Any AND-OR Formula of Size N Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer
Abstract
Consider the problem of evaluating an AND-OR formula on an N-bit black-box input. We present a bounded-error quantum algorithm that solves this problem in time $N^{1/2+o(1)}$. In particular, approximately balanced formulas can be evaluated in $O(\sqrt{N})$ queries, which is optimal. The idea of the algorithm is to apply phase estimation to a discrete-time quantum walk on a weighted tree whose spectrum encodes the value of the formula.
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Copyright © 2010 Society for Industrial and Applied Mathematics.
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Submitted: 2 January 2008
Accepted: 16 July 2009
Published online: 30 April 2010
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