NUMERICAL SIMULATION AND ERROR ESTIMATION OF INCHWORM MONTE CARLO METHOD FOR OPEN QUANTUM SYSTEMS

Abstract

We investigate a recently proposed diagrammatic quantum Monte Carlo method known as the inchworm Monte Carlo method for open quantum systems. The work is divided into three parts. In Part I, we establish the validity of the algorithm rigorously based on resummation of Dyson series. Moreover, we introduce an integro-differential equation formulation for open quantum systems, which leads to an improvement of the inchworm algorithm by introducing classical deterministic time-integration schemes. Part II considers the numerical analysis of the inchworm Monte Carlo method. We focus on the growth of the numerical error with respect to the simulation time. Two types of exponential error growth are distinguished to reveal the underlying mechanism of the inchworm Monte Carlo method. In Part III, we present a fast algorithm applying the inclusion-exclusion principle to calculate the bosonic bath influence functional. The fast algorithm reduces the computational cost from double factorial to exponential.