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

The full configuration interaction quantum Monte Carlo method in the lens of inexact power iteration