Within ab initio Quantum Monte Carlo simulations, the leading numerical cost for large systems is the computation of the values of the Slater determinants in the trial wavefunction. Each Monte Carlo step requires finding the determinant of a dense matrix. This is most commonly iteratively evaluated using a rank-1 Sherman-Morrison updating scheme to avoid repeated explicit calculation of the inverse. The overall computational cost is, therefore, formally cubic in the number of electrons or matrix size. To improve the numerical efficiency of this procedure, we propose a novel multiple rank delayed update scheme. This strategy enables probability evaluation with an application of accepted moves to the matrices delayed until after a predetermined number of moves, K. The accepted events are then applied to the matrices en bloc with enhanced arithmetic intensity and computational efficiency via matrix-matrix operations instead of matrix-vector operations. This procedure does not change the underlying Monte Carlo sampling or its statistical efficiency. For calculations on large systems and algorithms such as diffusion Monte Carlo, where the acceptance ratio is high, order of magnitude improvements in the update time can be obtained on both multi-core central processing units and graphical processing units.

中文翻译：

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高效量子蒙特卡洛的延迟Slater行列式更新算法

在从头算起的量子蒙特卡洛模拟中，大型系统的主要数值成本是对试验波函数中Slater行列式值的计算。每个蒙特卡洛步骤都需要找到一个密集矩阵的行列式。最常见的方法是使用1级Sherman-Morrison更新方案来迭代评估，以避免重复进行明确的逆运算。因此，总的计算成本在电子数量或矩阵尺寸上形式上是立方的。为了提高此过程的数值效率，我们提出了一种新颖的多秩延迟更新方案。该策略通过将接受的移动应用到矩阵直到预定数量的移动K之后才能够进行概率评估。。然后，通过矩阵矩阵运算（而不是矩阵矢量运算）将接受的事件以增强的算术强度和计算效率应用于整体矩阵。此过程不会更改基础的蒙特卡洛采样或其统计效率。对于接受率很高的大型系统和算法（例如扩散蒙特卡洛）的计算，可以在多核中央处理单元和图形处理单元上获得更新时间的数量级改进。