dorsal/arxiv
View SchemaYang--Baxterizations, Universal Quantum Gates and Hamiltonians
| Authors | Yong Zhang, Louis H. Kauffman, Mo-Lin Ge |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0502015 |
| URL | https://arxiv.org/abs/quant-ph/0502015 |
| Journal | Quant. Inf. Proc. 4 (2005) 159-197 |
Abstract
The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinskis's theorem, the unitary solutions of the quantum Yang--Baxter equation can be also related to universal quantum gates. This paper derives the unitary solutions of the quantum Yang--Baxter equation via Yang--Baxterization from the solutions of the braided relation. We study Yang--Baxterizations of the non-standard and standard representations of the six-vertex model and the complete solutions of the non-vanishing eight-vertex model. We construct Hamiltonians responsible for the time-evolution of the unitary braiding operators which lead to the Schr{\"o}dinger equations.
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"abstract": "The unitary braiding operators describing topological entanglements can be\nviewed as universal quantum gates for quantum computation. With the help of the\nBrylinskis\u0027s theorem, the unitary solutions of the quantum Yang--Baxter\nequation can be also related to universal quantum gates. This paper derives the\nunitary solutions of the quantum Yang--Baxter equation via Yang--Baxterization\nfrom the solutions of the braided relation. We study Yang--Baxterizations of\nthe non-standard and standard representations of the six-vertex model and the\ncomplete solutions of the non-vanishing eight-vertex model. We construct\nHamiltonians responsible for the time-evolution of the unitary braiding\noperators which lead to the Schr{\\\"o}dinger equations.",
"arxiv_id": "quant-ph/0502015",
"authors": [
"Yong Zhang",
"Louis H. Kauffman",
"Mo-Lin Ge"
],
"categories": [
"quant-ph",
"hep-th",
"math-ph",
"math.MP"
],
"journal_ref": "Quant. Inf. Proc. 4 (2005) 159-197",
"title": "Yang--Baxterizations, Universal Quantum Gates and Hamiltonians",
"url": "https://arxiv.org/abs/quant-ph/0502015"
},
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