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Optimal 4-bit Reversible Mixed-Polarity Toffoli Circuits

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Reversible Computation (RC 2012)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 7581))

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Abstract

Optimal synthesis of reversible circuits is a very hard task. For example, up to year 2009 this problem had not been solved even for 4-bit reversible functions, in spite of intensive research during previous decade. In 2010, a method and a tool of practical usage for finding optimal circuits for any 4-bit reversible specification were finally developed. Namely, with sophisticated optimizations it was possible to find gate count optimal circuits for any 4-bit reversible function built from multi-control Toffoli gates. Last year, we published an extension to the algorithm, which allows to reduce the quantum cost of the resulting circuits. In this paper we present another extension to this approach. Namely, we have extended the reversible gate library to mixed-polarity multi-control Toffoli gates (i.e. with both positive and negative controls). Our experimental results for the known reversible benchmarks show that using mixed-polarity Toffoli gates gives significant savings in gate count. The paper presents results of different computational experiments including optimal 4-bit circuits for the known reversible benchmarks with respect to both gate count and quantum cost criteria.

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Author information

Authors and Affiliations

  1. Institute of Computer Science, Department of Electronics and Information, Technology Warsaw University of Technology, Nowowiejska 15/19, 00-665, Warsaw, Poland

    Marek Szyprowski & Paweł Kerntopf

  2. Department of Theoretical Physics and Informatics, University of Łódź, Pomorska 149/153, 90-236, Łódź, Poland

    Paweł Kerntopf

Authors
  1. Marek Szyprowski
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  2. Paweł Kerntopf
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Editor information

Editors and Affiliations

  1. DIKU, Department of Computer Science, University of Copenhagen, Universitetsparken 1, 2100, Copenhagen, Denmark

    Robert Glück

  2. Department of Software Engineering, Nanzan University, 489-0863, Seto, Japan

    Tetsuo Yokoyama

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Szyprowski, M., Kerntopf, P. (2013). Optimal 4-bit Reversible Mixed-Polarity Toffoli Circuits. In: Glück, R., Yokoyama, T. (eds) Reversible Computation. RC 2012. Lecture Notes in Computer Science, vol 7581. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36315-3_11

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  • DOI: https://doi.org/10.1007/978-3-642-36315-3_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36314-6

  • Online ISBN: 978-3-642-36315-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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