Hamiltonian Learning at Heisenberg Limit for Hybrid Quantum Systems

Hybrid quantum systems, describing the interaction between different particle species, are central to quantum materials and quantum information science. In this work, we present the first algorithm capable of learning general hybrid Hamiltonians at the Heisenberg limit. Given access to an unknown hybrid Hamiltonian, our algorithm estimates all parameters up to error $\epsilon$ using only O(ε^-1) total evolution time and O(polylog(ε^-1)) measurements, while remaining robust under small SPAM error. In addition, we introduce the first Hamiltonian learning algorithm based on distributed quantum sensing, which significantly reduces the number of gates required for experimental realization. We numerically verify the efficiency of our algorithm via two generic models, whose extension encompasses various examples from AMO, condensed matter to high energy physics. Moreover, we demonstrate that our algorithm can be used for a new learning task named spectrum learning, allowing the modeling of non-Markovian dissipation directly from experimental measurements.