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Neural Networks for Quantum Inverse Problems

Quantum Inverse Problem (QIP) is the problem of estimating an unknown quantum system $ρ$ from a set of measurements, whereas the classical counterpart is the Inverse Problem of estimating a distribution from a set of observations. In this paper, we present a neural network based method for QIPs, which has been widely explored for its classical counterpart. The proposed method utilizes the quantum-ness of the QIPs and takes advantage of the computational power of neural networks to achieve higher efficiency for the quantum state estimation. We test the method on the problem of Maximum Entropy Estimation of an unknown state $ρ$ from partial information. Our method yields high fidelity, efficiency and robustness for both numerical experiments and quantum optical experiments.