Linear-scaling and parallelisable algorithms for stochastic quantum chemistry
Linear-scaling and parallelisable algorithms for stochastic quantum chemistry
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DOI：
10.1080/00268976.2013.877165
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发表时间：
2014-01-01
影响因子：
1.7
通讯作者：
Alavi, Ali
中科院分区：
文献类型：
--
作者：
Booth, George H.;Smart, Simon D.;Alavi, Ali
几十年来，量子化学方法的发展一直由涉及单电子轨道空间上日益复杂的一系列张量收缩的算法主导。他们的推导和实施程序已经发展到需要最少的逻辑量，并在很大程度上依赖于计算效率高的图书馆为基础的矩阵代数和优化的分页方案。在这方面，最近开发的精确随机量子化学算法，以减少计算缩放和内存开销需要一个对比的算法哲学，但一个有效地实现时，可以实现更高的精度/成本比与小的随机误差。此外，他们可以利用大规模并行化的持续趋势，这阻碍了确定性高级量子化学算法的进展。在量子蒙特卡罗社区，随机算法是无处不在的，但量子化学方法的离散福克空间往往是不熟悉的，方法引入算法效率所需的新概念。在本文中，我们将探讨这些概念和详细的算法用于全组态相互作用量子蒙特卡罗（FCIQMC），这是实现和可用的MOLPRO和作为一个独立的代码，是专为高层次的并行性和线性缩放与步行者数。许多算法也用于或可以转移到其他随机量子化学方法和实现中。我们将这些算法应用于强相关的铬二聚体，以证明其效率和并行性。
For many decades, quantum chemical method development has been dominated by algorithms which involve increasingly complex series of tensor contractions over one-electron orbital spaces. Procedures for their derivation and implementation have evolved to require the minimum amount of logic and rely heavily on computationally efficient library-based matrix algebra and optimised paging schemes. In this regard, the recent development of exact stochastic quantum chemical algorithms to reduce computational scaling and memory overhead requires a contrasting algorithmic philosophy, but one which when implemented efficiently can achieve higher accuracy/cost ratios with small random errors. Additionally, they can exploit the continuing trend for massive parallelisation which hinders the progress of deterministic high-level quantum chemical algorithms. In the Quantum Monte Carlo community, stochastic algorithms are ubiquitous but the discrete Fock space of quantum chemical methods is often unfamiliar, and the methods introduce new concepts required for algorithmic efficiency. In this paper, we explore these concepts and detail an algorithm used for Full Configuration Interaction Quantum Monte Carlo (FCIQMC), which is implemented and available in MOLPRO and as a standalone code, and is designed for high-level parallelism and linear-scaling with walker number. Many of the algorithms are also in use in, or can be transferred to, other stochastic quantum chemical methods and implementations. We apply these algorithms to the strongly correlated chromium dimer to demonstrate their efficiency and parallelism.