Phase matching in quantum searching

Details Phase matching in quantum searching Phase matching in quantum searching

1999-06-05

arxiv.org/abs/quant-ph/9906020v1

Phys.Lett. A262 (1999) 27-34

Physics

Quantum Physics

13 pages, 7 figures

Scientific paper

10.1016/S0375-9601(99)00631-3

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 \theta and the inversion for the prepared state |\gamma> is replaced by rotation through \phi, we found that these phase rotations must satisfy a matching condition \theta=\phi. 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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