Optimal and Robust In-situ Quantum Hamiltonian Learning through Parallelization

Hamiltonian learning is essential for advancing accurate many-body simulations, improving quantum device performance, and enabling quantum-enhanced sensing. Existing quantum metrology techniques achieve Heisenberg-limited precision only for small systems, while general Hamiltonian learning approaches are often inefficient due to the lack of prior information about system structure. There remains a lack of efficient and practically realizable Hamiltonian learning algorithms that directly exploit the known structure of the Hamiltonian. In this work, we present a Hamiltonian learning algorithm that achieves Cramér-Rao-limited optimal precision and robustness to realistic noise, while exploiting device structure to obtain a quadratic reduction in experimental cost for fully connected Hamiltonians. The method allows simultaneous in-situ estimation of all coupling parameters without decoupling non-learnable interactions, enabling direct characterization of intrinsic contextual errors. Notably, our algorithm does not require deep circuits and remains robust against both depolarizing and time-dependent coherent noise. We demonstrate its effectiveness with a detailed experimental proposal along with supporting numerical simulations on Rydberg atom quantum simulators, showcasing its potential for high-precision Hamiltonian learning in the NISQ era.