A polynomial quantum query lower bound for the set equality problem

Details A polynomial quantum query lower bound for the set equality problem A polynomial quantum query lower bound for the set equality problem

2004-01-13

arxiv.org/abs/quant-ph/0401073v2

Physics

Quantum Physics

10 pages, improved presentation, modified proof of one lemma

Scientific paper

The set equality problem is to tell whether two sets $A$ and $B$ are equal or disjoint under the promise that one of these is the case. This problem is related to the Graph Isomorphism problem. It was an open problem to find any $\omega(1)$ query lower bound when sets $A$ and $B$ are given by quantum oracles. We will show that any error-bounded quantum query algorithm that solves the set equality problem must evaluate oracles $\Omega(\sqrt[5]{\frac{n}{\ln n}})$ times, where $n=|A|=|B|$.

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