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Phase matching in quantum searching

Gui Lu Long·Yan Song Li·Wei Lin Zhang·Li Niu
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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 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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Gui Lu Long, Yan Song Li, Wei Lin Zhang, Li Niu. 1999-06-05. Phase matching in quantum searching. https://doi.org/10.1016/s0375-9601(99)00631-3

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