A Linear Least Squares Method to Identify the Damping Rate Function for a Non-Markovian Single Qubit System

Abstract

In this paper, we present a linear least squares method to identify a damping rate function for a non-Markovian single qubit system. The dynamics of the system is described by a time-convolutionless master equation where the unknown damping rate function contains all the information of the environment. By expressing the function as a polynomial of time with unknown coefficients, we convert the identification problem into a parameter estimation problem. We transform the master equation into a Bloch differential equation, and obtain a reduced system whose output is the time trace of an observable. Then we use a linear least squares method to estimate unknown coefficients in the polynomial by utilizing the measured outputs. Finally, the effectiveness of our method is shown in an example of a two-level atom non-Markovian system.