## Abstract

Grover’s algorithm for quantum searching of a database is generalized to deal with arbitrary initial amplitude distributions. First order linear difference equations are found for the time evolution of the amplitudes of the r marked and N − r unmarked states. These equations are solved exactly. An expression for the optimal measurement time T ∼ O(√N/r) is derived which is shown to depend only on the initial average amplitudes of the marked and unmarked states. A bound on the probability of measuring a marked state is derived, which depends only on the standard deviation of the initial amplitude distributions of the marked or unmarked states.

Original language | American English |
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Title of host publication | Quantum Computing and Quantum Communications - 1st NASA International Conference, QCQC 1998, Selected Papers |

Editors | Colin P. Williams |

Publisher | Springer Verlag |

Pages | 140-147 |

Number of pages | 8 |

ISBN (Print) | 354065514X, 9783540655145 |

DOIs | |

State | Published - 1999 |

Event | 1st NASA International Conference on Quantum Computing and Quantum Communications, QCQC 1998 - Palm Springs, United States Duration: 17 Feb 1998 → 20 Feb 1998 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 1509 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 1st NASA International Conference on Quantum Computing and Quantum Communications, QCQC 1998 |
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Country/Territory | United States |

City | Palm Springs |

Period | 17/02/98 → 20/02/98 |

### Bibliographical note

Publisher Copyright:© Springer-Verlag Berlin Heidelberg 1999.

## Keywords

- Exact solution
- Grover’s algorithm
- Quantum searching