An analytic sifting approach to optimization of LNN reversible circuits

In this paper we propose an analytic approach to the variable sifting based on weighting of qubits and gates. The proposed scheme allows to optimally sift gates (multi-control single-target reversible gates) within a linear number of steps of computation and provides in general smaller amount of SWAP gates required to transform a reversible circuit into an Linear Nearest Neighbor (LNN) model than other competing approaches. The method is analyzed for two different models of implementations, is verified on experimental data and results are compared to the state of the art algorithms for the design of LNN circuits.