Quantum Algorithms for Element Distinctness

2000/07/31 by Harry Buhrman, Christoph Durr, Mark Heiligman +4 · 1 citation
Physics and Astronomy · #quant-ph

paper · pdf · doi:10.1137/s0097539702402780

published as SIAM Journal on Computing, 34(6), 1324-1330, 2005 · 15 pages. Supersedes quant-ph/007016v1 and quant-ph/0006136

arxiv created 2000/09/01 · arxiv updated 2017/01/10

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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