Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution
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 \sim O(\sqrt{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.
Keywords
Cite
@article{arxiv.quant-ph/9801066,
title = {Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution},
author = {David Biron and Ofer Biham and Eli Biham and Markus Grassl and Daniel A. Lidar},
journal= {arXiv preprint arXiv:quant-ph/9801066},
year = {2016}
}
Comments
8 pages, llncs style. To be published in the proceedings of the 1st NASA International Conference on Quantum Computing and Quantum Communications