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

## TL;DR

This paper introduces FCI-FRI, a stochastic method for quantum chemistry that reduces error and improves efficiency over existing algorithms like FCIQMC by imposing sparsity during iterations.

## Contribution

The paper presents a new FCI-FRI approach that generalizes FCIQMC, with a systematic excitation sampling scheme that significantly enhances statistical efficiency.

## Key findings

- Systematic FCI-FRI is 11 to 45 times more efficient than multinomial FCI-FRI.
- Multinomial FCI-FRI outperforms original FCIQMC by 1.4 to 178 times.
- Method tested on five small molecules at fixed computational cost.

## 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.