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arXiv · 1206.3178

Quantum Walks on Trees with Disorder: Decay, Diffusion, and Localization

Steven R. Jackson·Teng Jian Khoo·Frederick W. Strauch
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Abstract

Quantum walks have been shown to have impressive transport properties compared to classical random walks. However, imperfections in the quantum walk algorithm can destroy any quantum mechanical speed-up due to Anderson localization. We numerically study the effect of static disorder on a quantum walk on the glued trees graph. For small disorder, we find that the dominant effect is a type of quantum decay, and not quantum localization. For intermediate disorder, there is a crossover to diffusive transport, while a localization transition is observed at large disorder, in agreement with Anderson localization on the Cayley tree.

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Steven R. Jackson, Teng Jian Khoo, Frederick W. Strauch. 2012-06-14. Quantum Walks on Trees with Disorder: Decay, Diffusion, and Localization. https://doi.org/10.1103/physreva.86.022335

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