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We prove that on any two-dimensional lattice of qudits of a prime dimension, every translation invariant Pauli stabilizer group with local generators and with code distance being the linear system size, is decomposed by a local Clifford circuit of constant depth into a finite number of copies of the toric code (abelian discrete gauge theory) stabilizer group.
1902
Earlier work this paper cites.
1907
Earlier work this paper cites.
A. M. Polyakov, “Compact gauge fields and the infrared catestrophe,” Physics Letters B 59
1975
Earlier work this paper cites.
Robbert Dijkgraaf and Edward Witten, “Topological gauge theories and group cohomology,” Communications in Mathematical Physics 129
1990
Earlier work this paper cites.
F. Gabbiani J. Fröhlich, “Braid statistics in local quantum theory,” Rev. Math. Phys. 2
1990
Earlier work this paper cites.
Xiao-Gang Wen, “Mean-field theory of spin-liquid states with finite energy gap and topological orders,” Phys. Rev. B 44
1991
Earlier work this paper cites.
A. R. Calderbank and Peter W. Shor, “Good quantum error-correcting codes exist,” Phys. Rev. A 54
1996
Earlier work this paper cites.
Andrew Steane, “Multiple particle interference and quantum error correction,” Proc. Roy. Soc. Lond. A 452
1996
Earlier work this paper cites.
Daniel Gottesman, “A class of quantum error-correcting codes saturating the quantum hamming bound,” Phys. Rev. A 54
1996
Earlier work this paper cites.
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
Cited alongside, same era.
Bojko Bakalov and Alexander Kirillov Jr., Lectures on Tensor Categories and Modular Functors , University Lecture Series, Vol. 21 (American Mathematical Society, 2001)
2001
Cited alongside, same era.
A.Yu. Kitaev, “Fault-tolerant quantum computation by anyons,” Annals of Physics 303
2003
Cited alongside, same era.
Xiao-Gang Wen, “Quantum orders in an exact soluble model,” Phys. Rev. Lett. 90
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.
2008
Later among the works it cites.
2010
Later among the works it cites.
Kevin Walker and Zhenghan Wang, “(3+1)-TQFTs and topological insulators,” Frontiers of Physics 7
2011
Later among the works it cites.
Jeongwan Haah, “Commuting Pauli hamiltonians as maps between free modules,” Commun. Math. Phys. 324
2013
Later among the works it cites.
M. B. Hastings, “Classifying quantum phases with the torus trick,” Phys. Rev. B 88
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T. Y. Lam, Introduction to Quadratic Forms over Fields , Graduate studies in mathematics 67 (American Mathematical Society, 2004)
2004
Cited alongside, same era.
Michael A. Levin and Xiao-Gang Wen, “String-net condensation: a physical mechanism for topological phases,” Physical Review B 71
2005
Cited alongside, same era.
A. Kitaev, “Anyons in an exactly solved model and beyond,” Annals of Physics 321
2006
Cited alongside, same era.
Richard Elman, Nikita Karpenko, and Alexander Merkurjev, The Algebraic and Geometric Theory of Quadratic Forms , Colloquium Publications, Vol. 56 (American Mathematical Society, 2008)
2008
Cited alongside, same era.
Cited in the paper.
Cited in the paper.
2013
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Héctor Bombín, “Structure of 2D topological stabilizer codes,” Commun. Math. Phys. 327
2014
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2016
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2016
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2017
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