Analysing correlated noise on the surface code using adaptive decoding algorithms

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