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Topological Quantum Computing

Attractor-repeller pair of topological zero-modes in a nonlinear quantum walk

arXiv
Authors: Y. Gerasimenko, B. Tarasinski, C. W. J. Beenakker

Year

2015

Paper ID

26022

Status

Preprint

Abstract Read

~2 min

Abstract Words

100

Citations

N/A

Abstract

The quantum-mechanical counterpart of a classical random walk offers a rich dynamics that has recently been shown to include topologically protected bound states (zero-modes) at boundaries or domain walls. Here we show that a topological zero-mode may acquire a dynamical role in the presence of nonlinearities. We consider a one-dimensional discrete-time quantum walk that combines zero-modes with a particle-conserving nonlinear relaxation mechanism. The presence of both particle-hole and chiral symmetry converts two zero-modes of opposite chirality into an attractor-repeller pair of the nonlinear dynamics. This makes it possible to steer the walker towards a domain wall and trap it there.

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  • This paper contributes to the Topological Quantum Computing research area in the Quantum Articles archive.
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  • The quantum-mechanical counterpart of a classical random walk offers a rich dynamics that has recently been shown to include topologically protected bound states (zero-modes)...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1511.06657 [2] arXiv https://arxiv.org/abs/1511.06657 [3] Publisher https://arxiv.org/abs/1511.06657

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