# Making the most of data: Quantum Monte Carlo Post-Analysis Revisited

## TL;DR

This paper evaluates and compares different error estimation methods for energy estimators in quantum Monte Carlo simulations, proposing a hybrid approach for reliable error analysis across various series lengths.

## Contribution

It introduces a hybrid error estimation method and heuristic schemes for identifying the equilibrated phase in QMC energy series analysis.

## Key findings

- Hybrid analysis provides reliable error estimates for all series lengths.
- MSER heuristic effectively identifies the start of the equilibrated phase.
- Comparison of three error estimation methods demonstrates their strengths and limitations.

## Abstract

In quantum Monte Carlo (QMC) methods, energy estimators are calculated as the statistical average of the Markov chain sampling of energy estimator along with an associated statistical error. This error estimation is not straightforward and there are several choices of the error estimation methods. We evaluate the performance of three methods, Straatsma, an autoregressive model, and a blocking analysis based on von Neumann's ratio test for randomness, for the energy time-series given by Diffusion Monte Carlo, Full Configuration Interaction Quantum Monte Carlo and Coupled Cluster Monte Carlo methods. From these analyses we describe a hybrid analysis method which provides reliable error estimates for series of all lengths. Equally important is the estimation of the appropriate start point of the equilibrated phase, and two heuristic schemes are tested, establishing that MSER (mean squared error rule) gives reasonable and constant estimations independent of the length of time-series.