论文标题
使用神经解码器确定半码阈值
Determination of the Semion Code Threshold using Neural Decoders
论文作者
论文摘要
我们计算半码的错误阈值，这是Kitaev旋转代码的同伴，带有相同的规格对称组$ \ mathbb {z} _2 $。由于代码是非Pauli和非CSS，因此高度不建议使用统计机械映射方法的应用。因此，我们使用机器学习方法，利用某些神经网络解码器的近乎最佳性能：多层感知和卷积神经网络（CNNS）。我们找到值$ p _ {\ text {eff}} = 9.5 \％$，用于不相关的位flip和phope-flip噪声，以及$ p _ {\ text {eff}} = 10.5 \％$ for deallalialized噪声。我们将这些值与对六角形晶格上的基塔夫旋转代码的类似分析与相同的方法进行了对比。对于卷积神经网络，我们使用Resnet体系结构，这使我们能够实现非常深的网络，并与多层感知器方法相比，可以实现更深入的性能和可扩展性。我们分析和比较两种方法，并提供一个明确的论点，其中有利于CNN作为半代码的最佳数值方法。
We compute the error threshold for the semion code, the companion of the Kitaev toric code with the same gauge symmetry group $\mathbb{Z}_2$. The application of statistical mechanical mapping methods is highly discouraged for the semion code, since the code is non-Pauli and non-CSS. Thus, we use machine learning methods, taking advantage of the near-optimal performance of some neural network decoders: multilayer perceptrons and convolutional neural networks (CNNs). We find the values $p_{\text {eff}}=9.5\%$ for uncorrelated bit-flip and phase-flip noise, and $p_{\text {eff}}=10.5\%$ for depolarizing noise. We contrast these values with a similar analysis of the Kitaev toric code on a hexagonal lattice with the same methods. For convolutional neural networks, we use the ResNet architecture, which allows us to implement very deep networks and results in better performance and scalability than the multilayer perceptron approach. We analyze and compare in detail both approaches and provide a clear argument favoring the CNN as the best suited numerical method for the semion code.
