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<p>Quantum computing can solve problems faster than classical computing, but the decoherence problem still affects the accuracy of calculations. Quantum error correction uses the method of encoding the information of multiple physical qubits into a single logical qubit, so that quantum information is no longer determined by a single data qubit, and the error is corrected by the decoding algorithm to achieve fault-tolerant quantum computing. The decoder based on machine learning has shown excellent performance, but most of them are based on multi-layer perceptron (MLP), and gradient explosion or gradient disappearance is unavoidable during the training process. We apply Kolmogorov–Arnold network to rotated surface codes, which can avoid the above problems in the model training process. Based on the experiments, the thresholds for the symmetric depolarization noise model were established for various code distances and error rates. These thresholds were then compared with the performance of the minimum weight perfect matching (MWPM) and the feedforward neural network (FFNN). The thresholds for KAN, MWPM, and FFNN are 0.157, 0.142, and 0.152, respectively. The results show that the decoder threshold using the KAN architecture is improved by 3<InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11128_2025_4826_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">\(\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mo>%</mo> </math></EquationSource> </InlineEquation> compared to FFNN. Finally, the performance of the three decoders under different noise error models is analyzed. Empirical results consistently show that our proposed decoder outperforms MWPM and FFNN approaches, achieving superior performance on the evaluated metrics.</p>

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Quantum error correction with Kolmogorov–Arnold network for rotated surface codes decoding

  • 期刊论文

  • 发表日期：

    2025年7月5日

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  • Zaixu Fan,
  • Cewen Tian,
  • Bo Xiao,
  • Xiaoxuan Guo,
  • Hongyang Ma

摘要

Quantum computing can solve problems faster than classical computing, but the decoherence problem still affects the accuracy of calculations. Quantum error correction uses the method of encoding the information of multiple physical qubits into a single logical qubit, so that quantum information is no longer determined by a single data qubit, and the error is corrected by the decoding algorithm to achieve fault-tolerant quantum computing. The decoder based on machine learning has shown excellent performance, but most of them are based on multi-layer perceptron (MLP), and gradient explosion or gradient disappearance is unavoidable during the training process. We apply Kolmogorov–Arnold network to rotated surface codes, which can avoid the above problems in the model training process. Based on the experiments, the thresholds for the symmetric depolarization noise model were established for various code distances and error rates. These thresholds were then compared with the performance of the minimum weight perfect matching (MWPM) and the feedforward neural network (FFNN). The thresholds for KAN, MWPM, and FFNN are 0.157, 0.142, and 0.152, respectively. The results show that the decoder threshold using the KAN architecture is improved by 3 \(\%\) % compared to FFNN. Finally, the performance of the three decoders under different noise error models is analyzed. Empirical results consistently show that our proposed decoder outperforms MWPM and FFNN approaches, achieving superior performance on the evaluated metrics.