Efficient implementation of quantum arithmetic operation circuits

Realization of robust quantum computing is a tremendous task. On one hand, one must reduce errors as many as possible using various means [1-3]; on the other hand, one may make large error rates tolerable via fault-tolerant implementation. In achieving tolerant against noises, the cost to pay is the increased number of gates used. Therefore, an efficient implementation of fault-tolerant gates is crucial. As already evidenced, Clifford gates with a T gate can form a universal set of fault-tolerant gates.