发表机构
ICFO–Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology; Simulacra Research Inc.（ICFO——光子科学研究所，巴塞罗那科学技术研究院; Simulacra研究公司）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明纯态基础神经量子态在拓扑上受阻碍，无法表示非平凡基态丛，而算子值模型可避免此问题并保留拓扑信息。
AI 中文摘要
自旋-1/2系统中基态的基础模型是一种有前景的方法，可应用于从量子化学到识别新相图等问题。目前几乎所有此类模型都是纯态模型，它们以哈密顿量的参数为条件，其蒙特卡洛样本根据变分原理给出能量估计。在本贡献中，我们证明这种表示在拓扑上受到阻碍。对于任何基态丛非平凡的带隙哈密顿量族，每个连续的归一化态矢量模型在哈密顿量族中的某个参数值处与基态的保真度为零。对于该值，能量至少为一个谱隙Δ，且在该点的开邻域内存在O(Δ)的间隙。我们证明这也是退化基态流形、时间动力学以及具有混合时空拓扑的周期系统情况下的充分的不可能性定理，并在单量子比特和双量子比特系统上展示了这些阻碍。我们讨论了这如何导致保真度磁化率出现尖峰，从而给出一个并不存在的相变的数值特征。然后我们证明算子值模型能够规范地避免这些阻碍并保留拓扑信息，这意味着基础神经量子态在表示上存在结构性必要性。
英文摘要
Foundation models for ground states in spin-1/2 systems are a promising method for problems ranging from quantum chemistry to identifying new phase diagrams. Nearly all such models are currently pure-states that condition on the Hamiltonian's parameters, whose Monte Carlo samples give energy estimates according to the variational principle. In this contribution, we show that this representation is topologically obstructed. For any gapped Hamiltonian family whose ground-state bundle is non-trivial, every continuous normalized state-vector model has zero fidelity with the ground state at some parameter value in the Hamiltonian family. For that value, the energy is at least one spectral gap, $Δ$, with an $O(Δ)$ gap in an open-neighbourhood of that point. We show that this is a sufficient no-go also in the case of degenerate ground-state manifolds, time dynamics, and periodic systems with mixed space-time topology, demonstrating these obstructions on one- and two-qubit systems. We discuss how this causes a spike in the fidelity susceptibility, giving a numerical signature of a phase-transition where there is none. We then show that operator-valued models canonically avoid these obstructions and preserve topological information, implying a structural necessity in representation for foundation neural quantum states.
Comments10 pages, 5 pages main text
