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This is a note from a series of lectures at Encuentro Colombiano de Computacion Cuantica, Universidad de los Andes, Bogota, Colombia, 2015.
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1969
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N. Read and Subir Sachdev, “Large- n n expansion for frustrated quantum antiferromagnets,” Phys. Rev. Lett. 66
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Peter W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52
1995
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H. Park and C. Woodburn, “An algorithmic proof of Suslin’s stability theorem over polynomial rings,” Journal of Algebra 178
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Peter W. Shor, “Fault-tolerant quantum computation,” in Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on (1996) pp. 56–65, quant-ph/9605011
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A. R. Calderbank and Peter W. Shor, “Good quantum error-correcting codes exist,” Phys. Rev. A 54
1996
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Andrew Steane, “Multiple particle interference and quantum error correction,” Proc. Roy. Soc. Lond. A 452
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Daniel Gottesman, “A class of quantum error-correcting codes saturating the quantum hamming bound,” Phys. Rev. A 54
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A. R. Calderbank, E. M Rains, P. W. Shor, and N. J. A. Sloane, “Quantum error correction and orthogonal geometry,” Phys. Rev. Lett. 78
1997
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Emanuel Knill and Raymond Laflamme, “Theory of quantum error-correcting codes,” Phys. Rev. A 55
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Daniel Gottesman, “Fault-tolerant quantum computation with higher-dimensional systems,” in Quantum Computing and Quantum Communications , Lecture Notes in Computer Science, Vol. 1509, edited by ColinP. Williams (Springer Berlin Heidelberg, 1999) pp. 302–313
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E.M. Rains, “Nonbinary quantum codes,” Information Theory, IEEE Transactions on 45
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Bojko Bakalov and Alexander Kirillov Jr., Lectures on Tensor Categories and Modular Functors , University Lecture Series, Vol. 21 (American Mathematical Society, 2001)
2001
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A. Klappenecker and M. Roetteler, “Beyond stabilizer codes ii: Clifford codes,” IEEE Transactions on Information Theory 48
2002
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Serge Lang, Algebra , revised 3rd ed. (Springer, 2002)
2002
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Allen Hatcher, Algebraic Topology (Cambridge University Press, 2002)
2002
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Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill, “Topological quantum memory,” J. Math. Phys. 43
2002
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A. Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Annals of Physics 303
Morou Amidou and Ihsen Yengui, “An algorithm for unimodular completion over laurent polynomial rings,” Linear Algebra and its Applications 429
2008
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2010
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2011
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2011
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Isaac H. Kim, “3d local qupit quantum code without string logical operator,” (2012), 1202.0052
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2003
Cited alongside, same era.
Michael Levin and Xiao-Gang Wen, “Fermions, strings, and gauge fields in lattice spin models,” Phys. Rev. B 67
2003
Cited alongside, same era.
David Fattal, Toby S. Cubitt, Yoshihisa Yamamoto, Sergey Bravyi, and Isaac L. Chuang, “Entanglement in the stabilizer formalism,” (2004), quant-ph/0406168
2004
Cited alongside, same era.
Hyungju Park, “Symbolic computation and signal processing,” Journal of Symbolic Computation 37
2004
Cited alongside, same era.
Claudio Chamon, “Quantum glassiness,” Phys. Rev. Lett. 94
2005
Cited alongside, same era.
Alioscia Hamma, Radu Ionicioiu, and Paolo Zanardi, “Bipartite entanglement and entropic boundary law in lattice spin systems,” Phys. Rev. A 71
2005
Cited alongside, same era.
M. Grassl and M. Roetteler, “Non-catastrophic encoders and encoder inverses for quantum convolutional codes,” in Information Theory, 2006 IEEE International Symposium on (2006) pp. 1109–1113
2006
Cited alongside, same era.
2012
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2012
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Beni Yoshida, “Exotic topological order in fractal spin liquids,” Phys. Rev. B 88
2013
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2013
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Jeongwan Haah, “Commuting Pauli Hamiltonians as maps between free modules,” Commun. Math. Phys. 324
2013
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Héctor Bombín, “Structure of 2D topological stabilizer codes,” Commun. Math. Phys. 327
2014
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J. M. Farinholt, “An ideal characterization of the clifford operators,” J. Phys. A: Math. Theor. 47
2014
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2015
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2016
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