Nonadiabatic quantum search algorithms
Armando Pérez, A. Romanelli · Physical Review A · 2007
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)].