Optimality of Grover's Algorithm

It is not directly proved, but simply stated in Grover's 1996 paper that his result was optimal.

It was established in [BBBV96] that any quantum algorithm can not identify a single marked element in fewer than $\Omega$($\sqrt{{N}}$). Grover's algorithm takes O($\sqrt{{n}}$) iterations, and is thus asymptotically optimal.

It has been shown since that any quantum algorithm would require at least $\pi$/4$\sqrt{{N}}$ queries, which is precisely the number queries required by Grover's algorithm. [Grover99]