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Information processing technology based on the basic principle of quantum mechanics shows great potential applications in computing, sensing and other fields, and is far superior to classical technology. With the advance of experimental technology, quantum control technology develops rapidly. Compared with other quantum information processing platforms, the superconducting system based on solid materials has the advantages of accurate quantum controllability, excellent quantum coherence and the potential for large-scale integration. Therefore, superconducting quantum system is one of the most promising platforms for quantum information processing. The existing superconducting circuits, which can integrate about one hundred qubits, have already demonstrated the advantages of quantum systems, but further development is limited by system noise. In order to break through this bottleneck, quantum error correction technology, which is developed from the classical error correction technology, has attracted extensive attention. Here, we mainly summarize the research progress of quantum error correction in superconducting quantum systems including the basic principles of superconducting quantum systems, the quantum error correction codes, the related control techniques and the recent applications. At the end of the article, we summarize seven key problems in this field.
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Keywords:
- quantum error correction/
- superconducting circuits/
- fault-tolerant quantum computation/
- bosonic codes
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时间 文献 编码 逻辑$ T_{1} $(物理$ T_{1} $)$/\text{µ} {\rm{s}}$ 逻辑 $ T_{2} $(物理$ T_{2} $)$/\text{µ} {\rm{s}}$ 2012 耶鲁大学[68] $ \left[3, 1, 3\right] $重复码 / / 2014 加州大学圣芭芭拉分校[69] $ \left[3, 1, 3\right] $, $ \left[5, 1, 5\right] $重复码 / / 2015 代尔夫特理工大学[25] $ \left[3, 1, 3\right] $重复码 / / 2017 IBM[71] 4比特颜色码 / / 2018 巴塞尔大学(University of Basel)[72] $ \left[8, 1, 8\right] $重复码 / / 2018 德国于利希研究中心(Forschungszentrum Jülich)[90] 4比特颜色码 / / 2019 悉尼大学[91] $ [4, 2, 2] $错误检测码 / / 2019 中国科学技术大学[92] $ [[5, 1, 3]] $编码 / / 2020 苏黎世联邦理工学院[93] $ [[4, 1, 2]] $表面码 $ 62.7\pm9.4 $($ 16.8^{*} $) $ 72.5\pm32.9 $($ 21.5^{*} $) 2021 谷歌公司[84] 实现表面码的基态 / / 2021 中国科学技术大学[31] $ [[9, 1, 3]] $表面码 $ 137.8 $($ 36.6^{*} $) / 2021 苏黎世联邦理工学院[94] $ [[9, 1, 3]] $表面码 $ 16.4 $($ 32.5 $) $ 18.2 $($ 37.5 $) 2021 谷歌公司[73] $ [11, 1, 11] $重复码以及$ [[4, 1, 2]] $表面码 / / 2022 苏黎世联邦理工学院[24] $ [[4, 1, 2]] $表面码 / / 2022 IBM[95] $ [[9, 1, 3]] $Heavy-hexagon编码 / / 2022 谷歌公司[8] $ [[25, 1, 5]] $表面码以及$ [25, 1, 25] $重复码 / / 
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