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Quantum error correction plays a prominent role in the realization of quantum computation, and quantum low-density parity-check (qLDPC) codes are believed to be practically useful stabilizer codes.
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
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Stabilizer codes and quantum error correction
Daniel Gottesman · 1997
Earlier work this paper cites.
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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String and membrane condensation on three-dimensional lattices
Alioscia Hamma, Paolo Zanardi, and Xiao-Gang Wen · 2005
Earlier work this paper cites.
Operator quantum error-correcting subsystems for self-correcting quantum memories
Dave Bacon · 2006
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Subsystem fault tolerance with the bacon-shor code
Panos Aliferis and Andrew W Cross · 2007
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Topological subsystem codes
Héctor Bombín · 2010
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Fault-tolerant quantum computing with color codes
Andrew J Landahl, Jonas T Anderson, and Patrick R Rice · 2011
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Subsystem surface codes with three-qubit check operators
Sergey Bravyi, Guillaume Duclos-Cianci, David Poulin, and Martin Suchara · 2012
Earlier work this paper cites.
Surface codes: Towards practical large-scale quantum computation
Austin G Fowler, Matteo Mariantoni, John M Martinis, and Andrew N Cleland · 2012
Earlier work this paper cites.
Michael H Freedman and Matthew B Hastings · 2013
Earlier work this paper cites.
Quantum ldpc codes with positive rate and minimum distance proportional to the square root of the blocklength
Jean-Pierre Tillich and Gilles Zémor · 2013
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Homological product codes
Sergey Bravyi and Matthew B Hastings · 2014
Earlier work this paper cites.
Quantum locally testable codes
Dorit Aharonov and Lior Eldar · 2015
Cited alongside, same era.
Weight reduction for quantum codes
Matthew B Hastings · 2016
Cited alongside, same era.
Sparse quantum codes from quantum circuits
Dave Bacon, Steven T Flammia, Aram W Harrow, and Jonathan Shi · 2017
Cited alongside, same era.
Local hamiltonians whose ground states are hard to approximate
Lior Eldar and Aram W Harrow · 2017
Cited alongside, same era.
Higher-dimensional quantum hypergraph-product codes with finite rates
Weilei Zeng and Leonid P Pryadko · 2019
Cited alongside, same era.
Critical faults of leakage errors on the surface code
Natalie C Brown, Andrew Cross, and Kenneth R Brown · 2020
Cited alongside, same era.
Quantum tanner codes
Anthony Leverrier and Gilles Zémor · 2022
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Asymptotically good quantum and locally testable classical ldpc codes
Pavel Panteleev and Gleb Kalachev · 2022
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Reshape: A decoder for hypergraph product codes
Armanda O Quintavalle and Earl T Campbell · 2022
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Logical blocks for fault-tolerant topological quantum computation
Hector Bombin, Chris Dawson, Ryan V Mishmash, Naomi Nickerson, Fernando Pastawski, and Sam Roberts · 2023
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Spacetime codes of clifford circuits
Nicolas Delfosse and Adam Paetznick · 2023
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A pair measurement surface code on pentagons
Craig Gidney · 2023
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Building manifolds from quantum codes
Michael Freedman and Matthew Hastings · 2021
Cited alongside, same era.
Matthew B Hastings · 2021
Cited alongside, same era.
Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead
Oscar Higgott and Nikolas P Breuckmann · 2021
Cited alongside, same era.
Dynamically generated logical qubits
Matthew B Hastings and Jeongwan Haah · 2021
Cited alongside, same era.
Four-dimensional toric code with non-clifford transversal gates
Tomas Jochym-O’Connor and Theodore J. Yoder · 2021
Cited alongside, same era.
Fault-tolerant gates on hypergraph product codes
Anirudh Krishna and David Poulin · 2021
Cited alongside, same era.
Distance-preserving stabilizer measurements in hypergraph product codes
Argyris Giannisis Manes and Jahan Claes · 2023
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General distance balancing for quantum locally testable codes
Adam Wills, Ting-Chun Lin, and Min-Hsiu Hsieh · 2023
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Tradeoff constructions for quantum locally testable codes
Adam Wills, Ting-Chun Lin, and Min-Hsiu Hsieh · 2023
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Dynamical weight reduction of pauli measurements
Julio C Magdalena de la Fuente · 2024
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Expansion of higher-dimensional cubical complexes with application to quantum locally testable codes
Irit Dinur, Ting-Chun Lin, and Thomas Vidick · 2024
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Improved pairwise measurement-based surface code
Linnea Grans-Samuelsson, Ryan V Mishmash, David Aasen, Christina Knapp, Bela Bauer, Brad Lackey, Marcus P da Silva, and Parsa Bonderson · 2024
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Weight reduced stabilizer codes with lower overhead
Eric Sabo, Lane G Gunderman, Benjamin Ide, Michael Vasmer, and Guillaume Dauphinais · 2024
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Fast and parallelizable logical computation with homological product codes
Qian Xu, Hengyun Zhou, Guo Zheng, Dolev Bluvstein, J Ataides, Mikhail D Lukin, and Liang Jiang · 2025
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A theory of single-shot error correction for adversarial noise
Earl T Campbell · 2058
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