A promising strategy to protect quantum information from noise-induced errors is to encode it into the low-energy states of a topological quantum memory device. However, readout errors from such memory under realistic settings is less understood. We study the problem of decoding quantum information encoded in the groundspaces of topological stabilizer Hamiltonians in the presence of generic perturbations, such as quenched disorder. We first prove that the standard stabilizer-based error correction and decoding schemes work adequately well in such perturbed quantum codes by showing that the decoding error diminishes exponentially in the distance of the underlying unperturbed code. We then prove that Quantum Neural Network (QNN) decoders provide an almost quadratic improvement on the readout error. Thus, we demonstrate provable advantage of using QNNs for decoding realistic quantum error-correcting codes, and our result enables the exploration of a wider range of non-stabilizer codes in the near-term laboratory settings.

翻译：将量子信息编码到拓扑量子存储器的低能态中，是保护量子信息免受噪声诱导错误的一种有前景策略。然而，在实际条件下，此类存储器的读出错误尚不明确。我们研究在存在淬火无序等一般性扰动时，从拓扑稳定子哈密顿量基态空间中解码量子信息的问题。首先，我们证明在受扰动的量子码中，基于标准稳定子的纠错与解码方案仍能有效工作——显示解码错误随底层未扰动码的距离呈指数级衰减。接着，我们证明量子神经网络解码器可将读出错误实现近二次方改进。由此，我们展示了使用QNN解码实际量子纠错码的可靠优势，这一结果将推动在近期实验室环境中探索更广泛的非稳定子码。