Adaptive Online Learning of Quantum States

The problem of efficient quantum state learning, also called shadow tomography, aims to comprehend an unknown d -dimensional quantum state through POVMs. Yet, these states are rarely static; they evolve due to factors such as measurements, environmental noise, or inherent Hamiltonian state transitio...

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Bibliographic Details
Published inQuantum (Vienna, Austria) Vol. 8; p. 1471
Main Authors Chen, Xinyi, Hazan, Elad, Li, Tongyang, Lu, Zhou, Wang, Xinzhao, Yang, Rui
Format Journal Article
LanguageEnglish
Published Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften 12.09.2024
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Summary:The problem of efficient quantum state learning, also called shadow tomography, aims to comprehend an unknown d -dimensional quantum state through POVMs. Yet, these states are rarely static; they evolve due to factors such as measurements, environmental noise, or inherent Hamiltonian state transitions. This paper leverages techniques from adaptive online learning to keep pace with such state changes.The key metrics considered for learning in these mutable environments are enhanced notions of regret, specifically adaptive and dynamic regret. We present adaptive and dynamic regret bounds for online shadow tomography, which are polynomial in the number of qubits and sublinear in the number of measurements. To support our theoretical findings, we include numerical experiments that validate our proposed models.
ISSN:2521-327X
2521-327X
DOI:10.22331/q-2024-09-12-1471