Q-Residual Physics: Hamiltonian-Structured Quantum Residual Learning for Embodied Dynamics

Embodied agents in contact-rich environments must model dynamics affectedby frictional uncertainty, contact discontinuities, compliance, actuator imperfec-tions, perception noise, and mass or inertia mismatch. Existing residual dynamicslearning methods correct nominal physics predictions with unconstrained neuralresiduals, which often generalize poorly under unseen contact regimes, changingphysical parameters, long-horizon rollouts, and few-shot adaptation. We proposeQ-Residual Physics, a Hamiltonian-structured quantum residual learning frame-work for embodied dynamics. The method represents residual errors through astructured quantum residual layer whose qubits correspond to physically inter-pretable modes, including contact impulse, friction, slip, compliance, damping,perception error, and mass or inertia mismatch. A physical interaction graphinduces a Hamiltonian residual structure, implemented with a Trotterized param-eterized quantum circuit whose components capture mode activation, physicalcoupling, uncertain switching, dynamic mode exchange, and higher-order interac-tions. Quantum measurements are decoded to correct nominal physics predictions.Across embodied dynamics and manipulation benchmarks, including OMNIPUSH,MANISKILL2, ROBOMIMIC, D4RL, and PHYSION, Q-Residual Physics achievesstronger generalization than physics-only, neural residual, graph residual, andquantum-circuit baselines. It reduces long-horizon rollout error by 23.8%, im-proves contact transition prediction by 16.4%, lowers out-of-distribution parametererror by 21.7%, and improves few-shot adaptation by 28.5%. The code is availableat https://anonymous.4open.science/r/QRP-0205