Adaptive Code-Distance Control for Surface-Code Quantum Error Correction Under Non-Stationary Noise: A Validated Closed-Loop Simulation Study

Surface-code quantum error correction (QEC) is typically deployed at a single, statically chosen code distance d, sized for a worst-case physical error rate. This is resource-inefficient whenever the true noise level is time-varying, as is characteristic of 1/fα flux noise and burst-type two-level-system defects in superconducting qubits. This paper develops and numerically validates a closed-loop variable topological coding (VTC) controller that adjusts the rotated surface-code distance dt ∈ {3, 5, 7, 9} online, using only locally measurable syndrome-defect density, and evaluates it against every fixed-distance baseline under a common, independently validated minimum-weight perfect-matching (MWPM) decoder implemented from first principles (an explicit lattice-adjacency graph with Dijkstra/Jansen-Sobol-verified shortest-path corrections, not a black-box library). All numerical results in this paper, logical failure rates, qubit-cycle costs, Sobol sensitivity indices, and bootstrap confidence intervals, are the direct output of Monte Carlo simulation code that is validated against three independent, closed-form sanity checks (zero-noise perfect recovery, monotonic single-qubit-error correctability, and the expected sub-threshold/super-threshold crossover of the code family) and is reproduced in full in Appendix A. Under stationary depolarizing and spatially correlated 1/f noise at a representative physical error rate p = 0.02, the adaptive controller matches the logical failure rate of the best-performing fixed-distance baseline while using on average 45 % to 50 % fewer physical qubits than that baseline requires as a static allocation. Under explicitly non-stationary (bursty) noise, the regime for which no single fixed distance is simultaneously optimal, the adaptive controller achieves the lowest logical failure rate of every option tested (PL = 0.0292, 95% CI [0.0250, 0.0332]) while using a mean of 10.9 physical qubits, versus 25 qubits for the best fixed baseline (d = 5, PL = 0.0307). A Saltelli/Jansen variance-based sensitivity analysis over four controller hyperparameters shows that total-order sensitivity indices substantially exceed first-order indices for all four parameters (ST ≈ 0.77–1.01 versus S1 ≈ 0.11–0.24), indicating the controller's failure rate is governed predominantly by parameter interactions rather than any single hyperparameter in isolation, a finding with direct implications for how such controllers should be tuned and reported. We give a full accounting of the method's present limitations (single-shot, code-capacity-level decoding without repeated-round temporal matching; no physical qubit-routing or crosstalk model; classical, not learned, control policy) and lay out a falsifiable, staged experimental roadmap toward circuit-level and hardware validation.