The quantum query complexity of certification
Quantum Physics
2018-12-20 v2 Computational Complexity
Abstract
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.
Cite
@article{arxiv.0903.1291,
title = {The quantum query complexity of certification},
author = {Andris Ambainis and Andrew M. Childs and François Le Gall and Seiichiro Tani},
journal= {arXiv preprint arXiv:0903.1291},
year = {2018}
}
Comments
8 pages; Updated to reflect changes in final journal version and to point out that the main result only applies for k>1