<p>Das et al. proposed a kind of system Hamiltonian with general form for quantum adiabatic computation and gave a specific example for it to show how to further reduce the time complexity of quantum adiabatic search problem compared with the optimality of square root speedup provided by previous quantum computation. In this paper, we study the implementation of the quantum algorithms given by Das et al. on the quantum circuit model. The main result is that, contrary to common belief, the total time slices thus needed are not necessarily equal to the time complexity of the quantum algorithm. As far as we know, this finding has not been noticed in the related studies previously, and the correct way to understand it is that the total time slices should equal to the time of the algorithm multiplying the increasing energy of the system compared to that of usual adiabatic evolution. We hope the result presented here may be helpful for us further grasping the relationship between these two models of quantum computation, although the equivalence between them is well known.</p>