Tensor networks for quantum machine learning

Once developed for quantum theory, tensor networks (TNs) have been established as a successful machine learning (ML) paradigm. Now, they have been ported back to the quantum realm in the emerging field of quantum ML to assess problems that classical computers are unable to solve efficiently. Their nature at the interface between physics and ML makes TNs 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 ML. In particular, we discuss how layouts like matrix product state, projected entangled pair states, tree tensor networks and multi-scale entanglement renormalization ansatz can be mapped to a quantum computer, how they can be used for ML and data encoding and which implementation techniques improve their performance.