发表机构
Stanford; Caltech; MIT（斯坦福大学; 加州理工学院; 麻省理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文证明SYK模型在高温下具有与系统大小无关的谱间隙的量子吉布斯采样器，实现多项式时间制备吉布斯态，引入伪林德布拉德方法并基于经典动力学比较简化分析。
AI 中文摘要
Sachdev-Ye-Kitaev (SYK) 模型是一个强相互作用的费米子系统。由于其全对全无序相互作用，其动力学难以用Lieb-Robinson界和簇展开进行分析。我们证明，在无序上以高概率，SYK模型在足够高的常数温度下允许一个具有与系统大小无关的谱间隙的量子吉布斯采样器。这导致在量子计算机上多项式时间内制备SYK吉布斯态。虽然先前建议SYK热化的非严格计算仅限于研究局部关联函数，但我们强调我们的结果在任意逆多项式迹距离内成立。我们的证明引入了费米子的伪林德布拉德方法，并使用了一种基于与经典动力学比较的特别简单的SYK分析。
英文摘要
The Sachdev-Ye-Kitaev (SYK) model is a strongly interacting fermionic system. Its dynamics are difficult to analyze with Lieb-Robinson bounds and cluster expansions due to its all-to-all disordered interactions. We prove that, with high probability over the disorder, the SYK model admits a quantum Gibbs sampler with a system-size-independent spectral gap at sufficiently high constant temperatures. This yields polynomial-time preparation of SYK Gibbs states on a quantum computer. While prior non-rigorous computations that suggested SYK thermalization were limited to studying local correlators, we emphasize that our result holds up to arbitrary inverse polynomial trace distance. Our proof introduces the pseudo-Lindbladian approach to fermions and uses an especially simple SYK analysis based on a comparison to classical dynamics.
Comments32 pages
