dorsal/arxiv
View SchemaQuantum Algorithms for Element Distinctness
| Authors | Harry Buhrman, Christoph Durr, Mark Heiligman, Peter Hoyer, Frederic Magniez, Miklos Santha, Ronald de Wolf |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0007016 |
| URL | https://arxiv.org/abs/quant-ph/0007016 |
| DOI | 10.1137/S0097539702402780 |
| Journal | SIAM Journal on Computing, 34(6), 1324-1330, 2005 |
Abstract
We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard, Hoyer, and Tapp, and imply an O(N^{3/4} log N) quantum upper bound for the element distinctness problem in the comparison complexity model (contrasting with Theta(N log N) classical complexity). We also prove a lower bound of Omega(N^{1/2}) comparisons for this problem and derive bounds for a number of related problems.
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"abstract": "We present several applications of quantum amplitude amplification to finding\nclaws and collisions in ordered or unordered functions. Our algorithms\ngeneralize those of Brassard, Hoyer, and Tapp, and imply an O(N^{3/4} log N)\nquantum upper bound for the element distinctness problem in the comparison\ncomplexity model (contrasting with Theta(N log N) classical complexity). We\nalso prove a lower bound of Omega(N^{1/2}) comparisons for this problem and\nderive bounds for a number of related problems.",
"arxiv_id": "quant-ph/0007016",
"authors": [
"Harry Buhrman",
"Christoph Durr",
"Mark Heiligman",
"Peter Hoyer",
"Frederic Magniez",
"Miklos Santha",
"Ronald de Wolf"
],
"categories": [
"quant-ph"
],
"doi": "10.1137/S0097539702402780",
"journal_ref": "SIAM Journal on Computing, 34(6), 1324-1330, 2005",
"title": "Quantum Algorithms for Element Distinctness",
"url": "https://arxiv.org/abs/quant-ph/0007016"
},
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