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We construct and analyze a family of low-density parity check (LDPC) quantum codes with a linear encoding rate, polynomial scaling distance and efficient decoding schemes.
C. Weber and H. Seifert, “Die beiden Dodekaederräume,” Mathematische Zeitschrift , vol. 37, no. 1, pp. 237–253, Dec 1933. [Online]. Available: https://doi.org/10.1007/BF01474572
1933
Earlier work this paper cites.
A. Schönhage, “On the power of random access machines,” in International Colloquium on Automata, Languages, and Programming . Springer, 1979, pp. 520–529
1979
Earlier work this paper cites.
M. T. Anderson, “Complete minimal varieties in hyperbolic space,” Inventiones mathematicae , vol. 69, no. 3, pp. 477–494, 1982
1982
Earlier work this paper cites.
M. Gromov, “Volume and bounded cohomology,” Publications Mathématiques de l’IHÉS , vol. 56, pp. 5–99, 1982
1982
Earlier work this paper cites.
M. W. Davis, “A hyperbolic 4 4 -manifold,” Proc. Amer. Math. Soc. , vol. 93, no. 2, pp. 325–328, 1985. [Online]. Available: https://doi.org/10.2307/2044771
1985
Earlier work this paper cites.
U. Abresch and V. Schroeder, “Graph manifolds, ends of negatively curved spaces and the hyperbolic 120-cell space,” Journal of Differential Geometry , vol. 35, no. 2, pp. 299–336, 1992
1992
Earlier work this paper cites.
C. C. Sims, Computation with Finitely Presented Groups . Cambridge University Press, 1994, vol. 48
1994
Earlier work this paper cites.
J. G. Ratcliffe, Foundations of hyperbolic manifolds . Springer, 1994, vol. 3
1994
Earlier work this paper cites.
P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Physical review A , vol. 52, no. 4, p. R2493, 1995
1995
Earlier work this paper cites.
S. B. Bravyi and A. Y. Kitaev, “Quantum codes on a lattice with boundary,” arXiv preprint quant-ph/9811052 , 1998
1998
Earlier work this paper cites.
M. H. Freedman and D. A. Meyer, “Projective plane and planar quantum codes,” Foundations of Computational Mathematics , vol. 1, no. 3, pp. 325–332, 2001
2001
Earlier work this paper cites.
J. Širáň, “Triangle Group Representations and Constructions of Regular Maps,” Proceedings of the London Mathematical Society , vol. 82, no. 3, pp. 513–532, 2001
2001
Earlier work this paper cites.
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill, “Topological quantum memory,” Journal of Mathematical Physics , vol. 43, no. 9, pp. 4452–4505, 2002
2002
Earlier work this paper cites.
P. McMullen and E. Schulte, Abstract Regular Polytopes . Cambridge University Press, 2002, vol. 92
2002
Cited alongside, same era.
M. Nakahara, Geometry, Topology and Physics . CRC Press, 2003
2003
Cited alongside, same era.
C. Wang, J. Harrington, and J. Preskill, “Confinement-higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory,” Annals of Physics , vol. 303, no. 1, pp. 31–58, 2003
2003
Cited alongside, same era.
M. Belolipetsky, “On volumes of arithmetic quotients of SO(1,n),” Annali della Scuola Normale Superiore di Pisa-Classe di Scienze , vol. 3, no. 4, pp. 749–770, 2004
2004
Cited alongside, same era.
G. Grinstein, “Can complex structures be generically stable in a noisy world?” IBM Journal of Research and Development , vol. 48, no. 1, pp. 5–12, 2004
2004
Cited alongside, same era.
L. Guth and A. Lubotzky, “Quantum Error Correcting Codes and 4-dimensional Arithmetic Hyperbolic Manifolds,” Journal of Mathematical Physics , vol. 55, no. 8, p. 082202, 2014
2014
Later among the works it cites.
H. Bombín, “Single-shot fault-tolerant quantum error correction,” Physical Review X , vol. 5, no. 3, p. 031043, 2015
2015
Later among the works it cites.
N. P. Breuckmann and B. M. Terhal, “Constructions and noise threshold of hyperbolic surface codes,” IEEE transactions on Information Theory , vol. 62, no. 6, pp. 3731–3744, 2016
2016
Later among the works it cites.
M. B. Hastings, “Weight reduction for quantum codes,” arXiv preprint arXiv:1611.03790 , 2016
2016
Later among the works it cites.
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M. Conder and C. Maclachlan, “Compact hyperbolic 4-manifolds of small volume,” Proceedings of the American Mathematical Society , vol. 133, no. 8, pp. 2469–2476, 2005
2005
Cited alongside, same era.
T. Richardson and R. Urbanke, Modern Coding Theory . Cambridge University Press, 2008
2008
Cited alongside, same era.
G. Zémor, “On cayley graphs, surface codes, and the limits of homological coding for quantum error correction,” in International Conference on Coding and Cryptology . Springer, 2009, pp. 259–273
2009
Cited alongside, same era.
R. Wilson, The Finite Simple Groups . Springer Science & Business Media, 2009, vol. 251
2009
Cited alongside, same era.
G. Duclos-Cianci and D. Poulin, “Fast decoders for topological quantum codes,” Physical review letters , vol. 104, no. 5, p. 050504, 2010
2010
Cited alongside, same era.
E. Fetaya, “Bounding the distance of quantum surface codes,” Journal of Mathematical Physics , vol. 53, no. 6, p. 062202, 2012
2012
Cited alongside, same era.
N. Delfosse, “Tradeoffs for reliable quantum information storage in surface codes and color codes,” in 2013 IEEE International Symposium on Information Theory . IEEE, 2013, pp. 917–921
2013
Cited alongside, same era.
2017
Later among the works it cites.
N. P. Breuckmann, “Homological quantum codes beyond the toric code,” Ph.D. dissertation, RWTH Aachen University, 2017
2017
Later among the works it cites.
N. P. Breuckmann, C. Vuillot, E. Campbell, A. Krishna, and B. M. Terhal, “Hyperbolic and Semi-Hyperbolic Surface Codes for Quantum Storage,” Quantum Science and Technology , vol. 2, no. 3, p. 035007, 2017
2017
Later among the works it cites.
N. P. Breuckmann, K. Duivenvoorden, D. Michels, and B. M. Terhal, “Local decoders for the 2d and 4d toric code,” Quantum Information and Computation , vol. 17, no. 3 and 4, pp. 0181–0208, 2017
2017
Later among the works it cites.
2018
Later among the works it cites.
2018
Later among the works it cites.
2018
Later among the works it cites.