@article {1256,
title = {The quantum query complexity of certification},
year = {2009},
month = {2009/03/06},
abstract = { We study the quantum query complexity of finding a certificate for a
d-regular, k-level balanced NAND formula. Up to logarithmic factors, we show
that the query complexity is Theta(d^{(k+1)/2}) for 0-certificates, and
Theta(d^{k/2}) for 1-certificates. In particular, this shows that the
zero-error quantum query complexity of evaluating such formulas is
O(d^{(k+1)/2}) (again neglecting a logarithmic factor). Our lower bound relies
on the fact that the quantum adversary method obeys a direct sum theorem.
},
url = {http://arxiv.org/abs/0903.1291v2},
author = {Andris Ambainis and Andrew M. Childs and Fran{\c c}ois Le Gall and Seiichiro Tani}
}