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Discrete-query quantum algorithm for NAND trees

Andrew M. Childs·Richard Cleve·Stephen P. Jordan·David Yonge-Mallo
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Abstract

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.

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Andrew M. Childs, Richard Cleve, Stephen P. Jordan, David Yonge-Mallo. 2007-02-16. Discrete-query quantum algorithm for NAND trees. https://doi.org/10.4086/toc.2009.v005a005

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