Toffoli Gate Implementation Using the Billiard Ball Model

In this paper we review the Billiard Ball Model (BBM) introduced by Toffoli and Fredkin. The analysis of a previous approach to design reversible networks based on BBM it shown to ignored physical realities. We prove that some logic function cannot be realized without additional control balls. For example, to realize the logical OR operation, at least three control balls are needed. We show how reversible Toffoli gates can be constructed with this model. Finally, a Toffoli gate module is proposed that can be used in a cascade of gates and thus implement arbitrary reversible functions.