  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.
