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.

The Ground State Electronic Energy of Benzene

“…[61][62][63][64][65][66][67] (SHCI), and iterative CI with selection[68][69][70][71] (iCI) methods all belong to a wider class of selected CI (SCI) methods,[96][97][98][99][100][101][102][103][104][105][106][107][108] which approximate the full linear expansion of the FCI wave function by selecting only important determinants in conjunction with perturbative corrections to account for any residual correlation. The FCI Quantum Monte Carlo[72][73][74][75] (FCIQMC) method offers another approach for sampling the wave function, namely, a stochastic QMC propagation of the wave function in the many-electron Hilbert space aimed at projecting out the FCI ground state.…”

Full Configuration Interaction Excited-State Energies in Large Active Spaces from Subspace Iteration with Repeated Random Sparsification

“…Thus, one can control the cost of multiplication by tuning m. In practice, however, m cannot be chosen to be arbitrarily small. As has been demonstrated previously in the context of related methods, statistical error can increase very rapidly as m is decreased, 25,36,[94][95][96][97] rendering it impossible to achieve accurate energy estimates, even after averaging over many iterations. For the large quantum chemistry problems of interest in this work, the values of m required for acceptable accuracy render this approach too computationally expensive.…”

“…trial vectors) to estimate energies and maintain orthogonality. In ref 33, we applied this approach to the full configuration interaction problem using a simple implementation of our fast randomized iteration approach (FCI-FRI) [35][36][37] to accelerate matrix-vector multiplications. Like FCIQMC and other discrete-space QMC methods, FCI-FRI is a stochastic implementation of an iterative linear algebra scheme involving sequential matrix-vector multiplication operations.…”

Polaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity

“…[56] and is similar in spirit but more efficient than the modifications discussed in Refs. [72][73][74]. It will be described in greater detail elsewhere [75].…”