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.

这项研究检查了不同的量子状态重构技术的性能，并证明了可以通过应用方差减少技术来系统地减少算法的量子资源需求。作者比较了两种主要的神经量子态编码方法，即神经密度算符和正算子值测量表示，并阐述了它们在混杂度不同的情况下表现出不同的性能。

神经网络混合态重建的经验样本复杂度

Empirical Sample Complexity of Neural Network Mixed State Reconstruction

We introduce an approach for performing quantum state reconstruction on
systems of $n$ qubits using a machine-learning-based reconstruction system
trained exclusively on $m$ qubits, where $m\geq n$. This approach removes the
necessity of exactly matching the dimensionality of a system under
consideration with the dimension of a model used for training. We demonstrate
our technique by performing quantum state reconstruction on randomly sampled
systems of one, two, and three qubits using machine-learning-based methods
trained exclusively on systems containing at least one additional qubit. The
reconstruction time required for machine-learning-based methods scales
significantly more favorably than the training time; hence this technique can
offer an overall savings of resources by leveraging a single neural network for
dimension-variable state reconstruction, obviating the need to train dedicated
machine-learning systems for each Hilbert space.

本文介绍了一种利用基于机器学习的重建系统，在只使用包含至少一个额外量子比特的系统训练的情况下，对 n 量子比特系统进行量子态重建的方法，证明了该方法比需要匹配模型维度的方法更节省资源。