A light weight regularization for wave function parameter gradients in quantum Monte Carlo

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 na\"ive 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 na\"ive 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.