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Quantum walk algorithm for element distinctness

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1 Author(s)
A. Ambainis ; Sch. of Math., Inst. for Adv. Study, Princeton, NJ, USA

We use quantum walks to construct a new quantum algorithm for element distinctness and its generalization. For element distinctness (the problem of finding two equal items among N given items), we get an O(N23/) query quantum algorithm. This improves the previous O(N34/) quantum algorithm of Buhrman et al. and matches the lower bound by Shi. We also give an O(Nk(k+1)/) query quantum algorithm for the generalization of element distinctness in which we have to find k equal items among N items.

Published in:

Foundations of Computer Science, 2004. Proceedings. 45th Annual IEEE Symposium on

Date of Conference:

17-19 Oct. 2004