2001/06/13 by G. L. Long · 1 citation
Physics and Astronomy · #quant-ph
paper · pdf · doi:10.1103/physreva.64.022307
published as Phys. Rev. A64 (2001) 022307 · 5 pages. Accepted for publication in Physical Review A
arxiv created 2001/06/13 · arxiv updated 2009/12/01
In standard Grover's algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this Letter we present a modified version of Grover's algorithm that searches a marked state with full successful rate. The modification is done by replacing the phase inversion by two phase rotation through angle ϕ. The rotation angle is given analytically to be ϕ=2 \arcsin(sinπ\over (4J+6)\over sinβ), where sinβ=1\over √(N), N the number of items in the database, and J an integer equal to or greater than the integer part of (π\over 2-β)/(2β). Upon measurement at (J+1)-th iteration, the marked state is obtained with certainty.