dorsal/arxiv
View SchemaHidden Subhypergroup Problem
| Authors | Massoud Amini, Mehrdad Kalantar, Mahmood M. Roozbehani |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0609220 |
| URL | https://arxiv.org/abs/quant-ph/0609220 |
Abstract
The Hidden Subgroup Problem is used in many quantum algorithms such as Simon's algorithm and Shor's factoring and discrete log algorithms. A polynomial time solution is known in case of abelian groups, and normal subgroups of arbitrary finite groups. The general case is still open. An efficient solution of the problem for symmetric group $S_n$ would give rise to an efficient quantum algorithm for Graph Isomorphism Problem. We formulate a hidden sub-hypergroup problem for finite hypergroups and solve it for finite commutative hypergroups. The given algorithm is efficient if the corresponding QFT could be calculated efficiently.
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"date_created": "2026-03-02T18:02:31.141000Z",
"date_modified": "2026-03-02T18:02:31.141000Z",
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"abstract": "The Hidden Subgroup Problem is used in many quantum algorithms such as\nSimon\u0027s algorithm and Shor\u0027s factoring and discrete log algorithms. A\npolynomial time solution is known in case of abelian groups, and normal\nsubgroups of arbitrary finite groups. The general case is still open. An\nefficient solution of the problem for symmetric group $S_n$ would give rise to\nan efficient quantum algorithm for Graph Isomorphism Problem. We formulate a\nhidden sub-hypergroup problem for finite hypergroups and solve it for finite\ncommutative hypergroups. The given algorithm is efficient if the corresponding\nQFT could be calculated efficiently.",
"arxiv_id": "quant-ph/0609220",
"authors": [
"Massoud Amini",
"Mehrdad Kalantar",
"Mahmood M. Roozbehani"
],
"categories": [
"quant-ph"
],
"title": "Hidden Subhypergroup Problem",
"url": "https://arxiv.org/abs/quant-ph/0609220"
},
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"source": {
"execution_id": "ae685327-0ec4-4ad3-b95a-6374ca87ff1a",
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"variant": "snapshot-2026-03-01",
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