A highly efficient delayed update algorithm for evaluating Slater determinants in quantum Monte Carlo

As cutting edge quantum Monte Carlo simulations demand thousands of electrons in a simulation cell, matrix operations related to Slater determinants lead the computational cost. McDaniel et at. [1] proposed a delayed update algorithm to maximize computational efficiency by leveraging matrix-matrix multiplication when updating the inverse matrices of Slater determinants. However, preparing intermediate matrices for applying the Sherman-Morrison-Woodbury formula remains a bottleneck. In this work, we eliminate that bottleneck by iteratively updating those intermediate matrices and also show the full scheme of integrating the delayed update algorithm into a step of single electron move. In addition, we also extend our algorithm to accommodate the compute characteristics of GPUs. We will demonstrate the high efficiency of our algorithm, as implemented in QMCPACK, on CPUs and GPUs

[1] T. McDaniel, E. F. D’Azevedo,Y. W. Li, K. Wong, and P. R. C. Kent, The Journal of Chemical Physics 147, 174107 (2017)