Quantum Algorithms for Element Distinctness

Quantum Algorithms for Element Distinctness (2001)

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by Harry Buhrman , Christoph Dürr , Mark Heiligman , Peter Høyer , Frédéric Magniez , Miklos Santha , Ronald Wolf

Venue:	SIAM Journal of Computing
Citations:	58 - 11 self

BibTeX

@INPROCEEDINGS{Buhrman01quantumalgorithms,
    author = {Harry Buhrman and Christoph Dürr and Mark Heiligman and Peter Høyer and Frédéric Magniez and Miklos Santha and Ronald Wolf},
    title = {Quantum Algorithms for Element Distinctness},
    booktitle = {SIAM Journal of Computing},
    year = {2001},
    pages = {131--137}
}

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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, Høyer, and Tapp, and imply an O(N 3/4 log N) quantum upper bound for the element distinctness problem in the comparison complexity model. This contrasts with Θ(N log N) classical complexity. We also prove a lower bound of Ω ( √ N) comparisons for this problem and derive bounds for a number of related problems. 1

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