The quantum query complexity of certification (pp0181-0189)
          Andris Ambainis, Andrew M. Childs, Francois Le Gall, and Seiichiro Tani
          doi: https://doi.org/10.26421/QIC10.3-4-1
Abstracts: We study the quantum query complexity of finding a certificate for a d-regular, klevel balanced nandformula. We show that the query complexity is Θ(d^{(k+1)/2}) for 0-certificates, and Θ(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}). Our lower bound relies on the fact that the quantum adversary method obeys a direct sum theorem.
Key words: Quantum query complexity, formula evaluation, certificates