Many recent developments in chemistry and material science utilize systems that exhibit unique quantum properties. A quantum optimal control strategy can maximize the performance of electronic devices that rely on quantum properties, e.g., minimizing the currents in molecular junctions. Computationally, solving the control problem requires visiting the time-dependent Schrödinger equation frequently, and the corresponding solutions will be combined with an optimization method. In this talk, we examine the overall approximation error and estimate the complexity given the error tolerance. We focus on various methods for integrating optimization algorithms and Hamiltonian simulations to achieve provable accuracy.