When the reference is not the signal: state-dependent damping and a pre-flight test for error mitigation of collective observables

On a superconducting processor, the damping that reference-based error mitigation must carry from a reference circuit to a signal circuit is not a property of the circuit: at identical depth, routing and gate content, changing only a rotation angle moves it by twenty to thirty standard deviations (χ²/dof = 116), while three repetitions of one and the same circuit agree within shot noise (1.5). The transfer assumption behind most mitigation schemes is seldom testable, because the exact answer on the signal circuit is usually unknown. Here it is known on every circuit. The observable is collective, ⟨K²⟩ of a 24-qubit nuclear shell-model state on ibm_marrakesh, read inside a postselected symmetry sector. At 161 two-qubit gates it is reconstructed to about one unit. At 465 gates two independent corrections fail: a mixture estimator with an in-situ calibrated false-positive kernel loses identifiability, and an operator-level renormalization without any shape model misses the known values by −69 to +283 units. From this diagnosis follows a pre-flight test, costing about ten seconds of processor time, that decides before a production run whether reference-based mitigation can work for a given observable and depth. Data and code: doi:10.5281/zenodo.22953020.