A High-Efficiency Delayed Update Algorithm for Evaluating Slater Determinants in Quantum Monte Carlo

Area of Science:

• Computational chemistry
• Quantum mechanics
• Materials science

Background:

• Quantum Monte Carlo (QMC) simulations are crucial for studying molecular systems and supercells.
• Matrix operations involving Slater determinants represent a significant computational bottleneck in QMC.
• Existing delayed update algorithms improve efficiency but face challenges with intermediate matrix preparation.

Purpose of the Study:

• To introduce an enhanced algorithm for QMC simulations that addresses the bottleneck in updating inverse matrices of Slater determinants.
• To improve computational efficiency for large-scale QMC calculations on both CPUs and GPUs.
• To demonstrate the algorithm's effectiveness across various acceptance ratios.

Main Methods:

• Developed an iterative approach to update intermediate matrices, circumventing the Sherman-Morrison-Woodbury formula bottleneck.
• Integrated the delayed update algorithm into a single-electron move scheme.
• Implemented and tested the algorithm on both central processing units (CPUs) and graphics processing units (GPUs).

Main Results:

• Achieved significant speed-ups in QMC simulations for large systems (512 atoms/6144 valence electrons).
• Demonstrated a 12x speed-up on CPUs and a 2x speed-up on GPUs compared to traditional rank-1 update schemes.
• The algorithm shows efficiency across all acceptance ratios, with negligible cost for rejected moves on CPUs and minimal cost on GPUs.

Conclusions:

• The improved delayed update algorithm substantially enhances computational efficiency in QMC simulations.
• This method offers a practical solution for accelerating large-scale electronic structure calculations.
• The algorithm's performance on both CPUs and GPUs makes it broadly applicable in computational science.