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This paper provides a detailed account of the numerical implementation of thestochastic equation of motion (SEOM) method for the dissipative dynamics offermionic open quantum systems. To enable direct stochastic calculations, aminimal auxiliary space (MAS) mapping scheme is adopted, with which thetime-dependent Grassmann fields are represented by c-numbers noises and a setof pseudo-operators. We elaborate on the construction of the system operatorsand pseudo-operators involved in the MAS-SEOM, along with the analyticexpression for the particle current. The MASSEOM is applied to study therelaxation and voltage-driven dynamics of quantum impurity systems described bythe single-level Anderson impurity model, and the numerical results arebenchmarked against those of the highly accurate hierarchical equations ofmotion (HEOM) method. The advantages and limitations of the present MAS-SEOMapproach are discussed extensively.

Stochastic Equation of Motion Approach to Fermionic Dissipative Dynamics. II. Numerical Implementation