Optimality
It is known that Grover's algorithm is optimal. That is, any algorithm that accesses the database only by using the operator Uω must apply Uω at least as many times as Grover's algorithm. This result is important in understanding the limits of quantum computation. If the Grover's search problem was solvable with logc N applications of Uω, that would imply that NP is contained in BQP, by transforming problems in NP into Grover-type search problems. The optimality of Grover's algorithm suggests (but does not prove) that NP is not contained in BQP.
The number of iterations for k matching entries, π(N/k)1/2/4, is also optimal.
Read more about this topic: Grover's Algorithm