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 Nr 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.
 Publication:

arXiv eprints
 Pub Date:
 January 1998
 DOI:
 10.48550/arXiv.quantph/9801066
 arXiv:
 arXiv:quantph/9801066
 Bibcode:
 1998quant.ph..1066B
 Keywords:

 Quantum Physics
 EPrint:
 8 pages, llncs style. To be published in the proceedings of the 1st NASA International Conference on Quantum Computing and Quantum Communications