### Abstract

Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.

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

Article number | 022304 |

Journal | Physical Review A |

Volume | 94 |

Issue number | 2 |

DOIs | |

State | Published - Aug 4 2016 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*94*(2), [022304]. https://doi.org/10.1103/PhysRevA.94.022304

**Engineering the success of quantum walk search using weighted graphs.** / Wong, Thomas; Philipp, Pascal.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 94, no. 2, 022304. https://doi.org/10.1103/PhysRevA.94.022304

}

TY - JOUR

T1 - Engineering the success of quantum walk search using weighted graphs

AU - Wong, Thomas

AU - Philipp, Pascal

PY - 2016/8/4

Y1 - 2016/8/4

N2 - Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.

AB - Continuous-time quantum walks are natural tools for spatial search, where one searches for a marked vertex in a graph. Sometimes the structure of the graph causes the walker to get trapped, such that the probability of finding the marked vertex is limited. We give an example with two linked cliques, proving that the captive probability can be liberated by increasing the weights of the links. This allows the search to succeed with probability 1 without increasing the energy scaling of the algorithm. Further increasing the weights, however, slows the runtime, so the optimal search requires weights that are neither too weak nor too strong.

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UR - http://www.scopus.com/inward/citedby.url?scp=84983469990&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.94.022304

DO - 10.1103/PhysRevA.94.022304

M3 - Article

VL - 94

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

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

SN - 1050-2947

IS - 2

M1 - 022304

ER -