that a noise model can have. At the level of a single qubit, the evolution operator is described by 12 real parameters, the bias being only one of them. That number grows exponentially with the number of qubits, the growth being mainly attributed to the number of inequivalent ways in which errors can be correlated across different qubits. Temporal correlations and non-Markovian effects will further increase that number of parameters, resulting in an extremely high-dimensional noise model manifold.

Thus, it is technically impossible to fully characterize the noise affecting more than, say, 3 qubits [@FIP97; @KGK17]. Techniques have been developed over the past decade to extract coarse information about the noise inflicting a system [@WT14; @MGE11; @AJJ16; @BWCO11; @CMBL16]. The simplest of these techniques will describe the noise by a single parameter $0<p<1$, which gives some indication of its strength, and more elaborate schemes will provide more parameters [@KLDF16]. These parameters define hypersurfaces in the high-dimensional noise manifold, leaving many noise parameters unspecified. One is left to wonder if knowledge about these few parameters can be of any help in designing tailored fault-tolerant protocols.

One of the key messages of this article is that unfortunately, no, there appears to be 