Inchworm Monte Carlo method for open quantum systems

TL;DR

This paper rigorously analyzes and improves the inchworm Monte Carlo method for open quantum systems, introducing a new integro-differential formulation and deterministic schemes, validated on the spin-boson model.

Contribution

The paper provides a rigorous validation of the inchworm Monte Carlo method and introduces an integro-differential formulation with deterministic time-integration schemes for enhanced performance.

Findings

Validated the inchworm Monte Carlo method for open quantum systems.

Developed a new integro-differential formulation of the algorithm.

Improved the algorithm with classical deterministic time-integration schemes.

Abstract

We investigate in this work a recently proposed diagrammatic quantum Monte Carlo method --- the inchworm Monte Carlo method --- for open quantum systems. We establish its validity rigorously based on resummation of Dyson series. Moreover, we introduce an integro-differential equation formulation for open quantum systems, which illuminates the mathematical structure of the inchworm algorithm. This new formulation leads to an improvement of the inchworm algorithm by introducing classical deterministic time-integration schemes. The numerical method is validated by applications to the spin-boson model.