<![CDATA[Fault-tolerant quantum computing is essential for realizing scalable quantum processors capable of executing reliable computations despite unavoidable physical errors and environmental disturbances. Conventional threshold theory predominantly assumes independent stochastic noise, whereas practical quantum hardware increasingly exhibits spatially and temporally correlated error processes that may significantly degrade logical qubit performance. This study aimed to evaluate the robustness of surface-code logical qubit operations under correlated noise models while examining the influence of decoder performance, syndrome extraction fidelity, code distance, and correlated error dynamics on fault-tolerant computation beyond conventional threshold assumptions. A mixed-methods sequential explanatory design was employed using 15,000 large-scale quantum simulations complemented by experimental benchmark datasets, quantum hardware calibration records, decoder implementation reports, and expert evaluations. Quantitative data were analyzed through generalized linear mixed-effects modeling, threshold analysis, Monte Carlo uncertainty estimation, and multivariate statistical techniques, whereas qualitative evidence was interpreted using thematic analysis of experimental observations and technical documentation. Findings demonstrated that optimized surface-code architectures maintained high logical gate fidelity and effective logical error suppression under moderate correlated noise conditions through accurate syndrome extraction and advanced decoding strategies. Decoder adaptation substantially mitigated correlated error propagation, preserving logical qubit stability despite realistic hardware imperfections. Results indicate that practical fault tolerance depends on the integrated interaction among correlated noise characterization, decoder intelligence, logical encoding, and hardware architecture rather than physical error rates alone. The proposed framework provides a comprehensive foundation for designing scalable, experimentally robust, and resource-efficient fault-tolerant quantum computing systems.]]>
