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机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文分类了有限多项式盒上复稳定性保持半群的生成元，证明多项式时间识别，给出谱间隙，并设计经典算法计算 Suzuki-Fisher 及 EPR 等哈密顿量的基态性质，解决多个猜想。
AI 中文摘要
我们在有限多项式盒上对复稳定性保持半群的生成元进行了分类，并证明了从高斯有理二元单点和双点输入进行多项式时间识别的可行性。下界为 $\mu>0$ 的阻尼保证了严格的零自由性和一个尖锐的、与容量无关的实部谱间隙，扩展了 Bravyi、Gosset、Liu 和 Wong 的 Hermitian $2\mu$ 间隙。在有界度和局部强度下，确定性经典算法可近似计算具有固定正纵向场的 Suzuki-Fisher 哈密顿量的基态能量和相对于稳定乘积态的相对振幅；场微扰给出了零场能量值多项式时间近似方案，适用于有界度无权图上的 Einstein-Podolsky-Rosen (EPR) 和二分量子最大割问题。一个全温度逆定理将完整 Gibbs 张量表征为，在固定基下，精确地是逐边相位旋转的 Suzuki-Fisher 族（模去标量）。结合严格正场 Gibbs 半径，这回答了 Wong、Bravyi、Gosset 和 Liu 的两个问题。加权令牌图谱凹性解决了 Apte、Parekh 和 Sud 的邻接矩阵和符号无拉普拉斯猜想。一个精确的证书否证了所提出的更强的 EPR 基态半径。
英文摘要
We classify the generators of stability-preserving semigroups on polynomial spaces with bounded coordinate degrees. The generators have differential order at most two, with principal coefficients characterized by low-degree nonnegativity conditions. In disk coordinates, positive degree damping gives strict zero-freeness and a sharp spectral gap, extending the Hermitian gap of Bravyi, Gosset, Liu, and Wong to complex generators. The resulting analytic domain yields deterministic classical algorithms for ground energies and stable product-state queries for bounded-degree Suzuki-Fisher Hamiltonians with bounded local strength and fixed positive fields. Field perturbation gives zero-field energy-value approximation schemes for bounded-degree unweighted EPR and bipartite Quantum MaxCut. We also prove that, up to scalars, the Hermitian qubit Hamiltonians whose full Gibbs tensors are Lee-Yang at every temperature in a fixed basis are precisely the edgewise phase-rotated Suzuki-Fisher family. With strictly positive longitudinal fields, these tensors are zero-free on a polydisk of radius greater than one at each positive inverse temperature. These two statements answer questions of Wong, Bravyi, Gosset, and Liu. Degree-preserving, coefficient-positive stability semigroups have concave sector growth rates, yielding token-graph concavity. We also give a counterexample to a proposed explicit ground-state radius.
Comments64 pages. Substantially reorganized and rewritten for clarity; references updated, including independent work by Jiang (arXiv:2609.25037). Mathematical results unchanged; theorem numbering changed. Exact verification scripts included as ancillary files
