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.

翻译：Grover算法在量子计算机上求解NP完全问题的速度快于经典计算机上所有已知算法。然而，Grover算法仍需指数级时间。根据BBBV定理，当函数被用作黑箱时，Grover算法在函数定义域内的搜索中是最优的。我们分析NP完全集合 \[\{ (\langle M \rangle, 1^n, 1^t ) \mid \text{图灵机}M\text{在}t\text{步内接受某个}x\in\{0,1\}^n\}\]。若$t$足够大，则M在$t$步内接受$L(M)$中每个长度为$n$的单词，因此可利用可计算性理论方法证明黑箱搜索是寻找解的最快方式。从而Grover算法对于NP完全问题是最优的。