Templates for Positive and Negative Control Toffoli Networks

Abstract

This paper proposes templates for positive and negative control Toffoli gates for post synthesis optimization of reversible circuits. Templates 1 − 5 can be applied to two adjacent Toffoli gates T 1(C 1,t 1) and T 2(C 2,t 2) where C i is the set of controls, |C 1| = |C 2|, and |t 1| = |t 2|. Templates 6 − 7 can be applied to two different size Toffoli gates T 1(C 1,t 1) and T 2(C 2,t 2) where C i is the set of controls, |C 1| = |C 2| and t i is the target, |t 1| = |t 2|. When applying our templates to circuits generated by the improved shared cube synthesis approach [14] a reduction in quantum cost was achieved for 98 of the 122 circuits. On average a 16.82% reduction in quantum cost was achieved, and in some cases up to 49.60% reduction was obtained.