Dominant gate imperfection in Grover’s quantum search algorithm

Abstract

It is found that systematic errors in phase inversions and random errors in Hadmard-Walsh transformations are the dominant gate imperfection in Grover's quantum search algorithm. They lead to reductions in the maximum probability of the marked state and affect the efficiency of the algorithm. Given the degree of inaccuracy, we find that to guarantee a half-rate of success, the size of the database should be on the order of $O(1/{\ensuremath{\delta}}^{2}),$ where $\ensuremath{\delta}$ is the uncertainty.