The quantum query complexity of certification

TitleThe quantum query complexity of certification
Publication TypeJournal Article
Year of Publication2009
AuthorsAmbainis, A, Childs, AM, Le Gall, F, Tani, S
Date Published2009/03/06

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.

Short TitleQuantum Information and Computation 10