Discrete-query quantum algorithm for NAND trees. (arXiv:quant-ph/0702160v2 UPDATED)
Andrew M. Childs, Richard Cleve, Stephen P. Jordan, David L. Yonge-Mallo · arXiv (Cornell University) · 2019
Recently, Farhi, Goldstone, and Gutmann gave a quantum algorithm for evaluating NAND trees that runs in time O(sqrt(N log N)) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm using O(N^{1/2 + epsilon}) queries in the conventional quantum query model, for any fixed epsilon > 0.