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Realizing repeated quantum error correction in a distance-three surface code


Quantum computers hold the promise of solving computational problems that are intractable using conventional methods1. For fault-tolerant operation, quantum computers must correct errors occurring owing to unavoidable decoherence and limited control accuracy2. Here we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors3,4,5,6. Using 17 physical qubits in a superconducting circuit, we encode quantum information in a distance-three logical qubit, building on recent distance-two error-detection experiments7,8,9. In an error-correction cycle taking only 1.1 μs, we demonstrate the preservation of four cardinal states of the logical qubit. Repeatedly executing the cycle, we measure and decode both bit-flip and phase-flip error syndromes using a minimum-weight perfect-matching algorithm in an error-model-free approach and apply corrections in post-processing. We find a low logical error probability of 3% per cycle when rejecting experimental runs in which leakage is detected. The measured characteristics of our device agree well with a numerical model. Our demonstration of repeated, fast and high-performance quantum error-correction cycles, together with recent advances in ion traps10, support our understanding that fault-tolerant quantum computation will be practically realizable.

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Fig. 1: Device concept, architecture and performance.
Fig. 2: Stabilizer circuits and their characterization.
Fig. 3: The surface-code cycle, fidelity of logical-state initialization and average error syndromes.
Fig. 4: Logical-state preservation and error per cycle.

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All data are available from the corresponding author on reasonable request.


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We are grateful for valuable discussions with Q. Ficheux and C. Lledó. We acknowledge the contributions of R. Boell to the experimental setup and M. Kerschbaum for early work on the two-qubit gate implementation. The team in Zurich acknowledges financial support by the Office of the Director of National Intelligence (ODNI), Intelligence Advanced Research Projects Activity (IARPA), through the U.S. Army Research Office grant W911NF-16-1-0071, by the EU Flagship on Quantum Technology H2020-FETFLAG-2018-03 project 820363 OpenSuperQ, by the National Center of Competence in Research ‘Quantum Science and Technology’ (NCCR QSIT), a research instrument of the Swiss National Science Foundation (SNSF, grant number 51NF40-185902), by the SNSF R’Equip grant 206021-170731, by the EU programme H2020-FETOPEN project 828826 Quromorphic and by ETH Zurich. S.K. acknowledges financial support from Fondation Jean-Jacques et Félicia Lopez-Loreta and the ETH Zurich Foundation. The work in Sherbrooke was undertaken thanks in part to funding from NSERC, Canada First Research Excellence Fund, ARO grant W911NF-18-1-0411, the Ministère de l’Économie et de l’Innovation du Québec and U.S. Department of Energy, Office of Science, National Quantum Information Science Research Centers, Quantum Systems Accelerator. M.M. acknowledges support by the U.S. Army Research Office grant W911NF-16-1-0070. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the ODNI, IARPA or the U.S. Government.

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Authors and Affiliations



S.K., N.L. and A.R. planned the experiments, S.K. and N.L. performed the main experiment and S.K. and N.L. analysed the data. F.S., A.R. and C.K.A. designed the device and S.K., A.R. and G.J.N. fabricated the device. N.L., C.H. and S.L. developed the experimental software framework and A.R., C.H., N.L., S.K. and S.L. developed the control and calibration software routines. A.R., J.H., S.K. and C.H. designed and built elements of the room-temperature setup and S.K., A.R., C.H., S.L., N.L. and F.S. maintained the experimental setup. S.K., N.L., A.R., C.H., S.L. and C.K.A. characterized and calibrated the device and the experimental setup. E.G., A.D.P. and C.L. performed the numerical simulations. M.M. provided guidance on logical qubit evaluation methodology aspects. S.K., N.L., A.R., C.H. and S.L. prepared the figures for the manuscript and S.K., N.L., A.R., C.E. and A.W. wrote the manuscript, with inputs from all co-authors. A.B., C.E. and A.W. supervised the work.

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Correspondence to Sebastian Krinner.

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This file contains sections I–XIII, including Supplementary Figs. 1–14, Supplementary Tables 1–3 and Supplementary References.

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Krinner, S., Lacroix, N., Remm, A. et al. Realizing repeated quantum error correction in a distance-three surface code. Nature 605, 669–674 (2022).

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