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Quantum walk on the line through potential barriers

Quantum Information Processing volume 15, pages 675–688 (2016)Cite this 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.

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Acknowledgments

Thanks to Andris Ambainis and Alexander Rivosh for useful discussions. This work was partially supported by the European Union Seventh Framework Programme (FP7/2007-2013) under the QALGO (Grant Agreement No. 600700) project and the ERC Advanced Grant MQC.

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  1. Faculty of Computing, University of Latvia, Raiņa bulv. 19, Riga, 1586, Latvia

    Thomas G. Wong

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  1. Thomas G. Wong
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Correspondence to Thomas G. Wong.

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Wong, T.G. Quantum walk on the line through potential barriers. Quantum Inf Process 15, 675–688 (2016). https://doi.org/10.1007/s11128-015-1215-6

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  • DOI: https://doi.org/10.1007/s11128-015-1215-6

Keywords

  • Quantum walks
  • Quantum tunneling
  • Faulty shift
  • Fourier transform