Making the most of data: Quantum Monte Carlo postanalysis revisited

Area of Science:

• Computational Physics
• Quantum Chemistry

Background:

• Quantum Monte Carlo (QMC) methods rely on statistical averages for energy estimation.
• Accurate estimation of statistical errors is crucial but challenging in QMC.
• Various methods exist for error estimation, each with limitations.

Purpose of the Study:

• To evaluate the performance of three distinct error estimation techniques.
• To compare these methods across different QMC algorithms: diffusion Monte Carlo, full configuration interaction Quantum Monte Carlo (FCIQMC), and coupled cluster Monte Carlo (CCMC).
• To develop a robust hybrid method for reliable error estimation in QMC energy time series.

Main Methods:

• Evaluation of the Straatsma method for error estimation.
• Application of an autoregressive model for time series analysis.
• Utilizing blocking analysis with von Neumann's ratio test for randomness.
• Development of a hybrid analysis method integrating multiple techniques.
• Assessment of the mean squared error rule for determining equilibration start points.

Main Results:

• The Straatsma method, autoregressive model, and blocking analysis show varying performance for QMC energy time series.
• A novel hybrid analysis method is proposed, yielding reliable error estimates for FCIQMC and CCMC.
• The mean squared error rule effectively identifies the equilibrated phase start point in time series.

Conclusions:

• The hybrid analysis method provides dependable error estimates for FCIQMC and CCMC.
• Accurate determination of the equilibrated phase is essential for reliable QMC results.
• This work enhances the accuracy and reliability of error estimation in advanced QMC simulations.