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  • Letter
  • Open Access

Forecasting quantum observables: A compressed sensing approach with performance guarantees

Víctor Valls1,*, Albert Akhriev1, Olatz Sanz Larrarte2, Javier Oliva del Moral2,3, Štěpán Šmíd4,5, Josu Etxezarreta Martinez2, Sergiy Zhuk1, and Dmytro Mishagli5

  • *Contact author: victor.valls@ibm.com
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Phys. Rev. Research 8, L032030 – Published 26 August, 2026

DOI: https://doi.org/10.1103/9qp3-33cs

Abstract

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.

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Outline

Information

Phys. Rev. Research 8, L032030– Published 26 August, 2026
  • Received 24 December 2025
  • Accepted 3 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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