Many variations of Grover’s algorithm attempt to improve iteration count using a technique known as phase matching, replacing Grover’s phase-flip oracle with an \(\alpha \) -rotation oracle that cannot be simulated using only one Grover oracle call. Previously it was shown that phase matching can always achieve 100% success probability with an iteration count within one step from the Grover algorithm. In this paper, we show that this is actually the optimal iteration count, hence finding the first proof of the minimal number of queries to solve the search problem with a known number of solutions whether we use an \(\alpha \) -rotation or the Grover flip.
