dorsal/arxiv
View SchemaLower Bounds of Quantum Search for Extreme Point
| Authors | Yuri Ozhigov |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9806001 |
| URL | https://arxiv.org/abs/quant-ph/9806001 |
| DOI | 10.1098/rspa.1999.0397 |
| Journal | Proc.Roy.Soc.Lond. A455 (1999) 2165-2172 |
Abstract
We show that Durr-Hoyer's quantum algorithm of searching for extreme point of integer function can not be sped up for functions chosen randomly. Any other algorithm acting in substantially shorter time $o(\sqrt{2^n})$ gives incorrect answer for the functions with the single point of maximum chosen randomly with probability converging to 1. The lower bound as $\Omega (\sqrt{2^n /b})$ was established for the quantum search for solution of equations $f(x)=1$ where $f$ is a Boolean function with $b$ such solutions chosen at random with probability converging to 1.
{
"annotation_id": "c70007d6-3609-4502-90eb-df7ba75f88c9",
"date_created": "2026-03-02T18:02:45.244000Z",
"date_modified": "2026-03-02T18:02:45.244000Z",
"file_hash": "dd65b5f8e18398c91433cc35f94d0d5d82625eca4f6531714f9f4788ca7c9e33",
"private": false,
"record": {
"abstract": "We show that Durr-Hoyer\u0027s quantum algorithm of searching for extreme point of\ninteger function can not be sped up for functions chosen randomly. Any other\nalgorithm acting in substantially shorter time $o(\\sqrt{2^n})$ gives incorrect\nanswer for the functions with the single point of maximum chosen randomly with\nprobability converging to 1. The lower bound as $\\Omega (\\sqrt{2^n /b})$ was\nestablished for the quantum search for solution of equations $f(x)=1$ where $f$\nis a Boolean function with $b$ such solutions chosen at random with probability\nconverging to 1.",
"arxiv_id": "quant-ph/9806001",
"authors": [
"Yuri Ozhigov"
],
"categories": [
"quant-ph"
],
"doi": "10.1098/rspa.1999.0397",
"journal_ref": "Proc.Roy.Soc.Lond. A455 (1999) 2165-2172",
"title": "Lower Bounds of Quantum Search for Extreme Point",
"url": "https://arxiv.org/abs/quant-ph/9806001"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "29938875-7926-40c0-97c5-21fa0eaa9488",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}