Effect of multiqubit correlated noise on surface-code thresholds

Surface codes are promising for practical quantum error correction due to their high threshold and experimental feasibility. However, their performance under realistic noise conditions, particularly those involving correlated errors, requires further investigation. In this study, we systematically investigate the effect of several distinct types of correlated errors that could potentially arise from next-nearest-neighbor coupling in quantum systems. Our analytical results reveal that these correlated errors exhibit lower logical error rates due to their inherent structural symmetries. We further perform circuit-level simulations that incorporate realistic circuit level errors alongside correlated noise components, demonstrating that surface code performance is intimately related to the structural characteristics of the correlation patterns. This deepens our insights into the threshold of surface code and hence facilitates a more robust design of quantum circuits with a higher noise threshold.