Completing or Refusing Low-Dimensional Records of Structured Quantum Circuits: Measurement Loss, Compression Loss, and Hardware Drift

Abstract: Structured quantum circuits are often summarized by low-dimensional records. Records lose control-dependent information when they merge outcomes whose probabilities respond differently to circuit parameters. We assess this loss without a parametric hardware-noise model or low-dimensional statistical family. Quantum Fisher information bounds premeasurement sensitivity; Fisher metrics of measurements and records describe device-attainable sensitivity. A Hellinger residual measures the response removed by a record, while its local quadratic term is the conditional covariance of the full-outcome score. Simultaneous confidence bounds support approval, refusal, or deferral. We prove a finite-library completion theorem: executable augmentations terminate with either a record preserving every declared response or proof that no library augmentation removes the loss. For an analytic control germ, integral closures characterize preservation along every analytic control arc, and finitely many Rees valuations detect failure. This state--measurement--record chain connects an all-arc criterion to executable completion or refusal, an attainable-Fisher local kernel criterion, and finite-sample decisions. A three-qubit calculation separates measurement loss from record loss. IBM experiments on Kingston and Marrakesh test decisions in fixed-particle-number and GHZ families, including negative controls. An end-to-end Kingston experiment reduces calibration shots by 33.3% while meeting prespecified noninferiority criteria on two held-out objectives. In two-epoch IQM Garnet data, median record-level drift is 0.0797 times full-distribution drift, but a significant residual remains in 35 of 36 settings. These experiments validate failure detection on the tested circuits; they do not establish universal compression performance or device quantum Fisher information.