arXiv：cs.LG· Zhen Qin, Qing Qu, Alfred O. Hero III·· 5 小时前AI 评分39
Transformer 神经量子态的上下文学习泛化理论分析
Generalization of Transformer-Based Neural Quantum States via In-Context Learning
AI 导读
研究者为基于 Transformer 的神经量子态建立了上下文学习泛化理论框架，证明推理时泛化误差（MSE）随上下文示例数量和 Transformer 深度增加而反比下降。达到该保证所需的 Transformer 深度仅随系统规模线性增长，即连续系统的粒子数或离散系统的 qudit 数。该分析进一步扩展到秩一密度算符表示的完整量子态，数值模拟验证了理论结果。
正文
Abstract:Neural quantum states based on modern deep learning architectures have emerged as powerful representations for quantum many-body systems. In particular, Transformer-based neural quantum states provide expressive models capable of capturing long-range correlations, and their empirical generalization performance has recently been demonstrated. However, a theoretical understanding of their generalization behavior remains largely unexplored. In this paper, we develop a theoretical framework to analyze the generalization properties of Transformer-based neural quantum states under in-context learning. We establish a rigorous inference-time generalization error bound in terms of mean squared error (MSE), showing that the pointwise prediction error decreases inversely with both the number of in-context examples and the depth of the Transformer. We further show that the Transformer depth required to achieve this guarantee scales only linearly with the system size--namely, the number of particles in continuous systems or the number of qudits in discrete systems. Building on this result, we extend our analysis to full quantum states formulated as rank-one density operators, and derive MSE-based generalization bounds over both continuous and discrete domains under physical constraints. Finally, numerical simulations corroborate our theoretical analysis.
| Subjects: | Quantum Physics (quant-ph); Machine Learning (cs.LG) |
| Cite as: | arXiv:2610.03463 [quant-ph] |
| (or arXiv:2610.03463v1 [quant-ph] for this version) | |
| https://doi.org/10.48550/arXiv.2610.03463 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Zhen Qin [view email]
[v1]
Fri, 2 Oct 2026 15:38:10 UTC (120 KB)
来源：arXiv：cs.LG · arxiv.org