Exploiting Negative Control Lines in the Optimization of Reversible Circuits

Abstract

Abstract. The development of approaches for synthesis and optimization of reversible circuits received significant attention in the past. This is partly due to the increasing emphasis on low power design methodologies, and partly motivated by recent works in quantum computation. While most of them relied on a gate library composed of multiple-control Toffoli (MCT) gates with positive control lines, some initial works also exist which additionally incorporate negative control lines. This usually leads to smaller circuits with respect to the number of gates as well as the corresponding quantum costs. However, despite these benefits, negative control lines have hardly been considered in post-synthesis optimization of reversible circuits so far. In this paper, we address this issue. We are presenting an optimization scheme inspired by template matching which explicitly makes use of negative control lines. Experimental evaluations demonstrate that exploiting negative control lines in fact lead to a reduction in the number of gates and the quantum costs by up to 60% and 25%, respectively.

Templates for Positive and Negative Control Toffoli Networks

“…Table 5. 4 we can see that the quantum cost of sym9 148 is 798 [32] which is much lower than all previously obtained results [4,5,32] and the results from the proposed approach. The same situation is also observed for the circuit sym6 145.…”

“…Templates and rules using both positive and negative control Toffoli gates were proposed in [4]. Templates were introduced that allow for a substitution of a cascade of (pos- these patterns, 7 generalized rules were proposed for post synthesis optimization to reduce both the number of gates and the quantum costs [4].…”

“…Templates were introduced that allow for a substitution of a cascade of (pos- these patterns, 7 generalized rules were proposed for post synthesis optimization to reduce both the number of gates and the quantum costs [4]. The proposed algorithm traverses the given reversible circuit and checks for any possible rules and the algorithm is iterated until no further reduction is possible.…”

“…The merging rules for adjacent gates were also discussed as merging rules in [2] and [32]. In [5], the authors proposed an optimization algorithm using the merging and replacement rules to optimize the circuits and showed that the algorithm performs better than the algorithm proposed in [4].…”

“…In this case the two CNOT gates can be replaced by a single NOT gate [4]. An example is shown in Figure 4.2 and the proof is given below.…”