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Quantum Simulation

Searching via nonlinear quantum walk on the 2D-grid

arXiv

Authors: Basile Herzog, Giuseppe Di Molfetta

Year

2020

Paper ID

20655

Status

Preprint

Abstract Read

~2 min

Abstract Words

127

Citations

N/A

Abstract

We provide numerical evidence that the nonlinear searching algorithm introduced by Wong and Meyer \cite{meyer2013nonlinear}, rephrased in terms of quantum walks with effective nonlinear phase, can be extended to the finite 2-dimensional grid, keeping the same computational advantage \BHg{with} respect to the classical algorithms. For this purpose, we have considered the free lattice Hamiltonian, with linear dispersion relation introduced by Childs and Ge \cite{Childs_2014}. The numerical simulations showed that the walker finds the marked vertex in O\(N^1/4 log^3/4 N\) steps, with probability O\(1/log N\), for an overall complexity of O\(N^1/4log^7/4N\). We also proved that there exists an optimal choice of the walker parameters to avoid that the time measurement precision affects the complexity searching time of the algorithm.

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We provide numerical evidence that the nonlinear searching algorithm introduced by Wong and Meyer citemeyer2013nonlinear, rephrased in terms of quantum walks with effective...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2009.07800 [2] arXiv https://arxiv.org/abs/2009.07800 [3] Publisher https://arxiv.org/abs/2009.07800

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