Quantum Algorithms for Evaluating Min-Max Trees

Authors:
Richard Cleve;Dmitry Gavinsky;D. L. Yonge-Mallo
Affiliations:
David R. Cheriton School of Computer Science and Institute for Quantum Computing, University of Waterloo, and Perimeter Institute for Theoretical Physics,;David R. Cheriton School of Computer Science and Institute for Quantum Computing, University of Waterloo,;David R. Cheriton School of Computer Science and Institute for Quantum Computing, University of Waterloo,
Venue:
Theory of Quantum Computation, Communication, and Cryptography
Year:
2008

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Abstract

We present a bounded-error quantum algorithm for evaluating Min -Max trees with $N^{\frac{1}{2}+o(1)}$ queries, where N is the size of the tree and where the allowable queries are comparisons of the form [x j x k ]. This is close to tight, since there is a known quantum lower bound of $\Omega(N^{\frac{1}{2}})$.