We introduce a new method to derive lower bounds on randomized and quantum communication complexity. Our method is based on factorization norms, a notion from Banach Space theory....
We consider the quantum complexities of the following three problems: searching an ordered list, sorting an un-ordered list, and deciding whether the numbers in a list are all dis...
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 describe a quantum black-box network computing the majority of N bits with zerosided error using only 2 3 N + O( N log( -1 log N)) queries: the algorithm returns the correct an...
Thomas P. Hayes, Samuel Kutin, Dieter van Melkebee...
Although it is known that quantum computers can solve certain computational problems exponentially faster than classical computers, only a small number of quantum algorithms have ...