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Boolean Hierarchical Tucker Networks on Quantum Annealers

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Large-Scale Scientific Computing (LSSC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13127))

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Abstract

Quantum annealing is an emerging technology with the potential to solve some of the computational challenges that remain unresolved as we approach an era beyond Moore’s Law. In this work, we investigate the capabilities of the quantum annealers of D-Wave Systems, Inc., for computing a certain type of Boolean tensor decomposition called Boolean Hierarchical Tucker Network (BHTN). Boolean tensor decomposition problems ask for finding a decomposition of a high-dimensional tensor with categorical, [true, false], values, as a product of smaller Boolean core tensors. As the BHTN decompositions are usually not exact, we aim to approximate an input high-dimensional tensor by a product of lower-dimensional tensors such that the difference between both is minimized in some norm. We show that BHTN can be calculated as a sequence of optimization problems suitable for the D-Wave 2000Q quantum annealer. Although current technology is still fairly restricted in the problems they can address, we show that a complex problem such as BHTN can be solved efficiently and accurately.

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Acknowledgments

The research presented in this article was supported by the Laboratory Directed Research and Development program of Los Alamos National Laboratory under the project numbers 20190020DR and 20190065DR. The work of Hristo Djidjev has been also partially supported by Grant No BG05M2OP001-1.001-0003, financed by the Science and Education for Smart Growth Operational Program (2014–2020) and co-financed by the European Union through the European structural and Investment funds.

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Correspondence to Georg Hahn .

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Pelofske, E., Hahn, G., O’Malley, D., Djidjev, H.N., Alexandrov, B.S. (2022). Boolean Hierarchical Tucker Networks on Quantum Annealers. In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing. LSSC 2021. Lecture Notes in Computer Science, vol 13127. Springer, Cham. https://doi.org/10.1007/978-3-030-97549-4_40

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  • DOI: https://doi.org/10.1007/978-3-030-97549-4_40

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-97548-7

  • Online ISBN: 978-3-030-97549-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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