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Laboratory hardware is rapidly progressing towards a state where quantumerror-correcting codes can be realised. As such, we must learn how to deal withthe complex nature of the noise that may occur in real physical systems. Singlequbit Pauli errors are commonly used to study the behaviour of error-correctingcodes, but in general we might expect the environment to introduce correlatederrors to a system. Given some knowledge of structures that errors commonlytake, it may be possible to adapt the error-correction procedure to compensatefor this noise, but performing full state tomography on a physical system toanalyse this structure quickly becomes impossible as the size increases beyonda few qubits. Here we develop and test new methods to analyse blue a particularclass of spatially correlated errors by making use of parametrised families ofdecoding algorithms. We demonstrate our method numerically using a diffusivenoise model. We show that information can be learnt about the parameters of thenoise model, and additionally that the logical error rates can be improved. Weconclude by discussing how our method could be utilised in a practical settingblue and propose extensions of our work to study more general error models.

Analysing correlated noise on the surface code using adaptive decoding algorithms