The full configuration interaction quantum Monte Carlo method in 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 the proposed framework, we establish the convergence theorems for several recently proposed randomized algorithms, including the full configuration interaction quantum Monte Carlo (FCIQMC) and the fast randomized iteration (FRI). The analysis is consistent with numerical experiments for physical systems such as Hubbard model and small chemical molecules. We also compare the algorithms both in convergence analysis and numerical results.

References in corpus (2)

• Semistochastic Heat-bath Configuration Interaction method: selected configuration interaction with semistochastic perturbation theory
• A Projector Quantum Monte Carlo Method for non-linear wavefunctions

Cited by in corpus (6)

• Coordinate descent full configuration interaction
• The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up
• Optimal Orbital Selection for Full Configuration Interaction (OptOrbFCI): Pursuing the Basis Set Limit under a Budget
• Approximating matrix eigenvalues by subspace iteration with repeated random sparsification
• Beyond Walkers in Stochastic Quantum Chemistry: Reducing Error using Fast Randomized Iteration
• Improved Fast Randomized Iteration Approach to Full Configuration Interaction