Optimal ensemble control of open quantum systems with a pseudospectral method

In this paper, we extend our previous results concerning the application of the Legendre pseudospectral method to optimal pulse design problems for open quantum systems. We now consider the more realistic case in which systems are characterized by variations in parameter values, such as relaxation rates and coupling constants. Such dispersions in system parameters motivate us to consider an ensemble of systems, each member distinct due to distinct parameter values. We demonstrate the method with systems from nuclear magnetic resonance (NMR) spectroscopy in liquid. In particular, we highlight the flexibility and robustness of the pseudospectral method approach by developing pulses that minimize the energy or total duration of the pulse sequence.