Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo

Area of Science:

• Computational Physics
• Quantum Chemistry

Background:

• Ab initio Quantum Monte Carlo (QMC) simulations are crucial for electronic structure calculations.
• The primary computational bottleneck in QMC for large systems is the repeated calculation of Slater determinants.
• Current methods often rely on iterative rank-1 updates, leading to cubic scaling.

Purpose of the Study:

• To introduce a more efficient numerical method for QMC simulations.
• To reduce the computational cost associated with determinant calculations in large quantum systems.

Main Methods:

• A novel multiple rank delayed update scheme is proposed.
• Accepted Monte Carlo moves are applied to matrices in batches after K steps.
• This enables the use of efficient matrix-matrix operations instead of matrix-vector operations.

Main Results:

• The new scheme significantly improves numerical efficiency, especially for large systems.
• Order of magnitude improvements in update time are achievable on CPUs and GPUs.
• The statistical efficiency of the Monte Carlo sampling remains unchanged.

Conclusions:

• The delayed update scheme offers a substantial speedup for QMC calculations.
• This method enhances computational performance without compromising simulation accuracy.
• It is particularly beneficial for diffusion Monte Carlo and high acceptance ratio algorithms.