Diagnosing Device Performance in Rydberg-Ladder Gauge Simulators with Cumulative Probabilities and Filtered Mutual Information

We study bitstring measurements from the publicly available Aquila Rydberg-atom platform using a two-leg ladder that encodes a truncated lattice gauge model as a practical benchmark that can be directly implemented and simulated on current hardware. Our goal is diagnostic: we analyze how errors propagate into bitstring probability distributions and downstream information measures, focusing on ladders with 6, 8, and 10 rungs and $\mathcal{O}(10^3)$ shots. We introduce cumulative probability distributions as a compact way to compare Aquila data with high-accuracy density matrix renormalization group (DMRG) and exact references, and we use optimally filtered mutual information primarily as a robust device-data diagnostic rather than a direct entanglement estimator. By isolating finite sampling, sorting fidelity, adiabatic ramp-up, Rabi-frequency ramp-down, and readout errors, we find that readout mitigation performs well in controlled DMRG tests. Applying the same procedure on hardware shows accuracy limitations for the leading probabilities estimation, indicating that readout errors are not dominant and that residual error is instead driven by imperfect state preparation.