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Hypergraph product codes are a class of constant-rate quantum low-density parity-check (LDPC) codes equipped with a linear-time decoder called small-set-flip (SSF).
Expander codes
Michael Sipser and Daniel A Spielman · 1994
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Soft-decision decoding of linear block codes based on ordered statistics
Marc PC Fossorier and Shu Lin · 1995
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Good quantum error-correcting codes exist
A Robert Calderbank and Peter W Shor · 1996
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Andrew Steane · 1996
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Dorit Aharonov and Michael Ben-Or · 1997
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Daniel Gottesman · 1997
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A Yu Kitaev · 1997
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Resilient quantum computation: error models and thresholds
Emanuel Knill, Raymond Laflamme, and Wojciech H Zurek · 1998
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Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Michael H Freedman, David A Meyer, and Feng Luo · 2002
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Asymptotic enumeration of 0–1 matrices with equal row sums and equal column sums
Brendan D McKay and Xiaoji Wang · 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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On the iterative decoding of sparse quantum codes
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Modern coding theory
Tom Richardson and Ruediger Urbanke · 2008
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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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Strong resilience of topological codes to depolarization
Héctor Bombin, Ruben S Andrist, Masayuki Ohzeki, Helmut G Katzgraber, and Miguel A Martin-Delgado · 2012
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Improved quantum hypergraph-product LDPC codes
Alexey A Kovalev and Leonid P Pryadko · 2012
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Tradeoffs for reliable quantum information storage in surface codes and color codes
Nicolas Delfosse · 2013
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Fault tolerance of quantum low-density parity check codes with sublinear distance scaling
Alexey A Kovalev and Leonid P Pryadko · 2013
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Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength
Statistical mechanical models for quantum codes with correlated noise
Christopher T Chubb and Steven T Flammia · 2018
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Constant overhead quantum fault-tolerance with quantum expander codes
Omar Fawzi, Antoine Grospellier, and Anthony Leverrier · 2018
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Numerical study of hypergraph product codes
Antoine Grospellier and Anirudh Krishna · 2018
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Numerical and analytical bounds on threshold error rates for hypergraph-product codes
Alexey A Kovalev, Sanjay Prabhakar, Ilya Dumer, and Leonid P Pryadko · 2018
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Golden codes: quantum LDPC codes built from regular tessellations of hyperbolic 4-manifolds
Vivien Londe and Anthony Leverrier · 2019
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Jean-Pierre Tillich and Gilles Zémor · 2013
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Fault-tolerant quantum computation with constant overhead
Daniel Gottesman · 2014
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Quantum error correcting codes and 4-dimensional arithmetic hyperbolic manifolds
Larry Guth and Alexander Lubotzky · 2014
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Thresholds for correcting errors, erasures, and faulty syndrome measurements in degenerate quantum codes
Ilya Dumer, Alexey A Kovalev, and Leonid P Pryadko · 2015
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Quantum expander codes
Anthony Leverrier, Jean-Pierre Tillich, and Gilles Zémor · 2015
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Constructions and noise threshold of hyperbolic surface codes
Nikolas P Breuckmann and Barbara M Terhal · 2016
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Fault-tolerant error correction with the gauge color code
Benjamin J Brown, Naomi H Nickerson, and Dan E Browne · 2016
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Degenerate quantum ldpc codes with good finite length performance
Pavel Panteleev and Gleb Kalachev · 2019
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Higher-dimensional quantum hypergraph-product codes with finite rates
Weilei Zeng and Leonid P Pryadko · 2019
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Single-Shot Decoding of Linear Rate LDPC Quantum Codes with High Performance
Nikolas P Breuckmann and Vivien Londe · 2020
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Topological wormholes: Nonlocal defects on the toric code
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A numerical study of bravyi-bacon-shor and subsystem hypergraph product codes
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Instantaneous braids and dehn twists in topologically ordered states
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Fault-tolerant gates on hypergraph product codes
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