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- Title
THE REPRESENTATIONS OF TEMPERLEY-LIEB ALGEBRA AND ENTANGLEMENT IN A YANG-BAXTER SYSTEM.
- Authors
CHUNFANG SUN; GANGCHENG WANG; TAOTAO HU; CHENGCHENG ZHOU; QINGYONG WANG; KANG XUE
- Abstract
A method of constructing Temperley-Lieb algebra (TLA) representations has been introduced in [Xue et al. arXiv:0903.3711]. Using this method, we can obtain another series of n2 × n2 matrices U which satisfy the TLA with the single loop $d=\sqrt{n}$. Specifically, we present a 9 × 9 matrix U with $d=\sqrt{3}$. Via Yang-Baxterization approach, we obtain a unitary $ \breve{R}(\theta ,\varphi_{1},\varphi_{2})$-matrix, a solution of the Yang-Baxter equation. This 9 × 9 Yang-Baxter matrix is universal for quantum computing.
- Subjects
MATRICES (Mathematics); YANG-Baxter equation; QUANTUM computers; ABSTRACT algebra; ALGEBRA
- Publication
International Journal of Quantum Information, 2009, Vol 7, Issue 6, p1285
- ISSN
0219-7499
- Publication type
Article
- DOI
10.1142/S0219749909005614