Quantum Information Processing

, Volume 15, Issue 2, pp 675–688 | Cite as

Quantum walk on the line through potential barriers

Article

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 that 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.

Keywords

Quantum walks Quantum tunneling Faulty shift Fourier transform 

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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Faculty of ComputingUniversity of LatviaRigaLatvia

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