Decomposing fredkin gate into simple reversible elements with memory

The Fredkin gate (Fredkin & Toffoli, 1982) is a Boolean logic gate that consists of 3 inputs and 3 outputs. This gate is universal for computational logic, and more importantly, it is reversible in the sense that the mapping between its inputs and outputs is bijective. In this paper, we realize the logic function of a Fredkin gate based upon two simple reversible elements (Lee, et al. 2008) that are mutually inverse. In addition, both elements have 2 inputs, 2 outputs, and 2 states that can record one- bit information.