Quantum search with resonances

We present a continuous time quantum search algorithm analogous to Groverʹs. In particular, the optimal search time for this algorithm is proportional to , where N is the database size. This search algorithm can be implemented using any Hamiltonian with a discrete energy spectrum through excitation of resonances between an initial and the searched state. This algorithm is robust and, as in the case of Groverʹs, it allows for an error in the determination of the searched state. A discrete time version of this continuous time search algorithm is built, and the connection between the search algorithms with discrete and continuous times is established.