Tensor networks for quantum computing

Tensor networks have become a useful tool in many areas of physics, especially in quantum information science and quantum computing, where they are used to represent and manipulate quantum states and processes. The original use of tensor networks is the simulation of quantum systems, where tensor networks provide compressed representations of the structured systems. As research into quantum computing and tensor networks progresses, a plethora of new applications are becoming increasingly relevant. This Technical Review discusses the diverse applications of tensor networks to demonstrate that they are an important instrument for quantum computing. Specifically, we summarize the application of tensor networks in various domains of quantum computing, including simulation of quantum computation, quantum circuit synthesis, quantum error correction and mitigation, and quantum machine learning. Finally, we provide an outlook on the opportunities that tensor-network techniques provide and the challenges they may face in the future. Tensor networks provide a powerful tool for understanding and improving quantum computing. This Technical Review discusses applications in simulation, circuit synthesis, error correction and mitigation, and quantum machine learning.