Damped quantum search in an Ising spin system


We seek on 8 and a 12 spins Ising systems at least one of their eigenstates of a certain eigenvalue by applying the damped quantum search. In particular, without the knowledge of the number of degeneracy, it requires 150 queries to find at least one of the characteristic states having an eigenvalue of -11ε in a database of 4096 items with a probability of 99.1%. The average number of queries are compared with that of the undamped quantum search. It is found that for a small number of target states, the damped quantum search still preserves the quantum results, while for a large number of target states the classical limit is approached. Moreover, the damped quantum search is shown to increase monotonically as the number of iteration is increased.