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The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead.
P. L. homeomorphic manifolds are equivalent by elementary shellings
Udo Pachner · 1991
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Stabilizer Codes and Quantum Error Correction
Daniel Gottesman · 1997
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Quantum codes on a lattice with boundary
Sergey B Bravyi and A Yu Kitaev · 1998
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Z 2 Z_{2} -systolic freedom and quantum codes
Michael H Freedman, David A Meyer, and Feng Luo · 2002
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Fault-tolerant quantum computation by anyons
Alexei Yu. Kitaev · 2003
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Quantum orders in an exact soluble model
Xiao-Gang Wen · 2003
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Geometry, Topology and Physics
Mikio Nakahara · 2003
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Quantum field theory of many-body systems: from the origin of sound to an origin of light and electrons
Xiao-Gang Wen · 2004
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Anyons in an exactly solved model and beyond
Alexei Kitaev · 2005
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Topological quantum distillation
Hector Bombín and Miguel A. Martin-Delagado · 2006
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A fault-tolerant one-way quantum computer
R. Raussendorf, J. Harrington, and K. Goyal · 2006
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Topological entanglement entropy
Alexei Kitaev and John Preskill · 2006
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Topological quantum error correction with optimal encoding rate
H Bombín and MA Martin-Delgado · 2006
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Lieb-Robinson bounds and the generation of correlations and topological quantum order
S. Bravyi, M. B. Hastings, and F. Verstraete · 2006
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Exact topological quantum order in d=3 and beyond: Branyons and brane-net condensates
H Bombín and MA Martin-Delgado · 2007
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Topological computation without braiding
H. Bombín and M. A. Martin-Delagado · 2007
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Non-Abelian anyons and topological quantum computation
Chetan Nayak, Steven H. Simon, Ady Stern, Michael Freedman, and Sankar Das Sarma · 2008
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Topological entanglement entropy in Chern-Simons theories and quantum Hall fluids
Shiying Dong, Eduardo Fradkin, Robert G. Leigh, and Sean Nowling · 2008
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Quantum measurements and gates by code deformation
H. Bombín and M. A. Martin-Delgado · 2009
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On classification of modular tensor categories
Eric Rowell, Richard Stong, and Zhenghan Wang · 2009
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U ( 1 ) × U ( 1 ) ⋊ ℤ 2 U(1)\times U(1)\rtimes\mathbb{Z}_{2} Chern-Simons theory and Z 4 {Z}_{4} parafermion fractional quantum Hall states
Maissam Barkeshli and Xiao-Gang Wen · 2010
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Topological order with a twist: Ising anyons from an Abelian model
Hector Bombín · 2010
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Tradeoffs for reliable quantum information storage in 2D systems
Sergey Bravyi, David Poulin, and Barbara Terhal · 2010
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Local unitary transformation, long-range quantum entanglement, wave function renormalization and topological order
Xie Chen, Zheng-Cheng Gu, and Xiao-Gang Wen · 2010
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Topological subsystem codes
H. Bombín · 2010
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The quantum double model with boundary: Condensations and symmetries
Salman Beigi, Peter W. Shor, and Daniel Whalen · 2011
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Clifford gates by code deformation
Hector Bombín · 2011
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Two-dimensional color-code quantum computation
Austin G Fowler · 2011
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Fault-tolerant quantum computing with color codes
Andrew J. Landahl, Jonas T. Anderson, and Patrick R. Rice · 2011
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Introduction to topological quantum computation
Jiannis K Pachos · 2012
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Model for gapped boundaries and domain walls
Alexei Kitaev and Liang Kong · 2012
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Surface code quantum computing by lattice surgery
Clare Horsman, Austin G. Fowler, Simon Devitt, and Rodney Van Meter · 2012
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Realization of three-qubit quantum error correction with superconducting circuits
M. D. Reed, L. DiCarlo, S. E. Nigg, L. Sun, L. Frunzio, S. M. Girvin, and R. J. Schoelkopf · 2012
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Strong resilience of topological codes to depoloarization
H. Bombín, Ruben S. Andrist, Masayuki Ohzeki, Helmut G. Katzgraber, and M. A. Martin-Delgado · 2012
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From majorana fermions to topological order
Barbara M. Terhal, Fabian Hassler, and David P. DiVincenzo · 2012
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Universal topological phase of two-dimensional stabilizer codes
Hector Bombín, Guillaume Duclos-Cianci, and David Poulin · 2012
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Fractionalizing majorana fermions: Non-abelian statistics on the edges of abelian quantum hall states
Netanel H Lindner, Erez Berg, Gil Refael, and Ady Stern · 2012
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Projective non-abelian statistics of dislocation defects in a ℤ N {\mathbb{Z}}_{N} rotor model
Milestones toward majorana-based quantum computing
D. Aasen, M. Hell, R. V. Mishmash, A. Higginbotham, J. Danon, M. Leijnse, T. S. Jespersen, J. A. Folk, C. M. Marcus, K. Flensberg, and J. Alicea · 2016
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Roadmap to majorana surface codes
S. Plugge, L. A. Landau, E. Sela, A. Altland, K. Flensberg, and R. Egger · 2016
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Towards realistic implementations of a majorana surface code
L. A. Landau, S. Plugge, E. Sela, A. Altland, S. M. Albrecht, and R. Egger · 2016
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Noise thresholds for the [[4, 2, 2]]-concatenated toric code
Ben Criger and Barbara Terhal · 2016
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Transversal Clifford gates on folded surface codes
Jonathan E. Moussa · 2016
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Y.-Z. You and X.-G. Wen · 2012
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Classification of topologically protected gates for local stabilizer codes
Sergey Bravyi and Robert König · 2013
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Protected edge modes without symmetry
M. Levin · 2013
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Topological entanglement entropy with a twist
Benjamin J. Brown, Stephen D. Bartlett, Andrew C. Doherty, and Sean D. Barrett · 2013
Cited alongside, same era.
Tradeoffs for reliable quantum information storage in surface codes and color codes
Nicolas Delfosse · 2013
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Changing topology by topological defects in three-dimensional topologically ordered phases
Andrej Mesaros, Yong Baek Kim, and Ying Ran · 2013
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Symmetry, defects, and gauging of topological phases
Maissam Barkeshli, Parsa Bonderson, Meng Cheng, and Zhenghan Wang · 2014
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Iris Cong, Meng Cheng, and Zhenghan Wang · 2016
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Symmetry fractionalization and twist defects
Nicolas Tarantino, Netanel H Lindner, and Lukasz Fidkowski · 2016
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Globally symmetric topological phase: from anyonic symmetry to twist defect
J. C. Y. Teo · 2016
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Protected gates for topological quantum field theories
Michael E Beverland, Oliver Buerschaper, Robert Koenig, Fernando Pastawski, John Preskill, and Sumit Sijher · 2016
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Topological quantum computation, 2017
J. Preskill · 2017
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Roads towards fault-tolerant universal quantum computation
Earl T Campbell, Barbara M Terhal, and Christophe Vuillot · 2017
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The surface code with a twist
Theodore J. Yoder and Isaac H. Kim · 2017
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Poking holes and cutting corners to achieve Clifford gates with the surface code
B. J. Brown, K. Laubscher, M. S. Kesselring, and J. R. Wootton · 2017
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Symmetry-protected topological order at nonzero temperature
Sam Roberts, Beni Yoshida, Aleksander Kubica, and Stephen D. Bartlett · 2017
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Quantum origami: Applying fault-tolerant transversal gates and measuring topological order
Guanyu Zhu, Mohammad Hafezi, and Maissam Barkeshli · 2017
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Tensor networks with a twist: Anyon-permuting domain walls and defects in peps
Jacob C. Bridgeman, Stephen D. Bartlett, and Andrew C. Doherty · 2017
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Symmetry-enriched topological order in tensor networks: Defects, gauging and anyon condensation
Dominic J Williamson, Nick Bultinck, and Frank Verstraete · 2017
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Fault-tolerant quantum error detection
Norbert M. Linke, Mauricio Gutierrez, Kevin A. Landsman, Caroline Figgatt, Shantanu Debnath, Kenneth R. Brown, and Christopher Monroe · 2017
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Combining topological hardware and topological software: Color code quantum computing with topological superconductor networks
D. Litinski, M. Kesselring, J. Eisert, and F. von Oppen · 2017
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Braiding by Majorana tracking and long-range CNOT gates with color codes
Daniel Litinski and Felix von Oppen · 2017
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private communication, 2017
Zhenghan Wang · 2017
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Anyon condensation and its applications
FJ Burnell · 2017
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Exotic non-Abelian topological defects in lattice fractional quantum Hall states
Zhao Liu, Gunnar Möller, and Emil J. Bergholtz · 2017
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Anyonic entanglement and topological entanglement entropy
Parsa Bonderson, Christina Knapp, and Kaushal Patel · 2017
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Fault-tolerant interface between quantum memories and quantum processors
Hendrik Poulsen Nautrup, Nicolai Friis, and Hans J Briegel · 2017
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Daniel Barter, Jacob C. Bridgeman, and Corey Jones · 2018
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Low overhead Clifford gates from joint measurements in surface, color, and hyperbolic codes
Ali Lavasani and Maissam Barkeshli · 2018
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Universal quantum computing with 3D surface codes
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Disjointness of stabilizer codes and limitations on fault-tolerant logical gates
Tomas Jochym-O’Connor, Aleksander Kubica, and Theodore J Yoder · 2018
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Locality-preserving logical operators in topological stabilizer codes
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Lattice surgery with a twist: Simplifying clifford gates of surface codes
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Hyperbolic and semi-hyperbolic surface codes for quantum storage
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