Generalized Grover Search Algorithm for Arbitrary Initial Amplitude Distribution

Authors:
David Biron;Ofer Biham;Eli Biham;Markus Grassl;Daniel A. Lidar
Affiliations:
-;-;-;-;-
Venue:
QCQC '98 Selected papers from the First NASA International Conference on Quantum Computing and Quantum Communications
Year:
1998

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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.