Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate

Details Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate Temperley-Lieb Algebra, Yang-Baxterization and Universal Gate

2009-03-23

arxiv.org/abs/0903.3711v6

Physics

Quantum Physics

12 pages

Scientific paper

10.1007/s11128-009-0159-0

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 $\breve{R}(\theta,q_{1},q_{2})$ 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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