Realization and synthesis of reversible functions

نویسندگان

  • Guowu Yang
  • Fei Xie
  • William N. N. Hung
  • Xiaoyu Song
  • Marek A. Perkowski
چکیده

Reversible circuits play an important role in quantum computing. This paper studies the realization problem of reversible circuits. For any n-bit reversible function, we present a constructive synthesis algorithm. Given any n-bit reversible function, there are N distinct input patterns different from their corresponding outputs, where N ≤ 2n, and the other (2n − N) input patterns will be the same as their outputs. We show that this circuit can be synthesized by at most 2n · N ‘(n − 1)’-CNOT gates and 4n2 · N NOT gates. The time and space complexities of the algorithm are Ω(n · 4n) and Ω(n · 2n), respectively. The computational complexity of our synthesis algorithm is exponentially lower than that of breadth-first search based synthesis algorithms. © 2010 Elsevier B.V. All rights reserved.

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عنوان ژورنال:
  • Theor. Comput. Sci.

دوره 412  شماره 

صفحات  -

تاریخ انتشار 2011