Numerical simulations for open quantum system dynamics is a profound challenge. In this talk, we will present some recent works on diagrammatic algorithms for open quantum systems. The focus will be an interplay between the dynamical sign problem and error amplification in numerical integration. In particular, our analysis demonstrates that the technique of partial resummation provides a tool to balance these two types of error, and the recently introduced inchworm Monte Carlo method is a successful case to suppress the numerical sign problem. (Based on joint works with Zhenning Cai and Siyao Yang)
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