Correlations of an environment are crucial for the dynamics of non-Markovian quantum systems, which may not be known in advance. In this paper, we propose a gradient algorithm for identifying the correlations in terms of timevarying 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 to a differential approach for a two-qubit spin chain.
I. INTRODUCTIONTo exactly process quantum information, accurate models, including parameters, structures, and descriptions of dynamics, for quantum information carriers are required. With these models, sophisticated feedback control strategies can be designed, for example, feedback stabilization of a number state in a cavity [1], preservation of quantum coherence and entanglement for qubit systems [2] and linear quantum systems [3], or coherent feedback rejection of quantum colored noise [4], [5].However, in practice, an accurate model may not be obtainable since parts of the parameters, structures or dynamics of the quantum system may not be well understood. This would lead to unexpected experimental results or degraded control performance of a quantum control system. For example, in a recent experiment on quantum dots [6], a calculation based on the theoretical model has a discrepancy from the experimental data on the broadened resonator line-width under suitable parameters, which means that some unknown dynamics of the system are not included in the model. Correspondingly, it is shown that degraded estimation performance can be observed due to ignorance of a noise model for a quantum system [7]. Hence, the problem of how to determine the unknown parameters, structures or dynamics of a "dark" quantum system is an