Survey on Computational Applications of Tensor Network Simulations

Tensor networks are a popular and computationally efficient approach to simulate general quantum systems on classical computers and, in a broader sense, a framework for dealing with high-dimensional numerical problems. This paper presents a broad literature review of state-of-the-art applications of tensor networks and related topics across many research domains including: machine learning, mathematical optimisation, materials science, quantum chemistry and quantum circuit simulation. This review aims to clarify which classes of relevant applications have been proposed for which class of tensor networks, and how these perform compared with other classical or quantum simulation methods. We intend this review to be a high-level tour on tensor network applications which is easy to read by non-experts, focusing on key results and limitations rather than low-level technical details of tensor networks.