量子算法的50%高级信息规则
The 50% advanced information rule of the quantum algorithms
摘要：
神谕从已知的函数集合中选择一个函数，并给玩家一个黑盒子，给出一个参数，评估函数。玩家应该通过函数求值来找出函数的某个特征。这是量子算法解决的典型问题。在以前的理论工作中，我们证明了量子算法需要经典算法的函数求值次数，该经典算法预先知道指定问题解决方案的50%的信息。在这里，我们检查这个50%规则是否适用于主要的量子算法。在结构化问题中，经典算法要识别出缺失的信息，需要先进行一次函数求值。速度是指数级的，因为没有高级信息的经典算法应该执行指数数量的函数求值。在非结构化数据库搜索中，预先知道数据库位置的n位的50%以识别n/2个丢失位的经典算法应该执行Order（2幂n/2）函数求值。速度是二次的，因为没有高级信息的经典算法应该执行Order（2 power n）函数求值。50%规则确定了以完全经典的方式加速的量子可解决的问题，实际上是通过比较两个经典算法，有和没有先进的信息。
英文摘要：
The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation. This is the typical problem addressed by the quantum algorithms. In former theoretical work, we showed that a quantum algorithm requires the number of function evaluations of a classical algorithm that knows in advance 50% of the information that specifies the solution of the problem. Here we check that this 50% rule holds for the main quantum algorithms. In the structured problems, a classical algorithm with the advanced information, to identify the missing information should perform one function evaluation. The speed up is exponential since a classical algorithm without advanced information should perform an exponential number of function evaluations. In unstructured database search, a classical algorithm that knows in advance 50% of the n bits of the database location, to identify the n/2 missing bits should perform Order(2 power n/2) function evaluations. The speed up is quadratic since a classical algorithm without advanced information should perform Order(2 power n) function evaluations. The 50% rule identifies the problems solvable with a quantum sped up in an entirely classical way, in fact by comparing two classical algorithms, with and without the advanced information.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
