A digital combinational logic circuit is reversible if it maps each input pattern to a unique output pattern. Such circuits are of interest in quantum computing, optical computing, nanotechnology and low-power CMOS design. Synthesis approaches are not well developed for reversible circuits even for small numbers of inputs and outputs.In this paper, a transformation based algorithm for the synthesis of such a reversible circuit in terms of  n  ×  n  Toffoli gates is presented. Initially, a circuit is constructed by a single pass through the specification with minimal look-ahead and no back-tracking. Reduction rules are then applied by simple template matching. The method produces near-optimal results for 3-input circuits and also produces very good results for larger problems.
['D.M. Miller', 'Dmitri Maslov', 'Gerhard W. Dueck']
A transformation based algorithm for reversible logic synthesis