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We survey some recent work on topological quantum computation with gapped boundaries and boundary defects and list some open problems.
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M. Müger. Galois extensions of braided tensor categories and braided crossed G-categories
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S. Beigi, P. W. Shor, D. Whalen. The quantum double model with boundary: condensations and symmetries
2011
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M. Cheng. Phys. Rev. B, Superconducting Proximity Effect on the Edge of Fractional Topological Insulators
2012
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A. Davydov, M. Müger, D. Nikshych, V. Ostrik. The Witt group of non-degenerate braided fusion categories
2012
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A.G. Fowler, M. Mariantoni, J. M. Martinis, A. N. Cleland. Surface codes: Towards practical large-scale quantum computation
2012
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A. Kitaev, L. Kong, Models for Gapped Boundaries and Domain Walls
2012
Cited alongside, same era.
N. H. Lindner, E. Berg, G. Refael and A. Stern. Fractionalizing Majorana fermions: non-abelian statistics on the edges of abelian quantum Hall states
2012
Cited alongside, same era.
K. Walker, Z. Wang. ( 3 + 1 ) (3+1) -TQFTs and Topological Insulators
2012
Cited alongside, same era.
M. Barkeshli, C.-M. Jian, X.-L. Qi. Twist defects and projective non-Abelian braiding statistics
L. Chang. Kitaev models based on unitary quantum groupoids
2014
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A. Kapustin, Ground-state degeneracy for Abelian anyons in the presence of gapped boundaries
2014
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M. Barkeshli. Charge 2 e / 3 2e/3 superconductivity and topological degeneracies without localized zero modes in bilayer fractional quantum Hall states
2016
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2016
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I. Cong, M. Cheng, Z. Wang. Topological quantum computation with gapped boundaries
2016
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2013
Cited alongside, same era.
M. Barkeshli, C.-M. Jian, X.-L. Qi. Theory of defects in Abelian topological states
2013
Cited alongside, same era.
M. Barkeshli, C.-M. Jian, X.-L. Qi. Classification of topological defects in Abelian topological states
2013
Cited alongside, same era.
D. J. Clarke, J. Alicea and K. Shtengel. Exotic non-Abelian anyons from conventional fractional quantum Hall states
2013
Cited alongside, same era.
M. Levin, Protected edge modes without symmetry
2013
Cited alongside, same era.
M. Barkeshli, P. Bonderson, M. Cheng, Z. Wang. Symmetry, defects, and gauging of topological phases
2014
Cited alongside, same era.
Cited in the paper.
2016
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I. Cong, M. Cheng, Z. Wang. Hamiltonian and Algebraic Theories of Gapped Boundaries in Topological Phases of Matter
2017
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2017
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I. Cong, M. Cheng, Z. Wang. Universal Quantum Computation with Gapped Boundaries
2017
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2017
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D.-J. Williamson, and Z. Wang. Hamiltonian models for topological phases of matter in three spatial dimensions
2017
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