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

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 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 FRI scheme is about 10 to 60 times more statistically efficient than the multinomial FRI scheme, which is in turn about 1.4 to 200 times more statistically efficient than FCIQMC.

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