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 T1(C1,t 1) and T2(C2,t2) where Ci is the set of controls, |C1| = |C2|, and |t1| = |t2|. Templates 6 - 7 can be applied to two different size Toffoli gates T1(C1,t1) and T2(C 2,t2) where Ci is the set of controls, |C 1| = |C2| and ti is the target, |t1| = |t2|. 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. © 2014 Springer International Publishing.