TITLE:
Permutation Algebra for Constructing Reversible Circuits
AUTHORS:
Shah Mohammad Bahauddin, Abu Ashik Md. Irfan
KEYWORDS:
Control NOT; Taffoli-Fredkin Gate; Full Adder
JOURNAL NAME:
Journal of Quantum Information Science,
Vol.2 No.3,
September
28,
2012
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.