Perturbations Can Enhance Quantum Search

In general, a quantum algorithm wants to avoid decoherence or perturbation, since such factors may cause errors in 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.