发表机构
IBM Research（IBM 研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究揭示量子杂质模型平衡态性质可被经典算法高效近似，而时间演化则能实现通用量子计算，并提出了改进的经典算法与BQP完全性证明。
AI 中文摘要
量子杂质模型描述了一个嵌入在大型自由费米子浴中的小型相互作用子系统。在此，我们研究了计算这些模型的基态能量、热平衡和动力学性质的计算复杂性。我们的工作揭示了鲜明的对比：平衡态性质可以通过经典方法高效近似，而时间演化可以实现通用量子计算。更精确地说，设 $H$ 为具有 $n$ 个费米子模式和常数大小杂质的杂质模型的哈密顿量。我们证明：（1）$H$ 的基态能量可以通过经典算法以加性误差 $\varepsilon$ 近似，运行时间为 $\textsf{poly}(n,1/\varepsilon)$，改进了先前已知最佳算法的拟多项式运行时间；（2）在逆温度 $\beta$ 下，亥姆霍兹自由能和热场双态（thermofield double state）的经典描述可以在时间 $\textsf{poly}(n,\beta,1/\varepsilon)$ 内以精度 $\varepsilon$ 计算；（3）模拟时间演化 $e^{-iHt}$ 是 $\textsf{BQP}$-完全的，对于时间无关且具有固定常数大小杂质的 $H$。我们的算法利用了按能量尺度和Krylov深度组织的基中多粒子浴激发的指数抑制。我们的普适性构造实现了一个静态量子处理器，其程序以自由传播的费米子流形式到达。
英文摘要
A quantum impurity model describes a small interacting subsystem embedded into a large bath of free fermions. Here we study the computational complexity of calculating the ground energy, thermal equilibrium, and dynamical properties of these models. Our work reveals a sharp contrast: equilibrium properties can be efficiently approximated by classical means, whereas time evolution can implement a universal quantum computation. More precisely, let $H$ be the Hamiltonian of an impurity model with $n$ fermionic modes and a constant-size impurity. We show that: (1) the ground energy of $H$ can be approximated to additive error $\varepsilon$ by a classical algorithm with runtime $\textsf{poly}(n,1/\varepsilon)$, improving on the quasi-polynomial runtime of the best previously known algorithm; (2) at inverse temperature $β$, the Helmholtz free energy and a classical description of the thermofield double state can be computed to precision $\varepsilon$ in time $\textsf{poly}(n,β,1/\varepsilon)$; (3) simulating the time evolution $e^{-iHt}$ is $\textsf{BQP}$-complete, for $H$ that is time-independent and has a fixed, constant impurity size. Our algorithms exploit exponential suppression of multi-particle bath excitations in a basis organized by energy scale and Krylov depth. Our universality construction realizes a stationary quantum processor whose program arrives in a stream of freely propagating fermions.
Comments81 pages, 2 figures
