dorsal/arxiv
View SchemaIs Grover's Algorithm a Quantum Hidden Subgroup Algorithm ?
| Authors | Samuel J. Lomonaco, Jr., Louis H. Kauffman |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0603140 |
| URL | https://arxiv.org/abs/quant-ph/0603140 |
Abstract
The arguments given in this paper suggest that Grover's and Shor's algorithms are more closely related than one might at first expect. Specifically, we show that Grover's algorithm can be viewed as a quantum algorithm which solves a non-abelian hidden subgroup problem (HSP). But we then go on to show that the standard non-abelian quantum hidden subgroup (QHS) algorithm can not find a solution to this particular HSP. This leaves open the question as to whether or not there is some modification of the standard non-abelian QHS algorithm which is equivalent to Grover's algorithm.
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"abstract": "The arguments given in this paper suggest that Grover\u0027s and Shor\u0027s algorithms\nare more closely related than one might at first expect. Specifically, we show\nthat Grover\u0027s algorithm can be viewed as a quantum algorithm which solves a\nnon-abelian hidden subgroup problem (HSP). But we then go on to show that the\nstandard non-abelian quantum hidden subgroup (QHS) algorithm can not find a\nsolution to this particular HSP.\n This leaves open the question as to whether or not there is some modification\nof the standard non-abelian QHS algorithm which is equivalent to Grover\u0027s\nalgorithm.",
"arxiv_id": "quant-ph/0603140",
"authors": [
"Samuel J. Lomonaco, Jr.",
"Louis H. Kauffman"
],
"categories": [
"quant-ph"
],
"title": "Is Grover\u0027s Algorithm a Quantum Hidden Subgroup Algorithm ?",
"url": "https://arxiv.org/abs/quant-ph/0603140"
},
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