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Extensive quantum error correction is necessary in order to perform a useful computation on a noisy quantum computer.
The theory of error-correcting codes
Florence Jessie MacWilliams and Neil James Alexander Sloane · 1977
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A recursive approach to low complexity codes
R. Tanner · 1981
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Near shannon limit error-correcting coding and decoding: Turbo-codes. 1
Claude Berrou, Alain Glavieux, and Punya Thitimajshima · 1993
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Scheme for reducing decoherence in quantum computer memory
Peter W. Shor · 1995
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Good quantum error-correcting codes exist
Robert A. Calderbank and Peter W. Shor · 1996
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Bounds on the size of linear codes
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Efficient fault-tolerant quantum computing
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Low-density parity-check codes based on finite geometries: a rediscovery and new results
Yu Kou, Shu Lin, and Marc P.C. Fossorier · 2001
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Low-density parity-check codes based on finite geometries: a rediscovery and new results
Yu Kou, Shu Lin, and Marc P.C. Fossorier · 2001
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Design of capacity-approaching irregular low-density parity-check codes
Thomas J. Richardson, Mohammad Amin Shokrollahi, and Rüdiger L. Urbanke · 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
David J.C. MacKay, Graeme Mitchison, and Paul L. McFadden · 2004
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Quantum accuracy threshold for concatenated distance-3 codes
Panos Aliferis, Daniel Gottesman, and John Preskill · 2005
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A flow-map model for analyzing pseudothresholds in fault-tolerant quantum computing
Krysta M. Svore, Andrew W. Cross, Isaac L. Chuang, and Alfred V. Aho · 2005
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Searching for linear codes with large minimum distance
Markus Grassl · 2006
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Fault-tolerant quantum computation with constant error rate
Dorit Aharonov and Michael Ben-Or · 2008
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Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels
Erdal Arikan · 2009
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Anthony Leverrier, Jean-Pierre Tillich, and Gilles Zémor · 2015
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Alexei Ashikhmin, Ching-Yi Lai, and Todd A. Brun · 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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Local decoders for the 2D and 4D toric code
Nikolas P. Breuckmann, Kasper Duivenvoorden, Dominik Michels, and Barbara M. Terhal · 2016
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Elucidating reaction mechanisms on quantum computers
Markus Reiher, Nathan Wiebe, Krysta M. Svore, Dave Wecker, and Matthias Troyer · 2017
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An introduction to quantum error correction and fault-tolerant quantum computation
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Errors in flash-memory-based solid-state drives: Analysis, mitigation, and recovery
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