Can adiabatic algorithms with extra items always be efficient in quantum computation?

It has been known that when an assisted driving item is added to the Hamiltonian of the main system, the efficiency of the resultant adiabatic evolution can be significantly improved. In some special cases, it can be seen that, only by adding an assisted driving Hamiltonian can the resultant adiabatic evolution work. So it seems that, the additional driving Hamiltonian plays an important role in adiabatic computing. In this paper, we show five kinds of possible forms of the driving Hamiltonian, and analyses the performance of the algorithms. We find that the former fourth kinds of driving Hamiltonian may still cause the adiabatic algorithm lose their efficiency when the overlap of the initial and final states equals some special value. More importantly, we find that only the final kinds of the driving Hamiltonian can be extended. By modifying its interpolating functions, the final kind of adiabatic algorithm can suit any fidelity of the systems to keep the adiabatic evolution always be valid. Finally, the time complexity of the extended algorithm is better than the original adiabatic algorithm, which owns a constant running time complexity. Although the time complexity is shifted to the complexity of implementing the driving Hamiltonian added. [ABSTRACT FROM AUTHOR]