Determining the minimal number of lines for large reversible circuits

Synthesis of reversible circuits is an active research area motivated by its applications e.g. in quantum computation or low-power design. The number of used circuit lines is thereby a crucial criterion. In this paper, we introduce several methods (including a theoretical upper bound) for the efficient computation or at least approximation of the minimal number of lines needed to realize a given function in reversible logic. While the proposed exact approach requires a significant amount of run-time (exponential in the worst case), the heuristic methods lead to very precise approximations in very short run-time. Using this, it can be shown that current synthesis approaches for large functions are still far away from producing optimal circuits with respect to the number of lines.