Generalized Grover Search Algorithm for Arbitrary Initial Amplitude   Distribution
  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. 
David Biron (1), Ofer Biham (1), Eli Biham (2), Markus Grassl (3) and   Daniel A. Lidar (4) ((1) Racah Institute of Physics,...