Quantum Walk on the Line through Potential Barriers

Abstract

Quantum walks are well-known for their ballistic dispersion, traveling $\Theta (t)$ 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 $\Theta (t)$ dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments.

14 pages, 6 figures

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• Quantum Walk on the Line through Potential Barriers

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• Oscillatory Localization of Quantum Walks Analyzed by Classical Electric Circuits
• Full Characterization of Oscillatory Localization of Quantum Walks
• Quantum Walk on the Line through Potential Barriers
• Nonlinear flip-flop quantum walks through potential barriers
• Quantum Walk Search through Potential Barriers