A least squares identifier for a quantum non-Markovian environment model

In this paper, we present a least squares approach to identifying an unknown damping rate function in a time-convolution-less master equation describing the non-Markovian dynamics of a probing single qubit. For the purpose of identification, we measure two kinds of time trace observables and with which the identification problem can be solved via our least squares approach. In the case of measuring the time trace observable , a data-driven method is also developed to estimate the unmeasured such that the identification problem fits into the least squares framework. A physical example is given to show the effectiveness of our method.