Empirical Sample Complexity of Neural Network Mixed State Reconstruction
Haimeng Zhao Giuseppe Carleo Filippo Vicentini
Quantum state reconstruction using Neural Quantum States has been proposed as
a viable tool to reduce quantum shot complexity in practical applications, and
its advantage over competing techniques has been shown in numerical experiments
focusing mainly on the noiseless case. In this work, we numerically investigate
the performance of different quantum state reconstruction techniques for mixed
states: the finite-temperature Ising model. We show how to systematically
reduce the quantum resource requirement of the algorithms by applying variance
reduction techniques. Then, we compare the two leading neural quantum state
encodings of the state, namely, the Neural Density Operator and the positive
operator-valued measurement representation, and illustrate their different
performance as the mixedness of the target state varies. We find that certain
encodings are more efficient in different regimes of mixedness and point out
the need for designing more efficient encodings in terms of both classical and
quantum resources.