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Reliable quantum memory under circuit-level noise requires decoders that can process syndrome information continuously and at a rate comparable to its generation.
“Low-density parity-check codes”
Robert G. Gallager · 1963
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“Paths, trees, and flowers”
Jack Edmonds · 1965
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“A recursive approach to low complexity codes”
R. Tanner · 1981
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“Probabilistic reasoning in intelligent systems: networks of plausible inference”
Judea Pearl · 1988
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“Scheme for reducing decoherence in quantum computer memory”
Peter W. Shor · 1995
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“Error correcting codes in quantum theory”
Andrew M. Steane · 1996
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“Good quantum error-correcting codes exist”
A. Robert Calderbank and Peter W. Shor · 1996
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“Fault-tolerant error correction with efficient quantum codes”
David P. DiVincenzo and Peter W. Shor · 1996
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“Theory of quantum error-correcting codes”
E. Knill and R. Laflamme · 1997
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“Stabilizer codes and quantum error correction”
Daniel Gottesman · 1997
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“Theory of fault-tolerant quantum computation”
Daniel Gottesman · 1998
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“Quantum error correction via codes over GF(4)”
A. Robert Calderbank, Eric M. Rains, Peter W. Shor, and Neil J. A. Sloane · 1998
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“Quantum computation and quantum information”
Michael A. Nielsen and Isaac L. Chuang · 2000
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“Factor graphs and the sum-product algorithm”
Frank R. Kschischang, Brendan J. Frey, and Hans-Andrea Loeliger · 2001
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“Topological quantum memory”
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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“Fault-tolerant quantum computation by anyons”
A. Yu. Kitaev · 2003
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“Confinement-Higgs transition in a disordered gauge theory and the accuracy threshold for quantum memory”
Chenyang Wang, Jim Harrington, and John Preskill · 2003
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“Sparse-graph codes for quantum error correction”
David J. C. MacKay, Graeme Mitchison, and Paul L McFadden · 2004
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“Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes”
James William Harrington · 2004
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“Universal quantum computation with ideal Clifford gates and noisy ancillas”
Sergey Bravyi and Alexei Kitaev · 2005
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“Topological quantum distillation”
Hector Bombin and Miguel Angel Martin-Delgado · 2006
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“Optimal resources for topological two-dimensional stabilizer codes: Comparative study”
Héctor Bombin and Miguel A Martin-Delgado · 2007
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“Fault-tolerant quantum computation with high threshold in two dimensions”
Robert Raussendorf and Jim Harrington · 2007
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“Topological fault-tolerance in cluster state quantum computation”
Robert Raussendorf, Jim Harrington, and Kovid Goyal · 2007
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“Efficient serial message-passing schedules for LDPC decoding”
Eran Sharon, Simon Litsyn, and Jacob Goldberger · 2007
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“Fault-tolerant quantum computation with constant error rate”
Dorit Aharonov and Michael Ben-Or · 2008
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“On the iterative decoding of sparse quantum codes”
David Poulin and Yeojin Chung · 2008
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“Threshold error rates for the toric and planar codes”
D. S. Wang, A. G. Fowler, A. M. Stephens, and L. C. L. Hollenberg · 2010
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“Graphical algorithms and threshold error rates for the 2d color code”
David S. Wang, Austin G. Fowler, Charles D. Hill, and Lloyd C. L. Hollenberg · 2010
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“Design of additive quantum codes via the code-word-stabilized framework”
Alexey A Kovalev, Ilya Dumer, and Leonid P Pryadko · 2011
Cited alongside, same era.
“Surface code quantum computing with error rates over 1%”
David S Wang, Austin G Fowler, and Lloyd CL Hollenberg · 2011
Cited alongside, same era.
“Enhanced feedback iterative decoding of sparse quantum codes”
Yun-Jiang Wang, Barry C Sanders, Bao-Ming Bai, and Xin-Mei Wang · 2012
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
“Stim: a fast stabilizer circuit simulator”
Craig Gidney · 2021
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“Cost of universality: A comparative study of the overhead of state distillation and code switching with color codes”
Michael E Beverland, Aleksander Kubica, and Krysta M Svore · 2021
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“Single-shot error correction of three-dimensional homological product codes”
Armanda O Quintavalle, Michael Vasmer, Joschka Roffe, and Earl T Campbell · 2021
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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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“Comparison of 2D topological codes and their decoding performances”
Kao-Yueh Kuo and Ching-Yi Lai · 2022
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“On belief propagation decoding of quantum codes with quaternary reliability statistics”
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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.
“Quantum Kronecker sum-product low-density parity-check codes with finite rate”
Alexey A. Kovalev and Leonid P. Pryadko · 2013
Cited alongside, same era.
“Efficient fault-tolerant decoding of topological color codes” (2014)
Ashley M Stephens · 2014
Cited alongside, same era.
“Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength”
Jean-Pierre Tillich and Gilles Zémor · 2014
Cited alongside, same era.
“Fault-tolerant quantum computation with constant overhead”
Daniel Gottesman · 2014
Cited alongside, same era.
“Fault-tolerant thresholds for quantum error correction with the surface code”
Ashley M Stephens · 2014
Cited alongside, same era.
Ching-Feng Kung, Kao-Yueh Kuo, and Ching-Yi Lai · 2023
Later among the works it cites.
“Scalable surface-code decoders with parallelization in time”
Xinyu Tan, Fang Zhang, Rui Chao, Yaoyun Shi, and Jianxin Chen · 2023
Later among the works it cites.
“Parallel window decoding enables scalable fault tolerant quantum computation”
Luka Skoric, Dan E Browne, Kenton M Barnes, Neil I Gillespie, and Earl T Campbell · 2023
Later among the works it cites.
“Layered decoding of quantum ldpc codes”
Julien Du Crest, Francisco Garcia-Herrero, Mehdi Mhalla, Valentin Savin, and Javier Valls · 2023
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Mengyu Zhang, Xiangyu Ren, Guanglei Xi, Zhenxing Zhang, Qiaonian Yu, Fuming Liu, Hualiang Zhang, Shengyu Zhang, and Yi-Cong Zheng · 2023
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“Quantum two-block group algebra codes”
Hsiang-Ku Lin and Leonid P. Pryadko · 2024
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“High-threshold and low-overhead fault-tolerant quantum memory”
Sergey Bravyi, Andrew W Cross, Jay M Gambetta, Dmitri Maslov, Patrick Rall, and Theodore J Yoder · 2024
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“Lift-connected surface codes”
Josias Old, Manuel Rispler, and Markus Müller · 2024
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“Union-find quantum decoding without union-find”
Sam J Griffiths and Dan E Browne · 2024
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“Ambiguity clustering: an accurate and efficient decoder for QLDPC codes” (2024)
Stasiu Wolanski and Ben Barber · 2024
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Ching-Feng Kung, Kao-Yueh Kuo, and Ching-Yi Lai · 2024
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“Toward low-latency iterative decoding of QLDPC codes under circuit-level noise” (2024)
Anqi Gong, Sebastian Cammerer, and Joseph M Renes · 2024
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“A graph-based formalism for surface codes and twists”
Rahul Sarkar and Theodore J Yoder · 2024
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https://github.com/kywukuo/qLDPC_SM-BP (2024)
“Streaming mixed-alphabet BP” · 2024
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“Sparse blossom: correcting a million errors per core second with minimum-weight matching”
Oscar Higgott and Craig Gidney · 2025
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“Union-intersection union-find for decoding depolarizing errors in topological codes”
Tzu-Hao Lin and Ching-Yi Lai · 2025
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“Generalized quantum data-syndrome codes and belief propagation decoding for phenomenological noise”
Kao-Yueh Kuo and Ching-Yi Lai · 2025
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“Localized statistics decoding for quantum low-density parity-check codes”
Timo Hillmann, Lucas Berent, Armanda O Quintavalle, Jens Eisert, Robert Wille, and Joschka Roffe · 2025
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“Designing fault-tolerant circuits using detector error models”
Peter-Jan HS Derks, Alex Townsend-Teague, Ansgar G Burchards, and Jens Eisert · 2025
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“QUITS: A modular Qldpc code circUIT simulator”
Mingyu Kang, Yingjia Lin, Hanwen Yao, Mert Gökduman, Arianna Meinking, and Kenneth R Brown · 2025
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“High-threshold, low-overhead and single-shot decodable fault-tolerant quantum memory”
Thomas R Scruby, Timo Hillmann, and Joschka Roffe · 2026
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