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The current best asymptotic lower bound on the minimum distance of quantum LDPC codes with fixed non-zero rate is logarithmic in the blocklength.
Low Density Parity Check Codes
R. G. Gallager · 1963
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Graph theoretic error-correcting codes
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The theory of error-correcting codes
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Good quantum error-correcting codes exist
A. R. Calderbank and P. W. Shor · 1996
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Multiple particle interference and quantum error correction
A. M. Steane · 1996
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Stabilizer codes and quantum error correction
D. Gottesman · 1997
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Quantum error correction via codes over GF(4)
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane · 1998
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Quantum-channel capacity of very noisy channels
D. P. DiVincenzo, P. W. Shor, and J. A. Smolin · 1998
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A proposed quantum low density parity check code, 2001
M. S. Postol · 2001
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ℤ 2 {\mathbb{Z}}_{2} -systolic freedom and quantum codes
M. H. Freedman, D. A. Meyer, and F. Luo · 2002
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Fault-tolerant quantum computation by anyons
A. Y. Kitaev · 2003
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Sparse graph codes for quantum error-correction
D. J. C. MacKay, G. Mitchison, and P. L. MacFadden · 2004
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Constructions and performance of classes of quantum LDPC codes, 2005. http://arxiv.org/abs/quant-ph/0502086
T. Camara, H. Ollivier, and J.-P. Tillich · 2005
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Quantum error correcting subsystem codes from two classical linear codes
D. Bacon and A. Casaccino · 2006
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Topological quantum distillation
H. Bombin and M. A. Martin-Delgado · 2006
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On the application of error-correcting codes with low-density generator matrix over different quantum channels
H. Lou and J. Garcia-Frias · 2006
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A class of quantum LDPC codes derived from Latin squares and combinatorial objects
S. A. Aly · 2007
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Homological error correction: classical and quantum codes
H. Bombin and M. A. Martin-Delgado · 2007
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A class of quantum LDPC codes: construction and performances under iterative decoding
T. Camara, H. Ollivier, and J.-P. Tillich · 2007
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Quantum quasi-cyclic LDPC codes
M. Hagiwara and H. Imai · 2007
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Design of near-optimum quantum error-correcting codes based on generator and parity-check matrices of LDGM codes
J. Garcia-Frias and K. Liu · 2008
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Quantum quasi-cyclic low-density parity check codes, March 2008
M-H. Hsieh, T. A. Brun, and I. Devetak · 2008
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Asymmetric quantum LDPC codes
K. P. Sarvepalli, M.Rötteler, and A. Klappenecker · 2008
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Quantum LDPC codes with positive rate and minimum distance proportional to n 1 2 n^{\frac{1}{2}}
J.-P. Tillich and G. Zémor · 2009
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On Cayley graphs, surface codes and the limits of homological coding for quantum error correction
G. Zémor · 2009
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Topological color codes over higher alphabets
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Asymmetric quantum error-correcting codes
L. Ioffe and M. Mézard · 2007
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Quantum codes on Hurwitz surfaces
I. H. Kim · 2007
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Degenerate coding for Pauli channels
G. Smith and J. A. Smolin · 2007
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A class of quantum LDPC codes constructed from finite geometries
S. A. Aly · 2008
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Construction of topological quantum codes on compact surfaces
C. D. de Albuquerque, R. Palazzo, and E. B. da Silva · 2008
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Quantum LDPC codes from incomplete block designs
I. B. Djordjevic · 2008
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P. Sarvepalli · 2010
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Efficient quantum stabilizer codes: LDPC and LDPC-convolutional constructions
P. Tan and J. Li · 2010
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A construction of quantum LDPC codes from Cayley graphs
A. Couvreur, N. Delfosse, and G. Zémor · 2011
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Quantum LDPC codes obtained by non-binary constructions
I. Andriyanova, D. Maurice, and J. P. Tillich · 2012
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Spatially coupled quantum LDPC codes
I. Andriyanova, D. Maurice, and J. P. Tillich · 2012
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Quantum error correction beyond the bounded distance decoding limit
K. Kasai, M. Hagiwara, H. Imai, and Sakaniwa K · 2012
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Fault-tolerance of "bad" quantum low-density parity check codes, August 2012
A. Kovalev and L. Pryadko · 2012
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Improved quantum hypergraph-product LDPC codes
A. Kovalev and L. Pryadko · 2012
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