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

Ye Luo1, Jeongnim Kim2, Paul R C Kent3

  • 1Computational Science Division, Argonne National Laboratory, Argonne, Illinois 60439 United States.

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Summary
This summary is machine-generated.

We developed an improved algorithm for quantum Monte Carlo simulations, significantly speeding up calculations for large molecular systems by efficiently updating Slater determinant matrices on CPUs and GPUs.

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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.