Phase matching in quantum searching
arXiv:quant-ph/9906020 · doi:10.1016/S0375-9601(99)00631-3
Abstract
Each iteration in Grover's original quantum search algorithm contains 4 steps: two Hadamard-Walsh transformations and two amplitudes inversions. When the inversion of the marked state is replaced by arbitrary phase rotation θand the inversion for the prepared state |γ> is replaced by rotation through Ï, we found that these phase rotations must satisfy a matching condition θ=Ï. Approximate formula for the amplitude of the marked state after an arbitrary number of iterations are also derived. We give also a simple explanation of the phase matching requirement.
13 pages, 7 figures