Study on estimating quantum discord by neural network with prior knowledge

Machine learning has achieved success in many areas because of its powerful fitting ability, so we hope it can help us to solve some significant physical quantitative problems, such as quantum correlation. In this research, we will use neural networks to predict the value of quantum discord. Quantum discord is a measure of quantum correlation which is defined as the difference between quantum mutual information and classical correlation for a bipartite system. Since the definition contains an optimization term, it makes analytically solving hard. For some special cases and small systems, such as two-qubit systems and some X-states, the explicit solutions have been calculated. However, for general cases, we still know very little. Therefore, we study the feasibility of estimating quantum discord by machine learning method on two-qubit systems. In order to get an interpretable and high-performance model, we modify the ordinary neural network by introducing some prior knowledge which comes from the analysis about quantum discord. Our results show that prior knowledge actually improves the performance of neural network.