Phase matching in quantum searching
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 θ and the inversion for the prepared state |γ> is replaced by rotation through φ, we found that these phase rotations must satisfy a matching condition θ=φ. 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.
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