Van der Waals heterostructures — stacks of two-dimensional materials held together by weak, non-chemical bonding forces — have triggered immense interest in recent years because their layer-by-layer assembly enables combining materials with vastly different properties and tuning their environment with external fields. This vast combinatorial landscape for creating compounds with tailored properties has fueled the vision of using these materials as programmable quantum simulators.

Yet, the curse of dimensionality quickly sets in: identifying which heterostructure is best suited to realize a particular quantum phase has remained a formidable challenge. A quantum simulator not only requires tunable degrees of freedom, but crucially needs a guiding design principle to reach specific goals — and, once reached, sufficient experimental accessibility to probe it.

Here, I will describe how recent works have brought us closer to this design principle. After reviewing the architecture of van der Waals stacks and showcasing experimental probes that offer unique access to their physics, I will show how the motion and interactions of electrons within these heterostructures can be efficiently predicted. If time permits, I will briefly explore how these systems might transition from analog quantum simulators to digital quantum computers through methods such as inhomogeneous gating.