We review the development of generative modeling techniques in machine
learning for the purpose of reconstructing real, noisy, many-qubit quantum
states. Motivated by its interpretability and utility, we discuss in detail the
theory of the restricted Boltzmann machine. We demonstrate its practical use
for state reconstruction, starting from a classical thermal distribution of
Ising spins, then moving systematically through increasingly complex pure and
mixed quantum states. Intended for use on experimental noisy intermediate-scale
quantum (NISQ) devices, we review recent efforts in reconstruction of a cold
atom wavefunction. Finally, we discuss the outlook for future experimental
state reconstruction using machine learning, in the NISQ era and beyond.

论文综述了机器学习中生成建模技术在恢复实际、嘈杂和多量子比特量子态方面的发展，尤其是限制玻尔兹曼机器的理论，并演示了它在状态重建中的实际应用，从经典热力学分布的伊辛自旋开始，逐步移动到越来越复杂的纯态和混合量子态，通过对实验噪音中间规模量子设备的冷原子波函数重建的最近工作进行总结，最后讨论了未来在 NISQ 时代和以后使用机器学习进行状态重建的展望。