Analysis of the damped quantum search and its application to the one-dimensional Ising system

TL;DR

This paper analyzes the efficiency of damped quantum search in finding target states within a one-dimensional Ising system, showing it outperforms classical search for intermediate target sizes and when targets are few.

Contribution

It provides a comparative analysis of damped quantum search versus classical search, highlighting its advantages for specific target state sizes and quantities.

Findings

Damped quantum search outperforms classical search for intermediate target sizes.

Quantum search has higher success probability when the number of targets is small.

Both methods perform similarly when the target size is large or comparable to the sample size.

Abstract

An analysis on the damped quantum search by exploring the rate at which the target state is obtained. The results were compared with that of the classical search since the standard Grover's algorithm does not give a convergent result if the number of target state is unknown. For a large number of target states, the classical and the damped quantum search give a similar result. However, for intermediate values of the target size the damped quantum search gives a higher probability of success than the classical search. Furthermore, we also made an analysis on the average number of iterations needed to obtain at least one of the target states. As the number of target states is reduced, the damped quantum search gives a better result than the classical search. The results coincide if the size of target state is comparable to the size of the sample.