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Quantum low-density parity-check codes are a promising candidate for fault-tolerant quantum computing with considerably reduced overhead compared to the surface code.
“Low-density parity-check codes”
Robert G. Gallager · 1962
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Robert Endre Tarjan · 1975
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Geoffrey Grimmett · 1989
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“Soft-decision decoding of linear block codes based on ordered statistics”
Marc P. C. Fossorier and Shu Lin · 1995
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“Near shannon limit performance of low density parity check codes”
David J. C. MacKay and Radford M. Neal · 1997
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Marc P. C. Fossorier, Shu Lin, and Jakov Snyders · 1998
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“Topological quantum memory”
Eric Dennis, Alexei J. Kitaev, Andrew Landahl, and John Preskill · 2002
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“Fault-tolerant quantum computation by anyons”
Alexei J. Kitaev · 2003
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“Accuracy threshold for postselected quantum computation”
Panos Aliferis, Daniel Gottesman, and John Preskill · 2008
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“Matrix factorization techniques for recommender systems”
Yehuda Koren, Robert Bell, and Chris Volinsky · 2009
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“Blueprint for a scalable photonic fault-tolerant quantum computer”
J. Eli Bourassa, Rafael N. Alexander, Michael Vasmer, Ashlesha Patil, Ilan Tzitrin, Takaya Matsuura, Daiqin Su, Ben Q. Baragiola, Saikat Guha, Guillaume Dauphinais, Krishna K. Sabapathy, Nicolas C. Menicucci, and Ish Dhand · 2010
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“Surface codes: Towards practical large-scale quantum computation”
Austin G. Fowler, Matteo Mariantoni, John M. Martinis, and Andrew N. Cleland · 2012
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“Quantum Kronecker sum-product low-density parity-check codes with finite rate”
Alexey A. Kovalev and Leonid P. Pryadko · 2013
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“Upper bounds on the rate of low density stabilizer codes for the quantum erasure channel”
Nicolas Delfosse and Gilles Zémor · 2013
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“Fault-tolerant quantum computation with constant overhead” (2014)
Daniel Gottesman · 2014
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“Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength”
Jean-Pierre Tillich and Gilles Zémor · 2014
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“A survey of compressed sensing”
Holger Boche, Robert Calderbank, Gitta Kutyniok, and Jan Vybíral · 2015
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“Quantum error correction for quantum memories”
Barbara M. Terhal · 2015
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“Cellular-automaton decoders for topological quantum memories”
Michael Herold, Earl T. Campbell, Jens Eisert, and Michael J. Kastoryano · 2015
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“Single-shot fault-tolerant quantum error correction”
Héctor Bombín · 2015
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“Introduction to percolation theory: Second edition”
Dietrich Stauffer and Ammon Aharony · 2017
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“Design of low-density parity check codes for 5g new radio”
Tom Richardson and Shrinivas Kudekar · 2018
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“Work-efficient parallel union-find”
Natcha Simsiri, Kanat Tangwongsan, Srikanta Tirthapura, and Kun-Lung Wu · 2018
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“Quantum error correction with the toric Gottesman-Kitaev-Preskill code”
Christophe Vuillot, Hamed Asasi, Yang Wang, Leonid P. Pryadko, and Barbara M. Terhal · 2019
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“Decoding across the quantum low-density parity-check code landscape”
Joschka Roffe, David R. White, Simon Burton, and Earl Campbell · 2020
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“Quantum low-density parity-check codes”
Nikolas P. Breuckmann and Jens Niklas Eberhardt · 2021
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“Balanced product quantum codes”
Nikolas P. Breuckmann and Jens N. Eberhardt · 2021
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Pavel Panteleev and Gleb Kalachev · 2021
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“Fault-tolerant quantum computation with static linear optics”
Ilan Tzitrin, Takaya Matsuura, Rafael N. Alexander, Guillaume Dauphinais, J. Eli Bourassa, Krishna K. Sabapathy, Nicolas C. Menicucci, and Ish Dhand · 2021
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“Trapping sets of quantum LDPC codes”
“Parallel window decoding enables scalable fault tolerant quantum computation”
Luka Skoric, Dan E. Browne, Kenton M. Barnes, Neil I. Gillespie, and Earl T. Campbell · 2023
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Kirsten D. Morris, Tefjol Pllaha, and Christine A. Kelley · 2023
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“Symphase: Phase symbolization for fast simulation of stabilizer circuits” (2023)
Wang Fang and Mingsheng Ying · 2023
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“Improved single-shot decoding of higher-dimensional hypergraph-product codes”
Oscar Higgott and Nikolas P. Breuckmann · 2023
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“Improved decoding of circuit noise and fragile boundaries of tailored surface codes”
Oscar Higgott, Thomas C. Bohdanowicz, Aleksander Kubica, Steven T. Flammia, and Earl T. Campbell · 2023
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“Almost-linear time decoding algorithm for topological codes”
Nicolas Delfosse and Naomi H. Nickerson · 2021
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Ben Barber, Kenton M. Barnes, Tomasz Bialas, Okan Buğdaycı, Earl T. Campbell, Neil I. Gillespie, Kauser Johar, Ram Rajan, Adam W. Richardson, Luka Skoric, Canberk Topal, Mark L. Turner, and Abbas B. Ziad · 2023
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“Erasure qubits: Overcoming the T 1 T_{1} limit in superconducting circuits”
Aleksander Kubica, Arbel Haim, Yotam Vaknin, Harry Levine, Fernando Brandão, and Alex Retzker · 2023
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“Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons” (2023)
Harry Levine, Arbel Haim, Jimmy S. C. Hung, Nasser Alidoust, Mahmoud Kalaee, Laura DeLorenzo, E. Alex Wollack, Patricio Arrangoiz Arriola, Amirhossein Khalajhedayati, Yotam Vaknin, et al · 2023
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