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Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible.
“Low-density parity-check codes”
Robert G. Gallager · 1963
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“A recursive approach to low complexity codes”
R. Tanner · 1981
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“Scheme for reducing decoherence in quantum computer memory”
Peter W. Shor · 1995
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“Good codes based on very sparse matrices”
David J. C. MacKay and Radford M. Neal · 1995
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“Soft-decision decoding of linear block codes based on ordered statistics”
M.P.C. Fossorier and Shu Lin · 1995
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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
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“Near shannon limit performance of low density parity check codes”
D.J.C. MacKay and R.M. Neal · 1997
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“Fault-tolerant quantum computation with constant error rate” (1999)
Dorit Aharonov and Michael Ben-Or · 1999
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“Projective plane and planar quantum codes”
Michael H. Freedman and David A. Meyer · 2001
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“Factor graphs and the sum-product algorithm”
F.R. Kschischang, B.J. Frey, and H.-A. Loeliger · 2001
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“Topological quantum memory”
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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“Sparse-graph codes for quantum error correction”
D.J.C. MacKay, G. Mitchison, and P.L. McFadden · 2004
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“Topological quantum distillation”
H. Bombin and M. A. Martin-Delgado · 2006
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“Application and evaluation of the ldpc codes for the next generation communication systems”
Teodor B. Iliev, Georgi V. Hristov, Plamen Z. Zahariev, and Mihail P. Iliev · 2008
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“Modern coding theory”
Thomas J. Richardson · 2008
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“Finite fields”
Rudolf Lidl and Harald Niederreiter · 2008
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“Tradeoffs for reliable quantum information storage in 2d systems”
Sergey Bravyi, David Poulin, and Barbara Terhal · 2010
Cited alongside, same era.
“Surface codes: Towards practical large-scale quantum computation”
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland · 2012
Cited alongside, same era.
“Quantum error correction for beginners”
Simon J Devitt, William J Munro, and Kae Nemoto · 2013
Cited alongside, same era.
“Fault-tolerant quantum computation with constant overhead” (2013)
Daniel Gottesman · 2013
Cited alongside, same era.
“Fault tolerance of quantum low-density parity check codes with sublinear distance scaling”
Alexey A. Kovalev and Leonid P. Pryadko · 2013
Cited alongside, same era.
“Bounds on stabilizer measurement circuits and obstructions to local implementations of quantum ldpc codes” (2021)
Nicolas Delfosse, Michael E. Beverland, and Maxime A. Tremblay · 2021
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“Degenerate quantum ldpc codes with good finite length performance”
Pavel Panteleev and Gleb Kalachev · 2021
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“Quantum simulation and computing with rydberg-interacting qubits”
M. Morgado and S. Whitlock · 2021
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“Quantum information processing, quantum computing, and quantum error correction an engineering approach”
Ivan Djordjevic · 2021
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“Quantum tanner codes” (2022)
Anthony Leverrier and Gilles Zémor · 2022
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“Quantifying nonlocality: How outperforming local quantum codes is expensive”
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“Quantum kronecker sum-product low-density parity-check codes with finite rate”
Alexey A. Kovalev and Leonid P. Pryadko · 2013
Cited alongside, same era.
“Scaling the ion trap quantum processor”
C. Monroe and J. Kim · 2013
Cited alongside, same era.
“Quantum ldpc codes with positive rate and minimum distance proportional to the square root of the blocklength”
Jean-Pierre Tillich and Gilles Zemor · 2014
Cited alongside, same era.
“Simplified variable-scaled min sum ldpc decoder for irregular ldpc codes”
Ahmed A. Emran and Maha Elsabrouty · 2014
Cited alongside, same era.
“Quantum error correction for quantum memories”
Barbara M. Terhal · 2015
Cited alongside, same era.
“Why i am optimistic about the silicon-photonic route to quantum computing”
Terry Rudolph · 2017
Cited alongside, same era.
Nouédyn Baspin and Anirudh Krishna · 2022
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“Constant-overhead quantum error correction with thin planar connectivity”
Maxime A. Tremblay, Nicolas Delfosse, and Michael E. Beverland · 2022
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“Decoding quantum tanner codes” (2022)
Anthony Leverrier and Gilles Zémor · 2022
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“Co-design quantum simulation of nanoscale nmr”
Manuel G. Algaba, Mario Ponce-Martinez, Carlos Munuera-Javaloy, Vicente Pina-Canelles, Manish J. Thapa, Bruno G. Taketani, Martin Leib, Inés de Vega, Jorge Casanova, and Hermanni Heimonen · 2022
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“Ldpc: Python tools for low density parity check codes” (2022)
Joschka Roffe · 2022
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“The future of quantum computing with superconducting qubits”
Sergey Bravyi, Oliver Dial, Jay M. Gambetta, Darío Gil, and Zaira Nazario · 2022
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“Hierarchical memories: Simulating quantum ldpc codes with local gates” (2023)
Christopher A. Pattison, Anirudh Krishna, and John Preskill · 2023
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“Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays” (2023)
Qian Xu, J. Pablo Bonilla Ataides, Christopher A. Pattison, Nithin Raveendran, Dolev Bluvstein, Jonathan Wurtz, Bane Vasic, Mikhail D. Lukin, Liang Jiang, and Hengyun Zhou · 2023
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“High-threshold and low-overhead fault-tolerant quantum memory” (2023)
Sergey Bravyi, Andrew W. Cross, Jay M. Gambetta, Dmitri Maslov, Patrick Rall, and Theodore J. Yoder · 2023
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“Matching generalized-bicycle codes to neutral atoms for low-overhead fault-tolerance” (2023)
Joshua Viszlai, Willers Yang, Sophia Fuhui Lin, Junyu Liu, Natalia Nottingham, Jonathan M. Baker, and Frederic T. Chong · 2023
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“Logical quantum processor based on reconfigurable atom arrays”
Dolev Bluvstein, Simon J. Evered, Alexandra A. Geim, Sophie H. Li, Hengyun Zhou, Tom Manovitz, Sepehr Ebadi, Madelyn Cain, Marcin Kalinowski, Dominik Hangleiter, J. Pablo Bonilla Ataides, Nishad Maskara, Iris Cong, Xun Gao, Pedro Sales Rodriguez, Thomas Karolyshyn, Giulia Semeghini, Michael J. Gullans, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin · 2023
Later among the works it cites.