  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.
