Contemporary scientific studies often rely on the understanding of complex quantum systems via computer simulation. This paper initiates the statistical study of quantum simulation and proposes a Monte Carlo method for estimating analytically intractable quantities. We derive the bias and variance for the proposed Monte Carlo quantum simulation estimator and establish the asymptotic theory for the estimator. The theory is used to design a computational scheme for minimizing the mean square error of the estimator.
"Quantum Monte Carlo simulation." Ann. Appl. Stat. 5 (2A) 669 - 683, June 2011. https://doi.org/10.1214/10-AOAS406