### Abstract

An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers, and some amplitude of staying put. We investigate the algorithmic consequence of such barriers for the quantum walk formulation of Grover's algorithm. We prove that the failure amplitude must scale as for search to retain its quantum runtime; otherwise, it searches in classical O(N) time. Thus searching larger 'databases' requires increasingly reliable hop operations or error correction. This condition holds for both discrete- and continuous-time quantum walks.

Original language | English (US) |
---|---|

Article number | 484002 |

Journal | Journal of Physics A: Mathematical and Theoretical |

Volume | 49 |

Issue number | 48 |

DOIs | |

State | Published - Nov 9 2016 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Statistics and Probability
- Modeling and Simulation
- Mathematical Physics
- Physics and Astronomy(all)

### Cite this

**Quantum walk search through potential barriers.** / Wong, Thomas.

Research output: Contribution to journal › Article

*Journal of Physics A: Mathematical and Theoretical*, vol. 49, no. 48, 484002. https://doi.org/10.1088/1751-8113/49/48/484002

}

TY - JOUR

T1 - Quantum walk search through potential barriers

AU - Wong, Thomas

PY - 2016/11/9

Y1 - 2016/11/9

N2 - An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers, and some amplitude of staying put. We investigate the algorithmic consequence of such barriers for the quantum walk formulation of Grover's algorithm. We prove that the failure amplitude must scale as for search to retain its quantum runtime; otherwise, it searches in classical O(N) time. Thus searching larger 'databases' requires increasingly reliable hop operations or error correction. This condition holds for both discrete- and continuous-time quantum walks.

AB - An ideal quantum walk transitions from one vertex to another with perfect fidelity, but in physical systems, the particle may be hindered by potential energy barriers. Then the particle has some amplitude of tunneling through the barriers, and some amplitude of staying put. We investigate the algorithmic consequence of such barriers for the quantum walk formulation of Grover's algorithm. We prove that the failure amplitude must scale as for search to retain its quantum runtime; otherwise, it searches in classical O(N) time. Thus searching larger 'databases' requires increasingly reliable hop operations or error correction. This condition holds for both discrete- and continuous-time quantum walks.

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UR - http://www.scopus.com/inward/citedby.url?scp=84995414683&partnerID=8YFLogxK

U2 - 10.1088/1751-8113/49/48/484002

DO - 10.1088/1751-8113/49/48/484002

M3 - Article

AN - SCOPUS:84995414683

VL - 49

JO - Journal of Physics A: Mathematical and Theoretical

JF - Journal of Physics A: Mathematical and Theoretical

SN - 1751-8113

IS - 48

M1 - 484002

ER -