A novel SO(3) picture for quantum searching

Details A novel SO(3) picture for quantum searching A novel SO(3) picture for quantum searching

1999-11-03

arxiv.org/abs/quant-ph/9911004v1

Physics

Quantum Physics

6 pages, 2 eps figures

Scientific paper

An SO(3) picture of the generalized Grover's quantum searching algorithm,with arbitrary unitary transformation and with arbitrary phase rotations, is constructed. In this picture, any quantum search operation is a rotation in a 3 dimensional space. Exact formulas for the rotation angle and rotational axis are given. The probability of finding the marked state is just $(z+1)/2$, where z is the z-component of the state vector. Exact formulas for this probability is easily obtained. The phase matching requirement and the failure of algorithm when phase mismatches are clearly explained.

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