dorsal/arxiv
View SchemaA novel SO(3) picture for quantum searching
| Authors | Gui Lu Long, Chang Cun Tu, Yan Song Li, Wei Lin Zhang, Hai Yang Yan |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9911004 |
| URL | https://arxiv.org/abs/quant-ph/9911004 |
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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"date_created": "2026-03-02T18:02:47.944000Z",
"date_modified": "2026-03-02T18:02:47.944000Z",
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"abstract": "An SO(3) picture of the generalized Grover\u0027s quantum searching algorithm,with\narbitrary unitary transformation and with arbitrary phase rotations, is\nconstructed. In this picture, any quantum search operation is a rotation in a 3\ndimensional space. Exact formulas for the rotation angle and rotational axis\nare given. The probability of finding the marked state is just $(z+1)/2$, where\nz is the z-component of the state vector. Exact formulas for this probability\nis easily obtained. The phase matching requirement and the failure of algorithm\nwhen phase mismatches are clearly explained.",
"arxiv_id": "quant-ph/9911004",
"authors": [
"Gui Lu Long",
"Chang Cun Tu",
"Yan Song Li",
"Wei Lin Zhang",
"Hai Yang Yan"
],
"categories": [
"quant-ph"
],
"title": "A novel SO(3) picture for quantum searching",
"url": "https://arxiv.org/abs/quant-ph/9911004"
},
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"execution_id": "2d0f6cb9-38c8-4289-b359-9f852da2a39e",
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"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
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