"Code Name","Article Title","First Author","Link","Year","Code Parameters","Platform","Notes","Round count","Postselection rate","Number of ancillae","Half life of the logical qubit","Circuit runtime (s)","Total number of qubits involved","Total physical gates","Total two-qubit gates","Research Group"
"Repetition Code","Experimental Quantum Error Correction","Cory","https://arxiv.org/abs/quant-ph/9802018","1998","[3,1,3]","NMR","","","","","","","","","","Los Alamos / MIT"
"Repetition Code","Experimental Repetitive Quantum Error Correction","Schindler","https://jubarreiro.physics.ucsd.edu/files/Schindler-Science-332-1059-1061.pdf","2011","[3,1,3]","Ion traps","","","","","","","","","","Innsbruck (Blatt)"
"Repetition Code","Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid-State Ensemble Quantum Information Processor","Moussa","https://arxiv.org/abs/1108.4842","2011","[3,1,3]","NMR","","","","","","","","","","IQC Waterloo"
"Repetition Code","Experimental quantum error correction with high fidelity","Zhang","https://arxiv.org/abs/1109.4821","2011","[3,1,3]","NMR","","","","","","","","","","IQC Waterloo"
"Repetition Code","Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits","Reed","https://arxiv.org/abs/1109.4948","2012","[3,1,3]","Superconducting circuit","","","","","","","","","","Yale (Schoelkopf)"
"Repetition Code","State preservation by repetitive error detection in a superconducting quantum circuit","Kelly","https://arxiv.org/abs/1411.7403","2014","[3,1,3]-[5,1,5]","Superconducting circuit","","","","","","","","","","UCSB / Google"
"Repetition Code","Quantum error correction in a solid-state hybrid spin register","Waldherr","https://arxiv.org/abs/1309.6424","2014","[[3,1,3]]","NV centers","","","","","","","","","","Delft (Hanson)"
"Repetition Code","Detecting bit-flip errors in a logical qubit using stabilizer measurements","Riste","https://arxiv.org/abs/1411.5542","2015","[3,1,3]","Superconducting circuit","","","","","","","","","","Delft (DiCarlo)"
"Repetition Code","Repeated quantum error correction on a continuously encoded qubit by real-time feedback","Cramer","https://arxiv.org/abs/1508.01388","2016","[3,1,3]","Superconducting circuit","","","","","","","","","","Yale (Schoelkopf)"
"Repetition Code","A repetition code of 15 qubits","Wootton","https://arxiv.org/abs/1709.00990","2018","[3,1,3]-[8,1,8]","Superconducting circuit","","","","","","","","","","IBM Research"
"Repetition Code","Benchmarking near-term devices with quantum error correction","Wootton","https://arxiv.org/abs/2004.11037","2020","[3,1,3]-[22,1,22]","Superconducting circuit","","","","","","","","","","Google Quantum AI"
"Repetition Code","Exponential suppression of bit or phase flip errors with repetitive error correction","Chen","https://arxiv.org/abs/2102.06132","2020","[3,1,3]-[11,1,11]","Superconducting circuit","","","","","","","","","","Google Quantum AI"
"Four-qubit Code","Exponential suppression of bit or phase flip errors with repetitive error correction","Chen","https://arxiv.org/abs/2102.06132","2020","[[4,1,2]]","Superconducting circuit","","","","","","","","","","Google Quantum AI"
"Repetition Code","Suppressing quantum errors by scaling a surface code logical qubit","Acharya","https://arxiv.org/abs/2207.06431","2023","[3,1,3]-[25,1,25]","Superconducting circuit","Repetition codes below threshold","","","","","","","","","Google Quantum AI"
"Repetition Code","Hardware-efficient quantum error correction using concatenated bosonic qubits","Putterman","https://arxiv.org/abs/2409.13025","2024","[[3,1,3]], [[5,1,5]]","Superconducting circuit","Repetition cat codes below threshold","","","","","","","","","Amazon (AWS)"
"Repetition Code","Quantum error correction below the surface code threshold","Acharya","https://arxiv.org/abs/2408.13687","2024","[3,1,3]-[29,1,29]","Superconducting circuit","Repetition codes below threshold","1000","100%","2-28","","","","","","Google Quantum AI"
"[[5,1,3]] Perfect Code","Benchmarking Quantum Computers: The Five-Qubit Error Correcting Code","Knill","https://arxiv.org/abs/quant-ph/0101034","2001","[[5,1,3]]","NMR","","","","","","","","","","Los Alamos / MIT"
"[[5,1,3]] Perfect Code","Experimental implementation of encoded logical qubit operations in a perfect quantum error correcting code","Zhang","https://arxiv.org/abs/1208.4797","2012","[[5,1,3]]","NMR","","","","","","","","","","IQC Waterloo"
"[[5,1,3]] Perfect Code","Experimental exploration of five-qubit quantum error correcting code with superconducting qubits","Gong","https://arxiv.org/abs/1907.04507","2019","[[5,1,3]]","Superconducting circuit","","","","","","","","","","IBM Research"
"Surface Code","Experimental demonstration of a graph state quantum error-correction code","Bell","https://arxiv.org/abs/1404.5498","2014","[[4,1,2]]","Photons","","","","","","","","","","University of Bristol"
"Surface Code","Repeated Quantum Error Detection in a Surface Code","Andersen","https://arxiv.org/abs/1912.09410","2020","[[4,1,2]]","Superconducting circuit","","","","","","","","","","ETH Zurich"
"Surface Code","Realizing repeated quantum error correction in a distance-three surface code","Krinner","https://arxiv.org/abs/2112.03708","2021","[[9,1,3]]","Superconducting circuit","","","","","","","","","","ETH Zurich"
"Surface Code","Suppressing quantum errors by scaling a surface code logical qubit","Acharya","https://arxiv.org/abs/2207.06431","2023","[[9,1,3]]-[[25,1,5]]","Superconducting circuit","Repetition codes below threshold","","","","","","","","","Google Quantum AI"
"Surface Code","A quantum processor based on coherent transport of entangled atom arrays","Bluvstein","https://arxiv.org/abs/2112.03923","2021","[[13,1,3]] surface code, [[16,2,2]] toric code","Neutral atoms","","","","","","","","","","Harvard / QuEra"
"Surface Code","Logical quantum processor based on reconfigurable atom arrays","Bluvstein","https://arxiv.org/abs/2312.03982","2023","[[9,1,3]], [[25,1,5]], [[49,1,7]]","Neutral atoms","","","","","","","","","","Harvard / QuEra"
"Surface Code","Quantum error correction below the surface code threshold","Acharya","https://arxiv.org/abs/2408.13687","2024","[[9,1,3]], [[25,1,5]], [[49,1,7]]","Superconducting circuit","Surface codes below threshold","250","100%","8, 24, 52","83, 188, ","","","","","Google Quantum AI"
"Color Code","Experimental Quantum Computations on a Topologically Encoded Qubit","Nigg","https://arxiv.org/abs/1403.5426","2014","[[7,1,3]]","Ion traps","","","","","","","","","","Innsbruck (Blatt)"
"Color Code","Experimental demonstration of fault-tolerant state preparation with superconducting qubits","Takita","https://arxiv.org/abs/1705.09259","2017","[[4,2,2]]","Superconducting circuit","","","","","","","","","","IBM Research"
"Color Code","Fault-tolerant quantum error detection","Linke","https://arxiv.org/abs/1611.06946","2017","[[4,2,2]]","Ion traps","","","","","","","","","","Maryland (Monroe)"
"Color Code","A quantum processor based on coherent transport of entangled atom arrays","Bluvstein","https://arxiv.org/abs/2112.03923","2021","[[7,1,3]]","Neutral atoms","","","","","","","","","","Harvard / QuEra"
"Color Code","Logical quantum processor based on reconfigurable atom arrays","Bluvstein","https://arxiv.org/abs/2312.03982","2023","[[7,1,3]], [[8,3,2]]","Neutral atoms","","","","","","","","","","Harvard / QuEra"
"Bell State","Demonstration of a quantum error detection code using a square lattice of four superconducting qubits","Córcoles","https://www.nature.com/articles/ncomms7979","2015","[[2,0,2]]","Superconducting circuit","","","","","","","","","","IBM Research"
"Bell State","Entanglement stabilization using ancilla-based parity detection and real-time feedback in superconducting circuits","Andersen","https://www.nature.com/articles/s41534-019-0185-4","2019","[[2,0,2]]","Superconducting circuit","","","","","","","","","","ETH Zurich"
"Bell State","Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements","Bultink","https://arxiv.org/abs/1905.12731","2020","[[2,0,2]]","Superconducting circuit","","","","","","","","","","Delft (DiCarlo)"
"Bacon-Shor Code","Fault-Tolerant Operation of a Quantum Error-Correction Code","Egan","https://arxiv.org/abs/2009.11482","2020","[[9,1,3]]","Ion traps","","","","","","","","","","Maryland / Duke / IonQ"
"Bacon-Shor Code","Quantum teleportation of physical qubits into logical code-spaces","Luo","https://arxiv.org/abs/2009.06242","2020","[[9,1,3]]","Photons","","","","","","","","","","USTC"
"Bacon-Shor Code","Logical computation demonstrated with a neutral atom quantum processor","Reichardt","https://arxiv.org/abs/2411.11822","2024","[[9,1,3]]","Neutral atoms","","","","","","","","","","Microsoft / QuEra"
"Four-qubit Code","Logical computation demonstrated with a neutral atom quantum processor","Reichardt","https://arxiv.org/abs/2411.11822","2024","[[4,1,2]], [[4,2,2]]","Neutral atoms","","","","","","","","","","Microsoft / QuEra"
"Cluster State","A quantum processor based on coherent transport of entangled atom arrays","Bluvstein","https://arxiv.org/abs/2112.03923","2021","1D with 12 qubits","Neutral atoms","","","","","","","","","","Harvard / QuEra"
"Four-qubit Code","Fault-tolerant quantum error detection","Linke","https://arxiv.org/abs/1611.06946","2017","[[4,1,2]]","Ion traps","","","","","","","","","","Maryland (Monroe)"
"Four-qubit Code","Experimental demonstration of fault-tolerant state preparation with superconducting qubits","Takita","https://arxiv.org/abs/1705.09259","2017","[[4,1,2]]","Superconducting circuit","","","","","","","","","","IBM Research"
"Four-qubit Code","Protecting quantum memories using coherent parity check codes","Roffe","https://arxiv.org/abs/1709.01866","2018","[[4,2,2]]","Superconducting circuit","","","","","","","","","","Durham / Sheffield"
"Four-qubit Code","Is error detection helpful on IBM 5Q chips ?","Vuillot","https://arxiv.org/abs/1705.08957","2018","[[4,2,2]]","Superconducting circuit","","","","","","","","","","IBM Research"
"Four-qubit Code","Testing quantum fault tolerance on small systems","Willsch","https://arxiv.org/abs/1805.05227","2018","[[4,2,2]]","Superconducting circuit","","","","","","","","","","IBM Research"
"Four-qubit Code","Fault-Tolerant Logical Gates in the IBM Quantum Experience","Harper","https://arxiv.org/abs/1806.02359","2019","[[4,2,2]]","Superconducting circuit","","","","","","","","","","IBM Research"
"Four-qubit Code","Resource Optimal Realization of Fault-Tolerant Quantum Circuit","Goudarzi","https://ieeexplore.ieee.org/document/9171796","2020","[[4,2,2]]","Superconducting circuit","","","","","","","","","","Unknown"
"Four-qubit Code","Error detection on quantum computers improves accuracy of chemical calculations","Urbanek","https://arxiv.org/abs/1910.00129","2020","[[4,2,2]]","Superconducting circuit","","","","","","","","","","IBM Research"
"Four-qubit Code","Experimental Characterization of Fault-Tolerant Circuits in Small-Scale Quantum Processors","Cane","https://arxiv.org/abs/2112.04076","2021","[[4,2,2]]","Superconducting circuit","","","","","","","","","","Southampton"
"Four-qubit Code","Comparative analysis of error mitigation techniques for variational quantum eigensolver implementations on IBM quantum system","Zhang","https://arxiv.org/abs/2206.07907","2022","[[4,2,2]]","Superconducting circuit","","","","","","","","","","Unknown"
"Four-qubit Code","Optical demonstration of quantum fault-tolerant threshold","Sun","https://arxiv.org/abs/2012.08927","2022","[[4,2,2]]","Photons","","","","","","","","","","USTC"
"Four-qubit Code","Encoding a magic state with beyond break-even fidelity","Gupta","https://arxiv.org/abs/2305.13581","2024","[[4,2,2]]","Superconducting circuit","","1","","3","?","","7","106","40","IBM Quantum"
"Four-qubit Code","End-to-End Quantum Simulation of a Chemical System","Dam","https://arxiv.org/abs/2409.05835","2024","[[4,2,2]]","Ion traps","Error detection yielded a 3% rejection
rate and the use of teleportation flags was responsible for the additional 50% rejection rate.","?","47%","9","?","?","13","66","24","Microsoft"
"Four-qubit Code","Fault-Tolerant Operation and Materials Science with Neutral Atom Logical Qubits","Bedalov","https://arxiv.org/abs/2412.07670","2024","[[4,2,2]]","Neutral atoms","","0","?","2","","","","","","Atom Computing"
"Color Code","Experimental Demonstration of Logical Magic State Distillation","Rodriguez","https://arxiv.org/abs/2412.15165","2024","[[7, 1, 3]], [[17,1,5]]","Neutral atoms","","0","3%, 0.4%","0","","","","","","Harvard / QuEra"
"Color Code","Scaling and logic in the color code on a superconducting quantum processor","Lacroix","https://arxiv.org/abs/2412.14256","2024","[[7, 1, 3]], [[17,1,5]]","Superconducting circuit","","30","100%","6, 18","","","","","","Google Quantum AI"
"Surface Code","Demonstrating dynamic surface codes","Eickbusch","https://arxiv.org/abs/2412.14360","2024","[[9,1,3]], [[25,1,5]]","Superconducting circuit","","54","100%","8, 24","","","","","","Google Quantum AI"
"Repetition Code","Realization of quantum error correction","Chiaverini","https://doi.org/10.1038/nature03074","2004","[3,1,3]","Ion traps","","1","100%","0","?","?","","","","NIST"
"Four-qubit Code","Error detection without post-selection in adaptive quantum circuits","Chertkov","https://doi.org/10.48550/arXiv.2509.25326","2025","[[4,2,2]]","Ion traps","Quantinuum H2-2, adaptive logical simulation, detected errors converted into random resets instead of post-selection, 4 ancilla qubits reused, qubit-reuse compilation, break-even for t<=6; 1000 shots","7","100%","4","","","28","","1940","Quantinuum"
"Color Code","Magic state cultivation on a superconducting quantum processor","Rosenfeld","https://doi.org/10.48550/arXiv.2512.13908","2025","[[7,1,3]]","Superconducting circuit","Willow processor. Magic state cultivation via fault-tolerant logical H_L measurement + postselection, kickback tomography (KT) characterization, |T> fidelity 0.9999(1); 40x improvement over injection; fault distance 3; error scales as p^3, RL-calibrated control, each QEC cycle = 30 two-qubit gates + 6 measurements","3","0.08","6","","","14","","216","Google Quantum AI"
"Surface Code","Magic state cultivation on a superconducting quantum processor","Rosenfeld","https://doi.org/10.48550/arXiv.2512.13908","2025","[[25, 1, 5]]","Superconducting circuit","Willow processor, cultivated |T> state grafted from d=3 color code into d=5 surface-code-compatible encoding, proof-of-principle code switching, 1 extension cycle + N-1 grafted-code cycles, decoded with Tesseract (A* most-likely-error decoder), LER ~7x higher than SI1000 simulation (leakage suspected), memory experiment up to N=9 QEC cycles","9","100%","24","","","54","","","Google Quantum AI"
"Carbon Code","Improved quantum processor logical error rates via correction and detection","Paetznick","https://www.nature.com/articles/s41586-026-10628-y","2026","[[12,2,4]]","Ion traps","Carbon = [[12,2,4]] self-dual CSS code, concatenation of [[4,2,2]] and [[6,2,2]] (Knill C4/C6 scheme); threshold ~3%, rate 1/6 at d=4; Quantinuum H2 trapped-ion QCCD; repeated error correction (up to 3 rounds) combining correction + detection with pre- and post-selection; measured logical error 0.017% (1 round), 0.3% (2 rounds), 0.5% (3 rounds), ~0.006% per-round fit in Table 1; 4.7x-800x gain over physical baselines; two-qubit gate count is reported only per round (98 CNOTs/round, >100 physical CNOTs per EC cycle), no per-experiment total tabulated; carbon experiments from arXiv:2404.02280","3","40-71%","19","","","31","","98 per round","Microsoft / Quantinuum"
"Color Code","Improved quantum processor logical error rates via correction and detection","Paetznick","https://www.nature.com/articles/s41586-026-10628-y","2026","[[16,4,4]]","Ion traps","Tesseract subsystem colour code from self-dual [[16,6,4]] tesseract code (2 encoded qubits sacrificed as gauge qubits), distance 4, 4 logical qubits; one code block = 18 physical qubits (16 data + 2 reused ancillae); X and Z stabilisers measured in parallel, 8 CNOTs per weight-4 measurement pair = 64 CNOTs/round; Quantinuum H2; up to 5 rounds of post-selected fault-tolerant EC; graph states up to 12 logical qubits (cube graph = 12 logical CNOTs, 12-qubit cat = 11 logical CNOTs); acceptance >=50% (50-90%); logical error ~0.02% per round (2.1e-4/round fit); two-qubit gate count reported only per round (64 CNOTs/round), no per-experiment total tabulated; tesseract experiments from arXiv:2409.04628","5","50-90%","2","","","18","","64 per round","Microsoft / Quantinuum"