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

The parameter derivative of the expectation value of the energy, partial derivative E/partial derivative p, is a key ingredient in variational Monte Carlo (VMC) wave function optimization methods. In some cases, a naive 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 naive 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 derivative E/partial derivative p for a multi-Slater-Jastrow trial wave function on the LiH molecule and in the optimization of a multi-Slater-Jastrow trial wave function on the CuO molecule. This regularized estimator is a simple and efficient estimator of partial derivative E/partial derivative p for VMC optimization techniques.