Tensor networks in their canonical and isometric forms have a natural realisation as quantum circuits. Using them as a framework to construct code to run on quantum computers promises the potential to build upon advances in classical simulation and machine learning using tensor networks, with clear quantification of the resources used and identification of potential quantum advantage.
I will discuss the construction of some basic algorithms to do this, emphasising the differences between classical and quantum realisations. I will discuss how the resulting circuits can be structured to mitigate errors on NISQ devices and survey some recent implementations of these ideas on real devices.