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Quantum codes with low-weight stabilizers known as LDPC codes have been actively studied recently due to their simple syndrome readout circuits and potential applications in fault-tolerant quantum computing.
Low-density parity-check codes
R. Gallager · 1962
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Good quantum error-correcting codes exist
R. Calderbank and P. W. Shor · 1996
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Simple quantum error-correcting codes
A. M. Steane · 1996
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Mixed-state entanglement and quantum error correction
C. H. Bennett, D. DiVincenzo, J. Smolin, and W. Wootters · 1996
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Perfect quantum error correcting code
R. Laflamme, C. Miquel, J.P. Paz, and W. Zurek · 1996
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Quantum error correction via codes over GF(4)
R. Calderbank, E. Rains, P. Shor, and N. Sloane · 1998
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Good error-correcting codes based on very sparse matrices
D. MacKay · 1999
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Projective plane and planar quantum codes
M. Freedman and D. Meyer · 2001
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A proposed quantum low density parity check code
M. Postol · 2001
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Z2-systolic freedom and quantum codes
M.H. Freedman, D. Meyer, and F. Luo · 2002
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Algebraic topology
A. Hatcher · 2002
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Fault-tolerant quantum computation by anyons
A. Kitaev · 2003
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Sparse-graph codes for quantum error correction
D. MacKay, G. Mitchison, and P. McFadden · 2004
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Constructions and performance of classes of quantum LDPC codes
T. Camara, H. Ollivier, and J-P Tillich · 2005
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Stabilizer formalism for operator quantum error correction
D. Poulin · 2005
Cited alongside, same era.
Operator quantum error correction
D. W. Kribs, R. Laflamme, D. Poulin, and M. Lesosy · 2006
Cited alongside, same era.
Operator quantum error-correcting subsystems for self-correcting quantum memories
D. Bacon · 2006
Cited alongside, same era.
Fault-tolerant quantum computation with high threshold in two dimensions
R. Raussendorf and J. Harrington · 2007
Cited alongside, same era.
Homological error correction: classical and quantum codes
H. Bombin and M.A. Martin-Delgado · 2007
Cited alongside, same era.
Quantum codes on Hurwitz surfaces
I. H. Kim · 2007
Cited alongside, same era.
On the iterative decoding of sparse quantum codes
D. Poulin and Y. Chung · 2010
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On the complexity of commuting local hamiltonians, and tight conditions for topological order
D. Aharonov and L. Eldar · 2011
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Local stabilizer codes in three dimensions without string logical operators
J. Haah · 2011
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Subsystem codes with spatially local generators
S. Bravyi · 2011
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Logical-operator tradeoff for local quantum codes
J. Haah and J. Preskill · 2012
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Improved quantum hypergraph-product LDPC codes
A. Kovalev and L. Pryadko · 2012
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A class of quantum LDPC codes constructed from finite geometries
S. A. Aly · 2008
Cited alongside, same era.
High-threshold universal quantum computation on the surface code
A. Fowler, A. Stephens, and P. Groszkowski · 2009
Cited alongside, same era.
On Cayley graphs, surface codes, and the limits of homological coding for quantum error correction
G. Zémor · 2009
Cited alongside, same era.
Quantum LDPC codes with positive rate and minimum distance proportional to n 1 / 2 n^{1/2}
J-P Tillich and G. Zémor · 2009
Cited alongside, same era.
A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes
S. Bravyi and B. Terhal · 2009
Cited alongside, same era.
Tradeoffs for reliable quantum information storage in 2D systems
S. Bravyi, D. Poulin, and B. Terhal · 2010
Cited alongside, same era.
K. Michnicki · 2012
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Topological subsystem codes from graphs and hypergraphs
P. Sarvepalli and K. R. Brown · 2012
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What is the overhead required for fault-tolerant quantum computation?
D. Gottesman · 2013
Closest in time.
Tradeoffs for reliable quantum information storage in surface codes and color codes
N. Delfosse · 2013
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M.H. Freedman and M.B. Hastings · 2013
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Short random circuits define good quantum error correcting codes
W. Brown and O. Fawzi · 2013
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Subsystem surface codes with three-qubit check operators
S. Bravyi, G. Duclos-Cianci, D. Poulin, and M. Suchara · 2013
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Hardness of decoding quantum stabilizer codes
P. Iyer and D. Poulin · 2013
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