Structural Ordering of Observable Noise in Fixed-Workload Quantum Circuits

We present an empirical study of observable noise behavior in quantum circuits under fixedworkload constraints. Using publicly available circuit archives and measurement data, we showthat observable dispersion metrics are monotonically ordered by pre-measurement interactionstructure derived solely from circuit topology, and not by gate count or circuit depth alone.Structure is quantified using topology-derived interaction matrices constructed prior to measurement, while noise is quantified using observable-level statistics such as measurement distribution entropy and fidelity proxies. The observed ordering persists across multiple system sizesand hardware-inspired datasets. These results indicate that circuit-level noise cannot be fullycharacterized by workload-local or gate-independent models, and suggest that pre-measurementstructural organization plays a decisive role in shaping observable noise.