  Information obtained from noise characterization of a quantum device can be
used in classical decoding algorithms to improve the performance of quantum
error-correcting codes. Focusing on the surface code under local (i.e.
single-qubit) noise, we present a simple method to determine the maximum extent
to which adapting a surface-code decoder to a noise feature can lead to a
performance improvement. Our method is based on a tensor-network decoding
algorithm, which uses the syndrome information as well as a process matrix
description of the noise to compute a near-optimal correction. By selectively
mischaracterizing the noise model input to the decoder and measuring the
resulting loss in fidelity of the logical qubit, we can determine the relative
importance of individual noise parameters for decoding. We apply this method to
several physically relevant uncorrelated noise models with features such as
coherence, spatial inhomogeneity and bias. While noise generally requires many
parameters to describe completely, we find that to achieve near optimal
decoding it appears only necessary adapt the decoder to a small number of
critical parameters.
