Ordering techniques for ESOP-based Toffoli cascade generation

Abstract

This paper describes three techniques for ordering ESOP cubes prior to generation of a Toffoli gate generation. Two of these techniques are from earlier work, while the third is a new approach. The new approach applies rules to manipulate the cubes followed by a reordering process. Our experiments demonstrate that the new approach is much more effective than either of the two previous approaches. We apply template matching as a post-processing step, which results in even further reductions in the number of Toffoli gates.

An ESOP-Based Reversible Circuit Synthesis Flow Using Simulated Annealing

“…• As compared to [17], it may be noted that for most of the benchmarks where (PI + PO \ 20), [17] gives better results compared to the proposed approach, but for larger circuits (like apex2, apex4, apex5), our method gives far better results. Overall, out of 11 benchmarks, our method provides better results for 7.…”

“…Table 2 compares the synthesis results with five recent methods [6,[15][16][17]20]. It may be noted that the results of [17] that have been shown in the table are without template matching, which has not been used by the other four methods, and are expected to improve the quantum costs for all the methods. Also since all the papers have not shown their results for the same set of benchmarks, some entries in the table are shown as '-' (result not available).…”

“…In [17] Rice et al proposed an ordering-based technique to reorder the ESOP cube list to reduce the number of NOT gates. The method shows better results as compared to [7,18].…”

“…R1: Rice and Nayeem [17] if two cubes A and B differ in one position, where it is '1' in A and '-' in B, then we merge them into a single cube C by setting the differing position to '0'. For example, the cubes {110-, 1-0-} can be merged to {100-}.…”

“…3. The final .esop cube list is mapped to reversible gate cascade consisting of positive-and negative-control generalized Toffoli gates using optimization concepts as proposed in [7,17,20], along with some heuristics suggested in Sect. 4.2.…”