Lindblad evolution without the sign problem

Quantum Monte Carlo is one of the most powerful numerical tools for studying nonpeturbative properties of quantum many-body systems. However, its application to real-time problems is limited since the complex and highly-oscillating path-integral weight of the real-time evolution harms the important sampling. % , which is the notorious sign problem. In this Letter, we show that some real-time problems in open fermion systems can be simulated using the quantum Monte Carlo. To this end, we prescribe a mapping between a real-time problem in open quantum systems and a statistical problem in non-Hermitian quantum systems; for some cases, the latter can be solved without suffering from the complex measure problem. To explain our idea and demonstrate how it works, we compute the real-time evolution of fidelities in open fermion systems under dissipation.