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.

本文提出了一种基于神经网络的深度量子错误解码器，引入了综合编码对系统噪音的初始估计进行迭代优化，并实现了在重复综合抽样下的有效解码。通过以可微目标直接优化在有限场上计算的逻辑错误率，该方法实现了量子纠错码解码的高效性，超过了现有的神经网络和经典解码器。