用神经网络重拟合纠错数据，提升量子表面码解码精度。
A Symmetry-Integrated Approach to Surface Code Decoding
- 将纠错问题转为回归任务，用连续函数逼近测量结果
- 在距离5、7的表面码上，各类神经网络解码器准确率均提升
- 方法通用性强，不依赖具体模型或编码距离
量子纠错通过将逻辑量子比特编码为多个物理量子比特来检测和纠正错误，是实现实用化量子计算的关键。表面码因其高容错阈值（由稳定子生成元定义）被视为有前景的编码方式，但以往方法因输入无法唯一确定正确预测，仅能获得错误概率分布而受限。为此，我们提出一种新方法：通过神经网络对校验测量进行数学插值，构建连续函数以重新优化解码模型。我们在代码距离为5和7的情况下评估了基于多层感知机的解码器，并在距离5时测试了卷积、循环神经网络及变换器结构。所有情况下，优化后的解码器均优于原始模型，证明该方法在不同代码距离与网络架构下均具普适有效性。结果表明，将表面码解码重构为可由深度学习解决的回归问题是一种有效策略。
原文摘要 · Abstract (English)
Quantum error correction, which utilizes logical qubits that are encoded as redundant multiple physical qubits to find and correct errors in physical qubits, is indispensable for practical quantum computing. Surface code is considered to be a promising encoding method with a high error threshold that is defined by stabilizer generators. However, previous methods have suffered from the problem that the decoder acquires solely the error probability distribution because of the non-uniqueness of correct prediction obtained from the input. To circumvent this problem, we propose a technique to reoptimize the decoder model by approximating syndrome measurements with a continuous function that is mathematically interpolated by neural network. We evaluated the improvement in accuracy of a multilayer perceptron based decoder for code distances of 5 and 7 as well as for decoders based on convolutional and recurrent neural networks and transformers for a code distance of 5. In all cases, the reoptimized decoder gave better accuracy than the original models, demonstrating the universal effectiveness of the proposed method that is independent of code distance or network architecture. These results suggest that re-framing the problem of surface code decoding into a regression problem that can be tackled by deep learning is a useful strategy.
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