On braiding of su(2)-anyons providing universal quantum gates for topological quantum computation:
On topological quantum computation with anyons in Chern-Simons theory:
Michael Freedman, Alexei Kitaev, Michael Larsen, Zhenghan Wang, Topological quantum computation, Bull. Amer. Math. Soc. 40 (2003), 31-38 (arXiv:quant-ph/0101025, doi:10.1090/S0273-0979-02-00964-3, pdf)
Zhenghan Wang, Topological Quantum Computation, CBMS Regional Conference Series in Mathematics 112, AMS 2010 (ISBN-13: 978-0-8218-4930-9, pdf)
Eric Rowell, Zhenghan Wang, Mathematics of Topological Quantum Computing, Bull. Amer. Math. Soc. 55 (2018), 183-238 (arXiv:1705.06206, doi:10.1090/bull/1605)
and with focus on abelian anyons in terms of modular tensor categories:
Wade Bloomquist, Zhenghan Wang, On Topological Quantum Computing With Mapping Class Group Representations, J. Phys. A: Math. Theor. 52 (2019) 015301 (arXiv:1805.04622, doi:10.1088/1751-8121/aaeea1)
Liang Wang, Zhenghan Wang, In and around Abelian anyon models, J. Phys. A: Math. Theor. 53 505203 (2020) (doi:10.1088/1751-8121/abc6c0)
More on anyons:
Simon Trebst, Matthias Troyer, Zhenghan Wang, A. W. W. Ludwig, A short introduction to Fibonacci anyon models, Prog. Theor. Phys. Supp. 176 384 (2008) [arXiv:0902.3275, doi:10.1143/PTPS.176.384]
C. Gils, E. Ardonne, Simon Trebst, D. A. Huse, A. W. W. Ludwig, Matthias Troyer, Zhenghan Wang, Anyonic quantum spin chains: Spin-1 generalizations and topological stability, Phys. Rev. B 87 (2013), 235120 [doi:10.1103/PhysRevB.87.235120, arXiv:1303.4290]
On identifying topological order via topological entanglement entropy of the ground state:
Introducing the 4d TQFT Walker-Wang model:
On number theoretic aspects of modular tensor categories:
On Levin-Wen models:
On braid group representations (specifically the Burau representation and its relation to the Alexander polynomial) and their application to topological quantum computation:
A proposal for classifying symmetry-protected anyonic topological order in terms of 2-groupoidal-actions on modular tensor categories:
Zhenghan Wang, §2.2 of: Beyond Anyons, Modern Physics Letters A 33 28 (2018) 1830011 [arXiv:1710.00464, doi:10.1142/S0217732318300112]
Maissam Barkeshli, Parsa Bonderson, Meng Cheng, Zhenghan Wang, Symmetry Fractionalization, Defects, and Gauging of Topological Phases, Phys. Rev. B 100 115147 (2019) arXiv:1410.4540, doi:10.1103/PhysRevB.100.115147, talk pdf
Argument realizing anyonic topological order in the worldvolume-field theory on M5-branes via KK-compactification on closed 3-manifolds (Seifert manifolds) analogous to the 3d-3d correspondence (which instead uses hyperbolic 3-manifolds):
On adiabatic transformations of certain 2d topological insulators:
Last revised on June 29, 2024 at 22:11:19. See the history of this page for a list of all contributions to it.