发表机构
UC Berkeley; Sandia National Laboratories; University of Cambridge; University of New Mexico（加州大学伯克利分校; 桑迪亚国家实验室; 剑桥大学; 新墨西哥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究划定了量子杂质模型模拟的经典与量子可处理边界：静态性质可经典多项式时间计算，而动力学性质需量子计算优势，为量子优势提供途径。
AI 中文摘要
量子杂质模型是相互作用量子物质的范式模型，也是现代电子结构方法的关键计算原语。它们描述了一个由相互作用费米子组成的小型子系统与一个大型非相互作用浴的耦合。我们对模拟杂质模型的计算复杂性进行了全面研究，划定了此类问题在经典与量子可处理性之间的边界。我们的主要发现是，量子杂质模型的静态性质可以在经典计算机上高效计算。具体而言，我们给出了经典算法，其(1)在时间$\mathrm{poly}(n,\delta^{-1})$内以加性精度$\delta$估计基态能量，以及(2)在时间$\mathrm{poly}(n,\beta,\delta^{-1})$内以相对精度$\delta$估计逆温度$\beta$下的配分函数，其中$n$为系统尺寸。这些结果将基态能量估计的先前最佳已知复杂性从拟多项式时间改进为多项式时间，同时首次为热平衡下模拟杂质模型建立了严格的多项式时间保证。另一方面，我们发现模拟杂质模型的动力学性质对经典计算机而言是困难的，但在量子计算机上则是容易的。作为一个典型例子，我们表明计算其非平衡格林函数捕获了量子计算的完整能力，即使在有限温度下也是如此。综合来看，我们的结果排除了计算静态性质的超多项式量子加速，但为在非平衡状态下模拟杂质物理提供了量子优势的途径。
英文摘要
Quantum impurity models are paradigmatic models of interacting quantum matter, as well as key computational primitives for modern electronic-structure methods. They describe a small subsystem of interacting fermions coupled to a large, noninteracting bath. We perform a comprehensive study of the computational complexity of simulating impurity models, delineating the boundary between classical and quantum tractability for this class of problems. Our main finding is that static properties of quantum impurity models can be calculated efficiently on a classical computer. Specifically, we give classical algorithms that (1) estimate the ground-state energy to additive precision $δ$ in time $\mathrm{poly}(n,δ^{-1})$, and (2) estimate the partition function at inverse temperature $β$ to relative precision $δ$ in time $\mathrm{poly}(n,β,δ^{-1})$, where $n$ is the system size. These results improve the previous best-known complexity for ground-state energy estimation from quasipolynomial to polynomial time, while establishing for the first time rigorous polynomial-time guarantees for simulating impurity models in thermal equilibrium. On the other hand, we find that simulating dynamical properties of impurity models is hard for classical computers but easy on a quantum computer. As a canonical example, we show that computing their nonequilibrium Green's functions captures the full power of quantum computation, even at finite temperature. Taken together, our results rule out superpolynomial quantum speedups for computing static properties, but provide an avenue for quantum advantage in simulating impurity physics out of equilibrium.
Comments73 pages, 1 figure. Updated bibliography and font, fixed typos
