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Recent developments have shown the existence of quantum low-density parity check (qLDPC) codes with constant rate and linear distance.
Expander codes
M. Sipser and D.A. Spielman · 1996
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Good quantum error-correcting codes exist
A. R. Calderbank and Peter W. Shor · 1996
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Error correcting codes in quantum theory
A. M. Steane · 1996
Earlier work this paper cites.
Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
Earlier work this paper cites.
Topological quantum distillation
H. Bombin and M. A. Martin-Delgado · 2006
Earlier work this paper cites.
Robust locally testable codes and products of codes
Eli Ben-Sasson and Madhu Sudan · 2006
Earlier work this paper cites.
Elements of Information Theory (Wiley Series in Telecommunications and Signal Processing)
Thomas M. Cover and Joy A. Thomas · 2006
Earlier work this paper cites.
Fault-tolerant quantum computation with constant overhead
Daniel Gottesman · 2014
Cited alongside, same era.
Quantum expander codes
Anthony Leverrier, Jean-Pierre Tillich, and Gilles Zémor · 2015
Cited alongside, same era.
Local hamiltonians whose ground states are hard to approximate
Lior Eldar and Aram W Harrow · 2017
Cited alongside, same era.
Decodable quantum LDPC codes beyond the n \sqrt{n} distance barrier using high dimensional expanders
Shai Evra, Tali Kaufman, and Gilles Zémor · 2020
Cited alongside, same era.
Quantum LDPC codes with almost linear minimum distance
Pavel Panteleev and Gleb Kalachev · 2021
Cited alongside, same era.
Fiber Bundle Codes: Breaking the n 1 / 2 polylog ( n ) n^{1/2}\operatorname{polylog}(n) Barrier for Quantum LDPC Codes , page 1276–1288
Degenerate quantum LDPC codes with good finite length performance
Pavel Panteleev and Gleb Kalachev · 2021
Later among the works it cites.
Lifting decoders for classical codes to decoders for quantum codes
Armanda O Quintavalle and Earl T Campbell · 2021
Later among the works it cites.
Locally testable codes with constant rate, distance, and locality
Irit Dinur, Shai Evra, Ron Livne, Alexander Lubotzky, and Shahar Mozes · 2021
Later among the works it cites.
Anthony Leverrier and Gilles Zémor · 2022
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Good quantum LDPC codes with linear time decoder from lossless expanders
Ting-Chun Lin and Min-Hsiu Hsieh · 2022
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Matthew B. Hastings, Jeongwan Haah, and Ryan O’Donnell · 2021
Cited alongside, same era.
Balanced product quantum codes
Nikolas P. Breuckmann and Jens N. Eberhardt · 2021
Cited alongside, same era.
Asymptotically good quantum and locally testable classical LDPC codes
Pavel Panteleev and Gleb Kalachev
Cited in the paper.
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Toward a union-find decoder for quantum LDPC codes
Nicolas Delfosse, Vivien Londe, and Michael E Beverland · 2022
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