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

The parameter derivative of the expectation value of the energy is a key ingredient in variational quantum Monte Carlo (VMC) wave function optimization methods. A naive Monte Carlo estimate of this derivative suffers from an infinite variance which inhibits the efficiency of optimization methods which rely on a stable estimate of the derivative. In this work we derive a simple regularization of the naive estimator which is easy to implement and has a neglible bias. This regularization is trivial to implement in a standard VMC code without sampling complex distributions and it can be extrapolated to zero bias without extra computation.