A permutation-equivariant deep learning model for quantum state characterization

The characterization of quantum states is a fundamental step of any application of quantum technologies. Nowadays, there exist several approaches addressing this problem, also based on machine and deep learning techniques. However, all these approaches usually require a number of measurements that scale exponentially with the number of parties composing the system. Threshold quantum state tomography (tQST) addresses this problem and, in some cases of interest, can significantly reduce the number of measurements. In this paper, we study how to combine a permutation-equivariant deep learning model with the tQST protocol. We test the model on quantum state tomography and purity estimation. Finally, we validate the robustness of the model to noise. We show results up to 4 qubits.