Permutation Algebra for Constructing Reversible Circuits

Shah Mohammad Bahauddin, Abu Ashik Md. Irfan

Department of Applied Physics, Electronics & Communication Engineering, Faculty of Engineering & Technology, University of Dhaka, Dhaka, Bangladesh.

DOI: 10.4236/jqis.2012.23011                

Abstract

In this paper, we show that the algebra of permutation group is one of the inherent structures of reversible logic for quantum computation. In this venture, we discuss necessary properties of cycle and transposition to reveal the potential of permutation algebra for reversible logic. Then we present an efficient method which naturally interconnects the structure of reversible logic with the expression of cycle and corresponding transpositions. Finally we discuss several examples which show that the algebra can be effectively used to construct complex gates as well.

Keywords

Control NOT; Taffoli-Fredkin Gate; Full Adder

Conflicts of Interest

The authors declare no conflicts of interest.

References

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