Optimization of the damped quantum search

TL;DR

This paper analyzes and improves the damped quantum search by deriving a new damping parameter that enhances the probability of finding the target state, especially for certain target-to-database ratios, leading to better performance.

Contribution

A new iteration-dependent damping parameter was derived, improving the damped quantum search's efficiency over the critical damping approach for specific ratios.

Findings

The new damping parameter increases the effective range as iterations grow.

Application of the new parameter significantly improves search success for target ratios ≥ 50%.

The method offers a notable performance boost over previous critical damping schemes.

Abstract

The damped quantum search proposed in [A. Mizel, Phys. Rev. Lett., 102 150501 (2009)] was analyzed by calculating the highest possible probability of finding the target state in each iteration. A new damping parameter that depends on the number of iterations was obtained, this was compared to the critical damping parameter for different values of target to database size ratio. The result shows that the range of the new damping parameter as a function of the target to database size ratio increases as the number of iterations is increased. Furthermore, application of the new damping parameter per iteration on the damped quantum search scheme shows a significant improvement on some target to database size ratio (i.e. greater than or equal to 50% maximum percentage difference) over the critically damped quantum search.