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A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit.
“Quantum Error Correction with Imperfect Gates”
A. Y. Kitaev · 1997
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“Topological quantum memory”
E. Dennis, A. Kitaev, A. Landahl, and J. Preskill · 2002
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“Z2-systolic freedom and quantum codes”
M. H. Freedman, D. A. Meyer, and F. Luo · 2002
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“Trivalent symmetric graphs on up to 768 vertices”
M. Conder and P. Dobcsányi · 2002
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“Fault-tolerant quantum computation by anyons”
A. Y. Kitaev · 2003
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“On Cayley Graphs, Surface Codes, and the Limits of Homological Coding for Quantum Error Correction”
G. Zémor · 2009
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“Thresholds for Topological Codes in the Presence of Loss”
T. M. Stace, S. D. Barrett, and A. C. Doherty · 2009
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“Vertex-, face-, point-, Schläfli-, and Delaney-symbols in nets, polyhedra and tilings: Recommended terminology”
V. A. Blatov, M. O’Keeffe, and D. M. Proserpio · 2010
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“Error correction and degeneracy in surface codes suffering loss”
T. M. Stace and S. D. Barrett · 2010
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“Surface code quantum computing by lattice surgery”
D. Horsman, A. G. Fowler, S. Devitt, and R. V. Meter · 2012
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“Simulation of rare events in quantum error correction”
S. Bravyi and A. Vargo · 2013
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“Fault-Tolerant Quantum Computation with Constant Overhead” (2014) arXiv:1310.2984
D. Gottesman · 2014
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“Majorana zero modes and topological quantum computation”
S. D. Sarma, M. Freedman, and C. Nayak · 2015
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“Demonstration of Weight-Four Parity Measurements in the Surface Code Architecture”
M. Takita, A. D. Córcoles, E. Magesan, B. Abdo, M. Brink, A. Cross, J. M. Chow, and J. M. Gambetta · 2016
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“Constructions and Noise Threshold of Hyperbolic Surface Codes”
N. P. Breuckmann and B. M. Terhal · 2016
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“Robust surface code topology against sparse fabrication defects in a superconducting-qubit array”
Y.-C. Tang and G.-X. Miao · 2016
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“Hyperbolic and semi-hyperbolic surface codes for quantum storage”
N. P. Breuckmann, C. Vuillot, E. Campbell, A. Krishna, and B. M. Terhal · 2017
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“Surface code error correction on a defective lattice”
S. Nagayama, A. G. Fowler, D. Horsman, S. J. Devitt, and R. V. Meter · 2017
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“Tailoring Surface Codes for Highly Biased Noise”
D. K. Tuckett, A. S. Darmawan, C. T. Chubb, S. Bravyi, S. D. Bartlett, and S. T. Flammia · 2019
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“Optimization of the surface code design for Majorana-based qubits”
R. Chao, M. E. Beverland, N. Delfosse, and J. Haah · 2020
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“Probing topological spin liquids on a programmable quantum simulator”
G. Semeghini, H. Levine, A. Keesling, S. Ebadi, T. T. Wang, D. Bluvstein, R. Verresen, H. Pichler, M. Kalinowski, R. Samajdar, A. Omran, S. Sachdev, A. Vishwanath, M. Greiner, V. Vuletić, and M. D. Lukin · 2021
Cited alongside, same era.
“Dynamically Generated Logical Qubits”
M. B. Hastings and J. Haah · 2021
Cited alongside, same era.
“The XZZX surface code”
J. P. Bonilla Ataides, D. K. Tuckett, S. D. Bartlett, S. T. Flammia, and B. J. Brown · 2021
Cited alongside, same era.
“Quantum Low-Density Parity-Check Codes”
N. P. Breuckmann and J. N. Eberhardt · 2021
Cited alongside, same era.
“A Fault-Tolerant Honeycomb Memory”
C. Gidney, M. Newman, A. Fowler, and M. Broughton · 2021
Cited alongside, same era.
“A Pair Measurement Surface Code on Pentagons”
C. Gidney · 2023
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“Floquet codes with a twist” (2023) arXiv:2306.08027
T. D. Ellison, J. Sullivan, and A. Dua · 2023
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“Floquet Codes without Parent Subsystem Codes”
M. Davydova, N. Tantivasadakarn, and S. Balasubramanian · 2023
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“Floquet codes and phases in twist-defect networks”
J. Sullivan, R. Wen, and A. C. Potter · 2023
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“Measurement Quantum Cellular Automata and Anomalies in Floquet Codes” (2023) arXiv:2304.01277
D. Aasen, J. Haah, Z. Li, and R. S. K. Mong · 2023
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“Random-bond Ising model and its dual in hyperbolic spaces”
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“Planar Floquet Codes” (2021) arXiv:2110.05348
C. Vuillot · 2021
Cited alongside, same era.
“Logical-qubit operations in an error-detecting surface code”
J. F. Marques, B. M. Varbanov, M. S. Moreira, H. Ali, N. Muthusubramanian, C. Zachariadis, F. Battistel, M. Beekman, N. Haider, W. Vlothuizen, A. Bruno, B. M. Terhal, and L. DiCarlo · 2022
Cited alongside, same era.
“Realizing repeated quantum error correction in a distance-three surface code”
S. Krinner, N. Lacroix, A. Remm, A. Di Paolo, E. Genois, C. Leroux, C. Hellings, S. Lazar, F. Swiadek, J. Herrmann, G. J. Norris, C. K. Andersen, M. Müller, A. Blais, C. Eichler, and A. Wallraff · 2022
Cited alongside, same era.
“Realization of an Error-Correcting Surface Code with Superconducting Qubits”
Y. Zhao, Y. Ye, H.-L. Huang, Y. Zhang, D. Wu, H. Guan, Q. Zhu, Z. Wei, T. He, S. Cao, F. Chen, T.-H. Chung, H. Deng, D. Fan, M. Gong, C. Guo, S. Guo, L. Han, N. Li, S. Li, Y. Li, F. Liang, J. Lin, H. Qian, H. Rong, H. Su, L. Sun, S. Wang, Y. Wu, Y. Xu, C. Ying, J. Yu, C. Zha, K. Zhang, Y.-H. Huo, C.-Y. Lu, C.-Z. Peng, X. Zhu, and J.-W. Pan · 2022
Cited alongside, same era.
“A quantum processor based on coherent transport of entangled atom arrays”
D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, V. Vuletić, and M. D. Lukin · 2022
Cited alongside, same era.
“Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays”
Y. Wu, S. Kolkowitz, S. Puri, and J. D. Thompson · 2022
Cited alongside, same era.
B. Placke and N. P. Breuckmann · 2023
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“Quantum Computing is Scalable on a Planar Array of Qubits with Fabrication Defects”
A. Strikis, S. C. Benjamin, and B. J. Brown · 2023
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“Adaptive surface code for quantum error correction in the presence of temporary or permanent defects”
A. Siegel, A. Strikis, T. Flatters, and S. Benjamin · 2023
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“Fault-tolerant Hastings-Haah codes in the presence of dead qubits” (2023) arXiv:2307.03715
D. Aasen, J. Haah, P. Bonderson, Z. Wang, and M. Hastings · 2023
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“Enhancing detection of topological order by local error correction”
I. Cong, N. Maskara, M. C. Tran, H. Pichler, G. Semeghini, S. F. Yelin, S. Choi, and M. D. Lukin · 2024
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“High-threshold and low-overhead fault-tolerant quantum memory”
S. Bravyi, A. W. Cross, J. M. Gambetta, D. Maslov, P. Rall, and T. J. Yoder · 2024
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“Clifford-Deformed Surface Codes”
A. Dua, A. Kubica, L. Jiang, S. T. Flammia, and M. J. Gullans · 2024
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“Constant-overhead fault-tolerant quantum computation with reconfigurable atom arrays”
Q. Xu, J. P. Bonilla Ataides, C. A. Pattison, N. Raveendran, D. Bluvstein, J. Wurtz, B. Vasić, M. D. Lukin, L. Jiang, and H. Zhou · 2024
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“Anyon Condensation and the Color Code”
M. S. Kesselring, J. C. Magdalena De La Fuente, F. Thomsen, J. Eisert, S. D. Bartlett, and B. J. Brown · 2024
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“Quantum computation from dynamic automorphism codes”
M. Davydova, N. Tantivasadakarn, S. Balasubramanian, and D. Aasen · 2024
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“Constructions and Performance of Hyperbolic and Semi-Hyperbolic Floquet Codes”
O. Higgott and N. P. Breuckmann · 2024
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“Sparse Blossom: Correcting a million errors per core second with minimum-weight matching”
O. Higgott and C. Gidney · 2025
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“XYZ Ruby Code: Making a Case for a Three-Colored Graphical Calculus for Quantum Error Correction in Spacetime”
J. C. Magdalena de la Fuente, J. Old, A. Townsend-Teague, M. Rispler, J. Eisert, and M. Müller · 2025
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