School of Information Science, Japan Advanced Institute of Science and Technology, Ishikawa 923-1292, Japan.
J Chem Phys. 2010 Nov 7;133(17):174120. doi: 10.1063/1.3488651.
Quantum mechanics for many-body systems may be reduced to the evaluation of integrals in 3N dimensions using Monte Carlo, providing the Quantum Monte Carlo ab initio methods. Here we limit ourselves to expectation values for trial wave functions, that is to variational quantum Monte Carlo. Almost all previous implementations employ samples distributed as the physical probability density of the trial wave function, and assume the central limit theorem to be valid. In this paper we provide an analysis of random error in estimation and optimization that leads naturally to new sampling strategies with improved computational and statistical properties. A rigorous lower limit to the random error is derived, and an efficient sampling strategy presented that significantly increases computational efficiency. In addition the infinite variance heavy tailed random errors of optimum parameters in conventional methods are replaced with a Normal random error, strengthening the theoretical basis of optimization. The method is applied to a number of first row systems and compared with previously published results.
多体系统的量子力学可以通过蒙特卡罗方法在 3N 维空间中评估积分，从而提供量子蒙特卡罗从头计算方法。在这里，我们仅限于对试探波函数的期望值进行研究，也就是变分量子蒙特卡罗。几乎所有之前的实现都采用了作为试探波函数物理概率密度分布的样本，并假设中心极限定理是有效的。在本文中，我们提供了对随机误差的分析，这自然导致了具有改进的计算和统计特性的新采样策略。推导出了随机误差的严格下限，并提出了一种有效的采样策略，大大提高了计算效率。此外，用正态随机误差取代了传统方法中最优参数的无限方差重尾随机误差，增强了优化的理论基础。该方法应用于一些第一行体系，并与之前发表的结果进行了比较。
