Topology-Dependent Coherence Persistence in Noisy Random Quantum Circuits: A Modified Decay Law and Falsifiable Prediction

Random circuit sampling (RCS) on noisy quantum hardware is widely modeled as exhibiting exponential decay of fidelity metrics (e.g., XEB, HOG) with circuit depth, converging toward Haar-random statistics beyond a characteristic noise-limited scale. This work introduces a minimal phenomenological recurrence for a coarse-grained local coherence observable defined on the qubit connectivity graph. The recurrence reproduces standard exponential decay in unstructured (fully scrambled) circuits but predicts delayed thermalization and a nonzero plateau when repeated local motifs are engineered into circuit compilation. The model introduces a single topology-dependent memory parameter α(µ), where µ denotes motif density. A transcritical bifurcation occurs when α(µ) exceeds the effective per-layer decoherence rate γ, producing a calculable plateau height and build-up depth scale. A matched-pair experimental protocol—holding qubit count, two-qubit gate count per layer, and reported hardware error rates fixed while varying only motif density—provides a direct falsification criterion. Absence of statistically significant topology dependence would rule out the model in its minimal form. The recurrence is an effective coarse-grained description at the metric level and does not modify underlying quantum channel structure or violate complete positivity.