Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. QECC, as its classical counterpart (ECC), enables the reduction of error rates, by distributing quantum logical information across redundant physical qubits, such that errors can be detected and corrected. In this work, we efficiently train novel deep quantum error decoders. We resolve the quantum measurement collapse by augmenting syndrome decoding to predict an initial estimate of the system noise, which is then refined iteratively through a deep neural network. The logical error rates calculated over finite fields are directly optimized via a differentiable objective, enabling efficient decoding under the constraints imposed by the code. Finally, our architecture is extended to support faulty syndrome measurement, to allow efficient decoding over repeated syndrome sampling. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy, outperforming, for a broad range of topological codes, the existing neural and classical decoders, which are often computationally prohibitive.

翻译：量子纠错码（QECC）是实现量子计算潜力的关键组成部分。与经典纠错码（ECC）类似，QECC通过将量子逻辑信息分布到冗余物理量子比特上，从而检测并纠正错误，进而降低错误率。本文高效训练了新型深度量子纠错解码器。我们通过增强综合征解码以预测系统噪声的初始估计来解决量子测量坍缩问题，随后利用深度神经网络迭代优化该估计。基于有限域计算的逻辑错误率通过可微目标函数直接优化，从而在码字约束下实现高效解码。最终，我们将架构扩展至支持含噪综合征测量，通过重复综合征采样实现高效解码。所提方法通过实现拓扑码广泛范围内的最高精度（超越现有计算量往往过大的神经解码器与经典解码器），展现了神经解码器在量子纠错码中的强大能力。