This paper studies the gap between classical one-way communication complexity C(f) and its quantum counterpart Q(f), under the unbounded-error setting, i.e., it is enough that the ...
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...
A sequence fn(q) is q-holonomic if it satisfies a nontrivial linear recurrence with coefficients polynomials in q and qn . Our main theorem states that q-holonomicity is preserve...
We give an exponential separation between one-way quantum and classical communication protocols for two partial Boolean functions, both of which are variants of the Boolean Hidden...
Dmitry Gavinsky, Julia Kempe, Iordanis Kerenidis, ...
For any q > 1, let MODq be a quantum gate that determines if the number of 1’s in the input is divisible by q. We show that for any q, t > 1, MODq is equivalent to MODt (u...