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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2510.14897 |
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| _version_ | 1866911725643628544 |
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| author | Valls, Víctor Akhriev, Albert Larrarte, Olatz Sanz del Moral, Javier Oliva Šmíd, Štěpán Martinez, Josu Etxezarreta Zhuk, Sergiy Mishagli, Dmytro |
| author_facet | Valls, Víctor Akhriev, Albert Larrarte, Olatz Sanz del Moral, Javier Oliva Šmíd, Štěpán Martinez, Josu Etxezarreta Zhuk, Sergiy Mishagli, Dmytro |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_14897 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Forecasting Quantum Observables: A Compressed Sensing Approach with Performance Guarantees Valls, Víctor Akhriev, Albert Larrarte, Olatz Sanz del Moral, Javier Oliva Šmíd, Štěpán Martinez, Josu Etxezarreta Zhuk, Sergiy Mishagli, Dmytro Quantum Physics 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. |
| title | Forecasting Quantum Observables: A Compressed Sensing Approach with Performance Guarantees |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2510.14897 |