The exact description of real-time dynamics in many-body quantum systems continues to provide major challenges, especially for strongly correlated electronic systems and dissipative condensed phase charge and energy transfer problems. While the imaginary-time diagrammatic Quantum Monte Carlo (dQMC) method has proven efficient and accurate for obtaining thermodynamic properties, the realtime version of the dQMC method has been plagued by the dynamical sign problem, causing the computational cost to scale exponentially with increasing time. Recently, to overcome this problem, the “inchworm algorithm” has been developed to optimally recycle diagrammatic information and enable exact real-time simulation of many-body quantum dynamics. In this talk, I will introduce variants of
the inchworm dQMC method for dissipative quantum dynamics and discuss the benefits and drawbacks, as compared to other numerically exact approaches. This talk will provide an overview of my past work in this area with some thoughts on future directions.