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 {\emph{end-to-end}} 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, by efficient decoding of repeated syndrome sampling. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy, outperforming {for small distance topological codes,} the existing {end-to-end }neural and classical decoders, which are often computationally prohibitive.

翻译：量子纠错码是实现量子计算潜力的关键组成部分。与经典纠错码类似，量子纠错码通过将量子逻辑信息分布在冗余的物理量子比特上，从而能够检测和纠正错误，降低错误率。在本研究中，我们高效训练了新颖的端到端深度量子纠错解码器。我们通过增强综合征解码，先预测系统噪声的初始估计，再通过深度神经网络进行迭代优化，解决了量子测量坍缩问题。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，从而在代码约束下实现高效解码。最后，我们的架构通过高效解码重复综合征采样，扩展支持有故障的综合征测量。该方法展示了神经解码器在量子纠错码中的强大能力，实现了最先进的准确率，并超越了现有的端到端神经解码器和经典解码器（对于小距离拓扑码），而后者通常计算开销巨大。