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 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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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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Keywords

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