Experiments
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Quantum error correction
Implementations of QEC codes: code, [[n,k,d]] parameters, platform, rounds and more.
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| Paper | ||||||
|---|---|---|---|---|---|---|
| Improved quantum processor logical error rates via correction and detection · Paetznick et al. | 2026 | Ion traps | Carbon Code | [[12,2,4]] | Microsoft / Quantinuum | 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 |
| Improved quantum processor logical error rates via correction and detection · Paetznick et al. | 2026 | Ion traps | Color Code | [[16,4,4]] | Microsoft / Quantinuum | 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 |
| Error detection without post-selection in adaptive quantum circuits · Chertkov et al. | 2025 | Ion traps | Four-qubit Code | [[4,2,2]] | Quantinuum | 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 |
| Magic state cultivation on a superconducting quantum processor · Rosenfeld et al. | 2025 | Superconducting circuit | Color Code | [[7,1,3]] | Google Quantum AI | 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 |
| Magic state cultivation on a superconducting quantum processor · Rosenfeld et al. | 2025 | Superconducting circuit | Surface Code | [[25, 1, 5]] | Google Quantum AI | 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 |
| Hardware-efficient quantum error correction using concatenated bosonic qubits · Putterman et al. | 2024 | Superconducting circuit | Repetition Code | [[3,1,3]], [[5,1,5]] | Amazon (AWS) | Repetition cat codes below threshold |
| Quantum error correction below the surface code threshold · Acharya et al. | 2024 | Superconducting circuit | Repetition Code | [3,1,3]-[29,1,29] | Google Quantum AI | Repetition codes below threshold |
| Quantum error correction below the surface code threshold · Acharya et al. | 2024 | Superconducting circuit | Surface Code | [[9,1,3]], [[25,1,5]], [[49,1,7]] | Google Quantum AI | Surface codes below threshold |
| Logical computation demonstrated with a neutral atom quantum processor · Reichardt et al. | 2024 | Neutral atoms | Bacon-Shor Code | [[9,1,3]] | Microsoft / QuEra | |
| Logical computation demonstrated with a neutral atom quantum processor · Reichardt et al. | 2024 | Neutral atoms | Four-qubit Code | [[4,1,2]], [[4,2,2]] | Microsoft / QuEra | |
| Encoding a magic state with beyond break-even fidelity · Gupta et al. | 2024 | Superconducting circuit | Four-qubit Code | [[4,2,2]] | IBM Quantum | |
| End-to-End Quantum Simulation of a Chemical System · Dam et al. | 2024 | Ion traps | Four-qubit Code | [[4,2,2]] | Microsoft | Error detection yielded a 3% rejection rate and the use of teleportation flags was responsible for the additional 50% rejection rate. |
| Fault-Tolerant Operation and Materials Science with Neutral Atom Logical Qubits · Bedalov et al. | 2024 | Neutral atoms | Four-qubit Code | [[4,2,2]] | Atom Computing | |
| Experimental Demonstration of Logical Magic State Distillation · Rodriguez et al. | 2024 | Neutral atoms | Color Code | [[7, 1, 3]], [[17,1,5]] | Harvard / QuEra | |
| Scaling and logic in the color code on a superconducting quantum processor · Lacroix et al. | 2024 | Superconducting circuit | Color Code | [[7, 1, 3]], [[17,1,5]] | Google Quantum AI | |
| Demonstrating dynamic surface codes · Eickbusch et al. | 2024 | Superconducting circuit | Surface Code | [[9,1,3]], [[25,1,5]] | Google Quantum AI | |
| Suppressing quantum errors by scaling a surface code logical qubit · Acharya et al. | 2023 | Superconducting circuit | Repetition Code | [3,1,3]-[25,1,25] | Google Quantum AI | Repetition codes below threshold |
| Suppressing quantum errors by scaling a surface code logical qubit · Acharya et al. | 2023 | Superconducting circuit | Surface Code | [[9,1,3]]-[[25,1,5]] | Google Quantum AI | Repetition codes below threshold |
| Logical quantum processor based on reconfigurable atom arrays · Bluvstein et al. | 2023 | Neutral atoms | Surface Code | [[9,1,3]], [[25,1,5]], [[49,1,7]] | Harvard / QuEra | |
| Logical quantum processor based on reconfigurable atom arrays · Bluvstein et al. | 2023 | Neutral atoms | Color Code | [[7,1,3]], [[8,3,2]] | Harvard / QuEra | |
| Comparative analysis of error mitigation techniques for variational quantum eigensolver implementations on IBM quantum system · Zhang et al. | 2022 | Superconducting circuit | Four-qubit Code | [[4,2,2]] | Unknown | |
| Optical demonstration of quantum fault-tolerant threshold · Sun et al. | 2022 | Photons | Four-qubit Code | [[4,2,2]] | USTC | |
| Realizing repeated quantum error correction in a distance-three surface code · Krinner et al. | 2021 | Superconducting circuit | Surface Code | [[9,1,3]] | ETH Zurich | |
| A quantum processor based on coherent transport of entangled atom arrays · Bluvstein et al. | 2021 | Neutral atoms | Surface Code | [[13,1,3]] surface code, [[16,2,2]] toric code | Harvard / QuEra | |
| A quantum processor based on coherent transport of entangled atom arrays · Bluvstein et al. | 2021 | Neutral atoms | Color Code | [[7,1,3]] | Harvard / QuEra | |
| A quantum processor based on coherent transport of entangled atom arrays · Bluvstein et al. | 2021 | Neutral atoms | Cluster State | 1D with 12 qubits | Harvard / QuEra | |
| Experimental Characterization of Fault-Tolerant Circuits in Small-Scale Quantum Processors · Cane et al. | 2021 | Superconducting circuit | Four-qubit Code | [[4,2,2]] | Southampton | |
| Benchmarking near-term devices with quantum error correction · Wootton et al. | 2020 | Superconducting circuit | Repetition Code | [3,1,3]-[22,1,22] | Google Quantum AI | |
| Exponential suppression of bit or phase flip errors with repetitive error correction · Chen et al. | 2020 | Superconducting circuit | Repetition Code | [3,1,3]-[11,1,11] | Google Quantum AI | |
| Exponential suppression of bit or phase flip errors with repetitive error correction · Chen et al. | 2020 | Superconducting circuit | Four-qubit Code | [[4,1,2]] | Google Quantum AI | |
| Repeated Quantum Error Detection in a Surface Code · Andersen et al. | 2020 | Superconducting circuit | Surface Code | [[4,1,2]] | ETH Zurich | |
| Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements · Bultink et al. | 2020 | Superconducting circuit | Bell State | [[2,0,2]] | Delft (DiCarlo) | |
| Fault-Tolerant Operation of a Quantum Error-Correction Code · Egan et al. | 2020 | Ion traps | Bacon-Shor Code | [[9,1,3]] | Maryland / Duke / IonQ | |
| Quantum teleportation of physical qubits into logical code-spaces · Luo et al. | 2020 | Photons | Bacon-Shor Code | [[9,1,3]] | USTC | |
| Resource Optimal Realization of Fault-Tolerant Quantum Circuit · Goudarzi et al. | 2020 | Superconducting circuit | Four-qubit Code | [[4,2,2]] | Unknown | |
| Error detection on quantum computers improves accuracy of chemical calculations · Urbanek et al. | 2020 | Superconducting circuit | Four-qubit Code | [[4,2,2]] | IBM Research | |
| Experimental exploration of five-qubit quantum error correcting code with superconducting qubits · Gong et al. | 2019 | Superconducting circuit | [[5,1,3]] Perfect Code | [[5,1,3]] | IBM Research | |
| Entanglement stabilization using ancilla-based parity detection and real-time feedback in superconducting circuits · Andersen et al. | 2019 | Superconducting circuit | Bell State | [[2,0,2]] | ETH Zurich | |
| Fault-Tolerant Logical Gates in the IBM Quantum Experience · Harper et al. | 2019 | Superconducting circuit | Four-qubit Code | [[4,2,2]] | IBM Research | |
| A repetition code of 15 qubits · Wootton et al. | 2018 | Superconducting circuit | Repetition Code | [3,1,3]-[8,1,8] | IBM Research | |
| Protecting quantum memories using coherent parity check codes · Roffe et al. | 2018 | Superconducting circuit | Four-qubit Code | [[4,2,2]] | Durham / Sheffield | |
| Is error detection helpful on IBM 5Q chips ? · Vuillot et al. | 2018 | Superconducting circuit | Four-qubit Code | [[4,2,2]] | IBM Research | |
| Testing quantum fault tolerance on small systems · Willsch et al. | 2018 | Superconducting circuit | Four-qubit Code | [[4,2,2]] | IBM Research | |
| Experimental demonstration of fault-tolerant state preparation with superconducting qubits · Takita et al. | 2017 | Superconducting circuit | Color Code | [[4,2,2]] | IBM Research | |
| Fault-tolerant quantum error detection · Linke et al. | 2017 | Ion traps | Color Code | [[4,2,2]] | Maryland (Monroe) | |
| Fault-tolerant quantum error detection · Linke et al. | 2017 | Ion traps | Four-qubit Code | [[4,1,2]] | Maryland (Monroe) | |
| Experimental demonstration of fault-tolerant state preparation with superconducting qubits · Takita et al. | 2017 | Superconducting circuit | Four-qubit Code | [[4,1,2]] | IBM Research | |
| Repeated quantum error correction on a continuously encoded qubit by real-time feedback · Cramer et al. | 2016 | Superconducting circuit | Repetition Code | [3,1,3] | Yale (Schoelkopf) | |
| Detecting bit-flip errors in a logical qubit using stabilizer measurements · Riste et al. | 2015 | Superconducting circuit | Repetition Code | [3,1,3] | Delft (DiCarlo) | |
| Demonstration of a quantum error detection code using a square lattice of four superconducting qubits · Córcoles et al. | 2015 | Superconducting circuit | Bell State | [[2,0,2]] | IBM Research | |
| State preservation by repetitive error detection in a superconducting quantum circuit · Kelly et al. | 2014 | Superconducting circuit | Repetition Code | [3,1,3]-[5,1,5] | UCSB / Google | |
| Quantum error correction in a solid-state hybrid spin register · Waldherr et al. | 2014 | NV centers | Repetition Code | [[3,1,3]] | Delft (Hanson) | |
| Experimental demonstration of a graph state quantum error-correction code · Bell et al. | 2014 | Photons | Surface Code | [[4,1,2]] | University of Bristol | |
| Experimental Quantum Computations on a Topologically Encoded Qubit · Nigg et al. | 2014 | Ion traps | Color Code | [[7,1,3]] | Innsbruck (Blatt) | |
| Realization of Three-Qubit Quantum Error Correction with Superconducting Circuits · Reed et al. | 2012 | Superconducting circuit | Repetition Code | [3,1,3] | Yale (Schoelkopf) | |
| Experimental implementation of encoded logical qubit operations in a perfect quantum error correcting code · Zhang et al. | 2012 | NMR | [[5,1,3]] Perfect Code | [[5,1,3]] | IQC Waterloo | |
| Experimental Repetitive Quantum Error Correction · Schindler et al. | 2011 | Ion traps | Repetition Code | [3,1,3] | Innsbruck (Blatt) | |
| Demonstration of Sufficient Control for Two Rounds of Quantum Error Correction in a Solid-State Ensemble Quantum Information Processor · Moussa et al. | 2011 | NMR | Repetition Code | [3,1,3] | IQC Waterloo | |
| Experimental quantum error correction with high fidelity · Zhang et al. | 2011 | NMR | Repetition Code | [3,1,3] | IQC Waterloo | |
| Realization of quantum error correction · Chiaverini et al. | 2004 | Ion traps | Repetition Code | [3,1,3] | NIST | |
| Benchmarking Quantum Computers: The Five-Qubit Error Correcting Code · Knill et al. | 2001 | NMR | [[5,1,3]] Perfect Code | [[5,1,3]] | Los Alamos / MIT | |
| Experimental Quantum Error Correction · Cory et al. | 1998 | NMR | Repetition Code | [3,1,3] | Los Alamos / MIT |
Magic states
Magic state preparation, distillation and code switching, with fidelity and acceptance rate.
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Entangled state error
Bell-state and two-qubit gate errors over time.
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Qubit count
Physical qubit count records per platform.
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Coherence times
T1 and T2 of physical qubits.
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