Nonadiabatic quantum search algorithms

Abstract

We present two continuous-time quantum search algorithms similar to the adiabatic search algorithm, but now without the requirement of adiabatic evolution. Both algorithms can find the marked state in a time proportional to sqrt(N). The behavior of the first algorithm is, essentially, similar to Grover's algorithm, but the second model possesses the important property that one does not need to single out a given time in order to find the searched state. After a well-defined transition time, this second algorithm will converge towards the marked state with a high probability, provided the parameters of the Hamiltonian are chosen appropriately. This convergence shows a resemblance to quantum search algorithms with a fixed point [L. K. Grover, Phys. Rev. Lett. 95, 150501 (2005)].