compare it to the diamond norm distance for reference. We see that the machine-learned function is a more accurate predictor of the logical error than the diamond norm distance.[]{data-label="fig:prediction"}](Figures/fig6.pdf)

Discussion
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In Sec. \[sec:StandardMetrics\] we saw that standard noise metrics can only very crudely predict the logical noise strength, while further extends this conclusion to a set of optimized parameters. This shows that predicting the logical fault-rate of a fault-tolerant scheme for a given channel depends on multiple parameters of the channel $\cE_0$. We can conclude from the data presented in this section that the information about the noise cannot be compressed to a single critical parameter: the response of a fault-tolerance scheme depends critically on many parameters of the noise model. One future generalization of our approach would be to compress the information about $\cE_0$ to a few critical parameters rather than a single one. But as we begin to consider more realistic noise models with an exponentially growing number of noise parameters, our numerical experiments lead us to severely doubt that a few critical parameter will suffice to obtain an accurate predictor.

Notwithstanding the problem of experimentally determining the noise model, we could use numerical simulations, as we 