Advanced materials form the basis of modern technology. This is perhaps most apparent in information technology, where improved hardware depends on materials with optimized functionalities.

Designing such materials requires a solid understanding of how physical properties emerge from the fundamental interactions among electrons and nuclei. The underlying theory, many-particle quantum mechanics, is well known. Unfortunately, except in the very simplest cases, it is not exactly solvable in practice, neither on classical nor on (digital) quantum computers. To make progress we thus need approximate methods that are sufficiently accurate and can be implemented efficiently. A popular approach is to circumvent the many-body problem by considering non-interacting electrons moving in an effective mean-field. In many cases this gives quite satisfactory results. But for the materials with the most exciting functionalities, ranging from highly tunable magnetic and even orbital ordering to superconductivity at high temperatures, these simple approaches give qualitatively wrong results. In these cases we cannot avoid confronting the many-body problem.