Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error using Fast Randomized Iteration

Abstract

We introduce a family of methods for the full configuration interaction problem in quantum chemistry, based on the fast randomized iteration (FRI) framework [L.-H. Lim and J. Weare, SIAM Rev. 59, 547 (2017)]. These methods, which we term "FCI-FRI," stochastically impose sparsity during iterations of the power method and can be viewed as a generalization of full configuration interaction quantum Monte Carlo (FCIQMC) without walkers. In addition to the multinomial scheme commonly used to sample excitations in FCIQMC, we present a systematic scheme where excitations are not sampled independently. Performing ground-state calculations on five small molecules at fixed cost, we find that the systematic FCI-FRI scheme is 11 to 45 times more statistically efficient than the multinomial FCI-FRI scheme, which is in turn 1.4 to 178 times more statistically efficient than the original FCIQMC algorithm.

arXiv comment19 pages, 7 figures

References in corpus (24)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Continuum variational and diffusion quantum Monte Carlo calculations
• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• A deterministic alternative to the full configuration interaction quantum Monte Carlo method
• Semistochastic Projector Monte Carlo Method
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
• Introduction to the Diffusion Monte Carlo Method
• Unbiased Reduced Density Matrices and Electronic Properties from Full Configuration Interaction Quantum Monte Carlo
• Efficient heat-bath sampling in Fock space
• Linear-scaling and parallelizable algorithms for stochastic quantum chemistry
• An excited-state approach within full configuration interaction quantum Monte Carlo
• The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method
• Semi-stochastic full configuration interaction quantum Monte Carlo: developments and application
• Practical rare event sampling for extreme mesoscale weather
• Coordinate descent full configuration interaction
• Exciting determinants in Quantum Monte Carlo: Loading the dice with fast, low memory weights
• An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo
• The sign problem in full configuration interaction quantum Monte Carlo: Linear and sub-linear representation regimes for the exact wave function
• Stochastic Coupled Cluster Theory: Efficient Sampling of the Coupled Cluster Expansion
• Fast randomized iteration: diffusion Monte Carlo through the lens of numerical linear algebra
• Minimising biases in Full Configuration Interaction Quantum Monte Carlo
• Understanding and Improving the Efficiency of Full Configuration Interaction Quantum Monte Carlo
• The full configuration interaction quantum Monte Carlo method in the lens of inexact power iteration

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• Fully quantum embedding with density functional theory for full configuration interaction quantum Monte Carlo
• Optimal Orbital Selection for Full Configuration Interaction (OptOrbFCI): Pursuing the Basis Set Limit under a Budget
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