Summary: Quantum Certificate Complexity
Scott Aaronson #
Computer Science Division
University of California, Berkeley
Abstract
Given a Boolean function f , we study two natural gener­
alizations of the certificate complexity C (f): the random­
ized certificate complexity RC (f) and the quantum cer­
tificate complexity QC(f). Using Ambainis' adversary
method, we exactly characterize QC (f) as the square root
of RC(f). We then use this result to prove the new rela­
tion R 0 (f) = O # Q 2 (f) 2
Q 0 (f) log n # for total f , where
R 0 , Q 2 , and Q 0 are zero­error randomized, bounded­
error quantum, and zero­error quantum query complexi­
ties respectively. Finally we give asymptotic gaps be­
tween the measures, including a total f for which C(f) is
superquadratic in QC (f), and a symmetric partial f for
which QC (f) = O (1) yet Q 2 (f)
=# (n/ log n).

Source: Aaronson, Scott - Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT)

Collections: Physics; Computer Technologies and Information Sciences