量子端口哈密顿神经网络：通过测量诱导非线性学习保守和耗散动力学
Quantum Port-Hamiltonian Neural Networks: Learning Conservative and Dissipative Dynamics via Measurement-Induced Nonlinearity
- Mindverse Computing LLC（Mindverse计算有限责任公司）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
介绍量子端口哈密顿神经网络，其基于同构哈密顿映射，通过测量诱导非线性学习经典动力学，在四种架构中实例化，经非线性摆和阻尼谐振子实验，展示了能量漂移、单调性及阻尼系数识别等方面的成果。
AI中文摘要：
我们引入了量子端口哈密顿神经网络（Q-pHNNs），这是一族以结构保持方式学习经典动力学的参数化量子电路。该框架依赖于同构哈密顿映射（IHM）：反对称互连矩阵$\mathbf{J}$对应酉门演化，正半定耗散矩阵$\mathbf{R}$对应通过电路中测量和经典前馈实现的测量诱导非线性（MINL）。这确保了守恒和无源性通过构造而非惩罚项来强制执行。我们在四种架构中实例化了IHM：（1）学习保守能量流形并通过参数移位规则精确提取哈密顿方程的量子HNN；（2）使用玻恩规则测量进行耗散的Q-pHNN；（3）联合学习能量假设和阻尼系数的Q-pHNN；（4）用于N节点耦合相量网络的拓扑纠缠量子图神经网络。在非线性摆和阻尼谐振子上的实验表明：（i）使用辛积分器和尺度校正时相对能量漂移为1.35%；（ii）MINL电路的能量单调性为100%；（iii）在没有对阻尼系数进行直接监督的情况下，从矢量场快照中识别阻尼系数时误差为12.1%。
英文摘要：
We introduce Quantum Port-Hamiltonian Neural Networks (Q-pHNNs), parameterised quantum circuits that learn classical dynamics in a structure-preserving manner. The framework rests on the Isomorphic Hamiltonian Mapping (IHM): the skew-symmetric interconnection matrix $\mathbf{J}$ corresponds to unitary gate evolution, and the positive-semidefinite dissipation matrix $\mathbf{R}$ to Measurement-Induced NonLinearity (MINL), realised by mid-circuit measurement with classical feedforward. Conservation and passivity are then enforced by construction rather than by penalty terms, and dissipation becomes an intrinsically quantum effect: energy leaves through the act of measurement. We instantiate the IHM in three architectures: a Quantum HNN that extracts Hamilton's equations via the Parameter-Shift Rule; a Q-pHNN that dissipates through MINL; and a topology-entangled Quantum Graph Neural Network lifting both channels to $N$-node coupled-phasor networks. In simulation, where every model here was trained, we obtain $1.35\%$ relative energy drift under a symplectic integrator, $100\%$ energy monotonicity for the single-oscillator MINL circuit, and $92$--$98\%$ phase-space energy decay across ring, star and chain networks at $N\in\{3,6,9\}$. On an IBM Heron processor the trained energy surface and its parameter-shift gradients reproduce their simulated values, with an error budget dominated by readout rather than gate infidelity; the dissipative channel executes natively, but its decay is not separable from measurement back-action at these depths.
