Andris Ambainis Yaoyun Shi algorithm quantum computer computer
The element distinctness problem is the problem of determining whether all the elements of a list are distinct. Classically, Ω(N) queries are required for a list of size N. However, it can be solved in 



Θ
(

N

2

/

3


)


{\displaystyle \Theta (N^{2/3})}

 queries on a quantum computer. The optimal algorithm is by Andris Ambainis. Yaoyun Shi first proved a tight lower bound when the size of the range is sufficiently large. Ambainis and Kutin independently (and via different proofs) extended his work to obtain the lower bound for all functions.
