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 versatile, numerical method to quantify the performance improvement gained by adapting an optimal surface-code decoder to specific, user-defined features of the physical noise model. 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 to adapt the decoder to a small number of critical parameters.

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• Quantum error correction
• Tensor network methods