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Quantum state reconstruction using Neural Quantum States has been proposed asa viable tool to reduce quantum shot complexity in practical applications, andits advantage over competing techniques has been shown in numerical experimentsfocusing mainly on the noiseless case. In this work, we numerically investigatethe performance of different quantum state reconstruction techniques for mixedstates: the finite-temperature Ising model. We show how to systematicallyreduce the quantum resource requirement of the algorithms by applying variancereduction techniques. Then, we compare the two leading neural quantum stateencodings of the state, namely, the Neural Density Operator and the positiveoperator-valued measurement representation, and illustrate their differentperformance as the mixedness of the target state varies. We find that certainencodings are more efficient in different regimes of mixedness and point outthe need for designing more efficient encodings in terms of both classical andquantum resources.

Empirical Sample Complexity of Neural Network Mixed State Reconstruction