  In this paper, the Pontryagin-type maximum principle for optimal control of
quantum stochastic systems in fermion fields is obtained. These systems have
gained significant prominence in numerous quantum applications ranging from
physical chemistry to multi-dimensional nuclear magnetic resonance experiments.
Furthermore, we establish the existence and uniqueness of solutions to backward
quantum stochastic differential equations driven by fermion Brownian motion.
The application of noncommutative martingale inequalities and the martingale
representation theorem enables this achievement.
