The Full Configuration Interaction Quantum Monte Carlo Method through the Lens of Inexact Power Iteration

Abstract

In this paper, we propose a general analysis framework for inexact power iteration, which can be used to efficiently solve high-dimensional eigenvalue problems arising from quantum many-body problems. Under this framework, we establish the convergence theorems for several recently proposed randomized algorithms, including full configuration interaction quantum Monte Carlo and fast randomized iteration. The analysis is consistent with numerical experiments for physical systems such as the Hubbard model and small chemical molecules. We also compare the algorithms both in convergence analysis and numerical results.

Topics & Concepts