# Sparse Mamba Decoder

Surface-code decoders have processed the full $d^2 \times R$ syndrome array regardless of how many errors occurred, yet at roughly 0.1% physical error rate fewer than 5% of entries fire. The Sparse Mamba Decoder (SMD) processes only the k active detection events, each described by a 13-dimensional feature, and runs a Mamba state-space backbone in O(k) time. Under SI1000 noise at $p=1.5\times10^{-3}$, a three-checkpoint ensemble lowers the d=7 logical error rate by 16% relative to MWPM, and the single model reaches ratios of 0.65 at d=3 and 0.51 at d=5.

Surface-code decoders have processed the full $d^2 \times R$ syndrome array regardless of how many errors occurred, yet at roughly 0.1% physical error rate fewer than 5% of entries fire. The Sparse Mamba Decoder (SMD) processes only the k active detection events, each described by a 13-dimensional feature, and runs a Mamba state-space backbone in O(k) time. Under SI1000 noise at $p=1.5\times10^{-3}$, a three-checkpoint ensemble lowers the d=7 logical error rate by 16% relative to MWPM, and the single model reaches ratios of 0.65 at d=3 and 0.51 at d=5.