Physics-Informed Quantum Machine Learning for Parameter Recovery in the Underdamped Harmonic Oscillator

Abstract

Physics-informed neural networks are widely used for inverse problems governed by differential equations, whereas evidence for physics-informed quantum models remains limited. We study a hybrid quantum model for recovering the damping coefficient of an underdamped harmonic oscillator from sparse noisy observations. The model contains 109 architecture parameters in classical input and output layers and a six-qubit parameterised quantum circuit; the damping coefficient is optimised as one additional scalar. The main comparison uses 15 independent paired replicates in each of four oscillator regimes. Against a 2209-parameter classical multilayer perceptron, the quantum model has lower mean absolute damping error in all four regimes. Exact paired Wilcoxon tests with Holm correction support a difference only in the fourth regime (p Holm = 0.041); the other corrected tests are not significant. A tuned DeepXDE baseline has a descriptively lower mean error in the first regime, while the quantum model has lower means in the remaining three, but this cross-framework comparison was not included in the frozen confirmatory test. Ablations show that both data and physics terms are needed, that circuit-depth effects are regime dependent, and that the observed ranking is robust to the tested observation-noise and training-size changes. All quantum experiments use an analytic classical simulator.