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Efficient and scalable wave function compression using corner hierarchical matrices.

Kenneth O Berard1,2, Hongji Gao1,3, Alexander Teplukhin1,2

  • 1Institute for Advanced Computational Science, Stony Brook University, Stony Brook, New York 11794, USA.

The Journal of Chemical Physics
|November 25, 2024
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Summary
This summary is machine-generated.

Corner hierarchically approximated CI (CHACI) offers superior wave function compression for strongly correlated systems. This new method, based on corner hierarchical matrices, outperforms existing techniques for quantum chemistry simulations.

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Materials Science

Background:

  • Simulating strongly correlated systems is computationally intensive due to the exponential scaling of traditional methods like complete active space and full configuration interaction (CI).
  • Existing wave function compression techniques face limitations in efficiency and accuracy for complex electronic structures.

Purpose of the Study:

  • To introduce a novel wave function compression approach, corner hierarchically approximated CI (CHACI), for accurately simulating strongly correlated systems.
  • To demonstrate the effectiveness of CHACI in improving the efficiency of quantum chemical calculations.

Main Methods:

  • Developed corner hierarchical matrices (CH-matrices), a new variant of hierarchical matrices utilizing block-wise low-rank decomposition.
  • Applied CHACI to dodecacene, a known strongly correlated molecule, to evaluate its compression performance.
  • Compared CHACI compression ratios against truncated global singular value decomposition and other compression schemes.

Main Results:

  • CHACI demonstrated superior compression ratios compared to truncated global singular value decomposition for the dodecacene system.
  • The compression efficiency of CHACI was observed to improve with larger active space sizes.
  • Optimized compression strategies, including specific blocking, sorting, and rank optimization, further enhanced CHACI's performance.

Conclusions:

  • CHACI provides a significant advancement in wave function compression for strongly correlated electronic structures.
  • The method offers a more efficient pathway for quantum chemists to simulate complex molecular systems.
  • Further optimization of CHACI parameters can lead to even greater computational savings.