Interaction-aided continuous time quantum search

The continuous quantum search algorithm (based on the Farhi–Gutmann Hamiltonian evolution) is known to be analogous to the Grover (or discrete time quantum) algorithm. Any errors introduced in Grover algorithm are fatal to its success. In the same way the Farhi–Gutmann Hamiltonian algorithm has a severe difficulty when the Hamiltonian is perturbed. In this letter we will show that the interaction term in quantum search Hamiltonian (actually which is in the generalized quantum search Hamiltonian) can save the perturbed Farhi–Gutmann Hamiltonian that should otherwise fail. We note that this fact is quite remarkable since it implies that introduction of interaction can be a way to correct some errors on the continuous time quantum search.