Recent advances in classical machine learning have shown that creating models with inductive biases encoding the symmetries of a problem can greatly improve performance. Importation of these ideas, combined with an existing rich body of work at the nexus of quantum theory and symmetry, has given rise to the field of Geometric Quantum Machine Learning (GQML). Following the success of its classical counterpart, it is reasonable to expect that GQML will play a crucial role in developing problem-specific and quantum-aware models capable of achieving a computational advantage. Despite the simplicity of the main idea of GQML -- create architectures respecting the symmetries of the data -- its practical implementation requires a significant amount of knowledge of group representation theory. We present an introduction to representation theory tools from the optics of quantum learning, driven by key examples involving discrete and continuous groups. These examples are sewn together by an exposition outlining the formal capture of GQML symmetries via "label invariance under the action of a group representation", a brief (but rigorous) tour through finite and compact Lie group representation theory, a reexamination of ubiquitous tools like Haar integration and twirling, and an overview of some successful strategies for detecting symmetries.

翻译：古典机器学习(GQML)的最新进展表明,创建带有感性偏差的模型将问题对称性编码,可以极大地改善绩效。这些想法的进口,加上在量子理论和对称关系方面现有的大量工作,已经产生了几何量子量子机器学习领域(GQML ) 。 在古典机器学习领域取得成功之后,可以合理地预期,GQML将在制定能够实现计算优势的针对具体问题和量子识别模型方面发挥关键作用。尽管GQML的主要理念简单简单 -- -- 创建了尊重数据对称性的结构 -- -- 其实际实施需要大量群体代表性理论的知识。我们介绍了量子学习的光学理论工具,由涉及离散和连续群体的关键例子驱动。这些实例通过“在团体代表行动下的标签”来正式捕获GQML对称性模型。 一种简短(但严格)的通过有限和紧凑合称性小组代表理论进行巡回考察,对成功的集成工具进行重新审视。