantum annealers is the sparse connectivity of manufactured qubits in the hardware graph. This technological limitation has generated considerable interest, motivating efforts to design efficient and adroit minor-embedding procedures that bypass sparsity constraints. In this paper, starting from a previous equational formulation by Dridi et al. (arXiv:1810.01440), we propose integer programming (IP) techniques for solving the minor-embedding problem. The first approach involves a direct translation from the previous equational formulation to IP, while the second decomposes the problem into an assignment master problem and fiber condition checking subproblems. The proposed methods are able to detect instance infeasibility and provide bounds on solution quality, capabilities not offered by currently employed heuristic methods. We demonstrate the efficacy of our methods with an extensive computational assessment involving three families of random graphs of varying sizes and densities. The direct translation as a monolithic IP model can be solved with existing commercial solvers yielding valid minor-embeddings but it is outperformed, overall, by the decomposition approach. Our results demonstrate the promise of our methods for the studied benchmarks, highlighting the advantages of using IP technology for minor-embedding problems.
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Acknowledgements
We thank Prof. Ignacio Grossmann and Dr. Eleanor Rieffel for the constructive discussions during the preparation of this work. DB, KB, and DV are supported/partially supported by NASA NAMS (NNA16BD14C), AFRL NYSTEC Contract (FA8750-19-3-6101). DB is also supported by the USRA Feynman Quantum Academy and the Center for Advanced Process Decision Making (CAPD) at CMU. NASA QuAIL acknowledges support from the Office of the Director of National Intelligence (ODNI) and the Intelligence Advanced Research Projects Activity (IARPA), via IAA 145483. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of ODNI, IARPA, AFRL, or the U.S. Government.
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Bernal, D.E., Booth, K.E.C., Dridi, R., Alghassi, H., Tayur, S., Venturelli, D. (2020). Integer Programming Techniques for Minor-Embedding in Quantum Annealers. In: Hebrard, E., Musliu, N. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2020. Lecture Notes in Computer Science(), vol 12296. Springer, Cham. https://doi.org/10.1007/978-3-030-58942-4_8
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