A Note About Claw Function with a Small Range

Andris Ambainis, Kaspars Balodis, Janis Iraids

Abstract: In the claw detection problem we are given two functions f:D → R and g:D → R (|D| = n, |R| = k), and we have to determine if there is exist x,y ∈ D such that f(x) = g(y). We show that the quantum query complexity of this problem is between Ω(n^{1/2}k^{1/6}) and O(n^{1/2+ε}k^{1/4}) when 2 ≤ k < n.