dorsal/arxiv
View SchemaA polynomial quantum query lower bound for the set equality problem
| Authors | Gatis Midrijanis |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401073 |
| URL | https://arxiv.org/abs/quant-ph/0401073 |
Abstract
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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"abstract": "The set equality problem is to tell whether two sets $A$ and $B$ are equal or\ndisjoint under the promise that one of these is the case. This problem is\nrelated to the Graph Isomorphism problem. It was an open problem to find any\n$\\omega(1)$ query lower bound when sets $A$ and $B$ are given by quantum\noracles. We will show that any error-bounded quantum query algorithm that\nsolves the set equality problem must evaluate oracles\n$\\Omega(\\sqrt[5]{\\frac{n}{\\ln n}})$ times, where $n=|A|=|B|$.",
"arxiv_id": "quant-ph/0401073",
"authors": [
"Gatis Midrijanis"
],
"categories": [
"quant-ph"
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"title": "A polynomial quantum query lower bound for the set equality problem",
"url": "https://arxiv.org/abs/quant-ph/0401073"
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