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Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits.
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“Paths, trees, and flowers”
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P Shor · 1995
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P Shor · 1995
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“Universal Quantum Simulators”
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“Universal Quantum Simulators”
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“Topological Quantum Distillation”
H. Bombin and M.. Martin-Delgado · 2006
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“Topological Quantum Distillation”
H. Bombin and M.. Martin-Delgado · 2006
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H Bombin and M Martin-Delgado · 2007
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“Optimal resources for topological two-dimensional stabilizer codes: Comparative study”
H Bombin and M Martin-Delgado · 2007
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“Surface codes: Towards practical large-scale quantum computation”
Austin Fowler, Matteo Mariantoni, John Martinis and Andrew Cleland · 2012
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“Surface codes: Towards practical large-scale quantum computation”
Austin Fowler, Matteo Mariantoni, John Martinis and Andrew Cleland · 2012
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“Optimal complexity correction of correlated errors in the surface code”
Austin Fowler · 2013
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“Optimal complexity correction of correlated errors in the surface code”
Austin Fowler · 2013
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“Quantum error correction for quantum memories”
Barbara Terhal · 2015
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“Distilling the Knowledge in a Neural Network”
Geoffrey Hinton, Oriol Vinyals and Jeff Dean · 2015
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“Quantum error correction for quantum memories”
Barbara Terhal · 2015
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“Distilling the Knowledge in a Neural Network”
Geoffrey Hinton, Oriol Vinyals and Jeff Dean · 2015
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“Gaussian Error Linear Units (Gelus)”
D Hendrycks · 2016
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“Gaussian Error Linear Units (Gelus)”
D Hendrycks · 2016
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“Flag fault-tolerant error correction with arbitrary distance codes”
Christopher Chamberland and Michael Beverland · 2018
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“Flag fault-tolerant error correction with arbitrary distance codes”
Christopher Chamberland and Michael Beverland · 2018
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“Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization”
Ian Kivlichan et al · 2019
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“Neural network decoder for topological color codes with circuit level noise”
P Baireuther, M Caio, B Criger, C Beenakker and T O’Brien · 2019
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“Quantum supremacy using a programmable superconducting processor”
Google Quantum AI · 2019
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“Root mean square layer normalization”
Biao Zhang and Rico Sennrich · 2019
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“Bert: Pre-training of deep bidirectional transformers for language understanding”
Jacob Devlin, Ming-Wei Chang, Kenton Lee and Kristina Toutanova · 2019
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“Improved Fault-Tolerant Quantum Simulation of Condensed-Phase Correlated Electrons via Trotterization”
Ian Kivlichan et al · 2019
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“Neural network decoder for topological color codes with circuit level noise”
P Baireuther, M Caio, B Criger, C Beenakker and T O’Brien · 2019
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“Quantum supremacy using a programmable superconducting processor”
Google Quantum AI · 2019
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“Root mean square layer normalization”
Biao Zhang and Rico Sennrich · 2019
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“Bert: Pre-training of deep bidirectional transformers for language understanding”
Jacob Devlin, Ming-Wei Chang, Kenton Lee and Kristina Toutanova · 2019
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“Advances in quantum cryptography”
Stefano Pirandola et al · 2020
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“Advances in quantum cryptography”
Stefano Pirandola et al · 2020
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“PyMatching: A Python package for decoding quantum codes with minimum-weight perfect matching”
Oscar Higgott · 2021
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“A Fault-Tolerant Honeycomb Memory”
Craig Gidney, Michael Newman, Austin Fowler and Michael Broughton · 2021
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“Stim: a fast stabilizer circuit simulator”
Craig Gidney · 2021
Cited alongside, same era.
“Realization of Real-Time Fault-Tolerant Quantum Error Correction”
C Ryan-Anderson et al · 2021
Cited alongside, same era.
“The XZZX surface code”
J Bonilla, David Tuckett, Stephen Bartlett, Steven Flammia and Benjamin Brown · 2021
Cited alongside, same era.
“PyMatching: A Python package for decoding quantum codes with minimum-weight perfect matching”
Oscar Higgott · 2021
Cited alongside, same era.
“A Fault-Tolerant Honeycomb Memory”
Craig Gidney, Michael Newman, Austin Fowler and Michael Broughton · 2021
Cited alongside, same era.
“Stim: a fast stabilizer circuit simulator”
Craig Gidney · 2021
Cited alongside, same era.
“Efficient near-optimal decoding of the surface code through ensembling”, 2024
Noah Shutty, Michael Newman and Benjamin Villalonga · 2024
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“Decoding algorithms for surface codes”
Antonio deMarti iOlius, Patricio Fuentes, Román Orús, Pedro Crespo and Josu Etxezarreta · 2024
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“Color code decoder with improved scaling for correcting circuit-level noise”
Seok-Hyung Lee, Andrew Li and Stephen Bartlett · 2024
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“Griffin: Mixing gated linear recurrences with local attention for efficient language models”
Soham De et al · 2024
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“Efficient soft-output decoders for the surface code”, 2024
Nadine Meister, Christopher. Pattison and John Preskill · 2024
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“Realization of Real-Time Fault-Tolerant Quantum Error Correction”
C Ryan-Anderson et al · 2021
Cited alongside, same era.
“The XZZX surface code”
J Bonilla, David Tuckett, Stephen Bartlett, Steven Flammia and Benjamin Brown · 2021
Cited alongside, same era.
“Early fault-tolerant simulations of the Hubbard model”
Earl Campbell · 2022
Cited alongside, same era.
“Benchmarking the planar honeycomb code”
Craig Gidney, Michael Newman and Matt McEwen · 2022
Cited alongside, same era.
“Early fault-tolerant simulations of the Hubbard model”
Earl Campbell · 2022
Cited alongside, same era.
“Benchmarking the planar honeycomb code”
Craig Gidney, Michael Newman and Matt McEwen · 2022
Cited alongside, same era.
“Quantum error correction below the surface code threshold”
Google Quantum AI · 2025
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“Scaling and logic in the colour code on a superconducting quantum processor”
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“Colour codes reach surface code performance using vibe decoding”
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Google Quantum AI · 2025
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“Scaling and logic in the colour code on a superconducting quantum processor”
N Lacroix et al · 2025
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“Architectural mechanisms of a universal fault-tolerant quantum computer”
Dolev Bluvstein et al · 2025
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“Learning to decode logical circuits”
Yiqing Zhou et al · 2025
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“Neural decoders for universal quantum algorithms”
J Pablo, Gu Andi, F Susanne and D Mikhail · 2025
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“Generative decoding for quantum error-correcting codes”
Hanyan Cao, Feng Pan, Dongyang Feng, Yijia Wang and Pan Zhang · 2025
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“Decoding quantum low density parity check codes with diffusion”, 2025
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“Efficient and universal neural-network decoder for stabilizer-based quantum error correction”
Gengyuan Hu, Wanli Ouyang, Chao-Yang Lu, Chen Lin and Han-Sen Zhong · 2025
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“Learning Neural Decoding with Parallelism and Self-Coordination for Quantum Error Correction”
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“Tesseract: A search-based decoder for quantum error correction”
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“Colour codes reach surface code performance using vibe decoding”
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“How to factor 2048 bit RSA integers with less than a million noisy qubits”, 2025
Craig Gidney · 2025
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“Rare Event Simulation of Quantum Error-Correcting Circuits”, 2025
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