Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution

Details Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution

1998-01-28

arxiv.org/abs/quant-ph/9801066v2

"Quantum Computing & Quantum Communications; First NASA International Conference; selected papers, QCQC'98", C.P. Williams (ed

Physics

Quantum Physics

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

Scientific paper

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.

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