Efficient and Scalable Wave Function Compression Using Corner Hierarchical Matrices

TL;DR

This paper introduces CHACI, a wave function compression method using corner hierarchical matrices, which significantly reduces the computational complexity of strongly correlated quantum systems, demonstrated on dodecacene.

Contribution

The paper presents a novel wave function compression technique based on corner hierarchical matrices, outperforming traditional methods in quantum chemistry applications.

Findings

CH matrix compression yields better compression ratios than SVD.

Compression improves with larger active spaces.

Blocking and sorting strategies enhance compression efficiency.

Abstract

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.