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

Abstract

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 \(\langle \sigma _z\rangle \) and \(\langle \sigma _x\rangle \) with which the identification problem can be solved via our least squares approach. In the case of measuring the time trace observable \(\langle \sigma _x\rangle \), a data-driven method is also developed to estimate the unmeasured \(\langle \sigma _y\rangle \) such that the identification problem fits into the least squares framework. A physical example is given to show the effectiveness of our method.