证书复杂度与量子查询复杂度之间的近四次分离

中文摘要 AI 辅助

我们构造了一个全布尔函数$f$，使得$Q(f) = \widetilde{O}(\sqrt[4]{C(f)})$，其中$Q(f)$表示有界误差量子查询复杂度，$C(f)$表示证书复杂度。这解决了一个长期悬而未决的问题，并且在对数因子范围内是紧的。

英文摘要

We study how large the certificate complexity ${C}(f)$ of a total Boolean function can be relative to its randomized and quantum query complexities. We construct a total Boolean function $f$ whose randomized query complexity with one-sided error satisfies ${R}_1(f) = Θ(\sqrt{{C}(f)})$. This separation is optimal even when two-sided error is allowed. From this construction, we obtain another total Boolean function $F$ with bounded-error quantum query complexity ${Q}(F) = \widetilde O({C}(F)^{1/4})$, attaining the general quartic bound up to polylogarithmic factors. For the same function, both exact and zero-error quantum query complexities are $\widetilde O(\sqrt{{C}(F)})$. We also prove matching lower bounds for these two measures on $F$.

发表机构

• Center for Quantum Computer Science, Faculty of Science and Technology, University of Latvia（拉脱维亚大学科学与技术学院量子计算机科学中心）

机构由 AI 辅助整理，请以论文原文为准。