Performance of Equal Phase-Shift Search for One Iteration

Grover presented the phase-shift search by replacing the selective inversions by selective phase shifts of $\pi /3$. In this paper, we investigate the phase-shift search with general equal phase shifts. We show that for small uncertainties, the failure probability of the Phase-$\pi /3$ search is smaller than the general phase-shift search and for large uncertainties, the success probability of the large phase-shift search is larger than the Phase-$\pi /3$ search. Therefore, the large phase-shift search is suitable for large-size of databases.