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<p>Quantum computers provide exponential computational advantages over classical systems; however, their practical deployment remains constrained by elevated error rates. To tackle decoding challenges in quantum error correction (QEC), we propose the KAT decoder, a hybrid architecture that integrates Kolmogorov-Arnold Networks (KAN) with the Transformer framework for decoding rotated surface codes. Unlike conventional Transformer decoders that use multi-layer perceptrons (MLPs), KAT replaces MLP layers with spline-parameterized KANs, enabling adaptive nonlinear feature optimization and superior modeling of complex error correlations. Experiments demonstrate that KAT achieves thresholds of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbf {4.857} \varvec{\times } \textbf{10}^{\varvec{-3}}\)</EquationSource> </InlineEquation> (circuit-level noise) and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbf {0.1594}\)</EquationSource> </InlineEquation> (depolarizing noise), reducing logical error rates by 13% and 5% compared to the Minimum Weight Perfect Matching (MWPM) and Feedforward Neural Network (FFNN) decoders. For rotated surface codes with code distances <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathbf {d=3,5,7,9}\)</EquationSource> </InlineEquation>, KAT mitigates boundary connectivity and noise propagation by leveraging its multi-head attention mechanism to model global spatiotemporal correlations. Meanwhile, under the circuit-level noise model, KAT outperforms the Transformer across code distances <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\varvec{d=5,7,9,11}\)</EquationSource> </InlineEquation>. This result underscores KAT’s application potential in quantum error correction and demonstrates the extensive prospects of deep learning techniques in quantum information processing.</p>

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A Hybrid Architecture Decoder Integrating Kolmogorov-Arnold Network and Transformer for Decoding Rotating Surface Codes

  • 期刊论文

  • 发表日期：

    2025年11月8日

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

摘要

Quantum computers provide exponential computational advantages over classical systems; however, their practical deployment remains constrained by elevated error rates. To tackle decoding challenges in quantum error correction (QEC), we propose the KAT decoder, a hybrid architecture that integrates Kolmogorov-Arnold Networks (KAN) with the Transformer framework for decoding rotated surface codes. Unlike conventional Transformer decoders that use multi-layer perceptrons (MLPs), KAT replaces MLP layers with spline-parameterized KANs, enabling adaptive nonlinear feature optimization and superior modeling of complex error correlations. Experiments demonstrate that KAT achieves thresholds of \(\mathbf {4.857} \varvec{\times } \textbf{10}^{\varvec{-3}}\) (circuit-level noise) and \(\mathbf {0.1594}\) (depolarizing noise), reducing logical error rates by 13% and 5% compared to the Minimum Weight Perfect Matching (MWPM) and Feedforward Neural Network (FFNN) decoders. For rotated surface codes with code distances \(\mathbf {d=3,5,7,9}\) , KAT mitigates boundary connectivity and noise propagation by leveraging its multi-head attention mechanism to model global spatiotemporal correlations. Meanwhile, under the circuit-level noise model, KAT outperforms the Transformer across code distances \(\varvec{d=5,7,9,11}\) . This result underscores KAT’s application potential in quantum error correction and demonstrates the extensive prospects of deep learning techniques in quantum information processing.