logN) Quantum Algorithm for the 1-dimensional Closest-Pair Problem

Abstract

We present an algorithm for solving the closest pair problem using O(N log N) queries. This improves the simple approach using Dürr and Høyer’s minimum algorithm which would result in O(N) queries. The classical deterministic and probabilistic complexity is, respectively, of O(N logN) and O(N) queries. We also show a quantum lower bound of Ω(N) queries for… (More)

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