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Tanner codes are long error correcting codes obtained from short codes and a graph, with bits on the edges and parity-check constraints from the short codes enforced at the vertices of the graph.
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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Checking computations in polylogarithmic time
László Babai, Lance Fortnow, Leonid A Levin, and Mario Szegedy · 1991
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Nearly-linear size holographic proofs
Alexander Polishchuk and Daniel A Spielman · 1994
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Good quantum error-correcting codes exist
Robert Calderbank and Peter W Shor · 1996
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Expander codes
Michael Sipser and Daniel A. Spielman · 1996
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Error correcting codes in quantum theory
Andrew M. Steane · 1996
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Stabilizer codes and quantum error correction
Daniel Gottesman · 1997
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Z 2 Z_{2} -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
Alexei Yu Kitaev · 2003
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Locally Testable Codes and PCPs of Almost-Linear Length
Oded Goldreich and Madhu Sudan · 2006
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Expander graphs and their applications
Shlomo Hoory, Nathan Linial, and Avi Wigderson · 2006
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Short Locally Testable Codes and Proofs: A Survey in Two Parts
Oded Goldreich · 2010
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Expander codes and their decoding
Venkatesan Guruswami · 2010
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Guest column: the quantum PCP conjecture
Dorit Aharonov, Itai Arad, and Thomas Vidick · 2013
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Trivial low energy states for commuting Hamiltonians, and the quantum PCP conjecture
Matthew B Hastings · 2013
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Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength
Jean-Pierre Tillich and Gilles Zémor · 2014
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Matthew B Hastings, Jeongwan Haah, and Ryan O’Donnell · 2020
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Quantum LDPC codes with Ω ( n log k n ) \Omega(\sqrt{n}\log^{k}n) distance, for any k k
Tali Kaufman and Ran J Tessler · 2020
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Quantum LDPC Codes with Almost Linear Minimum Distance
Pavel Panteleev and Gleb Kalachev · 2020
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Balanced product quantum codes
Nikolas P Breuckmann and Jens N Eberhardt · 2021
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Quantum low-density parity-check codes
Nikolas P Breuckmann and Jens N Eberhardt · 2021
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Quantum locally testable codes
Dorit Aharonov and Lior Eldar · 2015
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Local Hamiltonians whose ground states are hard to approximate
Lior Eldar and Aram W Harrow · 2017
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Quantum codes from high-dimensional manifolds
Matthew B Hastings · 2017
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Decodable quantum LDPC codes beyond the square root distance barrier using high dimensional expanders
Shai Evra, Tali Kaufman, and Gilles Zémor · 2020
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Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, and Shahar Mozes · 2021
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Matthew B Hastings · 2021
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Towards Local Testability for Quantum Coding
Anthony Leverrier, Vivien Londe, and Gilles Zémor · 2021
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Asymptotically good quantum and locally testable classical LDPC codes
Pavel Panteleev and Gleb Kalachev · 2021
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c 3 c^{3} -local testable codes from lossless expanders
Ting-Chun Lin and Min-Hsiu Hsieh · 2022
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