We survey various recent results that rigorously study the complexity of learning quantum states. These include progress on quantum tomography, learning physical quantum states, alternate learning models to tomography and learning classical functions encoded as quantum states. We highlight how these results are paving the way for a highly successful theory with a range of exciting open questions. To this end, we distill 25 open questions from these results.

翻译：本文系统综述了近期关于量子态学习复杂性的严谨研究成果，涵盖量子层析成像、物理量子态学习、替代层析成像的学习模型以及编码为量子态的经典函数学习等领域的最新进展。我们着重阐释这些成果如何为构建高度成功的理论体系奠定基础，并由此衍生出系列富有前景的开放性问题。为此，我们提炼出25个源于这些成果的待解难题。