  Grover's algorithm can solve NP-complete problems on quantum computers faster
than all the known algorithms on classical computers. However, Grover's
algorithm still needs exponential time. Due to the BBBV theorem, Grover's
algorithm is optimal for searches in the domain of a function, when the
function is used as a black box.
  We analyze the NP-complete set \[\{ (\langle M \rangle, 1^n, 1^t ) \mid
\text{ TM }M\text{ accepts an }x\in\{0,1\}^n\text{ within }t\text{ steps}\}.\]
If $t$ is large enough, then M accepts each word in $L(M)$ with length $n$
within $t$ steps. So, one can use methods from computability theory to show
that black box searching is the fastest way to find a solution. Therefore,
Grover's algorithm is optimal for NP-complete problems.
