Identification of Non-Markovian Environments for Spin Chains

Correlations of an environment are crucial for the dynamics of non-Markovian quantum systems, which may not be known in advance. In this brief, we propose a gradient algorithm for identifying the correlations in terms of the time-varying damping rate functions in a time-convolution-less master equation for spin chains. By measuring time trace observables of the system, the identification procedure can be formulated as an optimization problem. The gradient algorithm is designed based on a calculation of the derivative of an objective function with respect to the damping rate functions, whose effectiveness is shown in a comparison with a differential approach for a two-qubit spin chain.