The adaptive decision-making strategy for surface code decoding

Abstract Achieving large-scale real-time decoding requires efficient and accurate decoders. However, conventional decoding strategies for surface codes struggle to balance speed with accuracy. In this work, we propose the adaptive decision-making (ADM) strategy, which optimizes the local decisions through intermediate information during the decoding process, while maintaining rapid decoding. We compare the performance of different real-time strategies by integrating them into the union-find (UF) decoding framework. Numerical simulations under different noises show that our ADM-UF decoder significantly improves the threshold, outperforming its highly relevant competitors. Empirical evidence confirms that ADM-UF achieves an almost-linear complexity, ensuring real-time decoding for large-scale quantum codes. These results validate the efficacy of our ADM strategy.