### Abstract

Shenvi, Kempe, and Whaleya's quantum random-walk search (SKW) algorithm is known to require O (N) number of oracle queries to find the marked element, where N is the size of the search space. The overall time complexity of the SKW algorithm differs from the best achievable on a quantum computer only by a constant factor. We present improvements to the SKW algorithm which yield a significant increase in success probability, and an improvement on query complexity such that the theoretical limit of a search algorithm succeeding with probability close to one is reached. We point out which improvement can be applied if there is more than one marked element to find.

Original language | English |
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Article number | 012325 |

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

Volume | 79 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 5 2009 |

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

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## Cite this

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

*79*(1), [012325]. https://doi.org/10.1103/PhysRevA.79.012325