Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity

2026-07-13

AI Summary

This work addresses the challenge of structurally preserving learning of classical dynamical systems that exhibit both conservative and dissipative properties within quantum neural networks. The authors propose Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), which employ an isomorphic Hamiltonian mapping to associate the system’s interconnection matrix with unitary quantum gate evolution and its dissipation matrix with measurement-induced nonlinear feedback. This approach uniquely leverages measurement-induced nonlinearity to model dissipative dynamics while intrinsically enforcing energy conservation and passivity through architectural design rather than penalty terms. Four novel quantum architectures are developed, including a quantum Hamiltonian Neural Network that exactly recovers Hamilton’s equations and a topologically entangled quantum graph neural network. Experiments on nonlinear pendulum and damped harmonic oscillator tasks demonstrate a relative energy drift of 1.35%, perfect energy monotonicity, and accurate identification of damping coefficients from vector field snapshots with only 12.1% error.

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.

Problem

• Quantum Neural Networks
• Port-Hamiltonian Systems
• Conservative Dynamics
• Dissipative Dynamics
• Measurement-Induced Nonlinearity

Innovation

• Quantum Port-Hamiltonian Neural Networks
• Measurement-Induced NonLinearity
• Isomorphic Hamiltonian Mapping
• Structure-Preserving Learning
• Quantum Graph Neural Network