"MSD Protocol","Article Title","First Author","Link","Year","Platform","Notes","Fidelity","Acceptance Rate (%)","Magic State","QEC Code"," ""Post selection""","Experiment Type"
"4 to 2","Experimental purification of two-atom entanglement","Reichle","https://doi.org/10.1038/nature05146","2006","Ion traps","9Be+ atomic ion qubits. Distillation: Two noisy entangled pairs were created and distilled into one higher-fidelity pair available for further use. Unpurified fidelity of 0.614 +- 0.0015, and a purified fidelity of 0.629 +- 0.0015","0.629-15+15","","","","","Distillation"
"","Realization of real-time fault-tolerant quantum error correction","Ryan-Anderson","https://doi.org/10.1103/PhysRevX.11.041058","2021","Ion traps","","0.978-6+6","100","|T>","Steane","","Preparation"
"","Demonstration of fault-tolerant universal quantum gate operations","Postler","https://doi.org/10.1038/s41586-022-04721-1","2021","Ion traps","","0.994-14+5","13.7","|H>","Steane","","Preparation"
"","Experimental fault-tolerant code switching","Pogorelov","https://doi.org/10.1038/s41567-024-02727-2","2024","Ion traps","","0.963-4+4","19","|T>","Steane, [[10,1,2]]","Yes","Code Switching"
"","Fault-tolerant control of an error-corrected qubit","Egan","https://doi.org/10.1038/s41586-021-03928-y","2020","Ion traps","","0.972-12+12","100","|H>","Bacon-Shor","","Preparation"
"","Logical-qubit operations in an error-detecting surface code","Marques","https://doi.org/10.1038/s41567-021-01423-9","2021","Superconducting qubits","","0.966","<25","|T>","Surface code","","Preparation"
"","Encoding a magic state with beyond break-even fidelity","Gupta","https://doi.org/10.1038/s41586-023-06846-3","2023","Superconducting qubits","","0.9877-11+11","17","|CZ>","Surface code","","Preparation"
"","Logical Magic State Preparation with Fidelity beyond the Distillation Threshold on a Superconducting Quantum Processor","Ye","https://doi.org/10.1103/PhysRevLett.131.210603","2023","Superconducting qubits","","0.8771-9+9","73.41","|T>","Surface code","","Preparation"
"","Logical Magic State Preparation with Fidelity beyond the Distillation Threshold on a Superconducting Quantum Processor","Ye","https://doi.org/10.1103/PhysRevLett.131.210603","2023","Superconducting qubits","","0.9090-9+9","73.41","|H>","Surface code","","Preparation"
"","Magic State Injection on IBM Quantum Processors Above the Distillation Threshold","Kim","https://arxiv.org/abs/2412.01446","2024","Superconducting qubits","","0.8806-2+2","36.3","|H>","Surface code","","Injection"
"5 to 1","Experimental Demonstration of Logical Magic State Distillation","Rodriguez","https://arxiv.org/abs/2412.15165","2024","Neutral atoms","","0.994-4+3","1","|M>","Steane","","Preparation and Distillation"
"","Scaling and logic in the color code on a superconducting quantum processor","Lacroix","https://arxiv.org/abs/2412.14256","2024","Superconducting qubits","Post-selected logical state tomography measurements","0.9992-15+3","75.2","|T>","Steane","Yes","Preparation and Injection"
"","Scaling and logic in the color code on a superconducting quantum processor","Lacroix","https://arxiv.org/abs/2412.14256","2024","Superconducting qubits","Post-selected logical state tomography measurements","0.9959-37+38","74.6","|H>","Steane","Yes","Preparation and Injection"
"","Experimental demonstration of high-fidelity logical magic states from code switching","Daguerre","https://doi.org/10.48550/arXiv.2506.14169","2025","Ion traps","","0.99949-27+27","82.58","|T>","[[15,1,3]], Steane","","Code Switching"
"","Magic state cultivation on a superconducting quantum processor","Rosenfeld","https://doi.org/10.48550/arXiv.2512.13908","2025","Superconducting qubits","Willow processor, fault-tolerant logical Hadamard measurement projects onto |T> axis, kickback tomography characterization, 40x improvement over injection, decoded with Tesseract, error scales as p^3, RL-calibrated, includes 3 QEC cycles + 2 cultivation rounds","0.9999-1+1","8","|T>","Steane code to d=5 (grafted) Surface code","Yes","Cultivation + Grafting"