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Reordering Decision Diagrams for Quantum Computing Is Harder Than You Might Think

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Reversible Computation (RC 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13354))

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Abstract

Decision diagrams have proven to be a useful data structure in both, conventional and quantum computing, to compactly represent exponentially large data in many cases. Several approaches exist to further reduce the size of decision diagrams, i.e., their number of nodes. Reordering is one such approach to shrink decision diagrams by changing the order of variables in the representation. In the conventional world, this approach is established and its availability taken for granted. For quantum computing however, first approaches exist, but could not fully exploit a similar potential yet. In this paper, we investigate the differences between reordering decision diagrams in the conventional and the quantum world and, afterwards, unveil challenges that explain why reordering is much harder in the latter. A case study shows that, also for quantum computing, reordering may lead to improvements of several orders of magnitude in the size of the decision diagrams, but also requires substantially more runtime.

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Acknowledgments

This work received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 101001318), was part of the Munich Quantum Valley, which is supported by the Bavarian state government with funds from the Hightech Agenda Bayern Plus, and has been supported by the BMK, BMDW, and the State of Upper Austria in the frame of the COMET program (managed by the FFG).

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Authors and Affiliations

  1. Institute for Integrated Circuits, Johannes Kepler University Linz, Linz, Austria

    Stefan Hillmich, Lukas Burgholzer & Florian Stögmüller

  2. Chair for Design Automation, Technical University of Munich, Munich, Germany

    Robert Wille

  3. Software Competence Center Hagenberg GmbH (SCCH), Hagenberg, Austria

    Robert Wille

Authors
  1. Stefan Hillmich
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  2. Lukas Burgholzer
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  3. Florian Stögmüller
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  4. Robert Wille
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Corresponding authors

Correspondence to Stefan Hillmich , Lukas Burgholzer or Robert Wille .

Editor information

Editors and Affiliations

  1. University of Urbino, Urbino, Pesaro-Urbino, Italy

    Claudio Antares Mezzina

  2. University of Łódź, Lodz, Poland

    Krzysztof Podlaski

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Hillmich, S., Burgholzer, L., Stögmüller, F., Wille, R. (2022). Reordering Decision Diagrams for Quantum Computing Is Harder Than You Might Think. In: Mezzina, C.A., Podlaski, K. (eds) Reversible Computation. RC 2022. Lecture Notes in Computer Science, vol 13354. Springer, Cham. https://doi.org/10.1007/978-3-031-09005-9_7

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  • DOI: https://doi.org/10.1007/978-3-031-09005-9_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-09004-2

  • Online ISBN: 978-3-031-09005-9

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