Quantum Monte Carlo simulation

TL;DR

This paper develops a Monte Carlo method for quantum simulation, providing theoretical analysis of its bias, variance, and asymptotic properties to improve estimation accuracy of complex quantum systems.

Contribution

It introduces a novel Monte Carlo approach for quantum simulation and derives its statistical properties, including bias, variance, and asymptotic behavior.

Findings

Derived bias and variance formulas for the estimator

Established asymptotic theory for the Monte Carlo quantum simulation

Designed a scheme to minimize mean square error

Abstract

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.