Phaseless Auxiliary-Field Quantum Monte Carlo on Graphical Processing Units

Abstract

We present an implementation of phaseless Auxiliary-Field Quantum Monte Carlo (ph-AFQMC) utilizing graphical processing units (GPUs). The AFQMC method is recast in terms of matrix operations which are spread across thousands of processing cores and are executed in batches using custom Compute Unified Device Architecture kernels and the GPU-optimized cuBLAS matrix library. Algorithmic advances include a batched Sherman-Morrison-Woodbury algorithm to quickly update matrix determinants and inverses, density-fitting of the two-electron integrals, an energy algorithm involving a high-dimensional precomputed tensor, and the use of single-precision floating point arithmetic. These strategies accelerate ph-AFQMC calculations with both single- and multideterminant trial wave functions, though particularly dramatic wall-time reductions are achieved for the latter. For typical calculations we find speed-ups of roughly 2 orders of magnitude using just a single GPU card compared to a single modern CPU core. Furthermore, we achieve near-unity parallel efficiency using 8 GPU cards on a single node and can reach moderate system sizes via a local memory-slicing approach. We illustrate the robustness of our implementation on hydrogen chains of increasing length and through the calculation of all-electron ionization potentials of the first-row transition metal atoms. We compare long imaginary-time calculations utilizing a population control algorithm with our previously published correlated sampling approach and show that the latter improves not only the efficiency but also the accuracy of the computed ionization potentials. Taken together, the GPU implementation combined with correlated sampling provides a compelling computational method that will broaden the application of ph-AFQMC to the description of realistic correlated electronic systems.

On Achieving High Accuracy in Quantum Chemical Calculations of 3d Transition Metal-Containing Systems: A Comparison of Auxiliary-Field Quantum Monte Carlo with Coupled Cluster, Density Functional Theory, and Experiment for Diatomic Molecules

“…Recently we have introduced a correlated sampling (CS) approach for quantities involving energy differences which is capable of reducing computational prefactors 46 and in some cases the severity of the phaseless approximation. 43 In this section, we show that significant reductions in statistical errors are obtained not only for hydrogen abstraction reactions, as shown previously, but also for bond breaking events between a transition metal and a heavier ligand atom.…”

“…46 The second advance is the development of an efficient implementation of ph-AFQMC on graphical processing units (GPUs), including the use of the Sherman-Morrison-Woodbury (SMW) algorithm to accelerate calculations using multideterminental trial wavefunctions. 43 For problems where correlated sampling is applicable, the combination of these two techniques can reduce the computational effort by more than two orders of magnitude, enabling the method to be applied to larger systems, and also to substantially larger data sets. Further efficiency improvements are feasible (reducing both the scaling and the prefactor), leading to the possibility that ph-AFQMC will emerge as a scalable benchmark methodology for transition metal-containing systems.…”

Singlet–Triplet Energy Gaps of Organic Biradicals and Polyacenes with Auxiliary-Field Quantum Monte Carlo

“…64 ST gaps are extrapolated to the complete basis set (CBS) limit using exponential and 1/x 3 forms for the mean-field and correlation energies, respectively, as detailed in, e.g., Ref. 61.…”

Efficient Ab Initio Auxiliary-Field Quantum Monte Carlo Calculations in Gaussian Bases via Low-Rank Tensor Decomposition

“…We also find that the memory requirements using this approach are significantly reduced from the conventional AFQMC algorithm using Cholesky decomposition alone. The algorithmic advances may also be used in conjunction with parallel efforts to accelerate AFQMC through improved hardware implementations [54]. While more work is necessary to establish the relative benefits in AFQMC of exposing sparsity through low rank, as in the current work, versus the direct utilization of sparse operations, we expect such combinations to greatly advance the practical possibilities for AFQMC calculations on large systems.…”