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Journal of Computational Chemistry

Manager–worker‐based model for the parallelization of quantum Monte Carlo on heterogeneous and homogeneous networks

Michael T. Feldmann, Julian C. Cummings, David R. Kent, Richard P. Muller, William A. Goddard

Published Oct 5, 2007• 10 citations
Publisher

Abstract

A manager-worker-based parallelization algorithm for Quantum Monte Carlo (QMC-MW) is presented and compared with the pure iterative parallelization algorithm, which is in common use. The new manager-worker algorithm performs automatic load balancing, allowing it to perform near the theoretical maximal speed even on heterogeneous parallel computers. Furthermore, the new algorithm performs as well as the pure iterative algorithm on homogeneous parallel computers. When combined with the dynamic distributable decorrelation algorithm (DDDA) [Feldmann et al., J Comput Chem 28, 2309 (2007)], the new manager-worker algorithm allows QMC calculations to be terminated at a prespecified level of convergence rather than upon a prespecified number of steps (the common practice). This allows a guaranteed level of precision at the least cost. Additionally, we show (by both analytic derivation and experimental verification) that standard QMC implementations are not "perfectly parallel" as is often claimed.

DOI
10.1002/jcc.20836

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A manager-worker-based parallelization algorithm for Quantum Monte Carlo (QMC-MW) is presented and compared with the pure iterative parallelization algorithm, which is in common use. The new manager-worker algorithm performs automatic load balancing, allowing it to perform near the theoretical maximal speed even on heterogeneous parallel computers. Furthermore, the new algorithm performs as well as the pure iterative algorithm on homogeneous parallel computers. When combined with the dynamic distributable decorrelation algorithm (DDDA) [Feldmann et al., J Comput Chem 28, 2309 (2007)], the new manager-worker algorithm allows QMC calculations to be terminated at a prespecified level of convergence rather than upon a prespecified number of steps (the common practice). This allows a guaranteed level of precision at the least cost. Additionally, we show (by both analytic derivation and experimental verification) that standard QMC implementations are not "perfectly parallel" as is often claimed.
The exponential growth in computer power over the past few decades has been a huge boon to computational chemistry, physics, biology, and materials science. Now, a standard workstation or Linux cluster can calculate semi-quantitative properties of moderately sized systems. The next step in computational science is developing better algorithms which allow quantitative calculations of a system's properties. A relatively new class of algorithms, known collectively as Quantum Monte Carlo (QMC), has the potential to quantitatively calculate the properties of molecular systems. Furthermore, QMC scales as O(N3)O(N^3)O(N3) or better. This makes possible very high-level calculations on systems that are too large to be examined using standard high-level methods. This thesis develops (1) an efficient algorithm for determining "on-the-fly" the statistical error in serially correlated data, (2) a manager-worker parallelization algorithm for QMC that allows calculations to run on heterogeneous parallel computers and computational grids, (3) a robust algorithm for optimizing Jastrow functions which have singularities for some parameter values, and (4) a proof-of-concept demonstrating that it is possible to find transferable parameter sets for large classes of compounds.
We reexamine some fundamental Quantum Monte Carlo (QMC) algorithms with the goal of making QMC more mainstream and efficient. Two major themes exist: (1) Make QMC faster and cheaper, and (2) Make QMC more robust and easier to use. A fast "on-the-fly" algorithm to extract uncorrelated estimators from serially correlated data on a huge network is presented, DDDA. A very efficient manager-worker algorithm for QMC parallelization is presented, QMC-MW. Reduced expense VMC optimization procedure is presented to better guess initial Jastrow parameter sets for hydrocarbons, GJ. I also examine the formation and decomposition of aminomethanol using a variety of methods including a test of the hydrocarbon GJ set on these oxygen- and nitrogen-containing systems. The QMC program suite QMcBeaver is available from the authors in its entirety while a user's and developer's manual is attached as supplementary material.
Ab initio quantum Monte Carlo (QMC) is a stochastic approach for solving the many-body Schrödinger equation without resorting to one-body approximations. QMC algorithms are readily parallelizable via ensembles of Nw walkers, making them well suited to large-scale high-performance computing. Among the QMC techniques, diffusion Monte Carlo (DMC) is widely regarded as the most reliable since it provides the projection onto the ground state of a given Hamiltonian under the fixed-node approximation. One practical realization of DMC is the lattice regularized diffusion Monte Carlo (LRDMC) method, which discretizes the Hamiltonian within the Green's function Monte Carlo framework. DMC methods-including LRDMC-employ the so-called branching technique to stabilize walker weights and populations. At the branching step, walkers must be synchronized globally; any imbalance in per-walker workload can leave central processing unit (CPU) or graphics processing unit (GPU) cores idle, thereby degrading overall hardware utilization. The conventional LRDMC algorithm intrinsically suffers from such load imbalance, which grows as log(Nw), rendering it less efficient on modern parallel architectures. In this work, we present an LRDMC algorithm that inherently addresses the load imbalance issue and achieves significantly improved weak-scaling parallel efficiency. Using the binding energy calculation of a water-methane complex as a test case, we demonstrated that the conventional and load-balanced LRDMC algorithms yield consistent results. Furthermore, by utilizing the Leonardo supercomputer equipped with NVIDIA A100 GPUs, we demonstrated that the load-balanced LRDMC algorithm can maintain extremely high parallel efficiency (∼98%) up to 512 GPUs (corresponding to Nw = 51 200), together with a speedup of ×1.24 if directly compared with the conventional LRDMC algorithm with the same number of walkers. The speedup stays sizable, i.e., × 1.18, even if the number of walkers is reduced to Nw = 400.
Various strategies to implement efficiently quantum Monte Carlo (QMC) simulations for large chemical systems are presented. These include: (i) the introduction of an efficient algorithm to calculate the computationally expensive Slater matrices. This novel scheme is based on the use of the highly localized character of atomic Gaussian basis functions (not the molecular orbitals as usually done), (ii) the possibility of keeping the memory footprint minimal, (iii) the important enhancement of single-core performance when efficient optimization tools are used, and (iv) the definition of a universal, dynamic, fault-tolerant, and load-balanced framework adapted to all kinds of computational platforms (massively parallel machines, clusters, or distributed grids). These strategies have been implemented in the QMC=Chem code developed at Toulouse and illustrated with numerical applications on small peptides of increasing sizes (158, 434, 1056, and 1731 electrons). Using 10-80 k computing cores of the Curie machine (GENCI-TGCC-CEA, France), QMC=Chem has been shown to be capable of running at the petascale level, thus demonstrating that for this machine a large part of the peak performance can be achieved. Implementation of large-scale QMC simulations for future exascale platforms with a comparable level of efficiency is expected to be feasible.
Quantum Monte Carlo (QMC) algorithms are among the most powerful classical methods for simulating quantum systems, yet their accuracy is often limited by the systematic errors in the approximations used, such as Trotterization. Here we introduce randomly compiled quantum Monte Carlo (RC-QMC) as a general framework that suppresses these systematic errors by averaging over a family of approximations rather than relying on a single fixed one. This strategy is grounded in the concept of randomized compiling from quantum computing, which suppresses errors by sampling over quantum gates, at essentially no additional computational cost. Consequently, our framework achieves a computational advantage over standard QMC methods when estimating a target state to a desired level of accuracy. We illustrate this advantage on two key Monte Carlo algorithms: (1) path integral quantum Monte Carlo for estimating thermal states, and (2) the quantum trajectories method for simulating open system dynamics. In aggregate, these results represent a cross-fertilization of quantum and classical algorithms, are readily generalizable to other QMC methods, and suggest wider applications in classical simulation.
We introduce a new high-performance design for parallelism within the Quantum Monte Carlo code QMCPACK. We demonstrate that the new design is better able to exploit the hierarchical parallelism of heterogeneous architectures compared to the previous GPU implementation. The new version is able to achieve higher GPU occupancy via the new concept of crowds of Monte Carlo walkers, and by enabling more host CPU threads to effectively offload to the GPU. The higher performance is expected to be achieved independent of the underlying hardware, significantly improving developer productivity and reducing code maintenance costs. Scientific productivity is also improved with full support for fallback to CPU execution when GPU implementations are not available or CPU execution is more optimal.