dorsal/arxiv
View SchemaAn efficient quantum algorithm for the hidden subgroup problem in extraspecial groups
| Authors | Gábor Ivanyos, Luc Sanselme, Miklos Santha |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0701235 |
| URL | https://arxiv.org/abs/quant-ph/0701235 |
| Journal | stacs 2007 |
Abstract
Extraspecial groups form a remarkable subclass of p-groups. They are also present in quantum information theory, in particular in quantum error correction. We give here a polynomial time quantum algorithm for finding hidden subgroups in extraspecial groups. Our approach is quite different from the recent algorithms presented in [17] and [2] for the Heisenberg group, the extraspecial p-group of size p3 and exponent p. Exploiting certain nice automorphisms of the extraspecial groups we define specific group actions which are used to reduce the problem to hidden subgroup instances in abelian groups that can be dealt with directly.
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"abstract": "Extraspecial groups form a remarkable subclass of p-groups. They are also\npresent in quantum information theory, in particular in quantum error\ncorrection. We give here a polynomial time quantum algorithm for finding hidden\nsubgroups in extraspecial groups. Our approach is quite different from the\nrecent algorithms presented in [17] and [2] for the Heisenberg group, the\nextraspecial p-group of size p3 and exponent p. Exploiting certain nice\nautomorphisms of the extraspecial groups we define specific group actions which\nare used to reduce the problem to hidden subgroup instances in abelian groups\nthat can be dealt with directly.",
"arxiv_id": "quant-ph/0701235",
"authors": [
"G\u00e1bor Ivanyos",
"Luc Sanselme",
"Miklos Santha"
],
"categories": [
"quant-ph"
],
"journal_ref": "stacs 2007",
"title": "An efficient quantum algorithm for the hidden subgroup problem in extraspecial groups",
"url": "https://arxiv.org/abs/quant-ph/0701235"
},
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