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A novel SO(3) picture for quantum searching

Gui Lu Long·Chang Cun Tu·Yan Song Li·Wei Lin Zhang·Hai Yang Yan
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Abstract

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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Gui Lu Long, Chang Cun Tu, Yan Song Li, Wei Lin Zhang, Hai Yang Yan. 1999-11-03. A novel SO(3) picture for quantum searching. https://arxiv.org/abs/quant-ph/9911004

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