Spectral Techniques for Reversible Logic Synthesis

Reversible circuits can lead to low-power CMOS implementations and are also of interest in optical and quantum computing. In this paper, we consider the synthesis of reversible logic assuming a generalized Toffoli gate. We make use of Rademacher-Walsh spectral techniques and in particular a spectral measure of function complexity used as a metric in guiding the search for a solution. The synthesis procedure introduced develops the circuit from inputs to outputs and from outputs to inputs simultaneously taking advantage of the best translation available at each step. No backtracking or lookahead is used. Preliminary results are given for reversible and nonreversible functions together with several ideas for future work.