Separability does not certify zero-noise extrapolation: Factorial diagnostics in dynamic quantum circuits

Abstract

Separately amplifying gate, latency, and mid-circuit measurement errors can simplify zero-noise extrapolation, but a weak interaction between amplification knobs does not establish an accurate zero-noise limit. We distinguish observable separability, response-model adequacy, and calibration of that limit, and test them in a pre-specified $2^3$ factorial experiment on three IBM dynamic circuits. For the primary echoed spectator observable, the latency-measurement coefficient is $b_{LM}=+0.0007$ with a nominal 95% bootstrap interval $[-0.0033,+0.0049]$. A separately planned follow-up meets a $\pm0.005$ equivalence criterion and recovers two injected interactions; both repeat runs nevertheless trigger the drift rule. Multi-knob extrapolations have smaller median absolute errors than the single-knob comparisons, yet all five original strategies exclude the known ideal value for three of six observables. Duration controls support a model-dependent contribution to the spectator deficit from unequal decay rates in native padding and added delay. We give an explicit construction showing why measurements at two measurement-knob levels cannot identify the extrapolated limit without response assumptions. A post-hoc precision analysis and an additive full-factorial estimator expose a further bias-variance trade-off hidden by point-error comparisons. The experiment provides a diagnostic of the implemented response surface, not a certification of physical channel independence or mitigation accuracy.