发表机构
Center for Theoretical Physics — a Leinweber Institute, MIT（麻省理工学院莱因韦伯理论物理中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出经典算法在多项式时间内计算平均场模型（包括SYK模型和经典自旋玻璃）在所有恒定温度下的局部热期望值，并发展了严格的量子空穴方法，同时给出从Gibbs态学习SYK哈密顿量的量子算法。
AI 中文摘要
Sachdev-Ye-Kitaev模型是一种强相互作用的费米子系统，已在凝聚态物理和高能物理中得到深入研究。它具有高度量子性：高斯态远离热态（Hastings和O'Donnell，STOC'22），并且表示热态需要大型多项式规模的量子电路（Anschuetz等人，QIP'25）。然而，最近证明，经典算法可以在准多项式时间内估计足够高温下的局部热期望值（Zlokapa，FOCS'26）。我们表明，经典算法实际上可以在所有恒定温度下以多项式时间估计局部可观测量。我们的技术也直接扩展到经典系统：我们解决了关于计算经典自旋玻璃直到其相变点的热期望值的开放问题（Bencs等人，STOC'26）。我们的证明发展了一种完全严格的量子空穴方法。由于经典空穴方法在优化、采样、推理和学习中的成功，我们期望量子空穴方法能发现其他独立应用的兴趣。作为示例，我们给出了一种量子算法，该算法可以从任意恒定温度下的Gibbs态学习SYK哈密顿量，具有多项式时间和样本复杂度。
英文摘要
The Sachdev-Ye-Kitaev model is a strongly interacting fermionic system that has been well-studied in condensed matter and high energy physics. It is highly quantum: Gaussian states are far from the thermal state (Hastings and O'Donnell, STOC'22) and representing the thermal state requires large polynomial-size quantum circuits (Anschuetz et al., QIP'25). Very recently, it was nonetheless proven that classical algorithms can estimate local thermal expectations at sufficiently high temperature in quasipolynomial time (Zlokapa, FOCS'26). We show that classical algorithms can in fact estimate local observables at all constant temperatures in polynomial time. Our techniques also extend straightforwardly to classical systems: we resolve an open question about computing thermal expectations of a classical spin glass up to its phase transition (Bencs et al., STOC'26). Our proof develops a fully rigorous quantum cavity method. Due to the success of the classical cavity method in optimization, sampling, inference and learning, we expect the quantum cavity method to find further applications of independent interest. As an example, we give a quantum algorithm that learns SYK Hamiltonians from the Gibbs state at any constant temperature with polynomial time and sample complexity.
Comments63 + 107 pages, 4 figures
