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Belief propagation (BP) is well-known as a low complexity decoding algorithm with a strong performance for important classes of quantum error correcting codes, e.g.
“Low-density parity-check codes”
R. Gallager · 1962
Earlier work this paper cites.
“On the inherent intractability of certain coding problems (corresp.)”
E. Berlekamp, R. McEliece, and H. van Tilborg · 1978
Earlier work this paper cites.
“A recursive approach to low complexity codes”
R. Tanner · 1981
Earlier work this paper cites.
“Reverend bayes on inference engines: A distributed hierarchical approach”
Judea Pearl · 1982
Earlier work this paper cites.
“Good quantum error-correcting codes exist”
A Robert Calderbank and Peter W Shor · 1996
Earlier work this paper cites.
“Multiple-particle interference and quantum error correction”
Andrew Steane · 1996
Earlier work this paper cites.
“Expander codes”
M. Sipser and D. A. Spielman · 1996
Earlier work this paper cites.
“Near shannon limit performance of low density parity check codes”
David JC MacKay and Radford M Neal · 1997
Earlier work this paper cites.
“Stabilizer codes and quantum error correction” (1997)
Daniel Gottesman · 1997
Earlier work this paper cites.
“Factor graphs and algorithms”
Brendan J Frey, Frank R Kschischang, Hans-Andrea Loeliger, and Niclas Wiberg · 1997
Earlier work this paper cites.
“Generalized belief propagation”
Jonathan S Yedidia, William T Freeman, and Yair Weiss · 2000
Earlier work this paper cites.
“Asymptotically good quantum codes”
Alexei Ashikhmin, Simon Litsyn, and Michael A Tsfasman · 2001
Earlier work this paper cites.
“Topological quantum memory”
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
Earlier work this paper cites.
“Information theory, inference and learning algorithms”
David JC MacKay · 2003
Earlier work this paper cites.
“Fault-tolerant quantum computation by anyons”
A.Yu. Kitaev · 2003
Earlier work this paper cites.
“Constructing free-energy approximations and generalized belief propagation algorithms”
Jonathan S Yedidia, William T Freeman, and Yair Weiss · 2005
Earlier work this paper cites.
“Fault-Tolerant Quantum Computation with High Threshold in Two Dimensions”
Robert Raussendorf and Jim Harrington · 2007
Cited alongside, same era.
“On the iterative decoding of sparse quantum codes”
David Poulin and Yeojin Chung · 2008
Cited alongside, same era.
“Quantum ldpc codes with positive rate and minimum distance proportional to n 1 / 2 n^{1/2} ”
J. Tillich and G. Zemor · 2009
Cited alongside, same era.
“Blossom v: a new implementation of a minimum cost perfect matching algorithm”
Vladimir Kolmogorov · 2009
Cited alongside, same era.
“Libdai: A free and open source c++ library for discrete approximate inference in graphical models”
Joris M. Mooij · 2010
Cited alongside, same era.
“Lemon – an open source c++ graph template library”
Balázs Dezső, Alpár Jüttner, and Péter Kovács · 2011
“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.
“Quantum Low-Density Parity-Check Codes”
Nikolas P. Breuckmann and Jens Niklas Eberhardt · 2021
Later among the works it cites.
“Trapping sets of quantum LDPC codes”
Nithin Raveendran and Bane Vasić · 2021
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.
“Almost-linear time decoding algorithm for topological codes”
Nicolas Delfosse and Naomi H Nickerson · 2021
Later among the works it cites.
“Combining hard and soft decoders for hypergraph product codes”
Antoine Grospellier, Lucien Grouès, Anirudh Krishna, and Anthony Leverrier · 2021
Later among the works it cites.
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Cited alongside, same era.
“On the choice of regions for generalized belief propagation” (2012)
Max Welling · 2012
Cited alongside, same era.
“Fixed initialization decoding of ldpc codes over a binary symmetric channel”
Manabu Hagiwara, Marc P. C. Fossorier, and Hideki Imai · 2012
Cited alongside, same era.
“Strong resilience of topological codes to depolarization”
H. Bombin, Ruben S. Andrist, Masayuki Ohzeki, Helmut G. Katzgraber, and M. A. Martin-Delgado · 2012
Cited alongside, same era.
“Fault-tolerant quantum computation with constant overhead”
Daniel Gottesman · 2014
Cited alongside, same era.
“Quantum expander codes”
A. Leverrier, J. Tillich, and G. Zémor · 2015
Cited alongside, same era.
code: xtensor-stack/xtensor
Johan Mabille, Sylvain Corlay, and Wolf Vollprecht (2016) · 2016
Cited alongside, same era.
“Single-shot error correction of three-dimensional homological product codes”
Armanda O Quintavalle, Michael Vasmer, Joschka Roffe, and Earl T Campbell · 2021
Later among the works it cites.
“Ntl: A library for doing number theory”
Victor Shoup · 2021
Later among the works it cites.
“Asymptotically good quantum and locally testable classical ldpc codes”
Pavel Panteleev and Gleb Kalachev · 2022
Closest in time.
“Quantum tanner codes”
Anthony Leverrier and Gilles Zémor · 2022
Closest in time.
“Good quantum ldpc codes with linear time decoder from lossless expanders” (2022)
Ting-Chun Lin and Min-Hsiu Hsieh · 2022
Closest in time.
“Gaussian belief propagation solvers for nonsymmetric systems of linear equations”
Vladimir Fanaskov · 2022
Closest in time.
“Exploiting degeneracy in belief propagation decoding of quantum codes”
Kao-Yueh Kuo and Ching-Yi Lai · 2022
Closest in time.
code: nlohmann v3.10.5
Niels Lohmann (2022) · 2022
Closest in time.
code: josiasold/gbp
Josias Old (2022) · 2022
Closest in time.