Quantum entanglement, unitary braid representation and Temperley-Lieb algebra

  title={Quantum entanglement, unitary braid representation and Temperley-Lieb algebra},
  author={C. L. Ho and Allan I. Solomon and C.H.Oh},
Important developments in fault-tolerant quantum computation using the braiding of anyons have placed the theory of braid groups at the very foundation of topological quantum computing. Furthermore, the realization by Kauffman and Lomonaco that a specific braiding operator from the solution of the Yang-Baxter equation, namely the Bell matrix, is universal implies that in principle all quantum gates can be constructed from braiding operators together with single qubit gates. In this paper we… Expand
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Encoding discrete quantum algebras in a hierarchy of binary words
  • T. Raptis
  • Mathematics, Physics
  • Journal of Physics: Conference Series
  • 2019
It is shown how to endow a hierarchy of sets of binary patterns with the structure of an abstract,normed C*-algebra. In the course we also recover an intermediate connection with the words of a DyckExpand
New classes of spin chains from (SÔ(q)(N), Sp̂(q)(N)) Temperley-Lieb algebras: Data transmission and (q, N) parametrized entanglement entropies
A Temperley-Lieb algebra is extracted from the operator structure of a new class of N2×N2 braid matrices presented and studied in previous papers and designated as SO(q)(N), Sp(q)(N) for theExpand
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Topological basis associated with B–M–W algebra: Two-spin-1/2 realization
Abstract In this letter, we study the two-spin-1/2 realization for the Birman–Murakami–Wenzl (B–M–W) algebra and the corresponding Yang–Baxter R ˘ ( θ , ϕ ) matrix. Based on the two-spin-1/2Expand
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