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Improved walker population control for full configuration interaction quantum Monte Carlo.

Mingrui Yang1, Elke Pahl2, Joachim Brand1

  • 1New Zealand Institute for Advanced Study and Centre for Theoretical Chemistry and Physics, Massey University, Auckland 0632, New Zealand.

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We improved the Full Configuration Interaction Quantum Monte Carlo (FCIQMC) method for more stable ground state energy calculations. This new protocol precisely controls walker numbers, enhancing efficiency and aiding automation.

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Area of Science:

  • Quantum many-body physics
  • Computational chemistry
  • Stochastic methods

Background:

  • Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a stochastic method for determining the ground state of quantum systems.
  • The original FCIQMC protocol by Booth et al. can suffer from walker number overshoots and difficulties in achieving stable equilibration.
  • Efficient walker population control is crucial for accurate and automated quantum many-body calculations.

Purpose of the Study:

  • To present a modified FCIQMC protocol for precise walker population control.
  • To achieve stable equilibration at a pre-defined average walker number, avoiding overshoots.
  • To introduce a population growth witness for detecting annihilation plateaus and addressing the FCIQMC sign problem.

Main Methods:

  • Modification of the original FCIQMC walker population control protocol.
  • Modeling walker population dynamics as a noisy damped harmonic oscillator with damping and forcing parameters.
  • Introduction of a population growth witness to identify annihilation plateaus.

Main Results:

  • Demonstration of precise walker number control and fast equilibration.
  • Confirmation that the standard error of the ground state energy shift estimator and population control bias are unaffected.
  • The new procedure effectively controls walker number, reducing memory consumption.

Conclusions:

  • The enhanced FCIQMC protocol offers superior walker number control and faster equilibration.
  • The method is robust, with no adverse effects on energy estimation accuracy or bias.
  • This improved control facilitates the automation of FCIQMC calculations with minimal code changes.