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.

翻译：利用神经量子态进行量子态重构已被提出作为在实际应用中降低量子测量复杂度的可行工具，其相较于竞争技术的优势已在主要针对无噪声情形下的数值实验中得到验证。本研究通过数值方法探究了不同量子态重构技术在混合态（有限温度伊辛模型）中的性能表现。我们展示了如何通过方差缩减技术系统性降低算法的量子资源需求。随后，我们比较了两种主流神经量子态编码方法——神经密度算符与正算子值测量表示，并阐明了目标态混合度变化时二者性能表现的差异。研究发现，不同混合度区间内特定编码方式具有更高效率，同时指出有必要从经典与量子资源两个维度设计更高效的编码方案。