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Topological quantum codes are intrinsically fault-tolerant to local noise, and underlie the theory of topological phases of matter.
A pair of generators for the unimodular group
Stanton M Trott · 1962
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Computing automorphism groups of error-correcting codes
J. Leon · 1982
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A probabilistic algorithm for computing minimum weights of large error-correcting codes
J.S. Leon · 1988
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Quantum error correction with imperfect gates
A Yu Kitaev · 1997
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Z2-systolic freedom and quantum codes
Michael H Freedman, David A Meyer, and Feng Luo · 2002
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Topological quantum computation
Michael Freedman, Alexei Kitaev, Michael Larsen, and Zhenghan Wang · 2003
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Fault-tolerant quantum computation by anyons
A Yu Kitaev · 2003
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Quantum orders in an exact soluble model
Xiao-Gang Wen · 2003
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Fault-tolerant postselected quantum computation: Schemes
Emanuel Knill · 2004
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Universal quantum computation with ideal clifford gates and noisy ancillas
Sergey Bravyi and Alexei Kitaev · 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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A comparative code study for quantum fault-tolerance, 2009
Andrew W. Cross, David P. DiVincenzo, and Barbara M. Terhal · 2009
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High-threshold universal quantum computation on the surface code
Austin G Fowler, Ashley M Stephens, and Peter Groszkowski · 2009
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On thermal stability of topological qubit in kitaev’s 4d model
Robert Alicki, Michal Horodecki, Pawel Horodecki, and Ryszard Horodecki · 2010
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Self-correcting quantum computers
Hector Bombin, Ravindra W Chhajlany, Michał Horodecki, and Miguel-Angel Martin-Delgado · 2013
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Homological product codes
Sergey Bravyi and Matthew B Hastings · 2014
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Single-shot fault-tolerant quantum error correction
Héctor Bombín · 2015
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Trading classical and quantum computational resources
Sergey Bravyi, Graeme Smith, and John A. Smolin · 2016
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Codes and Protocols for Distilling T T , controlled- S S , and Toffoli Gates
Jeongwan Haah and Matthew B. Hastings · 2018
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A theory of single-shot error correction for adversarial noise
Earl T Campbell · 2019
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A Game of Surface Codes: Large-Scale Quantum Computing with Lattice Surgery
Daniel Litinski · 2019
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Loops in 4+ 1d topological phases
Xie Chen, Arpit Dua, Po-Shen Hsin, Chao-Ming Jian, Wilbur Shirley, and Cenke Xu · 2023
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Higher cup products on hypercubic lattices: Application to lattice models of topological phases
Yu-An Chen and Sri Tata · 2023
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Multiscale architecture for fast optical addressing and control of large-scale qubit arrays
T_M Graham, E Oh, and M Saffman · 2023
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Quantum error correction below the surface code threshold
Rajeev Acharya, Dmitry A Abanin, Laleh Aghababaie-Beni, Igor Aleiner, Trond I Andersen, Markus Ansmann, Frank Arute, Kunal Arya, Abraham Asfaw, Nikita Astrakhantsev, et al · 2024
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Experiments with the four-dimensional surface code on a quantum charge-coupled device quantum computer
Noah Berthusen, Joan Dreiling, Cameron Foltz, John P Gaebler, Thomas M Gatterman, Dan Gresh, Nathan Hewitt, Michael Mills, Steven A Moses, Brian Neyenhuis, et al · 2024
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Magic State Distillation: Not as Costly as You Think
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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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Building manifolds from quantum codes
Michael Freedman and Matthew Hastings · 2021
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Fiber bundle codes: breaking the n 1/2 polylog (n) barrier for quantum ldpc codes
Matthew B Hastings, Jeongwan Haah, and Ryan O’Donnell · 2021
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Degenerate quantum LDPC codes with good finite length performance
Pavel Panteleev and Gleb Kalachev · 2021
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Surface code compilation via edge-disjoint paths
Michael Beverland, Vadym Kliuchnikov, and Eddie Schoute · 2022
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High-threshold and low-overhead fault-tolerant quantum memory
Sergey Bravyi, Andrew W Cross, Jay M Gambetta, Dmitri Maslov, Patrick Rall, and Theodore J Yoder · 2024
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Fold-transversal clifford gates for quantum codes
Nikolas P Breuckmann and Simon Burton · 2024
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High-performance fault-tolerant quantum computing with many-hypercube codes
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Compare the pair: Rotated vs. unrotated surface codes at equal logical error rates
Anthony Ryan O’Rourke and Simon Devitt · 2024
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Roadmap to fault tolerant quantum computation using topological qubit arrays
David Aasen, Morteza Aghaee, Zulfi Alam, Mariusz Andrzejczuk, Andrey Antipov, Mikhail Astafev, Lukas Avilovas, Amin Barzegar, Bela Bauer, Jonathan Becker, et al · 2025
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Geometrically enhanced topological quantum codes
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How to factor 2048 bit rsa integers with less than a million noisy qubits
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Computing efficiently in QLDPC codes
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Demonstration of low-overhead quantum error correction codes
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Resource analysis of low-overhead transversal architectures for reconfigurable atom arrays
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