Efficient and Scalable Wave Function Compression Using Corner Hierarchical Matrices

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Bibliographic Details
Main Authors:	Berard, Kenneth O., Gao, Hongji, Teplukhin, Alexander, Jiao, Xiangmin, Levine, Benjamin G.
Format:	Preprint
Published:	2024
Subjects:	Chemical Physics
Online Access:	Acceder al recurso
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author	Berard, Kenneth O. Gao, Hongji Teplukhin, Alexander Jiao, Xiangmin Levine, Benjamin G.
author_facet	Berard, Kenneth O. Gao, Hongji Teplukhin, Alexander Jiao, Xiangmin Levine, Benjamin G.
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2407_21134
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Efficient and Scalable Wave Function Compression Using Corner Hierarchical Matrices Berard, Kenneth O. Gao, Hongji Teplukhin, Alexander Jiao, Xiangmin Levine, Benjamin G. Chemical Physics 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.
title	Efficient and Scalable Wave Function Compression Using Corner Hierarchical Matrices
topic	Chemical Physics
url	https://arxiv.org/abs/2407.21134

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