Learning quantum Hamiltonians with high precision is important for quantum physics and quantum information science. We propose a multistage neural network framework that significantly enhances Hamiltonian learning precision through successive network optimization of residuals. Our approach utilizes time-series data from single-qubit Pauli measurements of random initial states, enabling the estimation of unknown Hamiltonian parameters without prior knowledge of initial states or a specific evolution ansatz. We demonstrate the framework on two-qubit systems, achieving improvement of several orders of magnitude in parameter accuracy, and further extend the method to larger systems by integrating dynamical decoupling techniques. Additionally, the protocol exhibits robustness against experimental noise. This work bridges the gap between scalable Hamiltonian learning and high-precision requirements, offering a practical tool for precise quantum control and metrology.

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• Quantum information processing
• Quantum measurements
• Quantum metrology
• Quantum parameter estimation
• Machine learning