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Algebraic Characterization of Reversible Logic Gates

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Abstract

Reversible logic plays an important role in quantum computing. This paper investigates the universality and composition power of various known and new reversible gates. We present the algebraic characterization of selected new families of Boolean reversible gates. Some theoretical results on the relation between reversible w*w gates and the corresponding symmetric group are derived. Different combinations of reversible gate classes are proven to generate the entire class of reversible w*w gates.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, Portland State University, Portland, OR 97207, USA

    Xiaoyu Song, Guowu Yang & Marek Perkowski

  2. Department of Computer Science, University of Texas at Dallas, Richardson, TX 75083-0688, USA

    Yuke Wang

Authors
  1. Xiaoyu Song
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  2. Guowu Yang
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  3. Marek Perkowski
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  4. Yuke Wang
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Corresponding authors

Correspondence to Xiaoyu Song, Marek Perkowski or Yuke Wang.

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Song, X., Yang, G., Perkowski, M. et al. Algebraic Characterization of Reversible Logic Gates. Theory Comput Syst 39, 311–319 (2006). https://doi.org/10.1007/s00224-004-1166-2

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  • DOI: https://doi.org/10.1007/s00224-004-1166-2

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