Tensor networks for quantum computing

Abstract

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. Tensor networks often provide efficient representations of mathematical objects encountered in quantum physics and quantum computing. Tensor networks are powerful tools for classical simulations of quantum computing, and they are crucial to the understanding of the potential of quantum computational advantage. Tensor networks are useful for synthesizing quantum circuits that prepare potentially interesting quantum states. Tensor networks are a useful mathematical tool for understanding quantum error correction and provide a powerful computational tool to implement quantum error correction and error mitigation. It is an open question whether tensor networks can provide advantage for machine learning using quantum computing. Tensor networks often provide efficient representations of mathematical objects encountered in quantum physics and quantum computing. Tensor networks are powerful tools for classical simulations of quantum computing, and they are crucial to the understanding of the potential of quantum computational advantage. Tensor networks are useful for synthesizing quantum circuits that prepare potentially interesting quantum states. Tensor networks are a useful mathematical tool for understanding quantum error correction and provide a powerful computational tool to implement quantum error correction and error mitigation. It is an open question whether tensor networks can provide advantage for machine learning using quantum computing.