Huang灵敏度定理的量子意义
Quantum Implications of Huang's Sensitivity Theorem
摘要：
基于Huang（2019）最近的突破，我们证明了对于任何全布尔函数$f$，确定性查询复杂度$D(f)$至多是量子查询复杂度$Q(f)$：$D(f) = O(Q(f)^4)$的四分之一。这与Ambainis，Balodis，Belovs，Lee，Santha和Smotrovs（2017）的已知分离（高达对数因子）相匹配。我们还利用这个结果解决了Aanderaa-Karp-Rosenberg猜想的量子类似问题。我们证明了如果$f$是由其邻接矩阵指定的$n$ -顶点图的非平凡单调图性质，则$Q(f) = Ω(n)$也是最优的。
英文摘要：
Based on the recent breakthrough of Huang (2019), we show that for any total Boolean function $f$, the deterministic query complexity, $D(f)$, is at most quartic in the quantum query complexity, $Q(f)$: $D(f) = O(Q(f)^4)$. This matches the known separation (up to log factors) due to Ambainis, Balodis, Belovs, Lee, Santha, and Smotrovs (2017). We also use the result to resolve the quantum analogue of the Aanderaa-Karp-Rosenberg conjecture. We show that if $f$ is a nontrivial monotone graph property of an $n$-vertex graph specified by its adjacency matrix, then $Q(f) = Ω(n)$, which is also optimal.
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。
