### Abstract

This paper addresses the question: what processes take polynomial time on a quantum computer that require exponential time classically? We show that the hitting time of the discrete time quantum walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum walks. We provide the basic framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs. We outline a possible application to sequential packet routing.

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

Pages (from-to) | 215-235 |

Number of pages | 21 |

Journal | Probability Theory and Related Fields |

Volume | 133 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2005 |

### Fingerprint

### ASJC Scopus subject areas

- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Probability Theory and Related Fields*,

*133*(2), 215-235. https://doi.org/10.1007/s00440-004-0423-2

**Discrete quantum walks hit exponentially faster.** / Kempe, Julia.

Research output: Contribution to journal › Article

*Probability Theory and Related Fields*, vol. 133, no. 2, pp. 215-235. https://doi.org/10.1007/s00440-004-0423-2

}

TY - JOUR

T1 - Discrete quantum walks hit exponentially faster

AU - Kempe, Julia

PY - 2005/1/1

Y1 - 2005/1/1

N2 - This paper addresses the question: what processes take polynomial time on a quantum computer that require exponential time classically? We show that the hitting time of the discrete time quantum walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum walks. We provide the basic framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs. We outline a possible application to sequential packet routing.

AB - This paper addresses the question: what processes take polynomial time on a quantum computer that require exponential time classically? We show that the hitting time of the discrete time quantum walk on the n-bit hypercube from one corner to its opposite is polynomial in n. This gives the first exponential quantum-classical gap in the hitting time of discrete quantum walks. We provide the basic framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs. We outline a possible application to sequential packet routing.

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UR - http://www.scopus.com/inward/citedby.url?scp=24644478594&partnerID=8YFLogxK

U2 - 10.1007/s00440-004-0423-2

DO - 10.1007/s00440-004-0423-2

M3 - Article

VL - 133

SP - 215

EP - 235

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

SN - 0178-8051

IS - 2

ER -