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