发表机构
Korea Institute for Advanced Study; Korea University; National Research Council of Science & Technology（韩国高等研究院; 高丽大学; 国家科学技术研究委员会）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出一个端到端量子模拟框架，结合粒子数守恒Trotter化与广义量子信号处理，估计正则热性质，并通过经典重加权实现巨正则重构，在特定温度区间优于经典Lanczos方法，数值验证于二维Hubbard模型。
AI 中文摘要
我们开发了一个端到端框架，利用量子模拟估计粒子数守恒的二次量子化哈密顿量的正则热性质。该框架整合了混合Dicke态的初始态制备、粒子数守恒的Trotter化模拟以及广义量子信号处理，以估计正则配分函数和可观测量。基于这一正则方案，我们引入了一种巨正则重构方案，其中相同的量子测量数据可通过经典重加权用于任意化学势，从而避免在化学势变化时重复执行量子电路。我们证明了存在与系统大小无关的温度区间，在此区间内，对于物理相关的哈密顿量，正则方案和重构的巨正则方案在渐近时间复杂度上均低于经典Lanczos方法（至多相差多项式因子）。我们针对二维Hubbard模型在弱耦合和中等耦合区间数值验证了我们的理论结果。
英文摘要
We develop an end-to-end framework for estimating canonical thermal properties of particle-number-conserving second-quantized Hamiltonians using quantum simulations. The framework integrates initial state preparation with mixed Dicke states, particle-number-preserving Trotterized simulation, and generalized quantum signal processing to estimate canonical partition functions and observables. Building on this canonical scheme, we introduce a grand-canonical reconstruction scheme in which the same quantum measurement data can be reused for arbitrary chemical potentials through classical reweighting, thereby avoiding repeated quantum circuit executions as the chemical potential is varied. We prove the existence of system-size-independent temperature regimes in which both the canonical and reconstructed grand-canonical schemes have lower asymptotic time complexity than classical Lanczos methods, up to polynomial factors, for physically relevant Hamiltonians. We numerically validate our theoretical results for the two-dimensional Hubbard model in both weak- and intermediate-coupling regimes.
