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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.

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