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Bibliographic Details
Main Authors: Valls, Víctor, Akhriev, Albert, Larrarte, Olatz Sanz, del Moral, Javier Oliva, Šmíd, Štěpán, Martinez, Josu Etxezarreta, Zhuk, Sergiy, Mishagli, Dmytro
Format: Preprint
Published: 2025
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Online Access:https://arxiv.org/abs/2510.14897
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Table of Contents:
  • Data-driven extrapolation methods aim to extend the dynamics of quantum observables from measurements, but they often lack guarantees on prediction accuracy. We introduce a framework based on atomic norm minimization that can certify whether the spectral model learned by a forecasting algorithm -- i.e., Bohr frequencies and amplitudes -- is consistent with unitary quantum time evolution. Certification holds when the dynamics are governed by a small number of well-separated Bohr frequencies. We validate the approach on multiple forecasting algorithms applied to spin-chain Hamiltonians with 8--20 sites. Comparing with exact diagonalization, certified models yield an average forecasting error below 0.1 (observable range $[-1, 1]$) in 97\% of cases and below 0.05 in 91--99\% of cases. Even in the presence of noise, certified models remain robust at the 0.1 error threshold.