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Quantum low-density parity-check (QLDPC) codes have emerged as a promising technique for quantum error correction.
“Low-density parity-check codes”
R. Gallager · 1962
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“On the inherent intractability of certain coding problems (corresp.)”
E. Berlekamp, R. McEliece, and H. van Tilborg · 1978
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“Reverend Bayes on inference engines: A distributed hierarchical approach”
Judea Pearl · 1982
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“Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Iinference (2nd ed.)”
Judea Pearl · 1988
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“Near Shannon limit error-correcting coding and decoding: Turbo-codes. 1”
C. Berrou, A. Glavieux, and P. Thitimajshima · 1993
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“Good quantum error-correcting codes exist”
A. R. Calderbank and Peter W. Shor · 1996
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“Multiple-particle interference and quantum error correction”
Andrew Steane · 1996
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“Quantum error correction and orthogonal geometry”
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane · 1997
Earlier work this paper cites.
“Stabilizer codes and quantum error correction” (1997)
Daniel Gottesman · 1997
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“Quantum computations: algorithms and error correction”
A Yu Kitaev · 1997
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“Quantum error correction via codes over GF(4)”
A.R. Calderbank, E.M. Rains, P.M. Shor, and N.J.A. Sloane · 1998
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“Turbo decoding as an instance of Pearl’s “belief propagation” algorithm”
R.J. McEliece, D.J.C. MacKay, and Jung-Fu Cheng · 1998
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“The generalized distributive law”
S.M. Aji and R.J. McEliece · 2000
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“Factor graphs and the sum-product algorithm”
F.R. Kschischang, B.J. Frey, and H.-A. Loeliger · 2001
Earlier work this paper cites.
“Efficient erasure correcting codes”
M.G. Luby, M. Mitzenmacher, M.A. Shokrollahi, and D.A. Spielman · 2001
Earlier work this paper cites.
“Improved low-density parity-check codes using irregular graphs”
M.G. Luby, M. Mitzenmacher, M.A. Shokrollahi, and D.A. Spielman · 2001
Earlier work this paper cites.
“The capacity of low-density parity-check codes under message-passing decoding”
T.J. Richardson and R.L. Urbanke · 2001
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“Design of capacity-approaching irregular low-density parity-check codes”
T.J. Richardson, M.A. Shokrollahi, and R.L. Urbanke · 2001
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“The Bethe lattice spin glass revisited”
Marc Mézard and Giorgio Parisi · 2001
Earlier work this paper cites.
“Topological quantum memory”
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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“Analytic and algorithmic solution of random satisfiability problems”
M. Mézard, G. Parisi, and R. Zecchina · 2002
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“Fault-tolerant quantum computation by anyons”
A.Yu. Kitaev · 2003
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“Algebraic codes for data transmission”
Richard E. Blahut · 2003
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“Sparse-graph codes for quantum error correction”
D.J.C. MacKay, G. Mitchison, and P.L. McFadden · 2004
Cited alongside, same era.
“Lossy source encoding via message-passing and decimation over generalized codewords of LDGM codes”
M.J. Wainwright and E. Maneva · 2005
Cited alongside, same era.
“Solving constraint satisfaction problems through belief propagation-guided decimation”
Andrea Montanari, Federico Ricci-Tersenghi, and Guilhem Semerjian · 2007
Cited alongside, same era.
“Binary quantization using belief propagation with decimation over factor graphs of LDGM codes”
Tomas Filler and Jessica Fridrich · 2007
Cited alongside, same era.
“On the iterative decoding of sparse quantum codes”
David Poulin and Yeojin Chung · 2008
Cited alongside, same era.
“Approaching the rate-distortion limit with spatial coupling, belief propagation, and decimation”
Vahid Aref, Nicolas Macris, and Marc Vuffray · 2015
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“Comparing the bit-MAP and block-MAP decoding thresholds of reed-muller codes on BMS channels”
Shrinivas Kudekar, Santhosh Kumar, Marco Mondelli, Henry D. Pfister, and Rüdiger Urbankez · 2016
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“Design of low-density parity check codes for 5G new radio”
Tom Richardson and Shrinivas Kudekar · 2018
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“Modified belief propagation decoders for quantum low-density parity-check codes”
Alex Rigby, J. C. Olivier, and Peter Jarvis · 2019
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“Neural belief-propagation decoders for quantum error-correcting codes”
Ye-Hua Liu and David Poulin · 2019
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“Neural-net decoding of quantum LDPC codes with straight-through estimators”
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European Telecommunications Standards Institute (ETSI) · 2009
Cited alongside, same era.
“Tradeoffs for reliable quantum information storage in 2D systems”
Sergey Bravyi, David Poulin, and Barbara Terhal · 2010
Cited alongside, same era.
“On the dynamics of the error floor behavior in (regular) LDPC codes”
Christian Schlegel and Shuai Zhang · 2010
Cited alongside, same era.
“Ising models on locally tree-like graphs”
Amir Dembo and Andrea Montanari · 2010
Cited alongside, same era.
“Local stabilizer codes in three dimensions without string logical operators”
Jeongwan Haah · 2011
Cited alongside, same era.
“On belief propagation guided decimation for random k k -sat”
Amin Coja-Oghlan · 2011
Cited alongside, same era.
“Surface codes: Towards practical large-scale quantum computation”
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland · 2012
Cited alongside, same era.
Xin Xiao, Nithin Raveendran, and Bane Vasić · 2019
Later among the works it cites.
“Decoding across the quantum low-density parity-check code landscape”
Joschka Roffe, David R. White, Simon Burton, and Earl Campbell · 2020
Later among the works it cites.
“Refined belief propagation decoding of sparse-graph quantum codes”
Kao-Yueh Kuo and Ching-Yi Lai · 2020
Later among the works it cites.
“Degenerate Quantum LDPC Codes With Good Finite Length Performance”
Pavel Panteleev and Gleb Kalachev · 2021
Later among the works it cites.
“Quantum low-density parity-check codes”
Nikolas P. Breuckmann and Jens Niklas Eberhardt · 2021
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“Fiber bundle codes: breaking the n 1 / 2 {n}^{1/2} polylog( n {n} ) barrier for quantum LDPC codes”
Matthew B. Hastings, Jeongwan Haah, and Ryan O’Donnell · 2021
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“Balanced product quantum codes”
Nikolas P. Breuckmann and Jens N. Eberhardt · 2021
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“Trapping Sets of Quantum LDPC Codes”
Nithin Raveendran and Bane Vasić · 2021
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“Log-domain decoding of quantum LDPC codes over binary finite fields”
Ching-Yi Lai and Kao-Yueh Kuo · 2021
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“Quantum LDPC codes with almost linear minimum distance”
Pavel Panteleev and Gleb Kalachev · 2022
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“Asymptotically good quantum and locally testable classical LDPC codes”
Pavel Panteleev and Gleb Kalachev · 2022
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“Exploiting degeneracy in belief propagation decoding of quantum codes”
Kao-Yueh Kuo and Ching-Yi Lai · 2022
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“Stabilizer inactivation for message-passing decoding of quantum LDPC codes”
Julien Du Crest, Mehdi Mhalla, and Valentin Savin · 2022
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“Spatially-coupled QDLPC codes” (2023)
Siyi Yang and Robert Calderbank · 2023
Closest in time.
“Neural belief propagation decoding of quantum LDPC codes using overcomplete check matrices”
Sisi Miao, Alexander Schnerring, Haizheng Li, and Laurent Schmalen · 2023
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“Generalized Belief Propagation Algorithms for Decoding of Surface Codes”
Josias Old and Manuel Rispler · 2023
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“Enhanced message-passing decoding of degenerate quantum codes utilizing trapping set dynamics”
Dimitris Chytas, Michele Pacenti, Nithin Raveendran, Mark F. Flanagan, and Bane Vasić · 2024
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