论文标题
量子蒙特卡洛中波函数参数梯度的轻巧正规化
A light weight regularization for wave function parameter gradients in quantum Monte Carlo
论文作者
论文摘要
能源期望值的参数衍生物，$ \ partial e/\ partial p $，是变异量子蒙特卡洛（VMC）波函数功能优化方法的关键成分。在某些情况下，该衍生物的幼稚蒙特卡洛估计受到无限差异的影响，该方差抑制了依赖于衍生物稳定估计值的优化方法的效率。在这项工作中，我们得出了一个简单的天真估计量的正规化，该估计量很难在现有的VMC代码中实现，具有有限的差异，并且可以忽略不计，可以将其推断至零偏差而无需额外成本。我们使用此估计器来构建$ \ partial e/\ partial p $的无偏，有限的方差估计，用于在LIH分子上的多间隙jastrow试验波函数。该正则化估计器是用于VMC优化技术的$ \部分E/\部分P $的简单有效估计器。
The parameter derivative of the expectation value of the energy, $\partial E/\partial p$, is a key ingredient in variational quantum Monte Carlo (VMC) wave function optimization methods. In some cases, a naïve Monte Carlo estimate of this derivative suffers from an infinite variance which inhibits the efficiency of optimization methods that rely on a stable estimate of the derivative. In this work, we derive a simple regularization of the naïve estimator which is trivial to implement in existing VMC codes, has finite variance, and a negligible bias which can be extrapolated to zero bias with no extra cost. We use this estimator to construct an unbiased, finite variance estimation of $\partial E/\partial p$ for a multi-Slater-Jastrow trial wave function on the LiH molecule. This regularized estimator is a simple and efficient estimator of $\partial E/\partial p$ for VMC optimization techniques.
