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Quantum-Classical Solution Methods for Binary Compressive Sensing Problems

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Computational Science – ICCS 2022 (ICCS 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13353))

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Abstract

Compressive sensing is a signal processing technique used to acquire and reconstruct sparse signals using significantly fewer measurement samples. Compressive sensing requires finding the most sparse solution to an underdetermined linear system, which is an NP-hard problem and as a consequence in practise is only solved approximately. In our work we restrict ourselves to the compressive sensing problem for the case of binary signals. For that case we have defined an equivalent formulation in terms of a quadratic binary optimisation (QUBO) problem, which we solve using classical and (hybrid-)quantum computing solving techniques based on quantum annealing. Phase transition diagrams show that this approach significantly improves the number of problem types that can be successfully reconstructed when compared to a more conventional \(\mathcal {L}_1\) optimisation method. A challenge that remain is how to select optimal penalty parameters in the QUBO formulation as was shown can heavily impact the quality of the solution.

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Notes

  1. 1.

    https://www.gurobi.com/products/gurobi-optimizer/.

  2. 2.

    https://github.com/dwavesystems/qbsolv/.

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Acknowledgements

This work was supported by the Dutch Ministry of Defense under Grant V2104.

Author information

Authors and Affiliations

  1. Department of Cyber Security and Robustness, The Netherlands Organisation for Applied Scientific Research, The Hague, Netherlands

    Robert S. Wezeman & Irina Chiscop

  2. Department of Radar Technology, The Netherlands Organisation for Applied Scientific Research, The Hague, Netherlands

    Laura Anitori & Wim van Rossum

Authors
  1. Robert S. Wezeman
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  2. Irina Chiscop
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  3. Laura Anitori
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  4. Wim van Rossum
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Corresponding author

Correspondence to Robert S. Wezeman .

Editor information

Editors and Affiliations

  1. Brunel University London, London, UK

    Derek Groen

  2. University of Amsterdam, Amsterdam, The Netherlands

    Clélia de Mulatier

  3. AGH University of Science and Technology, Krakow, Poland

    Maciej Paszynski

  4. University of Amsterdam, Amsterdam, The Netherlands

    Valeria V. Krzhizhanovskaya

  5. University of Tennessee at Knoxville, Knoxville, TN, USA

    Jack J. Dongarra

  6. University of Amsterdam, Amsterdam, The Netherlands

    Peter M. A. Sloot

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Wezeman, R.S., Chiscop, I., Anitori, L., van Rossum, W. (2022). Quantum-Classical Solution Methods for Binary Compressive Sensing Problems. In: Groen, D., de Mulatier, C., Paszynski, M., Krzhizhanovskaya, V.V., Dongarra, J.J., Sloot, P.M.A. (eds) Computational Science – ICCS 2022. ICCS 2022. Lecture Notes in Computer Science, vol 13353. Springer, Cham. https://doi.org/10.1007/978-3-031-08760-8_9

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  • DOI: https://doi.org/10.1007/978-3-031-08760-8_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-08759-2

  • Online ISBN: 978-3-031-08760-8

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