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Quantum LDPC codes are a promising direction for low overhead quantum computing.
Low-density parity-check codes
Robert Gallager · 1962
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A recursive approach to low complexity codes
R Tanner · 1981
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Complete minimal varieties in hyperbolic space
Michael T Anderson · 1982
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Complex functions: an algebraic and geometric viewpoint
Gareth A Jones and David Singerman · 1987
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Good quantum error-correcting codes exist
A. R. Calderbank and Peter W. Shor · 1996
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Expander codes
Michael Sipser and Daniel A Spielman · 1996
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Simple quantum error-correcting codes
A. M. Steane · 1996
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Stabilizer Codes and Quantum Error Correction
Daniel Gottesman · 1997
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Quantum bch codes
Thomas Beth Markus Grassl · 1999
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Quantum reed-muller codes
Andrew M Steane · 1999
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Z2-systolic freedom and quantum codes
Michael H Freedman, David A Meyer, and Feng Luo · 2002
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Fault-tolerant quantum computation by anyons
A Yu Kitaev · 2003
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Sparse-graph codes for quantum error correction
David JC MacKay, Graeme Mitchison, and Paul L McFadden · 2004
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Algebraic topology
Allen Hatcher · 2005
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On the iterative decoding of sparse quantum codes
David Poulin and Yeojin Chung · 2008
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Modern coding theory
Tom Richardson and Ruediger Urbanke · 2008
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Asymmetric quantum codes: constructions, bounds and performance
Pradeep Kiran Sarvepalli, Andreas Klappenecker, and Martin Rötteler · 2009
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Tradeoffs for reliable quantum information storage in 2d systems
Sergey Bravyi, David Poulin, and Barbara Terhal · 2010
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Analytic and numerical demonstration of quantum self-correction in the 3d cubic code. december 2011
Sergey Bravyi and Jeongwan Haah · 2011
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Tradeoffs for reliable quantum information storage in surface codes and color codes
Nicolas Delfosse · 2013
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Computational linear algebra over finite fields
Jean-Guillaume Dumas and Clément Pernet · 2013
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Decoding in hyperbolic spaces: Ldpc codes with linear rate and efficient error correction
A theory of single-shot error correction for adversarial noise
Earl T Campbell · 2019
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Cellular-automaton decoders with provable thresholds for topological codes
Aleksander Kubica and John Preskill · 2019
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Towards local testability for quantum coding
Anthony Leverrier, Vivien Londe, and Gilles Zémor · 2019
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Degenerate quantum ldpc codes with good finite length performance
Pavel Panteleev and Gleb Kalachev · 2019
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Balanced product quantum codes
Nikolas P Breuckmann and Jens N Eberhardt · 2020
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Matthew B Hastings · 2013
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Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
Larry Guth and Alexander Lubotzky · 2014
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Quantum locally testable codes
Dorit Aharonov and Lior Eldar · 2015
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Quantum expander codes
Anthony Leverrier, Jean-Pierre Tillich, and Gilles Zémor · 2015
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Local decoders for the 2d and 4d toric code
Nikolas P Breuckmann, Kasper Duivenvoorden, Dominik Michels, and Barbara M Terhal · 2016
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Quantum codes from high-dimensional manifolds
Matthew B Hastings · 2016
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Almost-linear time decoding algorithm for topological codes
Nicolas Delfosse and Naomi H Nickerson · 2017
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Nikolas P Breuckmann and Vivien Londe · 2020
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Union-find decoders for homological product codes
Nicolas Delfosse and Matthew B Hastings · 2020
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Linear-time maximum likelihood decoding of surface codes over the quantum erasure channel
Nicolas Delfosse and Gilles Zémor · 2020
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Combining hard and soft decoders for hypergraph product codes
Antoine Grospellier, Lucien Grouès, Anirudh Krishna, and Anthony Leverrier · 2020
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Matthew B Hastings, Jeongwan Haah, and Ryan O’Donnell · 2020
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Quasilinear-Time Decoding Algorithm for Topological Codes with High Decoding Performance
Shui Hu and David Elkouss · 2020
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Fault-tolerant weighted union-find decoding on the toric code
Shilin Huang, Michael Newman, and Kenneth R Brown · 2020
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Quantum ldpc codes with almost linear minimum distance
Pavel Panteleev and Gleb Kalachev · 2020
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Decoding across the quantum ldpc code landscape
Joschka Roffe, David R White, Simon Burton, and Earl T Campbell · 2020
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Universal fault-tolerant quantum computing with stabiliser codes, 2020
Paul Webster, Michael Vasmer, Thomas R. Scruby, and Stephen D. Bartlett · 2020
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Linear programming decoder for hypergraph product quantum codes
Omar Fawzi, Lucien Grouès, and Anthony Leverrier · 2021
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