  Ohya and Volovich have been proposed a new quantum computation model with
chaos amplification to solve the SAT problem, which went beyond usual quantum
algorithm. In this paper we study the complexity of the SAT algorithm by
counting the steps of computation algorithm rigorously, which was mentioned in
the paper [1,2,3,5,7]For this purpose, we refine the quantum gates treating the
SAT problem step by step.
