Physics-Anchored vs. Data-Driven Extrapolation of Superconducting-Qubit Dephasing Rates
Abstract
Abstract Several papers on physics-informed noise modeling for superconducting qubits report gains from embedding known physics into machine-learning models, but we found little discussion in that literature of the specific mechanism by which such gains arise, or of the conditions under which embedding a known relation could instead hurt. We do not claim this gap is unaddressed anywhere in the broader machine-learning literature — bias-variance behavior of physics-informed models and the importance of multi-seed evaluation are both studied elsewhere in adjacent settings, discussed in Section 2 — only that we did not find this specific mechanism characterized for noisy-input extrapolation in the quantum-noise-modeling papers we reviewed. We derive a leading-order (small-σ) bias-variance decomposition for anchoring a regression model to an exact analytic noise relation (here, the T1-relaxation-limited dephasing rate 1/(2T1)): to leading order in the relative input-noise magnitude σ, the exact plug-in estimator has a small positive relative bias of σ² and a variance scaling with the square of the anchored quantity's absolute magnitude. We validate both predictions in a controlled single-variable Monte Carlo experiment: the simulated relative bias (0.65%) matched the leading-order prediction (0.64%) closely, and the simulated variance ratio between two test points matched its prediction to within about 1%. We then test whether this single-variable picture transfers to a more…
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