TY - JOUR T1 - The quantum query complexity of certification Y1 - 2009 A1 - Andris Ambainis A1 - Andrew M. Childs A1 - François Le Gall A1 - Seiichiro Tani AB - 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. UR - http://arxiv.org/abs/0903.1291v2 J1 - Quantum Information and Computation 10 ER -