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arXiv:0903.3711 · Quantum Information Processing

Temperley–Lieb algebra, Yang-Baxterization and universal gate

Gangcheng Wang, Kang Xue, Chunfang Sun, Chengcheng Zhou, Taotao Hu, Qingyong Wang

Published Dec 17, 2009• 18 citations
arXivHTMLPDF
DOI
10.1007/s11128-009-0159-0

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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 [Formula: see text]. Specifically, we present a 9 × 9 matrix U with [Formula: see text]. Via Yang-Baxterization approach, we obtain a unitary [Formula: see text]-matrix, a solution of the Yang-Baxter equation. This 9 × 9 Yang-Baxter matrix is universal for quantum computing.