The auxiliary‐field quantum Monte Carlo (AFQMC) method provides a computational framework for solving the time‐independent Schrödinger equation in atoms, molecules, solids, and a variety of model systems. AFQMC has recently witnessed remarkable growth, especially as a tool for electronic structure computations in real materials. The method has demonstrated excellent accuracy across a variety of correlated electron systems. Taking the form of stochastic evolution in a manifold of nonorthogonal Slater determinants, the method resembles an ensemble of density‐functional theory (DFT) calculations in the presence of fluctuating external potentials. Its computational cost scales as a low‐power of system size, similar to the corresponding independent‐electron calculations. Highly efficient and intrinsically parallel, AFQMC is able to take full advantage of contemporary high‐performance computing platforms and numerical libraries. In this review, we provide a self‐contained introduction to the exact and constrained variants of AFQMC, with emphasis on its applications to the electronic structure of molecular systems. Representative results are presented, and theoretical foundations and implementation details of the method are discussed.

中文翻译：

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用辅助场量子蒙特卡洛方法从头算分子系统

辅助场量子蒙特卡洛（AFQMC）方法提供了一个计算框架，用于求解原子，分子，固体和各种模型系统中与时间无关的薛定ding方程。AFQMC最近见证了惊人的增长，特别是作为用于在真实材料中进行电子结构计算的工具。该方法在各种相关的电子系统中显示出极好的准确性。该方法以非正交Slater行列式形式的随机演化形式出现，类似于在外部势能波动的情况下密度泛函理论（DFT）计算的集合。与相应的独立电子计算类似，它的计算成本是系统规模的低功耗。高效且本质上是并行的，AFQMC能够充分利用现代高性能计算平台和数值库。在本文中，我们对AFQMC的确切和受限制的变体进行了全面的介绍，重点介绍了AFQMC在分子系统电子结构中的应用。给出了代表性的结果，并讨论了该方法的理论基础和实现细节。