  In general, a quantum algorithm wants to avoid decoherence or perturbation,
since such factors may cause errors in the algorithm. In this letter, we will
supply the answer to the interesting question: can the factors seemingly
harmful to a quantum algorithm(for example, perturbations) enhance the
algorithm? We show that some perturbations to the generalized quantum search
Hamiltonian can reduce the running time and enhance the success probability. We
also provide the narrow bound to the perturbation which can be beneficial to
quantum search. In addition, we show that the error induced by a perturbation
on the Farhi and Gutmann Hamiltonian can be corrected by another perturbation.
