Confidence and efficiency scaling in Variational Quantum Monte Carlo calculations

TL;DR

This paper introduces a robust method for evaluating statistical errors in Monte Carlo calculations, verifies equilibrium hypotheses, and derives efficiency scaling laws demonstrated through Variational Monte Carlo simulations of a two-dimensional electron gas.

Contribution

It presents a practical approach to determine effective variance and verify equilibrium in Monte Carlo methods, along with derived efficiency scaling laws for Variational Monte Carlo.

Findings

Effective variance determination method

Verification of equilibrium hypothesis using Kolmogorov-Smirnov test

Derived efficiency scaling laws for Variational Monte Carlo

Abstract

Based on the central limit theorem, we discuss the problem of evaluation of the statistical error of Monte Carlo calculations using a time discretized diffusion process. We present a robust and practical method to determine the effective variance of general observables and show how to verify the equilibrium hypothesis by the Kolmogorov-Smirnov test. We then derive scaling laws of the efficiency illustrated by Variational Monte Carlo calculations on the two dimensional electron gas.