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This research introduces Quantum Port-Hamiltonian Neural Networks that enforce physical laws like energy conservation and dissipation directly through quantum measurement protocols rather than penalty terms. By mapping unitary evolution to skew-symmetric matrices and using mid-circuit measurements for non-unitary decay, the architecture achieves high-fidelity modeling of classical dynamics with minimal numerical drift. The study validates these structure-preserving circuits on nonlinear oscillators and scalable network topologies, demonstrating a novel integration of quantum measurement effects into machine learning frameworks.
Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity
arXiv:2607.12269v2 Announce Type: replace 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, and it makes dissipation an intrinsically quantum effect: energy leaves the system through the act of measurement, not through any non-unitary term in the Hamiltonian. We instantiate the IHM in three 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 that realises dissipation through MINL-mid-circuit measurement of a bath ancilla with conditional feed-forward; and (3) a topology-entangled Quantum Graph Neural Network that lifts both channels to $N$-node coupled-phasor networks, with one bath ancilla per node. Experiments on the nonlinear pendulum and damped harmonic oscillator, and a network scaling study on GPU, demonstrate: (i)~$1.35\%$ relative energy drift with a symplectic integrator and scale correction; (ii)~$100\%$ energy monotonicity for the single-oscillator MINL circuit; and (iii)~$92$--$98\%$ phase-space energy decay from measurement-induced dissipation -- monotone at every step -- across ring, star, and chain networks at sizes $N\in\{3,6,9\}$, alongside exact machine-precision energy conservation in the conservative mode.
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, and it makes dissipation an intrinsically quantum effect: energy leaves the system through the act of measurement, not through any non-unitary term in the Hamiltonian. We instantiate the IHM in three 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 that realises dissipation through MINL-mid-circuit measurement of a bath ancilla with conditional feed-forward; and (3) a topology-entangled Quantum Graph Neural Network that lifts both channels to $N$-node coupled-phasor networks, with one bath ancilla per node. Experiments on the nonlinear pendulum and damped harmonic oscillator, and a network scaling study on GPU, demonstrate: (i)~$1.35\%$ relative energy drift with a symplectic integrator and scale correction; (ii)~$100\%$ energy monotonicity for the single-oscillator MINL circuit; and (iii)~$92$--$98\%$ phase-space energy decay from measurement-induced dissipation -- monotone at every step -- across ring, star, and chain networks at sizes $N\in\{3,6,9\}$, alongside exact machine-precision energy conservation in the conservative mode.
Machine Learning (cs.LG)
arXiv:2607.12269 [cs.LG]
(or arXiv:2607.12269v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2607.12269 Focus to learn more arXiv-issued DOI via DataCite
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