In the oracle identification problem we have oracle access to bits of an unknown string $x$ of length $n$, with the promise that it belongs to a known set $C\subseteq\{0,1\}^n$. The goal is to identify $x$ using as few queries to the oracle as possible. We develop a quantum query algorithm for this problem with query complexity $O\left(\sqrt{\frac{n\log M }{\log(n/\log M)+1}}\right)$, where $M$ is the size of $C$. This bound is already derived by Kothari in 2014, for which we provide a more elegant simpler proof.

中文翻译：

---

Oracle 识别问题的简化量子算法

在预言机识别问题中，我们让预言机访问长度为 $n$ 的未知字符串 $x$ 的位，并承诺它属于已知集合 $C\subseteq\{0,1\}^n$。目标是使用对 oracle 的尽可能少的查询来识别 $x$。我们针对这个问题开发了一个量子查询算法，查询复杂度为 $O\left(\sqrt{\frac{n\log M }{\log(n/\log M)+1}}\right)$，其中 $M $ 是 $C$ 的大小。这个界限已经由 Kothari 在 2014 年推导出来，为此我们提供了一个更优雅、更简单的证明。