Amplitude amplification of the marked states in quantum search simulation

Yoder et al. [1] proposed a quantum search algorithm that prevents the system to move away from the marked states when the number of target states M is unknown. This method uses a recursive approach that makes the target state act as a fixed-point. We simulate the algorithm in an Ising spin chain with first- and second-nearest neighbor interaction. Our method involves a selective phase-shift rotation per iteration to obtain the target state.