AI 中文总结
该研究针对量子处理器中含时哈密顿量的表征问题，开发了一种从连续弱测量记录学习含时多体哈密顿量的协议，利用相互作用稀疏性简化重构，推导相关定理并验证协议，为多体系统含时哈密顿量学习提供了严格基础。
AI 中文摘要
表征量子处理器实际实现的哈密顿量对于校准和验证当前量子硬件至关重要。许多设备的发生器设计为随时间变化。本文开发了一种严格且实验友好的协议，用于从连续弱测量记录中学习含时多体哈密顿量。关键在于相互作用稀疏性将全局重构简化为一组局部逆问题，其数量由相互作用连通性而非系统大小控制。纯可分探测态足以驱动这些反演，图着色构造将其嵌入少量全局积态制备中。我们推导了显式重构误差界和样本复杂度定理，将有限采样统计噪声与迭代态更新的确定性偏差清晰分开，并在多达\(n = 8\)个量子比特的含时自旋链上验证了该协议。此外，我们的分析为多体系统中从连续监测进行含时哈密顿量学习提供了严格基础，建立了一个自然扩展到许多平台和探测系综的框架。
英文摘要
Characterizing the Hamiltonian that a quantum processor actually implements is central to calibrating and validating current quantum hardware. Many devices, however, operate with generators that are time dependent by design. Here we develop a rigorous and experimentally friendly protocol for learning time-dependent many-body Hamiltonians from continuous weak measurement records. The key observation is that interaction sparsity reduces the global reconstruction to a set of local inverse problems, whose number is controlled by the interaction connectivity rather than by the system size. Pure separable probe states suffice to drive these inversions, and a graph-coloring construction embeds them into a small number of global product-state preparations. We derive explicit reconstruction-error bounds and a sample-complexity theorem that cleanly separates the finite-sampling statistical noise from the deterministic bias of the iterative state update, and we validate the protocol on time-dependent spin chains with up to $n=8$ qubits. Beyond these results, our analysis provides a rigorous foundation for time-dependent Hamiltonian learning from continuous monitoring in many-body systems, establishing a framework that extends naturally to many platforms and probe ensembles.
