Noncommutative optimal control and quantum networks

Optimal control is formulated based on a noncommutative calculus of operator derivatives. The use of optimal control methods in the design of quantum systems relies on the differentiation of an operator-valued function with respect to the relevant operator. Noncommutativity between the operator and its derivative leads to a generalization of the conventional method of control for classical systems. This formulation is applied to quantum networks of both spin and bosonic particles for the purpose of quantum state control via quantum random walks.