%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