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Braiding defects in topological stabiliser codes has been widely studied as a promising approach to fault-tolerant quantum computing.
D. Aharanov and M. Ben-Or, “Fault-tolerant quantum computation with constant error”, STOC ’97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing, pp. 176–188, 1997
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D. Gottesman, “Stabilizer Codes and Quantum Error Correction”, PhD Thesis, California Institute of Technology, 1997
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S. Bravyi and A. Yu. Kitaev, “Quantum codes on a lattice with boundary”, arXiv:quant-ph/9811052v1, 1998
1998
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M. H. Freedman, M. Larsen, Z. Wang, “A modular functor which is universal for quantum computation”, Commun. Math. Phys., 227(3)
2002
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M. Levin and X.-G. Wen, “Fermions, strings and gauge fields in lattice spin models”, Phys. Rev. B, 67
2003
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A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons”, Ann. Phys., 303
2003
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S. Bravyi and A. Kitaev, “Universal quantum computation with ideal Clifford gates and noisy ancillas”, Phys. Rev. A, 71
2005
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C. Chamon, “Quantum Glassiness in Strongly Correlated Clean Systems: An Example of Topological Overprotection”, Phys. Rev. Lett., 94
2005
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A. Kitaev, “Anyons in an exactly solved model and beyond”, Annals of Physics, 321
2006
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H. Bombin and M. A. Martin-Delgado, “Topological Quantum Distillation”, Phys. Rev. Lett., 97
2006
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H. Bombin and M. A. Martin-Delgado, “Topological Computation without Braiding”, Phys. Rev. Lett., 98
2007
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R. Raussendorf and J. Harrington, “Fault-tolerant quantum computation with high threshold in two dimensions”, Phys. Rev. Lett., 98
2007
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R. Raussendorf, J. Harrington and K. Goyal, “Topological fault-tolerance in cluster state quantum computation”, New J. Phys., 9
2007
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H. Bombin and M. A. Martin-Delgado, “An interferometry-free protocol for demonstrating topological order”, Phys. Rev. B, 78
2008
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B. Eastin and E. Knill, “Restrictions on Transversal Encoded Gate Sets”, Phys. Rev. Lett., 102
2009
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A. G. Fowler, A. M. Stephens and P. Groszkowski, “High threshold universal quantum computation on the surface code”, Phys. Rev. A, 80
2009
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H. Bombin and M. A. Martin-Delgado, “Quantum measurements and gates by code deformation”, J. Phys. Math. Theor., 42
2009
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H. Bombin, “Topological Order with a Twist: Ising Anyons from an Abelian Model”, Phys. Rev. Lett., 105
2010
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A. G. Fowler, “2-D color quantum computation”, Phys. Rev. A, 83
2011
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H. Bombin, “Clifford gates by code deformation”, New J. Phys., 13
2011
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J. Haah, “Local stabilizer code in three dimensions without string logical operators”, Phys. Rev. A, 83
2011
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A. G. Fowler, M. Mariantoni, J. M. Martinis and A. N. Cleland, “Surface codes: Towards practical large-scale quantum computation”, Phys. Rev. A, 86
2012
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C. Horsman, A. G. Fowler, S. Devitt and R. Van Meter, “Surface code quantum computing by lattice surgery”, New J. Phys., 14
2012
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S. Bravyi and R. König, “Classification of topologically protected gates for local stabilizer codes”, Phys. Rev. Lett., 110
2013
Cited alongside, same era.
M. Barkeshli, C.-M. Jian and X.-L. Qi, “Genons, twist defects, and projective non-Abelian braiding statistics”, Phys. Rev. B, 87
2013
Cited alongside, same era.
M. Barkeshli, C.-M. Jian and X.-L. Qi, “Theory of defects in Abelian topological states”, Phys. Rev. B, 88
2013
Cited alongside, same era.
M. Barkeshli, C.-M. Jian and X.-L. Qi, “Classification of topological defects in abelian topological states”, Phys. Rev. B, 88
2013
Cited alongside, same era.
H. Bombin, “An introduction to Topological Quantum Codes” in “Quantum Error Correction”, eds: D. A. Lidar and T. A. Brun, Cambridge University Press, New York, 2013
2013
Cited alongside, same era.
B. J. Brown, K. Laubscher, M. S. Kesselring and J. R. Wootton, “Poking holes and cutting corners to achieve Clifford gates with the surface code”, Phys. Rev. X, 7
2017
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I. Cong, M. Cheng and Z. Wang, “Universal quantum computation with gapped boundaries”, Phys. Rev. Lett., 119
2017
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T. J. Yoder and I. H. Kim, “The surface code with a twist”, Quantum, 1
2017
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D. V. Else and C. Nayak, “Cheshire charge in (3+1)-dimensional topological phases”, Phys. Rev. B, 96
2017
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B. Yoshida, “Gapped boundaries, group cohomology and fault-tolerant logical gates”, Annals of Physics, 337
2017
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A. Mesaros, Y. B. Kim and Y. Ran, “Changing topology by topological defects in three-dimensional topologically ordered phases”, Phys. Rev. B, 88
2013
Cited alongside, same era.
J. Haah, “Commuting Pauli Hamiltonians as maps between free modules”, Comm. Math. Phys., 324
2013
Cited alongside, same era.
2014
Cited alongside, same era.
C. Wang and M. Levin, “Braiding statistics of loop excitations in three dimensions”, Phys. Rev. Lett., 113
2014
Cited alongside, same era.
F. Pastawski and B. Yoshida, “Fault-tolerant logical gates in quantum error-correcting codes”, Phys. Rev. A, 91
2015
Cited alongside, same era.
A. Kubica and M. E. Beverland, “Universal transversal gates with color codes: A simplified approach”, Phys. Rev. A, 91
2015
Cited alongside, same era.
M. B. Hastings and A. Geller, “Reduced space-time and time costs using dislocation codes and arbitrary ancillas”, Quantum Information and Computation, 15
2015
Cited alongside, same era.
S. Roberts, B. Yoshida, A. Kubica and S. D. Bartlett, “Symmetry protected topological order at nonzero temperature”, Phys. Rev. A, 96
2017
Later among the works it cites.
2017
Later among the works it cites.
P. Webster and S. D. Bartlett, “Locality-preserving logical operators in topological stabilizer codes”, Phys. Rev. A, 97
2018
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H. Bombin, “2D quantum computation with 3D topological codes”, arXiv:1810.09571, 2018
2018
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2018
Later among the works it cites.
M. S. Kesselring, F. Pastawski, J. Eisert and B. J. Brown, “The boundaries and twist defects of the color code and their applications to topological quantum computation”, Quantum, 2
2018
Later among the works it cites.
H. Bombin, “Transversal gates and error propagation in 3D topological codes”, arXiv:1810:09575, 2018
2018
Later among the works it cites.
A. Kubica and B. Yoshida, “Ungauging quantum error-correcting codes”, arXiv:1805.01836, 2018
2018
Later among the works it cites.
2018
Later among the works it cites.
M. Vasmer and D. E. Browne, “Three-dimensional surface codes: Transversal gates and fault-tolerant architectures”, Phys. Rev. A, 100
2019
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W. Shirley, K. Slagle and X. Chen, “Foliated fracton order in the checkerboard model”, Phys. Rev. B, 99
2019
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A. Dua, I. H. Kim, M. Cheng and D. J. Williamson, “Sorting topological stabilizer models in three dimensions”, Phys. Rev. B, 100
2019
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W. Shirley, K. Slagle and X. Chen, “Fractional excitations in foliated fracton phases”, Annals of Physics, 410
2019
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A. Lavasani, G. Zhu and M. Barkeshli, “Universal logical gates with constant overhead: instantaneous Dehn twists for hyperbolic quantum codes”, Quantum, 3
2019
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N. Escobar-Velásquez, C. Galindo and Z. Wang, “Braid group representations from braiding gapped boundaries of Dijkgraaf-Witten theories”, Pacific Journal of Mathematics, 300
2019
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D. Litinski, “Magic State Distillation: Not as Costly as You Think”, Quantum, 3
2019
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B. J. Brown, “A fault-tolerant non-Clifford gate for the surface code in two dimensions”, Sci. Adv., 6
2020
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T. R. Scruby and D. E. Browne, “A Hierarchy of Anyon Models Realised by Twists in Stacked Surface Codes”, Quantum, 4
2020
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