Characterizing time-periodic Hamiltonians is important for validating and controlling driven quantum platforms, yet generic time-domain reconstruction methods, when applied directly, can require dense temporal sampling and overparametrized time-slice descriptions. Informed by the Floquet theorem, we study Hamiltonian learning for time-periodic Hamiltonians under a structured Fourier Ansatz and show that, when the Hamiltonian is well captured by a small number of harmonics and a local operator basis, the unknown parameters can be recovered from a linear inverse problem in the Floquet-band representation. In this formulation, the resource requirements of the assembled inverse problem are governed by the retained Fourier modes, sampled times, and local operator coefficients rather than directly by the Hilbert-space dimension. We also analyze the access assumptions, resource estimates, and a conditional stability statement for the assembled regression problem. Numerical experiments on driven Ising and Heisenberg models, together with waveform-dependent tests and a naive time-slice baseline, identify when the Fourier-informed description is accurate and when it fails because of truncation or model mismatch. These results provide a structured route to characterizing driven platforms whose dynamics admit a compact Fourier description.

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• Open quantum systems
• Quantum algorithms
• Quantum benchmarking
• Quantum parameter estimation
• Bloch-Floquet theorem