Identifying a damping rate function for a non-Markovian single qubit system

In this paper, we present a gradient algorithm to identify a damping rate function for a non-Markovian single qubit system. The dynamics of the single qubit system in a non-Markovian environment are assumed to obey a time convolutionless master equation, where all the non-Markovian effects of the environment are combined in the unknown damping rate function. To identify the damping rate function, we measure time trace observables of the qubit such that we can formulate the identification procedure as an optimization problem. Thus, we design a gradient algorithm to optimally reveal the damping rate function.