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arXiv · 1612.08958

Efficient quantum walk on the grid with multiple marked elements

Peter Hoyer·Mojtaba Komeili
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Abstract

We give a quantum algorithm for finding a marked element on the grid when there are multiple marked elements. Our algorithm uses quadratically fewer steps than a random walk on the grid, ignoring logarithmic factors. This is the first known quantum walk that finds a marked element in a number of steps less than the square-root of the extended hitting time. We also give a new tighter upper bound on the extended hitting time of a marked subset, expressed in terms of the hitting times of its members.

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Peter Hoyer, Mojtaba Komeili. 2016-12-28. Efficient quantum walk on the grid with multiple marked elements. https://doi.org/10.4230/lipics.stacs.2017.42

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