Understanding and Improving the Efficiency of Full Configuration Interaction Quantum Monte Carlo

Abstract

Within Full Configuration Interaction Quantum Monte Carlo, we investigate how the statistical error behaves as a function of the parameters which control the stochastic sampling. We define the inefficiency as a measure of the statistical error per particle sampling the space and per timestep and show there is a sizeable parameter regime where this is minimised. We find that this inefficiency increases sublinearly with Hilbert space size and can be reduced by localising the canonical Hartree--Fock molecular orbitals, suggesting that the choice of basis impacts the method beyond that of the sign problem.

7 pages, 4 figures, Supplementary material available as 'Ancillary Files'

References in corpus (8)

• Unbiased Reduced Density Matrices and Electronic Properties from Full Configuration Interaction Quantum Monte Carlo
• An excited-state approach within full configuration interaction quantum Monte Carlo
• Semi-stochastic full configuration interaction quantum Monte Carlo: developments and application
• Interaction Picture Density Matrix Quantum Monte Carlo
• Developments in Stochastic Coupled Cluster Theory: The initiator approximation and application to the Uniform Electron Gas
• The sign problem in full configuration interaction quantum Monte Carlo: Linear and sub-linear representation regimes for the exact wave function
• Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo
• Minimising biases in Full Configuration Interaction Quantum Monte Carlo

Cited by in corpus (10)

• The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up
• Exciting determinants in Quantum Monte Carlo: Loading the dice with fast, low memory weights
• Stochastic Coupled Cluster Theory: Efficient Sampling of the Coupled Cluster Expansion
• Linked Coupled Cluster Monte Carlo
• Diagrammatic Coupled Cluster Monte Carlo
• Approximating matrix eigenvalues by subspace iteration with repeated random sparsification
• Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error using Fast Randomized Iteration
• Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification
• Rapidly convergent quantum Monte Carlo using a Chebyshev projector
• Improved Fast Randomized Iteration Approach to Full Configuration Interaction