Runtime Calibration as State-Trajectory Feedback Control in Quantum-Classical Workflows

Abstract: In superconducting devices running variational workloads, gate and readout fidelities drift on hour timescales, while existing runtime schedulers treat backend quality as static. The temporal dimension of calibration remains unresolved. We formulate runtime calibration as a state-trajectory feedback-control problem under a fixed wall-clock budget, and investigate whether spending time on calibration now can improve the future optimization trajectory. Calibration quality proxy is represented as a drifting equivalent-age state, recovery action is modeled as costly state reset, and policies are evaluated by time-integrated optimization gap over the full execution window. Using a finite-horizon rollout controller, we compare feedback calibration against a strengthened family of open-loop baselines across three latency regimes: cloud-like (25 ms), local-millisecond (1 ms), and tight-loop (4 $\mathrmμ$s). The results show a clear ordering: cloud-like feedback is generally uncompetitive, while local-ms and tight-loop regimes open a positive-gain region that grows with workload quality-sensitivity and initial calibration age. Crucially, the gap between local-ms and tight-loop control is modest for single-target recovery. The advantage of tight-loop integration emerges under capacity pressure, when many calibration targets must be processed within the same control window.