Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity
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Computer Science > Machine Learning
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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2607.12269 [cs.LG] |
| (or arXiv:2607.12269v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2607.12269
arXiv-issued DOI via DataCite (pending registration)
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