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A. Barenco, C. H. Bennett, C. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin and H. Weinfurter, “Elementary Gates for Quantum Computation,” Physical Review A, Vol. 52, No. 5, 1995, pp. 3457-3467. doi:10.1103/PhysRevA.52.3457

has been cited by the following article:

• 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.