Temperley–Lieb algebra, Yang-Baxterization and universal gate

Temperley–Lieb algebra, Yang-Baxterization and universal gate A method of constructing n 2 × n 2 matrix realization of Temperley–Lieb algebras is presented. The single loop of these realizations are $${d=\sqrt{n}}$$ . In particular, a 9 × 9-matrix realization with single loop $${d=\sqrt{3}}$$ is discussed. A unitary Yang–Baxter $${\breve{R}\theta,q_{1},q_{2})}$$ matrix is obtained via the Yang-Baxterization process. The entanglement properties and geometric properties (i.e., Berry Phase) of this Yang–Baxter system are explored. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Temperley–Lieb algebra, Yang-Baxterization and universal gate

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Publisher
Springer US
Copyright
Copyright © 2009 by Springer Science+Business Media, LLC
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-009-0159-0
Publisher site
See Article on Publisher Site

Abstract

A method of constructing n 2 × n 2 matrix realization of Temperley–Lieb algebras is presented. The single loop of these realizations are $${d=\sqrt{n}}$$ . In particular, a 9 × 9-matrix realization with single loop $${d=\sqrt{3}}$$ is discussed. A unitary Yang–Baxter $${\breve{R}\theta,q_{1},q_{2})}$$ matrix is obtained via the Yang-Baxterization process. The entanglement properties and geometric properties (i.e., Berry Phase) of this Yang–Baxter system are explored.

Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 18, 2009

References

  • Quantum information and computation
    Bennett, C.H.; DiVincenzo, D.P.
  • S matrix for the one-dimensional N-body problem with repulsive or attractive-function interaction
    Yang, C.N.

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