Decoder Dependence in Surface-Code Threshold Estimation with Native Gottesman-Kitaev-Preskill Digitization and Parallelized Sampling
This study quantifies decoder dependence in surface-code threshold estimation under Pauli and native GKP noise regimes using LiDMaS+, demonstrating that while MWPM and Union-Find decoders achieve superior Pareto-optimal performance with stable crossing diagnostics, neural-guided and Belief Propagation decoders are significantly less accurate and robust, thereby establishing a framework for estimator-conditional threshold reporting coupled with runtime-fidelity checks.