Lowering the Quantum Gate Cost of Reversible Circuits

One approach to determining a quantum circuit is to first synthesize a circuit composed of binary reversible gates and to then map that circuit to an equivalent quantum gate realization. This paper considers the mapping phase with the goal of reducing the number of quantum gates required. Our method is based on novel line labeling and gate moving procedures. Results are presented for the quantum library: NOT, controlled-NOT, and the square-root-of-NOT gates (V and V⁺). The approach is applicable to other quantum gate libraries.