Hybrid global single-shot decoding for the 2D repetition code

Error-correction protocols can protect information even when the syndrome measurements themselves are faulty. In the presence of measurement noise, multiple rounds of faulty measurements are generally required before accurate corrections can be applied. However, there exist special "single-shot" protocols where sufficiently good corrections can be applied after just one round of measurements. Such protocols are always local in time but may be local or global in space, with important trade-offs: global decoders offer the possibility of higher thresholds but are more susceptible to correlated mistakes, especially when measurement noise dominates. Focusing on the 2D repetition code, we explore a family of efficient hybrid global single-shot decoders that consider physical and measurement errors simultaneously to provide improved performance in these situations. We compare our results against existing decoders for the 2D repetition code and discuss how our framework may be extended to quantum codes in higher dimensions.