Floquet-informed Learning of Periodically Driven Hamiltonians

Abstract: Characterizing time-periodic Hamiltonians is pivotal for validating and controlling driven quantum platforms, yet prevailing and unadjusted reconstruction methods demand dense time-domain sampling and heavy post-processing. We introduce a scalable Floquet-informed learning algorithm that represents the Hamiltonian as a truncated Fourier series and recasts parameter estimation as a compact linear inverse problem in the Floquet band picture. The algorithm is well-suited to problems satisfying mild smoothness/band-limiting. In this regime, its sample and runtime complexities scale polynomially with the Fourier cutoff, time resolution, and the number of unknown coefficients. For local Hamiltonian models, the coefficients grows polynomially with system size, yielding at most polylogarithmic dependence on the Hilbert-space dimension. Furthermore, numerical experiments on one- and two-dimensional Ising and Heisenberg lattices show fast convergence to time resolution and robustness to higher-order perturbations. An adaptive rule learns the cutoff of Fourier series, removing the need to set known truncation \textit{a priori}. These features enable practical certification and benchmarking of periodically driven platforms with rapidly decaying higher-order content, and extend naturally to near-periodic drives.