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This paper considers the extension of the non-Markovian stochastic approachfor quantum open systems strongly coupled to a fermionic bath, to the models inwhich the system operators commute with the fermion bath. This technique canalso be a useful tool for studying open quantum systems coupled to a spin-chainenvironment, which can be further transformed into an effective fermionic bath.We derive an exact stochastic Schr\"{o}dinger equation (SSE), called fermionicquantum state diffusion (QSD) equation, from the first principle by using thefermionic coherent state representation. The reduced density operator for theopen system can be recovered from the average of the solutions to the QSDequation over the Grassmann-type noise. By employing the exact fermionic QSDequation, we can derive the corresponding exact master equation. The power ofour approach is illustrated by the applications of our stochastic approach toseveral models of interest including the one-qubit dissipative model, thecoupled two-qubit dissipative model, the quantum Brownian motion model and theN-fermion model coupled to a fermionic bath. Different effects caused by thefermionic and bosonic baths on the dynamics of open systems are also discussed.

Fermionic Stochastic Schr\"{o}dinger Equation and Master Equation: An Open System Model