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arXiv · 1509.07112

Quantum Walk on the Line through Potential Barriers

Thomas G. Wong
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Abstract

Quantum walks are well-known for their ballistic dispersion, traveling $Θ(t)$ away in $t$ steps, which is quadratically faster than a classical random walk's diffusive spreading. In physical implementations of the walk, however, the particle may need to tunnel through a potential barrier to hop, and a naive calculation suggests this could eliminate the ballistic transport. We show by explicit calculation, however, that such a loss does not occur. Rather, the $Θ(t)$ dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments.

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Thomas G. Wong. 2015-12-07. Quantum Walk on the Line through Potential Barriers. https://doi.org/10.1007/s11128-015-1215-6

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