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Decision Diagrams for Quantum Computing

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Design Automation of Quantum Computers

Abstract

Quantum computing promises to solve some important problems faster than conventional computations ever could. Currently available NISQ devices on which first practical applications are already executed demonstrate the potential—with future fault-tolerant quantum hardware for more demanding applications on the horizon. Nonetheless, the advantages in computing power come with challenges to be addressed in the design automation and software development community. In particular, non-quantum representations of states and operations, which provide the basis, e.g., for quantum circuit simulation or verification, require an exponential amount of memory. We propose to use decision diagrams as data structure to conquer the exponential memory requirements in many cases. In this chapter, we review the fundamentals on decision diagrams and highlight their applicability in the tasks of quantum circuit simulation with and without errors as well as in verification of quantum circuits. The tools presented here are all available online as open source projects.

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Notes

  1. 1.

    The terminology most significant qubit refers to a position in the basis states of a quantum system and does not signify the importance of the qubit itself.

  2. 2.

    This does not limit the applicability of the following findings, since arbitrary single-qubit operations combined with CNOT form a universal gate-set [43].

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Acknowledgements

We sincerely thank all co-authors and collaborators who work(ed) with us in this exciting area. Special thanks go to Alwin Zulehner and Thomas Grurl.

This work received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (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 BMWK on the basis of a decision by the German Bundestag through project QuaST, as well as 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. Chair for Design Automation, Technical University of Munich, Munich, Germany

    Robert Wille

  2. Software Competence Center Hagenberg GmbH (SCCH), Linz, Austria

    Robert Wille

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

    Stefan Hillmich & Lukas Burgholzer

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  1. Robert Wille
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  2. Stefan Hillmich
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Correspondence to Robert Wille .

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  1. IBM, Poughkeepsie, NY, USA

    Rasit O. Topaloglu

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Wille, R., Hillmich, S., Burgholzer, L. (2023). Decision Diagrams for Quantum Computing. In: Topaloglu, R.O. (eds) Design Automation of Quantum Computers. Springer, Cham. https://doi.org/10.1007/978-3-031-15699-1_1

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  • DOI: https://doi.org/10.1007/978-3-031-15699-1_1

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