Quantum Information Processing

, Volume 15, Issue 2, pp 675–688

Quantum walk on the line through potential barriers


DOI: 10.1007/s11128-015-1215-6

Cite this article as:
Wong, T.G. Quantum Inf Process (2016) 15: 675. doi:10.1007/s11128-015-1215-6


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.


Quantum walks Quantum tunneling Faulty shift Fourier transform 

Funding information

Funder NameGrant NumberFunding Note
Seventh Framework Programme
European Research Council
  • MQC

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Faculty of ComputingUniversity of LatviaRigaLatvia

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