Yang--Baxterizations, Universal Quantum Gates and Hamiltonians

Details Yang--Baxterizations, Universal Quantum Gates and Hamiltonians Yang--Baxterizations, Universal Quantum Gates and Hamiltonians

2005-02-02

arxiv.org/abs/quant-ph/0502015v4

Quant. Inf. Proc. 4 (2005) 159-197

Physics

Quantum Physics

v1:36 pages, 3 figures, latex; v2: 35 pages, typo errors corrected and diagrams redrawn; v3: RevTex4, 24 pages, 3 .eps files;

Scientific paper

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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