发表机构
Harvard; IBM Research（哈佛大学; IBM研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究从吉布斯态学习稠密SYK哈密顿量，利用随机平均场结构克服非局域性障碍，证明多项式样本可达逆多项式精度，并构造拟多项式时间算法。
AI 中文摘要
我们研究从吉布斯态的副本中学习稠密Sachdev-Ye-Kitaev（SYK）哈密顿量的问题。现有的哈密顿量学习算法通常依赖于几何局域性或有限相互作用阶数，因此不适用于SYK，因为其中每个四次相互作用与$\Theta(n^3)$个其他相互作用重叠。我们表明，通过利用模型的随机平均场结构可以克服这一障碍。在任意常数温度下，我们证明对于SYK耦合，以高概率，整个哈密顿量可以使用多项式数量的样本学习到逆多项式精度。此外，当逆温度被限制为足够小的常数时，我们构造了一个拟多项式时间的学习算法，该算法在性质上与样本高效的算法不同。
英文摘要
We study the problem of learning the dense Sachdev--Ye--Kitaev (SYK) Hamiltonian from copies of its Gibbs state. Existing algorithms for Hamiltonian learning typically rely on geometric locality or bounded interaction degree and therefore do not apply to SYK, where each quartic interaction overlaps with $Θ(n^3)$ others. We show that this obstruction can be overcome by exploiting the random mean-field structure of the model. At any constant temperature, we prove that with high probability over the SYK couplings, the entire Hamiltonian can be learned to inverse-polynomial accuracy using polynomially many samples. Furthermore, when the inverse temperature is restricted to be a sufficiently small constant, we construct a quasipolynomial-time learning algorithm which is qualitatively different from the sample-efficient algorithm.
