使用角分层矩阵的高效且可扩展的波函数压缩
Efficient and Scalable Wave Function Compression Using Corner Hierarchical Matrices
AI总结：
针对CAS和CI计算的指数级标度限制，提出基于角分层矩阵的波函数压缩方法CHACI，通过逐块低秩分解等策略在强相关分子上实现了优于截断全局SVD的压缩效果。
摘要：
完全活性空间（CAS）和全组态相互作用（CI）计算的指数级标度限制了量子化学家模拟强相关体系电子结构的能力。在此，我们提出了角分层近似CI（CHACI），这是一种基于角分层矩阵（CH-matrices）的波函数压缩方法——这是一种基于逐块低秩分解的分层矩阵新变体。通过应用于强相关分子十二并苯，我们证明了CH矩阵压缩相比截断的全局奇异值分解提供了更优的压缩效果。结果表明，压缩比随着活性空间大小的增加而提高。通过比较几种替代方案，我们证明了更优的压缩通过以下方式实现：a）使用强调CI向量左上角的分块方法，b）在压缩前对CI向量进行排序，c）优化每个块的秩以最大化信息密度。
英文摘要：
The exponential scaling of complete active space (CAS) and full configuration interaction (CI) calculations limits the ability of quantum chemists to simulate the electronic structures of strongly correlated systems. Herein, we present corner hierarchically approximated CI (CHACI), an approach to wave function compression based on corner hierarchical matrices (CH-matrices) -- a new variant of hierarchical matrices based on a block-wise low-rank decomposition. By application to dodecacene, a strongly correlated molecule, we demonstrate that CH matrix compression provides superior compression compared to a truncated global singular value decomposition. The compression ratio is shown to improve with increasing active space size. By comparison of several alternative schemes, we demonstrate that superior compression is achieved by a) using a blocking approach that emphasizes the upper-left corner of the CI vector, b) sorting the CI vector prior to compression, and c) optimizing the rank of each block to maximize information density.
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