Discrete-Query Quantum Algorithm for NAND Trees

This is a comment on the article “A Quantum Algorithm for the Hamiltonian NAND Tree” by Edward Farhi, Jeffrey Goldstone, and Sam Gutmann, Theory of Computing 4 (2008) 169--190. That paper gave a quantum algorithm for evaluating NAND trees with running time O(√N) in the Hamiltonian query model. In this note, we point out that their algorithm can be converted into an algorithm using N^[1/2 + o(1)] queries in the conventional (discrete) quantum query model.

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