### Abstract

A randomly walking quantum particle searches in Grover’s (formula presented) iterations for a marked vertex on the complete graph of N vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a “coin” flip, and hopping. Physically, however, potential energy barriers can hinder the hop and cause the search to fail, even when the amplitude of not hopping decreases with N. We correct for these errors by interpreting the quantum walk search as an amplitude amplification algorithm and modifying the phases applied by the coin flip and oracle such that the amplification recovers the (formula presented) runtime.

Original language | English (US) |
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Pages (from-to) | 1365-1372 |

Number of pages | 8 |

Journal | Quantum Information and Computation |

Volume | 15 |

Issue number | 15-16 |

State | Published - Sep 21 2015 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Statistical and Nonlinear Physics
- Nuclear and High Energy Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Computational Theory and Mathematics

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## Cite this

Ambainis, A., & Wong, T. G. (2015). Correcting for potential barriers in quantum walk search.

*Quantum Information and Computation*,*15*(15-16), 1365-1372.