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Making the most of data: Quantum Monte Carlo postanalysis revisited

Tom Ichibha*

Verena A. Neufeld

Kenta Hongo

Ryo Maezono†

Alex J. W. Thom‡

  • School of Information Science, JAIST, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan

  • Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom and Department of Chemistry, Columbia University, New York, New York 10027, USA

  • Research Center for Advanced Computing Infrastructure, JAIST, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan

  • School of Information Science, JAIST, 1-1 Asahidai, Nomi, Ishikawa 923-1292, Japan

  • Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom

  • *ichibha@icloud.com
  • †rmaezono@mac.com
  • ‡ajwt3@cam.ac.uk
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Phys. Rev. E 105, 045313 – Published 19 April, 2022

DOI: https://doi.org/10.1103/PhysRevE.105.045313

Abstract

In quantum Monte Carlo (QMC) methods, energy estimators are calculated as (functions of) statistical averages of quantities sampled during a calculation. Associated statistical errors of these averages are often estimated. This error estimation is not straightforward and there are several choices of the error estimation methods. We evaluate the performance of three methods (the Straatsma method, an autoregressive model, and a blocking analysis based on von Neumann's ratio test for randomness) for the energy time series given by three QMC methods [diffusion Monte Carlo, full configuration interaction Quantum Monte Carlo (FCIQMC), and coupled cluster Monte Carlo (CCMC)]. From these analyses, we describe a hybrid analysis method which provides reliable error estimates for a series of various lengths of FCIQMC and CCMC's time series. Equally important is the estimation of the appropriate start point of the equilibrated phase. We establish that a simple mean squared error rule method as described by White [K. P. White, Jr., Simulation 69(6), 323 (1997)] can provide reasonable estimations.

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Phys. Rev. E 105, 045313– Published 19 April, 2022
  • Received 1 June 2021
  • Accepted 10 March 2022
Article part of CHORUS
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