量子搜索极值点的下界
Lower Bounds of Quantum Search for Extreme Point
摘要：
我们证明了对于随机选取的函数，Durr-Hoyer的求整数函数极值点的量子算法不能加速。任何其他算法在相当短的时间内起作用$o(\sqrt{2^n})$给出了函数的错误答案，该函数具有随机选择的最大值的单个点，概率收敛到1。建立了求解方程$f(x)=1$的量子搜索的下限$Ω(\sqrt{2^n /b})$，其中$f$是一个布尔函数，$b$是随机选择的，概率收敛到1的解。
英文摘要：
We show that Durr-Hoyer's quantum algorithm of searching for extreme point of integer function can not be sped up for functions chosen randomly. Any other algorithm acting in substantially shorter time $o(\sqrt{2^n})$ gives incorrect answer for the functions with the single point of maximum chosen randomly with probability converging to 1. The lower bound as $Ω(\sqrt{2^n /b})$ was established for the quantum search for solution of equations $f(x)=1$ where $f$ is a Boolean function with $b$ such solutions chosen at random with probability converging to 1.
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