  Quantum Brownian motion plays a fundamental role in many areas of modern
physics. In the path-integral formulation, the environmental quantum
fluctuations driving the system dynamics can be characterized by auxiliary
stochastic fields. For fermion bath environment the stochastic fields are
Grassmann-valued, and cannot be represented by conventional classical numbers.
In this Letter, we propose a strategy to map the nonclassical Grassmann fields
onto Gaussian white noises along with a set of quantized pseudo-states. This
results in a numerically feasible stochastic equation of motion (SEOM) method
for fermionic open systems. The SEOM yields exact physical observables for
noninteracting systems, and accurate approximate results for interacting
systems. The practicality and accuracy of the proposed SEOM are exemplified by
direct stochastic simulations conducted on a single-impurity Anderson model.
