We give an improved algorithm for learning a quantum Hamiltonian given copies of its Gibbs state, that can succeed at any temperature. Specifically, we improve over the work of Bakshi, Liu, Moitra, and Tang [BLMT24], by reducing the sample complexity and runtime dependence to singly exponential in the inverse-temperature parameter, as opposed to doubly exponential. Our main technical contribution is a new flat polynomial approximation to the exponential function, with significantly lower degree than the flat polynomial approximation used in [BLMT24].

翻译：我们提出了一种改进的算法，用于在给定其吉布斯态副本的情况下学习量子哈密顿量，该算法可在任意温度下成功。具体而言，我们改进了Bakshi、Liu、Moitra和Tang的工作[BLMT24]，将样本复杂度和运行时间对逆温度参数的依赖从双指数降低为单指数。我们的主要技术贡献是提出了一种新的指数函数平坦多项式逼近，其阶数显著低于[BLMT24]中使用的平坦多项式逼近。