Generalized grover search algorithm for arbitrary initial amplitude distribution

David Biron, Ofer Biham, Eli Biham, Markus Grassl, Daniel A. Lidar

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

42 Scopus citations

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 languageAmerican English
Title of host publicationQuantum Computing and Quantum Communications - 1st NASA International Conference, QCQC 1998, Selected Papers
EditorsColin P. Williams
PublisherSpringer Verlag
Pages140-147
Number of pages8
ISBN (Print)354065514X, 9783540655145
DOIs
StatePublished - 1999
Event1st NASA International Conference on Quantum Computing and Quantum Communications, QCQC 1998 - Palm Springs, United States
Duration: 17 Feb 199820 Feb 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1509
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference1st NASA International Conference on Quantum Computing and Quantum Communications, QCQC 1998
Country/TerritoryUnited States
CityPalm Springs
Period17/02/9820/02/98

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1999.

Keywords

  • Exact solution
  • Grover’s algorithm
  • Quantum searching

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