Hybrid quantum systems with different particle species are fundamental in quantum materials and quantum information science. In this work, we demonstrate that Hamiltonian learning in hybrid spin-boson systems can achieve the Heisenberg limit. Specifically, we establish a rigorous theoretical framework proving that, given access to an unknown hybrid Hamiltonian system, our algorithm can estimate the Hamiltonian coupling parameters up to root mean square error (RMSE) $\epsilon$ with a total evolution time scaling as $T \sim \mathcal{O}(\epsilon^{-1})$ using only $\mathcal{O}({\rm polylog}(\epsilon^{-1}))$ measurements. Furthermore, it remains robust against small state preparation and measurement (SPAM) errors. In addition, we also provide an alternative algorithm based on distributed quantum sensing, which significantly reduces the maximum evolution time per measurement. To validate our method, we apply it to the generalized Dicke model for Hamiltonian learning and the spin-boson model for spectrum learning, demonstrating its efficiency in practical quantum systems. These results provide a scalable and robust framework for precision quantum sensing and Hamiltonian characterization in hybrid quantum platforms.

翻译：由不同粒子种类构成的混合量子系统是量子材料与量子信息科学的基础。本工作证明，混合自旋-玻色子系统中的哈密顿量学习可以达到海森堡极限。具体而言，我们建立了一个严格的理论框架，证明在给定一个未知混合哈密顿量系统的访问权限下，我们的算法能够以总演化时间 $T \sim \mathcal{O}(\epsilon^{-1})$ 且仅需 $\mathcal{O}({\rm polylog}(\epsilon^{-1}))$ 次测量的代价，将哈密顿量耦合参数的估计均方根误差（RMSE）控制在 $\epsilon$ 以内。此外，该算法对小规模的态制备与测量（SPAM）误差保持鲁棒性。同时，我们还提出了一种基于分布式量子传感的替代算法，该算法显著降低了每次测量所需的最大演化时间。为验证我们的方法，我们将其应用于广义迪克模型进行哈密顿量学习，并应用于自旋-玻色子模型进行谱学习，从而证明了该方法在实际量子系统中的高效性。这些结果为混合量子平台中的精密量子传感与哈密顿量表征提供了一个可扩展且鲁棒的框架。