Validity of exponential polarization decay for compiled QUOPS circuits

Establish whether the mean process polarization of compiled QUOPS circuits generally decays approximately exponentially with circuit size at fixed circuit width, thereby validating the heuristic model used to extrapolate error-mitigated QUOPS capability regions.

Background

The paper extrapolates error-mitigated QUOPS capability regions by assuming that, at fixed circuit width, the mean process polarization follows the model ˉw,s=e−rws\bar{}_{w,s}=e^{-r_ws}. This assumption allows experimentally measured polarization data at finite circuit sizes to be fitted and then used to estimate capabilities at larger sizes.

The authors note that compiled QUOPS circuits may undergo broad and architecture-dependent compilation, and therefore existing results establishing exponential polarization decay for random circuits do not directly apply. Determining whether exponential decay remains a reliable approximation for such compiled circuits would substantiate the extrapolation methodology and its resulting error-mitigated QUOPS scores.

References

The extrapolated capability regions rely on the assumption that $\bar{}_{w,s}$ follows an approximately exponentially decay with $s$, for fixed $w$. We conjecture that this will often be a reasonable approximation in practice, but we note that this is heuristic.

— Benchmarking the computational power of quantum computers  (2609.12146 - Proctor et al., 10 Sep 2026) in Supplementary Information, Section "Extrapolated capability regions"