Quantum walk algorithm for element distinctness

@article{Ambainis2004QuantumWA,
  title={Quantum walk algorithm for element distinctness},
  author={Andris Ambainis},
  journal={45th Annual IEEE Symposium on Foundations of Computer Science},
  year={2004},
  pages={22-31}
}
  • A. Ambainis
  • Published 2004
  • Mathematics, Physics, Computer Science
  • 45th Annual IEEE Symposium on Foundations of Computer Science
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(N/sup 2/3/) query quantum algorithm. This improves the previous O(N/sup 3/4/) quantum algorithm of Buhrman et al. and matches the lower bound by Shi. We also give an O(N/sup k/(k+1)/) query quantum algorithm for the generalization of element distinctness in which we have to find k equal items… Expand
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