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The Turaev-Viro invariant for a closed 3-manifold is defined as the contraction of a certain tensor network.
Rational conformal field theory and invariants of 3-manifolds
M. Kontsevich · 1988
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Quantum field theory and the Jones polynomial
Edward Witten · 1989
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Ribbon graphs and their invaraints derived from quantum groups
N.Y. Reshetikhin and V.G. Turaev · 1990
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2-d physics and 3-d topology
L. Crane · 1991
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Invariants of 3-manifolds via link polynomials and quantum groups
N.Y. Reshetikhin and V.G. Turaev · 1991
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On Witten’s 3-manifold invariants, 1991
Kevin Walker · 1991
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Topological invariants of 3-manifolds using representations of mapping class groups I
Toshitake Kohno · 1992
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State sum invariants of 3 3 -manifold and quantum 6 j 6j -symbols
V.G. Turaev and O.Y. Viro · 1992
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Reshetikhin-Turaev and Crane-Kohno-Kontsevich 3-manifold invariants coincide
Sergey Piunikhin · 1993
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Quantum invariants of knots and 3-manifolds
V.G. Turaev · 1994
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Quantum Groups
Christian Kassel · 1995
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Skein theory and Turaev-Viro invariants
Justin D. Roberts · 1995
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Invariants of piecewise-linear 3-manifolds
John W. Barrett and Bruce W. Westbury · 1996
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Categories for the working mathematician
Saunders Mac Lane · 1998
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Spherical categories
John W. Barrett and Bruce W. Westbury · 1999
Cited alongside, same era.
Classical and Quantum Computation
A. Yu. Kitaev, A.H. Shen, and M.N. Vyalyi · 1999
Cited alongside, same era.
Quantum computation and the localization of modular functors, 2000, arXiv:quant-ph/0003128
Michael H. Freedman · 2000
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Simulation of topological field theories by quantum computers
Michael H. Freedman, Alexei Kitaev, and Zhenghan Wang · 2002
Cited alongside, same era.
A modular functor which is universal for quantum computation
Michael H. Freedman, Michael J. Larsen, and Zhenghan Wang · 2002
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String-net condensation: A physical mechanism for topological phases
Michael A. Levin and Xiao-Gang Wen · 2005
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Anyons in an exactly solved model and beyond
Alexei Kitaev · 2006
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A fault-tolerant one-way quantum computer
Robert Raussendorf, Jim Harrington, and Kovid Goyal · 2006
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Topological quantum compiling
L. Hormozi, G. Zikos, N.E. Bonesteel, and S.H. Simon · 2007
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Fault-tolerant quantum computation with high threshold in two dimensions
Robert Raussendorf and Jim Harrington · 2007
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Non-abelian anyons and topological quantum computation
Chetan Nayak, Steven H. Simon, Ady Stern, Michael H. Freedman, and Sankar Das Sarma · 2008
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Conformal Field Theory and Topology
Toshitake Kohno · 2002
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Topological quantum computation
Michael H. Freedman, Alexei Kitaev, Michael J. Larsen, and Zhenghan Wang · 2003
Cited alongside, same era.
Fault-tolerant quantum computation by anyons
Alexei Kitaev · 2003
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From subfactors to categories and topology I: Frobenius algebras in and Morita equivalence of tensor categories
Michael Müger · 2003
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From subfactors to categories and topology II: The quantum double of tensor categories and subfactors
Michael Müger · 2003
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Topological quantum computation
John Preskill · 2004
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From string nets to nonabelions
L. Fidkowski, M. Freedman, C. Nayak, K. Walker, and Z. Wang · 2009
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High threshold universal quantum computation on the surface code
Austin G. Fowler, Ashley M. Stephens, and Peter Groszkowski · 2009
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Composite anyon coding and the initialization of a topological quantum computer
Robert König · 2009
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Exact entanglement renormalization for string-net models
Robert König, Ben W. Reichardt, and Guifré Vidal · 2009
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On classification of modular tensor categories
E. Rowell, R. Stong, and Z. Wang · 2009
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Approximating the Turaev-Viro invariant is BQP-complete
Gorjan Alagic, Stephen P. Jordan, Robert König, and Ben W. Reichardt · 2010
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personal communication
V.G. Turaev, 2010 · 2010
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