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Quantum algorithms for element distinctness

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7 Author(s)
Buhrman, H. ; CWI, Amsterdam, Netherlands ; Durr, C. ; Heiligman, M. ; Hoyer, P.
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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 (1998), and imply an O(N3/4 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

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Computational Complexity, 16th Annual IEEE Conference on, 2001.

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