发表机构
Technische Universität Wien; Fujitsu Research of America（维也纳工业大学; 富士通美国研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对量子态在线学习问题，利用测量的结构性质改进了遗憾界，推导了与希尔伯特空间维度无关的界，证明结构假设可提升量子态在线学习的可学性。
AI 中文摘要
量子态层析是量子信息处理的基础，但由于态空间呈指数增长，在大规模场景下变得不可行。影子层析通过聚焦于预测测量结果而非重构完整态，缓解了这一挑战。其在线变体建模了自适应且可能为对抗性的测量场景，其中学习器依次预测结果，同时与事后最优的固定量子态竞争。我们证明，利用测量中的额外结构可得到显著更强的遗憾保证。具体而言，在对抗性测量具有有界Frobenius范数的假设下，我们分析了投影在线梯度下降（Projected Online Gradient Descent），并推导了依赖于秩或稀疏性等内在结构性质而非环境希尔伯特空间维度的遗憾界。作为补充结果，我们表明，在平方L₂损失下，对于多结果测量，可实现与量子比特数和测量结果数均无关的对数遗憾。这些结果表明，在在线环境中，结合现实的结构假设可大幅提升量子态的可学习性。
英文摘要
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.
Comments19 pages (including references)
