The general solution of many-particle quantum systems is exponentially complex, requiring a quantum computer to solve. But for many of the most important properties of realistic experimental systems, the exponential complexity is avoidable, because while the entanglement of the system is high enough to make the system interesting, it is much lower than quantum mechanics allows. Tensor network methods exploit this low entanglement to enable simulations of many quantum systems on an ordinary computer.

In this talk, I will give an overview of these ideas and methods and then detail our recent progress in simulating high temperature superconductors, systems with exotic entangled states which we are increasingly able to understand through simulation.