On figures of merit in reversible and quantum logic designs

Abstract

Five figures of merit including number of gates, quantum cost, number of constant inputs, number of garbage outputs, and delay are used casually in the literature to compare the performance of different reversible or quantum logic circuits. In this paper we propose new definitions and enhancements, and identify similarities between these figures of merit. We evaluate these measures to show their strength and weakness. Instead of the number of gates, we introduce the weighted number of gates, where a weighting factor is assigned to each quantum or reversible gate, based on its type, size and technology. We compare the quantum cost with weighted number of gates of a circuit and show three major differences between these measures. It is proved that it is not possible to define a universal reversible logic gate without adding constant inputs. We prove that there is an optimum value for number of constant inputs to obtain a circuit with minimum quantum cost. Some reversible logic benchmarks have been synthesized using Toffoli and Fredkin gates to obtain their optimum values of number of constant inputs. We show that the garbage outputs can also be used to decrease the quantum cost of the circuit. A new definition of delay in quantum and reversible logic circuits is proposed for music line style representation. We also propose a procedure to calculate the delay of a circuit, based on the quantum cost and the depth of the circuit. The results of this research show that to achieve a fair comparison among designs, figures of merit should be considered more thoroughly.