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Fast, reliable logical operations are essential for realizing useful quantum computers.
Error Correcting Codes in Quantum Theory
A. M. Steane · 1996
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Peter W. Shor · 1996
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Good quantum error-correcting codes exist
A. R. Calderbank and Peter W. Shor · 1996
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Sergey B Bravyi, Alexei Yu Kitaev, and L D Landau · 1998
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Dorit Aharonov and Michael Ben-Or · 1999
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A. Kitaev, Unpaired Majorana Fermions in Quantum Wires, arXiv preprint arXiv:cond-mat/0010440 10.1070/1063-7869/44/10S/S29 (2000)
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Topological quantum memory
Eric Dennis, Alexei Kitaev, Andrew Landahl, and John Preskill · 2002
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Fault-tolerant quantum computation by anyons
A. Yu Kitaev · 2003
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A new quantum ripple-carry addition circuit
Steven A. Cuccaro, Thomas G. Draper, Samuel A. Kutin, and David Petrie Moulton · 2004
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Quantum Computing with Very Noisy Devices
E. Knill · 2004
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Quantum computation via translation-invariant operations on a chain of qubits
Robert Raussendorf · 2005
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Universal quantum computation with ideal Clifford gates and noisy ancillas
Sergey Bravyi and Alexei Kitaev · 2005
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S. Bravyi and A. Kitaev, Universal quantum computation with ideal Clifford gates and noisy ancillas, Physical Review A 71
2005
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H. Bombin and M. A. Martin-Delgado, Topological quantum distillation, Physical Review Letters 97
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Accuracy threshold for postselected quantum computation
Panos Aliferis, Daniel Gottesman, and John Preskill · 2007
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P. Aliferis, D. Gottesman, and J. Preskill, Accuracy threshold for postselected quantum computation, Quantum Information and Computation 8
2007
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Modern coding theory
Tom Richardson and Ruediger Urbanke · 2008
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Restrictions on Transversal Encoded Quantum Gate Sets
Bryan Eastin and Emanuel Knill · 2009
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B. Eastin and E. Knill, Restrictions on Transversal Encoded Quantum Gate Sets, Physical Review Letters 102
2009
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An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation
Daniel Gottesman · 2010
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Fast decoders for topological quantum codes
Guillaume Duclos-Cianci and David Poulin · 2010
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Quantum Computation and Quantum Information
Michael A. Nielsen and Isaac L. Chuang · 2010
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Topological order at nonzero temperature
Matthew B. Hastings · 2011
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Fault-tolerant quantum computing with color codes
Andrew J. Landahl, Jonas T. Anderson, and Patrick R. Rice · 2011
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M. B. Hastings, Topological order at nonzero temperature, Physical Review Letters 107
2011
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Surface code quantum computing by lattice surgery
Clare Horsman, Austin G. Fowler, Simon Devitt, and Rodney Van Meter · 2012
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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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Time-optimal quantum computation
Austin G. Fowler · 2012
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Magic-state distillation with low overhead
Sergey Bravyi and Jeongwan Haah · 2012
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High threshold error correction for the surface code
James R. Wootton and Daniel Loss · 2012
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A. G. Fowler, M. Mariantoni, J. M. Martinis, and A. N. Cleland, Surface codes: Towards practical large-scale quantum computation, Physical Review A 86
2012
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Fault-Tolerant Quantum Computation with Constant Overhead
Daniel Gottesman · 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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Optimal complexity correction of correlated errors in the surface code
Austin G. Fowler · 2013
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Gauge Color Codes: Optimal Transversal Gates and Gauge Fixing in Topological Stabilizer Codes
Héctor Bombín · 2013
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D. Gottesman, Fault-Tolerant Quantum Computation with Constant Overhead, Quantum Information and Computation 14
2013
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2013
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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 Zemor · 2014
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Sparse Quantum Codes from Quantum Circuits
Dave Bacon, Steven T. Flammia, Aram W. Harrow, and Jonathan Shi · 2014
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J. P. Tillich and G. Zemor, Quantum LDPC codes with positive rate and minimum distance proportional to the square root of the blocklength, IEEE Transactions on Information Theory 60
2014
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Single-shot fault-tolerant quantum error correction
Héctor Bombín · 2015
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A magic state’s fidelity can be superior to the operations that created it
Ying Li · 2015
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Minimum weight perfect matching of fault-tolerant topological quantum error correction in average O(1) parallel time
Austin G. Fowler · 2015
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Quantum error correction for quantum memories
Barbara M. Terhal · 2015
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Gauge color codes: optimal transversal gates and gauge fixing in topological stabilizer codes
Héctor Bombín · 2015
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Unfolding the color code
Aleksander Kubica, Beni Yoshida, and Fernando Pastawski · 2015
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Sergey Bravyi and Andrew Cross · 2015
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A. Kubica, B. Yoshida, and F. Pastawski, Unfolding the color code, New Journal of Physics 17
2015
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H. Bombín, Single-shot fault-tolerant quantum error correction, Physical Review X 5
2015
Cited alongside, same era.
Y. Li, A magic state’s fidelity can be superior to the operations that created it, New Journal of Physics 17
2015
Cited alongside, same era.
Transversal Clifford gates on folded surface codes
Jonathan E. Moussa · 2016
Cited alongside, same era.
Trading classical and quantum computational resources
Sergey Bravyi, Graeme Smith, and John A. Smolin · 2016
Cited alongside, same era.
J. E. Moussa, Transversal Clifford gates on folded surface codes, Physical Review A 94
2016
Cited alongside, same era.
Constant Overhead Quantum Fault-Tolerance with Quantum Expander Codes
Omar Fawzi, Antoine Grospellier, and Anthony Leverrier · 2018
Cited alongside, same era.
Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules
Isaac H. Kim, Ye-Hua Liu, Sam Pallister, William Pol, Sam Roberts, and Eunseok Lee · 2022
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Asymptotically good Quantum and locally testable classical LDPC codes
Pavel Panteleev and Gleb Kalachev · 2022
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Toward a Union-Find Decoder for Quantum LDPC Codes
Nicolas Delfosse, Vivien Londe, and Michael E. Beverland · 2022
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A quantum processor based on coherent transport of entangled atom arrays
Dolev Bluvstein, Harry Levine, Giulia Semeghini, Tout T. Wang, Sepehr Ebadi, Marcin Kalinowski, Alexander Keesling, Nishad Maskara, Hannes Pichler, Markus Greiner, Vladan Vuletić, and Mikhail D. Lukin · 2022
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A. Kubica and M. Vasmer, Single-shot quantum error correction with the three-dimensional subsystem toric code, Nature Communications 2022 13:1 13
2022
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Disjointness of Stabilizer Codes and Limitations on Fault-Tolerant Logical Gates
Tomas Jochym-O’Connor, Aleksander Kubica, and Theodore J. Yoder · 2018
Cited alongside, same era.
Low overhead quantum computation using lattice surgery
Austin G. Fowler and Craig Gidney · 2018
Cited alongside, same era.
Transversal gates and error propagation in 3D topological codes
Hector Bombin · 2018
Cited alongside, same era.
Quantum advantage of unitary Clifford circuits with magic state inputs
Mithuna Yoganathan, Richard Jozsa, and Sergii Strelchuk · 2018
Cited alongside, same era.
Halving the cost of quantum addition
Craig Gidney · 2018
Cited alongside, same era.
Encoding Electronic Spectra in Quantum Circuits with Linear T Complexity
Ryan Babbush, Craig Gidney, Dominic W. Berry, Nathan Wiebe, Jarrod McClean, Alexandru Paler, Austin Fowler, and Hartmut Neven · 2018
Cited alongside, same era.
L. Lao and B. Criger, Magic state injection on the rotated surface code, ACM International Conference Proceeding Series , 113 (2022)
2022
Later among the works it cites.
I. H. Kim, Y.-H. Liu, S. Pallister, W. Pol, S. Roberts, and E. Lee, Fault-tolerant resource estimate for quantum chemical simulations: Case study on Li-ion battery electrolyte molecules, Physical Review Research 4
2022
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N. Delfosse, V. Londe, and M. E. Beverland, Toward a Union-Find Decoder for Quantum LDPC Codes, IEEE Transactions on Information Theory 68
2022
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L. Z. Cohen, I. H. Kim, S. D. Bartlett, and B. J. Brown, Low-overhead fault-tolerant quantum computing using long-range connectivity, Science Advances 8
2022
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T. R. Scruby, D. E. Browne, P. Webster, and M. Vasmer, Numerical Implementation of Just-In-Time Decoding in Novel Lattice Slices through the Three-Dimensional Surface Code, Quantum 6
2022
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Spacetime codes of Clifford circuits
Nicolas Delfosse and Adam Paetznick · 2023
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Looped Pipelines Enabling Effective 3D Qubit Lattices in a Strictly 2D Device
Zhenyu Cai, Adam Siegel, and Simon Benjamin · 2023
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Cleaner magic states with hook injection
Craig Gidney · 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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Guanyu Zhu, Shehryar Sikander, Elia Portnoy, Andrew W. Cross, and Benjamin J. Brown · 2023
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Partitioning qubits in hypergraph product codes to implement logical gates
Armanda O. Quintavalle, Paul Webster, and Michael Vasmer · 2023
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Modular decoding: parallelizable real-time decoding for quantum computers
Héctor Bombín, Chris Dawson, Ye-Hua Liu, Naomi Nickerson, Fernando Pastawski, and Sam Roberts · 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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Scalable Quantum Error Correction for Surface Codes using FPGA
Namitha Liyanage, Yue Wu, Alexander Deters, and Lin Zhong · 2023
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Fusion Blossom: Fast MWPM Decoders for QEC
Yue Wu and Lin Zhong · 2023
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Scalable Surface-Code Decoders with Parallelization in Time
Xinyu Tan, Fang Zhang, Rui Chao, Yaoyun Shi, and Jianxin Chen · 2023
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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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A. O. Quintavalle, P. Webster, and M. Vasmer, Partitioning qubits in hypergraph product codes to implement logical gates, Quantum 7
2023
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O. Higgott and N. P. Breuckmann, Improved Single-Shot Decoding of Higher-Dimensional Hypergraph-Product Codes, PRX Quantum 4
2023
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Correlated Decoding of Logical Algorithms with Transversal Gates
Madelyn Cain, Chen Zhao, Hengyun Zhou, Nadine Meister, J. Pablo Bonilla Ataides, Arthur Jaffe, Dolev Bluvstein, and Mikhail D Lukin · 2024
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Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays
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Time-Efficient Constant-Space-Overhead Fault-Tolerant Quantum Computation
Hayata Yamasaki and Masato Koashi · 2024
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High-threshold and low-overhead fault-tolerant quantum memory
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Constructions and Performance of Hyperbolic and Semi-Hyperbolic Floquet Codes
Oscar Higgott and Nikolas P. Breuckmann · 2024
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Single-Shot Decoding of Good Quantum LDPC Codes
Shouzhen Gu, Eugene Tang, Libor Caha, Shin Ho Choe, Zhiyang He, and Aleksander Kubica · 2024
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Logical quantum processor based on reconfigurable atom arrays
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What is Your Logical Qubit
Jeongwan Haah · 2024
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Gurobi Optimizer Reference Manual, 2024
Gurobi Optimization, LLC · 2024
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Fold-Transversal Clifford Gates for Quantum Codes
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Hypergraph Minimum-Weight Parity Factor Decoder for QEC
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S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder, High-threshold and low-overhead fault-tolerant quantum memory, Nature 627
2024
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2024
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2024
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2024
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