Realization and synthesis of reversible functions

Authors:
Guowu Yang;Fei Xie;William N. N. Hung;Xiaoyu Song;Marek A. Perkowski
Affiliations:
School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China;Department Computer Science, Portland State University, Portland, OR 97207, USA;Synopsys Inc., Mountain View, CA 94043, USA;Department Electrical & Computer Engineering, Portland State University, Portland, OR 97207, USA;Department Electrical & Computer Engineering, Portland State University, Portland, OR 97207, USA
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

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@?2^n, and the other (2^n-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 4n^2@?N NOT gates. The time and space complexities of the algorithm are @W(n@?4^n) and @W(n@?2^n), respectively. The computational complexity of our synthesis algorithm is exponentially lower than that of breadth-first search based synthesis algorithms.