Online learning of quantum states under structure
Abstract
Quantum state tomography is fundamental to quantum information processing but becomes infeasible at scale due to the exponential growth of the state space. Shadow tomography alleviates this challenge by focusing on predicting measurement outcomes rather than reconstructing the full state. Its online variant models adaptive and potentially adversarial measurement scenarios, where a learner sequentially predicts outcomes while competing with the best fixed quantum state in hindsight. We show that exploiting additional structure in the measurements leads to significantly stronger regret guarantees. In particular, under the assumption that the adversarial measurements have bounded Frobenius norm, we analyze online mirror descent and derive optimal regret bounds that depend on intrinsic structural properties, such as rank or sparsity in the standard basis, rather than the dimension of the measurement operators. As a complementary result, we also show that, even in the setting where adversarial measurements are known to be sparse in the Pauli basis commonly used in variational quantum eigensolvers and near-term quantum error mitigation, the underlying regret bound for learning quantum states is the same as that obtained in the generic setting, where the adversarial measurements are not known to possess any particular structure.
Related
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- Reinforcement learning to disentangle multiqubit quantum states from partial observations
- Learning Sparse Quantum States
- Efficient learning of quantum interactions from thermal metastable states
BibTeX
@misc{bansal2026online,
title = {{Online learning of quantum states under structure}},
author = {Akshay Bansal and Jiahui Liu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2608.05740},
eprint = {2608.05740},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.05740},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Online learning of quantum states under structure
AU - Akshay Bansal
AU - Jiahui Liu
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2608.05740
UR - https://arxiv.org/abs/2608.05740
AB - Quantum state tomography is fundamental to quantum information processing but becomes infeasible at scale due to the exponential growth of the state space. Shadow tomography alleviates this challenge by focusing on predicting measurement outcomes rather than reconstructing the full state. Its online variant models adaptive and potentially adversarial measurement scenarios, where a learner sequentially predicts outcomes while competing with the best fixed quantum state in hindsight. We show that exploiting additional structure in the measurements leads to significantly stronger regret guarantees. In particular, under the assumption that the adversarial measurements have bounded Frobenius norm, we analyze online mirror descent and derive optimal regret bounds that depend on intrinsic structural properties, such as rank or sparsity in the standard basis, rather than the dimension of the measurement operators. As a complementary result, we also show that, even in the setting where adversarial measurements are known to be sparse in the Pauli basis commonly used in variational quantum eigensolvers and near-term quantum error mitigation, the underlying regret bound for learning quantum states is the same as that obtained in the generic setting, where the adversarial measurements are not known to possess any particular structure.
ER -