Efficient simulation of a quantum system generally relies on structural properties of the quantum state. Motivated by the recent results by Bakshi et al. on the sudden death of entanglement in high-temperature Gibbs states of quantum spin systems, we study the high-temperature Gibbs states of bounded-degree local fermionic Hamiltonians, which include the special case of geometrically local fermionic systems. We prove that at a sufficiently high temperature that is independent of the system size, the Gibbs state is a probabilistic mixture of fermionic Gaussian states. This forms the basis of an efficient classical algorithm to prepare the Gibbs state by sampling from a distribution of fermionic Gaussian states. As a contrasting example, we show that high-temperature Gibbs states of the Sachdev-Ye-Kitaev (SYK) model are not convex mixtures of Gaussian states.

翻译：量子系统的高效模拟通常依赖于量子态的结构特性。受Bakshi等人最近关于量子自旋系统高温吉布斯态中纠缠猝死现象的研究启发，我们研究了有界度局域费米子哈密顿量的高温吉布斯态，其中包括几何局域费米子系统的特例。我们证明，在足够高且与系统尺寸无关的温度下，吉布斯态是费米子高斯态的概率混合。这构成了一个高效经典算法的基础，该算法通过从费米子高斯态的分布中采样来制备吉布斯态。作为对比示例，我们证明了Sachdev-Ye-Kitaev（SYK）模型的高温吉布斯态并非高斯态的凸混合。