Estimating thermal expectations of local observables is a natural target for quantum advantage. We give a simple classical algorithm that approximates thermal expectations, and we show it has quasi-polynomial cost $n^{O(\log n/ε)}$ for all temperatures above a phase transition in the free energy. For many natural models, this coincides with the entire fast-mixing, quantumly easy phase. Our results apply to the Sachdev-Ye-Kitaev (SYK) model at any constant temperature -- including when the thermal state is highly entangled and satisfies polynomial quantum circuit lower bounds, a sign problem, and nontrivial instance-to-instance fluctuations. Our analysis of the SYK model relies on the replica trick to control the complex zeros of the partition function.

翻译：估算局域可观测量热期望值是量子优势的一个自然目标。我们提出了一种近似计算热期望值的简单经典算法，并证明该算法在自由能相变点以上的所有温度下具有拟多项式复杂度$n^{O(\log n/ε)}$。对于许多自然模型，该温度范围与整个快速混合、量子易处理相重合。我们的结果适用于任意恒定温度下的Sachdev-Ye-Kitaev（SYK）模型——包括当热态处于高度纠缠且满足多项式量子电路下界、符号问题及非平凡实例间涨落的情形。我们对SYK模型的分析依赖于复本技巧来控制配分函数的复零点。