Alternative sampling for variational quantum Monte Carlo

Abstract

Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within Many-Body Quantum mechanics, and these multi-dimensional integrals may be estimated using Monte Carlo methods. In a previous publication it has been shown that for the simplest, most commonly applied strategy in continuum Quantum Monte Carlo, the random error in the resulting estimates is not well controlled. At best the Central Limit theorem is valid in its weakest form, and at worst it is invalid and replaced by an alternative Generalised Central Limit theorem and non-Normal random error. In both cases the random error is not controlled. Here we consider a new `residual sampling strategy' that reintroduces the Central Limit Theorem in its strongest form, and provides full control of the random error in estimates. Estimates of the total energy and the variance of the local energy within Variational Monte Carlo are considered in detail, and the approach presented may be generalised to expectation values of other operators, and to other variants of the Quantum Monte Carlo method.

14 pages, 9 figures

References in corpus (6)

• Jastrow correlation factor for atoms, molecules, and solids
• Inhomogeneous backflow transformations in quantum Monte Carlo calculations
• Zero-variance principle for Monte Carlo algorithms
• Zero-Variance Zero-Bias Principle for Observables in quantum Monte Carlo: Application to Forces
• Monte Carlo energy and variance minimization techniques for optimizing many-body wave functions
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Cited by in corpus (11)

• Heavy-tailed random error in quantum Monte Carlo
• Excited State Specific Multi-Slater Jastrow Wave Functions
• Methods for calculating forces within quantum Monte Carlo simulations
• A hybrid approach to excited-state-specific variational Monte Carlo and doubly excited states
• Excitation Variance Matching with Limited Configuration Interaction Expansions in Variational Monte Carlo
• Complementary First and Second Derivative Methods for Ansatz Optimization in Variational Monte Carlo
• Optimized structure and vibrational properties by error affected potential energy surfaces
• Reduced Scaling Hilbert Space Variational Monte Carlo
• Optimum and efficient sampling for variational quantum Monte Carlo
• Confidence and efficiency scaling in Variational Quantum Monte Carlo calculations
• Fast Evaluation of Unbiased Atomic Forces in ab initio Variational Monte Carlo via the Lagrangian Technique