Abstract
Entanglement is one of the most important resources in quantum computing, cryptography and sensing. However, entanglement is also fragile, and its potential advantages are hindered by decoherence effects in experiments. Here we experimentally realize entangled logical qubits with a bosonic quantum module by encoding quantum information into spatially separated microwave modes. The entanglement is protected by repetitive quantum error correction, which improves the coherence time of the entangled logical qubits compared with their unprotected counterparts by 45%. In addition, we demonstrate the violation of the Bell inequality by the purified entangled logical qubits via independent error detection and post-selection on each logical qubit, resulting in measured Bell signals that surpass the classical bound. The protected entangled logical qubits could be applied in future explorations of quantum foundations and applications of quantum networks.
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Data availability
The data generated in this study have been deposited in the Figshare database under accession code https://doi.org/10.6084/m9.figshare.22759031 ref. 43.
Code availability
The code used for this study is available from the corresponding authors upon reasonable request.
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Acknowledgements
This work was supported by the National Natural Science Foundation of China (grant nos. 92165209, 11925404, 12204052, 92265210, 12061131011, 92365301, 11890704 and 92365206), Innovation Program for Quantum Science and Technology (2021ZD0300203 and 2021ZD0301800), Natural Science Foundation of Beijing (grant no. Z190012), Fundamental Research Funds for the Central Universities, China Postdoctoral Science Foundation (BX2021167 and 2023M733409), grant no. 2019GQG1024 from the Institute for Guo Qiang, Tsinghua University and the National Key Research and Development Program of China (grant no. 2017YFA0304303). This work was partially carried out at the USTC Center for Micro and Nanoscale Research and Fabrication.
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L.S. and C.-L.Z. conceived the experiments. W.C., X.M. and W.W. performed the experiments and analysed the data with the assistance of J.Z., Y.M., X.P., Z.H. and X.L. L.S. directed the project. C.-L.Z. provided theoretical support. W.C., X.M., W.W. and J.Z. performed the numerical simulations. W.C., H.W. and Y.S. fabricated the 3D cavity. G.X. and H.Y. fabricated the tantalum transmon qubits and provided further experimental support. W.C., X.M., W.W., J.Z., C.-L.Z. and L.S. wrote the paper with feedback from all authors.
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Supplementary Figs. 1–15, Tables 1–9, Sects. I–VII, and References.
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Source data of Fig. 4b.
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Cai, W., Mu, X., Wang, W. et al. Protecting entanglement between logical qubits via quantum error correction. Nat. Phys. (2024). https://doi.org/10.1038/s41567-024-02446-8
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DOI: https://doi.org/10.1038/s41567-024-02446-8
