集合等式问题的量子下界
Quantum lower bounds for the set equality problems
摘要：
集合相等问题是在保证两个集合$A$和$B$中的一个是相等的情况下，决定两个集合是否相等或不相交。其他一些问题，如图同构问题，可以通过简化为集合质量问题来解决。当集合$A$和$B$由具有函数$a$和$b$的量子预言机给出时，如何找到任意$w(1)$查询下界是一个公开问题.当$B$和$A$中的每个元素的原像集都很小时，我们将证明集合等式问题的$Ω(\frac{n^{1/3}}{\log^{1/3} n})$下界.
英文摘要：
The set equality problem is to decide whether two sets $A$ and $B$ are equal or disjoint, under the promise that one of these is the case. Some other problems, like the Graph Isomorphism problem, is solvable by reduction to the set quality problem. It was an open problem to find any $w(1)$ query lower bound when sets $A$ and $B$ are given by quantum oracles with functions $a$ and $b$. We will prove $Ω(\frac{n^{1/3}}{\log^{1/3} n})$ lower bound for the set equality problem when the set of the preimages are very small for every element in $A$ and $B$.
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。
