Quantum Tensor Networks for NISQ - Simualtion and Machine Learning*

Tensor network methods permit efficient computation of 1D and 2D quantum systems by concentrating computing and entanglement resources into relevant regions of Hilbert Space. Quantum computing is an emerging technology which could provide great advances in simulations of quanutm systems. Currently available noisy quantum computers, so-called NISQ devices, are limited in the entanglement they can generate. Quantum tensor network methods provide a way of translating classical tensor network algorithms to NISQ devices, allowing them to use limited entanglement resources more effectively. Here I discuss how to translate tensor networks algorithms for time evolution and ground state optimisation onto NISQ devices, and show how these can be used to simulate quanutm systems that are much larger than the quanyum device. I discuss how the burgeoning field of machine learning with classical tensor networks can be used to improve the performance of machine learning and VQE tasks performed on NISQ devices.