Quantum walks are well known for their ballistic dispersion, traveling $$\Theta (t)$$ 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 that this could eliminate the ballistic transport. We show by explicit calculation, however, that such a loss does not occur. Rather, the $$\Theta (t)$$ Θ ( t ) dispersion is retained, with only the coefficient changing, which additionally gives a way to detect and quantify the hopping errors in experiments.
Quantum Information Processing – Springer Journals
Published: Dec 22, 2015
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