仿射布尔函数识别的快速量子算法
A Fast Quantum Algorithm for the Affine Boolean Function Identification
摘要：
Bernstein-Vazirani算法（一次查询算法）可以通过对预言机的一次查询来确定一个完全指定的线性布尔函数。本文的第一个目的是表明，如果所提供的布尔函数是仿射的，那么需要多一个查询的预言机（两个查询算法），以确定的亲和力的功能。本文的第二个目的是表明，如果所提供的布尔函数是不完全定义的，那么一个查询和两个查询算法可以被用来作为有界错误的量子多项式算法，以确定某些类的不完全定义的线性和仿射布尔函数分别与成功的概率至少$2/3$。
英文摘要：
Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean function is affine, then one more query to the oracle (the two-query algorithm) is required to identify the affinity of the function with certainty. The second aim of the paper is to show that if the provided Boolean function is incompletely defined, then the one-query and the two-query algorithms can be used as bounded-error quantum polynomial algorithms to identify certain classes of incompletely defined linear and affine Boolean functions respectively with probability of success at least $2/3$.
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。
