A common thread in physics is the existence of special length and time scales in which the behavior of a system can be described simply. One of those special scales is that of nuclei and electrons, where the equations are relatively easy to write down (quantum mechanics of charged particles), but notoriously difficult to solve. However, since almost everything we experience is made up of nuclei and electrons, it is tempting to push these solutions as far as we can go, since they tell us anything we would like to know about a condensed matter system. These techniques, called first principles, were tried on some of the first computers, but even now a general efficient solution has still not been found.

Even though we cannot simulate quantum mechanical systems for large number of particles in general and exactly, an important question is how large the errors are of modern approximations on modern computational resources. As it turns out, sustained progress over the past few decades has resulted in a collection of algorithms that are efficient and can get accuracies for many-electron systems that in some cases are comparable to experimental accuracy. Thus, these simulations on classical computers of quantum systems are good enough that with a grain of salt we can treat data from them with similar reverence as experimental data.

In this talk, I will give an update on progress in computing properties of quantum many body systems from first principles, including some new techniques developed only in the past few years that extend the reach significantly. I will then talk about using these calculations as a very advanced experimental system that will allow us to develop specific larger length scale descriptions of materials, including the very challenging strongly correlated regime. Machine learning and Monte Carlo techniques will make appearances.