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We present a scheme for universal topological quantum computation based on Clifford complete braiding and fusion of symmetry defects in the 3-Fermion anyon theory, supplemented with magic state injection.
1907
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2003
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2003
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2005
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2005
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Robert Raussendorf, Jim Harrington, and Kovid Goyal, “A fault-tolerant one-way quantum computer,” Annals of Physics 321
2006
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Maarten Van den Nest, Akimasa Miyake, Wolfgang Dür, and Hans J Briegel, “Universal resources for measurement-based quantum computation,” Physical review letters 97
2006
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Robert Raussendorf, Jim Harrington, and Kovid Goyal, “Topological fault-tolerance in cluster state quantum computation,” New Journal of Physics 9
2007
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Robert Raussendorf and Jim Harrington, “Fault-tolerant quantum computation with high threshold in two dimensions,” Phys. Rev. Lett. 98
2007
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Héctor Bombín and Miguel Angel Martin-Delgado, “Quantum measurements and gates by code deformation,” Journal of Physics A: Mathematical and Theoretical 42
2009
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2009
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2009
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Sergey Bravyi and Barbara Terhal, “A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes,” New Journal of Physics 11
2009
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2010
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Akimasa Miyake, “Quantum computation on the edge of a symmetry-protected topological order,” Physical Review Letters 105
2010
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H. Bombin, “Clifford gates by code deformation,” New Journal of Physics 13
2011
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Kevin Walker and Zhenghan Wang, “(3+ 1)-tqfts and topological insulators,” Frontiers of Physics 7
2012
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Hector Bombin, Guillaume Duclos-Cianci, and David Poulin, “Universal topological phase of two-dimensional stabilizer codes,” New Journal of Physics 14
2012
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Maissam Barkeshli, Chao-Ming Jian, and Xiao-Liang Qi, “Twist defects and projective non-abelian braiding statistics,” Physical Review B 87
2013
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CW Von Keyserlingk, FJ Burnell, and Steven H Simon, “Three-dimensional topological lattice models with surface anyons,” Physical Review B 87
2013
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FJ Burnell, X Chen, L Fidowski, and A Vishwanath, “Exactly soluble models of a 3d symmetry protected topological phase of bosons with surface topological order,” Physical Review B 90
2013
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Dave Bacon, Steven T Flammia, and Gregory M Crosswhite, “Adiabatic quantum transistors,” Physical Review X 3
2013
2018
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Trithep Devakul and Dominic J Williamson, “Universal quantum computation using fractal symmetry-protected cluster phases,” Physical Review A 98
2018
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Markus S Kesselring, Fernando Pastawski, Jens Eisert, and Benjamin J Brown, “The boundaries and twist defects of the color code and their applications to topological quantum computation,” Quantum 2
2018
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Kosuke Fukui, Akihisa Tomita, Atsushi Okamoto, and Keisuke Fujii, “High-threshold fault-tolerant quantum computation with analog quantum error correction,” Physical review X 8
2018
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Mayukh Nilay Khan, Jeffrey CY Teo, and Taylor L Hughes, “Anyonic symmetries and topological defects in abelian topological phases: An application to the a d e classification,” Physical Review B 90
2014
Cited alongside, same era.
Jeffrey CY Teo, Taylor L Hughes, and Eduardo Fradkin, “Theory of twist liquids: gauging an anyonic symmetry,” Annals of Physics 360
2015
Cited alongside, same era.
Hendrik Poulsen Nautrup and Tzu-Chieh Wei, “Symmetry-protected topologically ordered states for universal quantum computation,” Physical Review A 92
2015
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Beni Yoshida, “Topological color code and symmetry-protected topological phases,” Physical Review B 91
2015
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Ying Li, “A magic state’s fidelity can be superior to the operations that created it,” New Journal of Physics 17
2015
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Justyna Łodyga, Paweł Mazurek, Andrzej Grudka, and Michał Horodecki, “Simple scheme for encoding and decoding a qubit in unknown state for various topological codes,” Scientific reports 5
2015
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2015
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Maissam Barkeshli, Parsa Bonderson, Meng Cheng, and Zhenghan Wang, “Symmetry fractionalization, defects, and gauging of topological phases,” Physical Review B 100
2019
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Robert Raussendorf, Cihan Okay, Dong-Sheng Wang, David T Stephen, and Hendrik Poulsen Nautrup, “Computationally universal phase of quantum matter,” Physical review letters 122
2019
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Sam Roberts, Symmetry-Protected Topological Phases for Robust Quantum Computation , Doctor of philosophy ph.d. (2019-02-28)
2019
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2019
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Jeongwan Haah, “Clifford quantum cellular automata: Trivial group in 2d and witt group in 3d,” Journal of Mathematical Physics 62
2019
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Francesco Benini, Clay Cordova, and Po-Shen Hsin, “On 2-group global symmetries and their anomalies,” Journal of High Energy Physics 2019
2019
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