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Real-time quantum error correction beyond break-even


The ambition of harnessing the quantum for computation is at odds with the fundamental phenomenon of decoherence. The purpose of quantum error correction (QEC) is to counteract the natural tendency of a complex system to decohere. This cooperative process, which requires participation of multiple quantum and classical components, creates a special type of dissipation that removes the entropy caused by the errors faster than the rate at which these errors corrupt the stored quantum information. Previous experimental attempts to engineer such a process1,2,3,4,5,6,7 faced the generation of an excessive number of errors that overwhelmed the error-correcting capability of the process itself. Whether it is practically possible to utilize QEC for extending quantum coherence thus remains an open question. Here we answer it by demonstrating a fully stabilized and error-corrected logical qubit whose quantum coherence is substantially longer than that of all the imperfect quantum components involved in the QEC process, beating the best of them with a coherence gain of G = 2.27 ± 0.07. We achieve this performance by combining innovations in several domains including the fabrication of superconducting quantum circuits and model-free reinforcement learning.

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Fig. 1: Experimental system.
Fig. 2: QEC implementation and optimization.
Fig. 3: System coherence.
Fig. 4: Analysis of error syndromes.

Data availability

The data that support the findings of this study are available from the corresponding authors upon a request.

Code availability

The open-source implementation of the proximal policy optimization algorithm is available in ref. 29. The custom code used for quantum control optimization, data acquisition, analysis and visualization is available from the corresponding authors upon a request.


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We acknowledge discussions with R. Cortiñas, J. Claes and A. Mi. We thank B. Huard for feedback on the manuscript. This research was supported by the US Army Research Office under grants W911NF-18-1-0212 and W911NF-16-1-0349, and by the US Department of Energy, Office of Science, National Quantum Information Science Research Centers, Co-design Center for Quantum Advantage (C2QA) under contract number DE-SC0012704. The views and conclusions contained in this document are those of the authors and should not be interpreted as representing official policies, either expressed or implied, of the US Government. The US Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation herein. The use of fabrication facilities was supported by the Yale Institute for Nanoscience and Quantum Engineering and the Yale SEAS Cleanroom.

Author information

Authors and Affiliations



V.V.S., A.M. and A.E. built the experimental setup. R.J.S. contributed to experimental apparatus. I.T., S.G. and L.F. fabricated the transmon chip. B.R., S.S. and S.M.G. developed the theory. B.R., V.V.S., A.E. and B.L.B. developed dissipative oscillator cooling. A.E., V.V.S. and A.Z.D. developed the state initialization technique. V.V.S. implemented RL, carried out the experiments and analysed data. V.V.S., A.E., B.R. and M.H.D. regularly discussed the project and provided insight. M.H.D. supervised the project. V.V.S. and M.H.D. wrote the manuscript with feedback from all authors.

Corresponding authors

Correspondence to V. V. Sivak or M. H. Devoret.

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Competing interests

R.J.S., L.F. and M.H.D. are founders, and R.J.S. and L.F. are shareholders of Quantum Circuits, Inc.

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Nature thanks Atsushi Noguchi and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Supplementary information

Supplementary Information

This file contains the following four sections and additional references: I. Experimental setup and sample parameters; II. Calibration and characterization experiments; III. Quantum control optimization; and IV. QEC of the grid code.

Peer Review File

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Sivak, V.V., Eickbusch, A., Royer, B. et al. Real-time quantum error correction beyond break-even. Nature 616, 50–55 (2023).

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