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Quantum Certificate Complexity Scott Aaronson

Summary: Quantum Certificate Complexity
Scott Aaronson
Computer Science Division
University of California, Berkeley
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 R0 (f) = O Q2 (f)
Q0 (f) log n for total f, where
R0, Q2, and Q0 are zero-error randomized, bounded-
error quantum, and zero-error 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 Q2 (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