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Possible universal quantum algorithms for generalized Turaev-Viro invariants
SPIE Proceedings, 2011An emergent trend in quantum computation is the topological quantum computation (TQC). Briefly, TQC results from the application of quantum computation with the aim to solve the problems of quantum topology such as topological invariants for knots and links (Jones polynomials, HOMFLY polynomials, Khovanov polynomials); topological invariants for ...
Velez, Mario, Ospina, Juan
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TURAEV-VIRO AND KAUFFMAN-LINS INVARIANTS FOR 3-MANIFOLDS COINCIDE
Journal of Knot Theory and Its Ramifications, 1992The presentation of link polynomials, arising from representations of quantum group SLq(2) by SLq(2)-spin networks is given. The explicit form of cabling formula for these polynomials is written. The connection between 6j-symbols in q-spin network theory and Rakah-Wigner q-6j-symbols is shown.
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GRAPHICAL APPROACH TO THE 3-MANIFOLD INVARIANTS OF TURAEV-VIRO
Journal of Knot Theory and Its Ramifications, 1992This paper uses graphical techniques introduced by Kirillov and Reshetikhin to give an alternative approach to the construction of the Turaev-Viro invariants for links in \(S^ 3 \) and for closed 3- manifolds. The invariant is defined in terms of a regular diagram for the link (or for a framed link representing the manifold) and is shown to be ...
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Which lens spaces are distinguished by Turaev-Viro invariants
Mathematical Notes, 1997Using the works of \textit{S. Yamada} [J. Knot Theory Ramifications 4, No. 2, 319-327 (1995; Zbl 0843.57004)] and \textit{L. C. Jeffrey} [Commun. Math. Phys. 147, No. 3, 563-604 (1992; Zbl 0755.53054)], the author gives an explicit formula for the value of the Turaev-Viro invariants of the 3-dimensional lens spaces \(L_{p,q}\).
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The Turaev-viro Invariant for 3-Manifolds is a Sum of Three Invariants
Canadian Mathematical Bulletin, 1996AbstractWe show that every Turaev-Viro invariant for 3-manifolds is a sum of three new invariants and discuss their properties. We also find a solution of a conjecture of L. H. Kauffman and S. Lins. Tables of the invariants for closed orientable 3-manifolds of complexity ≤ 3 are presented at the end of the paper.
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Quantum Error Correction Thresholds for the Universal Fibonacci Turaev-Viro Code
Physical Review X, 2022Alexis Schotte +2 more
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Three-dimensional gravity from the Turaev-Viro invariant
Physical Review Letters, 1992Tsukasa Tada
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