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<p>Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise characteristics of real quantum devices, limiting their practical performance. This work introduces Variational Graphical Quantum Error Correction (VGQEC), a learning-based framework that enhances standard quantum codes by embedding tunable parameters into their associated Quon graphs. Consequently, VGQEC codes can adapt to device-specific noise models and interpolate between different code families, effectively integrating their respective strengths. As an application, we fine-tune the three-qubit repetition code and discover a compact code for amplitude damping noise. Furthermore, within a thermal relaxation model guided by experimental data, we refine the five-qubit [[5,1,3]] code, achieving near-optimal numerical performance. Finally, we experimentally demonstrate the effectiveness of the three-qubit VGQEC code in low-to-medium noise regime with a photonic system, highlighting its potential for real-world applications.</p>

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Variational graphical quantum error correction codes

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年5月15日

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  • Yuguo Shao,
  • Yong-Chang Li,
  • Fuchuan Wei,
  • Hao Zhan,
  • Ben Wang,
  • Zhaohui Wei,
  • Lijian Zhang,
  • Zhengwei Liu

摘要

Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise characteristics of real quantum devices, limiting their practical performance. This work introduces Variational Graphical Quantum Error Correction (VGQEC), a learning-based framework that enhances standard quantum codes by embedding tunable parameters into their associated Quon graphs. Consequently, VGQEC codes can adapt to device-specific noise models and interpolate between different code families, effectively integrating their respective strengths. As an application, we fine-tune the three-qubit repetition code and discover a compact code for amplitude damping noise. Furthermore, within a thermal relaxation model guided by experimental data, we refine the five-qubit [[5,1,3]] code, achieving near-optimal numerical performance. Finally, we experimentally demonstrate the effectiveness of the three-qubit VGQEC code in low-to-medium noise regime with a photonic system, highlighting its potential for real-world applications.