三对角化开放量子系统的低秩传播：随系统规模近线性扩展
Low-rank propagation for tridiagonalizable open quantum systems: near-linear scaling with system size
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中文总结 AI 辅助
针对三对角化开放量子系统，提出确定性低秩传播算法，消除密度矩阵二次增长，实现内存与成本随系统规模线性扩展，并在氮空位腔模型中验证了高精度与近线性加速。
中文摘要 AI 辅助
密度矩阵随希尔伯特空间维度D的二次增长是模拟大型开放量子系统的主要障碍。我们提出了一种确定性算法，针对哈密顿量由含时对角部分加上在基重排后呈三对角形式的项组成的Lindblad动力学，消除了这一障碍。该状态是一个低秩向量系综，通过三对角分裂算符步骤和短时Kraus分支的系综秩截断进行传播，从而在固定秩下，每步的内存和成本与D呈线性关系。对于驱动氮空位腔模型，秩16即可将完整密度矩阵可观测量复现至相对误差低于$10^{-5}$，该方法在D≈500时已比QuTiP快两个数量级，且其运行时间近线性扩展。
英文摘要
The quadratic growth of the density matrix with Hilbert-space dimension D is the central obstacle to simulating large open quantum systems. We introduce a deterministic algorithm that eliminates it for Lindblad dynamics whose Hamiltonian consists of a time-dependent diagonal part plus terms that are tridiagonal after reordering the basis. The state is a low-rank ensemble of vectors, propagated by tridiagonal split-operator steps and ensemble rank truncation of short-time Kraus branches, so that memory and cost per step are linear in D at fixed rank. For a driven nitrogen-vacancy-cavity model, rank 16 reproduces full density-matrix observables to relative error below $10^{-5}$, the method is up to two orders of magnitude faster than QuTiP already at $D \approx 500$, and its runtime scales nearly linearly.
发表机构
- Akhiezer Institute for Theoretical Physics, NSC KIPT（阿赫伊泽尔理论物理研究所，NSC KIPT）
- Advanced Photonic and Electronic Sciences Division, U.S. Army DEVCOM Army Research Laboratory（美国陆军DEVCOM陆军研究实验室先进光子与电子科学部）
- Department of Physics, University of Massachusetts at Boston（马萨诸塞大学波士顿分校物理系）
- Education and Research Institute “School of Physics and Technology”, Karazin Kharkiv National University（哈尔科夫国立大学教育与研究所“物理与技术学院”）
- Department of Physics and Engineering Physics, Tulane University（杜兰大学物理与工程物理系）
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