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...
We present several applications of quantum amplitude amplification to finding claws and collisions in ordered or unordered functions. Our algorithms generalize those of Brassard...
We exactly determine the formula size of the parity function. If n = 2 + k, where 0 ≤ k < 2 , then the formula size of parity on n bits is 2 (2 + 3k) = n2 + k2 − k2 . Khrap...
One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix— th...