Once developed for quantum theory, tensor networks have been established as a successful machine learning paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum machine learning to assess problems that classical computers are unable to solve efficiently. Their nature at the interface between physics and machine learning makes tensor networks easily deployable on quantum computers. In this review article, we shed light on one of the major architectures considered to be predestined for variational quantum machine learning. In particular, we discuss how layouts like MPS, PEPS, TTNs and MERA can be mapped to a quantum computer, how they can be used for machine learning and data encoding and which implementation techniques improve their performance.

翻译：张量网络最初为量子理论而发展，如今已成功确立为一种机器学习范式。在量子机器学习这一新兴领域中，它们被重新引入量子范畴，以解决经典计算机无法高效处理的问题。其位于物理学与机器学习交叉领域的特性，使得张量网络易于在量子计算机上部署。在这篇综述文章中，我们聚焦于被认为专为变分量子机器学习设计的主要架构之一。具体而言，我们讨论了MPS、PEPS、TTN和MERA等布局如何映射到量子计算机，如何用于机器学习与数据编码，以及哪些实现技术能提升其性能。