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arXiv · 0903.3711

Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate

Gangcheng Wang·Chengcheng Zhou·Chunfang Sun·Taotao Hu·Qingyong Wang·Kang Xue
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Abstract

A method of constructing $n^{2}\times n^{2}$ matrix solutions(with $n^{3}$ matrix elements) of Temperley-Lieb algebra relation is presented in this paper. The single loop of these solutions are $d=\sqrt{n}$. Especially, a $9\times9-$matrix solution with single loop d=$\sqrt{3}$ is discussed in detail. An unitary Yang-Baxter $\breve{R}(θ,q_{1},q_{2})$ matrix is obtained via the Yang-Baxterization process. The entanglement property and geometric property (\emph{i.e.} Berry Phase) of this Yang-Baxter system are explored.

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Gangcheng Wang, Chengcheng Zhou, Chunfang Sun, Taotao Hu, Qingyong Wang, Kang Xue. 2009-12-27. Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate. https://doi.org/10.1007/s11128-009-0159-0

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