Adaptive Online Learning of Quantum States
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910607513485312 |
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| author | Chen, Xinyi Hazan, Elad Li, Tongyang Lu, Zhou Wang, Xinzhao Yang, Rui |
| author_facet | Chen, Xinyi Hazan, Elad Li, Tongyang Lu, Zhou Wang, Xinzhao Yang, Rui |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_00220 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Adaptive Online Learning of Quantum States Chen, Xinyi Hazan, Elad Li, Tongyang Lu, Zhou Wang, Xinzhao Yang, Rui Machine Learning Quantum Physics 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. |
| title | Adaptive Online Learning of Quantum States |
| topic | Machine Learning Quantum Physics |
| url | https://arxiv.org/abs/2206.00220 |