Abstract. We compare classical and quantum query complexities of total Boolean functions. It is known that for worst-case complexity, the gap between quantum and classical can be a...
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...
We show that any 1-round 2-server Private Information Retrieval Protocol where the answers are 1-bit long must ask questions that are at least n - 2 bits long, which is nearly equa...
In this paper we study quantum computation from a complexity theoretic viewpoint. Our first result is the existence of an efficient universal quantum Turing machine in Deutsch’s...
In this note, we obtain a lower bound for the distance between the pseudospectrum of a matrix polynomial and a given point that lies out of it, generalizing a known result on pseu...