%0 Journal Article %D 2009 %T The quantum query complexity of certification %A Andris Ambainis %A Andrew M. Childs %A François Le Gall %A Seiichiro Tani %X 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. %8 2009/03/06 %G eng %U http://arxiv.org/abs/0903.1291v2 %! Quantum Information and Computation 10