### Abstract

A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

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

Article number | 032320 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 92 |

Issue number | 3 |

DOIs | |

State | Published - Sep 21 2015 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

### Cite this

**Faster quantum walk search on a weighted graph.** / Wong, Thomas.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Faster quantum walk search on a weighted graph

AU - Wong, Thomas

PY - 2015/9/21

Y1 - 2015/9/21

N2 - A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

AB - A randomly walking quantum particle evolving by Schrödinger's equation searches for a unique marked vertex on the "simplex of complete graphs" in time Θ(N3/4). We give a weighted version of this graph that preserves vertex transitivity, and we show that the time to search on it can be reduced to nearly Θ(N). To prove this, we introduce two extensions to degenerate perturbation theory: an adjustment that distinguishes the weights of the edges and a method to determine how precisely the jumping rate of the quantum walk must be chosen.

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U2 - 10.1103/PhysRevA.92.032320

DO - 10.1103/PhysRevA.92.032320

M3 - Article

VL - 92

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

SN - 1050-2947

IS - 3

M1 - 032320

ER -