The statistical mechanics mapping used to analyze the scrambling properties and XEB of the hIQP circuits has certain limitations that need to be addressed for a more comprehensive analysis. One limitation is the assumption of a simple noise model, which may not capture the full complexity of the noise present in practical quantum systems. To improve the mapping, more realistic noise models could be incorporated, taking into account various types of errors and their probabilities. Additionally, the mapping could be generalized to include a broader range of quantum circuits beyond IQP circuits, allowing for a more versatile analysis of quantum circuit properties. By refining the statistical mechanics model and extending its applicability to different circuit types, the analysis of scrambling properties and XEB could be enhanced and made more robust.