超立方体单调性检验的量子算法
Quantum Algorithm for Monotonicity Testing on the Hypercube
摘要：
在这篇文章中，我们开发了一个有界误差量子算法，该算法对布尔函数$f$进行$\tilde O(n^{1/4}\varepsilon^{-1/2})$查询，接受单调函数，并拒绝$\varepsilon$ -远离单调的函数。与所有$\varepsilon = o(1)$的最佳已知随机化算法相比，这给出了超二次改进。当使用$\varepsilon = 1/\sqrt{n}$ .
英文摘要：
In this note, we develop a bounded-error quantum algorithm that makes $\tilde O(n^{1/4}\varepsilon^{-1/2})$ queries to a Boolean function $f$, accepts a monotone function, and rejects a function that is $\varepsilon$-far from being monotone. This gives a super-quadratic improvement compared to the best known randomized algorithm for all $\varepsilon = o(1)$. The improvement is cubic when $\varepsilon = 1/\sqrt{n}$.
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。
