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2002
ACM

Quantum lower bound for the collision problem

15 years 12 days ago
Quantum lower bound for the collision problem
The collision problem is to decide whether a function X : {1, . . . , n} {1, . . . , n} is one-to-one or two-to-one, given that one of these is the case. We show a lower bound of 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 (1) was an open problem since 1997. Our proof uses the polynomial method augmented by some new ideas. We also give a lower bound of n1/7 for the problem of deciding whether two sets are equal or disjoint on a constant fraction of elements. Finally we give implications of these results for quantum complexity theory.
Scott Aaronson
Added 03 Dec 2009
Updated 03 Dec 2009
Type Conference
Year 2002
Where STOC
Authors Scott Aaronson
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