{"ID":6620440,"CreatedAt":"2026-07-15T01:01:48.440468303Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.12269","arxiv_id":"2607.12269","title":"Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity","abstract":"We introduce Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), a family of parameterised quantum circuits that learn classical dynamics in a structure-preserving manner. The framework relies on the Isomorphic Hamiltonian Mapping (IHM): the skew-symmetric interconnection matrix $\\mathbf{J}$ corresponds to unitary gate evolution, and the positive-semidefinite dissipation matrix $\\mathbf{R}$ corresponds to Measurement-Induced NonLinearity (MINL) realised via mid-circuit measurement and classical feedforward. This ensures conservation and passivity are enforced by construction rather than penalty terms. We instantiate the IHM in four architectures: (1) a Quantum HNN that learns conservative energy manifolds and extracts Hamilton's equations exactly via the Parameter-Shift Rule; (2) a Q-pHNN using Born-rule measurement for dissipation; (3) a Q-pHNN jointly learning the energy ansatz and damping coefficient; and (4) a topology-entangled Quantum Graph Neural Network for $N$-node coupled-phasor networks. Experiments on the nonlinear pendulum and damped harmonic oscillator demonstrate: (i)~$1.35\\%$ relative energy drift with a symplectic integrator and scale correction; (ii)~$100\\%$ energy monotonicity for the MINL circuit; and (iii)~$12.1\\%$ error in damping-coefficient identification from vector-field snapshots with no direct supervision on the damping coefficient.","short_abstract":"We introduce Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), a family of parameterised quantum circuits that learn classical dynamics in a structure-preserving manner. The framework relies on the Isomorphic Hamiltonian Mapping (IHM): the skew-symmetric interconnection matrix $\\mathbf{J}$ corresponds to unitary gate...","url_abs":"https://arxiv.org/abs/2607.12269","url_pdf":"https://arxiv.org/pdf/2607.12269v1","authors":"[\"Dibakar Sigdel\"]","published":"2026-07-14T02:16:20Z","proceeding":"cs.LG","tasks":"[\"cs.LG\"]","methods":"[\"Graph Neural Network\"]","has_code":false}