Abstract:
Circuit compression is a key requirement for near-term quantum computing, yet the factors that govern stability under gate removal are not fully understood. We study this problem via a large-scale numerical analysis of 300 structurally uniform circuits across 10, 12, and 14 qubits. Despite identical macroscopic resources, each ensemble separates into two stability classes under the compression settings considered here. We show that this discrete separation is not explained by structural descriptors alone, but is instead linked to the statistical properties of the gate rotation parameters. In particular, fragile circuits exhibit a consistent signature of statistical brittleness, characterized by reduced parameter variability and a lower prevalence of small-angle gates. We further identify a mechanism consistent with this behavior: paradoxical importance, where smaller-angle gates can be disproportionately critical to circuit function, an effect most pronounced in fragile circuits. These results suggest simple parameter-statistics-based diagnostics that complement macroscopic resource metrics when assessing stability under compilation-based and pruning-based compression.