The Lognormal Distribution and Quantum Monte Carlo Data

TL;DR

This paper introduces a method to analyze lognormal-like distributions in Quantum Monte Carlo data, improving error estimation for ground state energy calculations in quantum models.

Contribution

A novel method is proposed to estimate lognormal distributions in Quantum Monte Carlo data, enhancing statistical analysis beyond Gaussian assumptions.

Findings

Improved error estimates for quantum Monte Carlo data.

Application to a simple quantum model demonstrates effectiveness.

Better understanding of distribution characteristics in quantum simulations.

Abstract

Quantum Monte Carlo data are often afflicted with distributions that resemble lognormal probability distributions and consequently their statistical analysis can not be based on simple Gaussian assumptions. To this extent a method is introduced to estimate these distributions and thus give better estimates to errors associated with them. This method is applied to a simple quantum model utilizing the single-thread Monte Carlo algorithm to estimate ground state energies.