Numerical analysis for inchworm Monte Carlo method: Sign problem and error growth

Understand

We consider the numerical analysis of the inchworm Monte Carlo method, which is proposed recently to tackle the numerical sign problem for open quantum systems.

• We focus on the growth of the numerical error with respect to the simulation time, for which the inchworm Monte Carlo method shows a flatter curve than the direct application of Monte Carlo method to the classical Dyson series.
• To better understand the underlying mechanism of the inchworm Monte Carlo method, we distinguish two types of exponential error growth, which are known as the numerical sign problem and the error amplification.
• The former is due to the fast growth of variance in the stochastic method, which can be observed from the Dyson series, and the latter comes from the evolution of the numerical solution.