2013 IEEE 54th Annual Symposium on Foundations of Computer Science (2007)

Providence, Rhode Island

Oct. 21, 2007 to Oct. 23, 2007

ISSN: 0272-5428

ISBN: 0-7695-3010-9

pp: 363-372

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/FOCS.2007.57

ABSTRACT

For any AND-OR formula of size N, there exists a bounded-error N^{1/2 + o(1)} -time quantum algorithm, based on a discrete-time quantum walk, that evaluates this formula on a black-box input. Balanced, or "approximately balanced," formulas can be evaluated in {\rm O}(\sqrt N ) {\rm O}(\sqrt N ) (2 - o(1))th power of the quantum query complexity is a lower bound on the formula size, almost solving in the positive an open problem posed by Laplante, Lee and Szegedy.

INDEX TERMS

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CITATION

Robert Spalek,
Ben W. Reichardt,
Andris Ambainis,
Andrew M. Childs,
Shengyu Zhang,
"Any AND-OR Formula of Size N can be Evaluated in time N^{1/2 + o(1)} on a Quantum Computer",

*2013 IEEE 54th Annual Symposium on Foundations of Computer Science*, vol. 00, no. , pp. 363-372, 2007, doi:10.1109/FOCS.2007.57SEARCH