Quantum lower bound for the collision problem

@inproceedings{Aaronson2002QuantumLB,
  title={Quantum lower bound for the collision problem},
  author={Scott Aaronson},
  booktitle={STOC '02},
  year={2002}
}
  • S. Aaronson
  • Published in STOC '02 19 November 2001
  • Mathematics, Physics, Computer Science
(MATH) The collision problem is to decide whether a function X: { 1,&ldots;,n} → { 1, &ldots;,n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of Ω(n1/5) on the number of queries needed by a quantum computer to solve this problem with bounded error probability. The best known upper bound is O(n1/3), but obtaining any lower bound better than Ω(1) was an open problem since 1997. Our proof uses the polynomial method augmented by some new ideas. We also… 
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