Local decoder for the toric code with a high pseudo-threshold

Local decoders provide a promising approach to real-time quantum error-correction by replacing centralized classical processing, with significant hardware constraints, by a fully distributed architecture based on a simple, local update rule. We propose a new local decoder for Kitaev's toric code: the 2D signal-rule, that interprets odd parity stabilizer measurements as defects, attracted to each other via the exchange of binary signals. We present numerical evidence of exponential logical error suppression with system size below some critical error rate, under a phenomenological noise model, with data and measurement errors between each iteration. Compared to previously known local decoders, which exhibit suboptimal thresholds and scaling, our construction halves (in log scale) the threshold gap with state-of-the-art decoders, and achieves optimal scaling for experimentally relevant system sizes, enabling the practical realization of a two-dimensional local quantum memory.