Quantum Neural Networks Learn Classical Dynamics with Structure Preservation

A new class of parameterized quantum circuits, termed Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), has been developed to learn classical dynamic systems while inherently preserving their underlying physical structure. This innovative framework leverages the Isomorphic Hamiltonian Mapping (IHM) to ensure that fundamental principles like energy conservation and passivity are maintained by design, rather than through penalty terms in the optimization process. Specifically, unitary gate evolution within the quantum circuit corresponds to the skew-symmetric interconnection matrix, which governs conservative energy flow. Dissipative dynamics, on the other hand, are modeled through Measurement-Induced NonLinearity (MINL), achieved via mid-circuit measurements and classical feedback. The study demonstrates four distinct Q-pHNN architectures, including one that learns conservative energy manifolds and another that jointly learns energy and damping coefficients. Experimental results on systems like the nonlinear pendulum and damped harmonic oscillator show impressive performance. The Q-pHNNs exhibited minimal energy drift, perfect energy monotonicity for MINL circuits, and accurate identification of damping coefficients. These findings suggest a powerful new approach for quantum computers to simulate and understand complex classical physical systems with built-in physical consistency.