average infidelity or the diamond norm. Despite these relative improvements the accuracy of the predictions from machine learning algorithms remain poor. This provides further evidence that fine details of the noise model must be known to predict – and eventually optimize – the response of a fault tolerant scheme.

In , we will discuss the numerical difficulty of simulating an error correction process. While several problems related to classical and quantum error correction – such as optimal decoding – are notoriously hard computational problems [@BMT78; @IP15], the characterization of quantum protocols poses an extra computational challenge with no classical counterpart. This difficulty stems from the computational hardness of simulating quantum mechanics. From that perspective, it is rather surprising that numerical simulations can be of any use to simulate large quantum error-correcting schemes, but the Gottesman-Knill theorem [@G98] provides a means to efficiently simulate simple noise models. However, the assumptions of the Gottesman-Knill theorem pose severe limitations on the noise models which can be efficiently simulated, thus rendering numerical simulations rather useless for the design of fault tolerant schemes tailored to physical noise models.

In addition to this quantum hardness, the numerical characterization of error correcting schemes is plagued by the 