Iterative methods are generally necessary for solving the design equations to identify optimal quantum controls. Since iteration can be computationally intensive, it is significant to develop good approximate noniterative methods. In this paper we present noniterative techniques for achieving quantum optimal control over the expectation value of positive semidefinite operators. The noniterative methods are characterized by an order index. Zeroth-order methods involving no feedback from the objective are generally found to be inadequate. A proposed first-order noniterative algorithm is expected to often be a good approximation. Numerical tests verify the noniterative capabilities of the algorithm.