Transformation-based synthesis of networks of Toffoli/Fredkin gates

Abstract

Reversible logic has attracted significant attention in recent years. It has applications in low power CMOS, quantum computing, nanotechnology, and optical computing. Traditional gates such as AND, OR, and EXOR are not reversible. In fact NOT is the only reversible gate from the traditional set of gates. Several reversible gates have been proposed. Among them are the controlled NOT (also known as the Feynman gate), the Toffoli gate, and the Fredkin gate. An n-input Toffoli gate has n - 1 control lines which pass through the gate unaltered and a target line on which the value is inverted if all the control lines have value '1'. An n-input Fredkin gate has n - 2 control lines which pass through the gate unaltered and two target lines on which the values are swapped if all the control lines have value '1'. A NOT gate is the special case of a Toffoli gate with no control inputs. Likewise, a SWAP gate is the special case of a Fredkin gate with no control inputs. In this paper, we review a transformation-based synthesis procedure targeted to Toffoli gates and show how it can be extended to allow Fredkin gates. This extension results in circuits with fewer gates. The synthesis of reversible logic differs significantly from traditional irreversible logic synthesis approaches. Fan-outs and loops are not permitted due to the target technology. Outputs from one gate are used as inputs to the next gate. This results in a high degree of interdependence among gates. Our algorithm first finds an initial circuit with no backtracking and minimal look-ahead. We exploit reversibility directly in our synthesis approach. This method always finds a solution. Next we apply a set of template transforms that reduce the size of the circuit. We synthesize all three input, three output reversible functions and compare our results to those obtained previously.