参数化耗散量子系统的模型阶数约简
Model Order Reduction for Parametric Dissipative Quantum Systems
- Institute of Applied Analysis and Numerical Simulation, University of Stuttgart（斯图加特大学应用分析与数值模拟研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
该研究针对参数化耗散量子系统，提出残差驱动的约化基框架，推导误差估计与收敛性，经数值实验验证迹约束贪心方法的精度与计算成本平衡最优。
AI中文摘要：
我们考虑参数相关Lindbladian的非平衡稳态的约化基近似，其环境矩阵空间随系统大小呈指数增长。我们通过将问题表征为特征值问题或迹约束源问题，给出了该问题的统一结构视角。基于这些表征，我们为两种公式提出了残差驱动的约化基框架。在存在唯一稳态的假设下，我们推导了基于残差的状态误差估计，并在问题数据具有实解析参数依赖性的情况下，建立了贪心算法的（亚）指数收敛性。在边界驱动的费米-哈伯德（Fermi--Hubbard）模型和耗散XYZ链上的数值实验支持了该分析，表明迹约束贪心方法在精度和计算成本之间提供了最佳整体平衡。
英文摘要：
We consider reduced basis approximations of non-equilibrium steady states of parameter-dependent Lindbladians, whose ambient matrix space grows exponentially with system size. We give a unified structural view of the problem through its characterizations as an eigenvalue problem or as a trace-constrained source problem. Building on these characterizations, we propose a residual-driven reduced basis framework for both formulations. Under the assumption of a unique steady state, we derive residual-based state-error estimates, and establish (sub-)exponential convergence of the greedy algorithms under real-analytic parameter dependence of the problem data. Numerical experiments on boundary-driven Fermi--Hubbard and dissipative XYZ chains support the analysis and suggest that the trace-constrained greedy method offers the best overall balance of accuracy and computational cost.
