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Trapped Ion Quantum Computing Quantum Simulation

Spatial Search on Grids with Minimum Memory

arXiv

Authors: Andris Ambainis, Renato Portugal, Nikolay Nahimov

Year

2013

Paper ID

31653

Status

Preprint

Abstract Read

~2 min

Abstract Words

104

Citations

N/A

Abstract

We study quantum algorithms for spatial search on finite dimensional grids. Patel et al. and Falk have proposed algorithms based on a quantum walk without a coin, with different operators applied at even and odd steps. Until now, such algorithms have been studied only using numerical simulations. In this paper, we present the first rigorous analysis for an algorithm of this type, showing that the optimal number of steps is O\(sqrt{Nlog N}\) and the success probability is O\(1/log N\), where N is the number of vertices. This matches the performance achieved by algorithms that use other forms of quantum walks.

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This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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We study quantum algorithms for spatial search on finite dimensional grids.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1312.0172 [2] arXiv https://arxiv.org/abs/1312.0172 [3] Publisher https://arxiv.org/abs/1312.0172

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