Group Theory Based Synthesis of Binary Reversible Circuits

  • Guowu Yang
  • Xiaoyu Song
  • William N. N. Hung
  • Fei Xie
  • Marek A. Perkowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3959)

Abstract

This paper presents an important result addressing a fundamental question in synthesizing binary reversible logic circuits for quantum computation. We show that any even-reversible-circuit of n (n>3) qubits can be realized using NOT gate and Toffoli gate (‘2’-Controlled-Not gate), where the numbers of Toffoli and NOT gates required in the realization are bounded by \((n + \lfloor \frac{n}{3} \rfloor)(3 \times 2^{2n-3}-2^{n+2})\) and \(4n(n + \lfloor \frac{n}{3} \rfloor)2^n\), respectively. A provable constructive synthesis algorithm is derived. The time complexity of the algorithm is \(\frac{10}{3}n^2 \cdot 2^n\). Our algorithm is exponentially lower than breadth-first search based synthesis algorithms with respect to space and time complexities.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Guowu Yang
    • 1
  • Xiaoyu Song
    • 2
  • William N. N. Hung
    • 2
  • Fei Xie
    • 1
  • Marek A. Perkowski
    • 2
  1. 1.Dept. of Computer SciencePortland State UniversityPortlandUSA
  2. 2.Dept. of Electrical and Computer EngineeringPortland State UniversityPortlandUSA

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