Theory of Computing ------------------- Title : A Quantum Algorithm for the Hamiltonian NAND Tree Authors : Edward Farhi, Jeffrey Goldstone, and Sam Gutmann Volume : 4 Number : 8 Pages : 169-190 URL : https://theoryofcomputing.org/articles/v004a008 Abstract -------- We give a quantum algorithm for the binary NAND tree problem in the Hamiltonian oracle model. The algorithm uses a continuous time quantum walk with a running time proportional to sqrt{N}. We also show a lower bound of Omega(sqrt{N}) for the NAND tree problem in the Hamiltonian oracle model.