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We ask what is the general framework for a quantum error correcting code that is defined by a sequence of measurements.
“Operator quantum error-correcting subsystems for self-correcting quantum memories”
Dave Bacon · 2006
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“Restrictions on Transversal Encoded Quantum Gate Sets”
Bryan Eastin and Emanuel Knill · 2009
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“A no-go theorem for a two-dimensional self-correcting quantum memory based on stabilizer codes”
Sergey Bravyi and Barbara Terhal · 2009
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“Tradeoffs for Reliable Quantum Information Storage in 2D Systems”
Sergey Bravyi, David Poulin, and Barbara Terhal · 2010
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“Subsystem codes with spatially local generators”
Sergey Bravyi · 2011
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“Classification of topologically protected gates for local stabilizer codes”
Sergey Bravyi and Robert Koenig · 2013
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“Subsystem surface codes with three-qubit check operators” (2013)
Sergey Bravyi, Guillaume Duclos-Cianci, David Poulin, and Martin Suchara · 2013
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“Fault-Tolerant Conversion between the Steane and Reed-Muller Quantum Codes”
Jonas T. Anderson, Guillaume Duclos-Cianci, and David Poulin · 2014
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“Universal transversal gates with color codes - a simplified approach”
Aleksander Kubica and Michael E. Beverland · 2015
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“Fault-tolerant logical gates in quantum error-correcting codes”
Fernando Pastawski and Beni Yoshida · 2015
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Sergey Bravyi and Andrew Cross · 2015
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“Sparse Quantum Codes from Quantum Circuits”
Dave Bacon, Steven T. Flammia, Aram W. Harrow, and Jonathan Shi · 2017
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“Transversal switching between generic stabilizer codes” (2018)
Cupjin Huang and Michael Newman · 2018
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“Dynamically Generated Logical Qubits”
Matthew B. Hastings and Jeongwan Haah · 2021
Cited alongside, same era.
Christophe Vuillot · 2021
Cited alongside, same era.
“A fault-tolerant honeycomb memory”
Craig Gidney, Michael Newman, Austin Fowler, and Michael Broughton · 2021
Cited alongside, same era.
“Boundaries for the Honeycomb Code”
Jeongwan Haah and Matthew B. Hastings · 2022
Cited alongside, same era.
“Adiabatic paths of Hamiltonians, symmetries of topological order, and automorphism codes”
David Aasen, Zhenghan Wang, and Matthew B. Hastings · 2022
Cited alongside, same era.
“Opportunities and challenges in fault-tolerant quantum computation” (2022)
“Floquet codes and phases in twist-defect networks” (2023)
Joseph Sullivan, Rui Wen, and Andrew C. Potter · 2023
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“Spacetime codes of clifford circuits” (2023)
Nicolas Delfosse and Adam Paetznick · 2023
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“Anyon condensation and the color code” (2024)
Markus S. Kesselring, Julio C. Magdalena de la Fuente, Felix Thomsen, Jens Eisert, Stephen D. Bartlett, and Benjamin J. Brown · 2024
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“Constructions and performance of hyperbolic and semi-hyperbolic floquet codes” (2024)
Oscar Higgott and Nikolas P. Breuckmann · 2024
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“Topological error correcting processes from fixed-point path integrals” (2024)
Andreas Bauer · 2024
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“Designing fault-tolerant circuits using detector error models” (2024)
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Daniel Gottesman · 2022
Cited alongside, same era.
“Quantifying nonlocality: how outperforming local quantum codes is expensive”
Nouédyn Baspin and Anirudh Krishna · 2022
Cited alongside, same era.
“Floquet codes with a twist” (2023)
Tyler D. Ellison, Joseph Sullivan, and Arpit Dua · 2023
Cited alongside, same era.
“ x x -cube floquet code: A dynamical quantum error correcting code with a subextensive number of logical qubits”
Zhehao Zhang, David Aasen, and Sagar Vijay · 2023
Cited alongside, same era.
“Floquet codes without parent subsystem codes”
Margarita Davydova, Nathanan Tantivasadakarn, and Shankar Balasubramanian · 2023
Cited alongside, same era.
“Performance of planar floquet codes with majorana-based qubits”
Adam Paetznick, Christina Knapp, Nicolas Delfosse, Bela Bauer, Jeongwan Haah, Matthew B. Hastings, and Marcus P. da Silva · 2023
Cited alongside, same era.
“Measurement quantum cellular automata and anomalies in floquet codes” (2023)
David Aasen, Jeongwan Haah, Zhi Li, and Roger S. K. Mong · 2023
Cited alongside, same era.
Peter-Jan H. S. Derks, Alex Townsend-Teague, Ansgar G. Burchards, and Jens Eisert · 2024
Closest in time.
“Fault tolerance of stabilizer channels” (2024)
Michael E. Beverland, Shilin Huang, and Vadym Kliuchnikov · 2024
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“Quantum computation from dynamic automorphism codes” (2024)
Margarita Davydova, Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen · 2024
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“Improved rate-distance trade-offs for quantum codes with restricted connectivity” (2023)
Nouédyn Baspin, Venkatesan Guruswami, Anirudh Krishna, and Ray Li · 2024
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“Fault-tolerant hyperbolic floquet quantum error correcting codes” (2025)
Ali Fahimniya, Hossein Dehghani, Kishor Bharti, Sheryl Mathew, Alicia J. Kollár, Alexey V. Gorshkov, and Michael J. Gullans · 2025
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“Dynamical logical qubits in the bacon-shor code” (2025)
M. Sohaib Alam and Eleanor Rieffel · 2025
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“Fault-tolerant protocols through spacetime concatenation” (2025)
Yichen Xu and Arpit Dua · 2025
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