Efficient decomposition methods for controlled-R (n) using a single ancillary qubit

We consider decomposition for a controlled-R (n) gate with a standard set of universal gates. For this problem, a method exists that uses a single ancillary qubit to reduce the number of gates. In this work, we extend this method to three ends. First, we find a method that can decompose into fewer gates than the best known results in decomposition of controlled-R (n) . We also confirm that the proposed method reduces the total number of gates of the quantum Fourier transform. Second, we propose another efficient decomposition that can be mapped to a nearest-neighbor architecture with only local CNOT gates. Finally, we find a method that can minimize the depth to 5 gate steps in a nearest-neighbor architecture with only local CNOT gates.