Universality is one of the guiding principles unifying the description of seemingly unrelated physical systems.

Kardar-Parisi-Zhang (KPZ) universality is a celebrated example, describing disparate phenomena such as interface growth or propagating shock waves.

Recently, KPZ was conjectured to also describe spin transport in one-dimensional Heisenberg quantum magnets near equilibrium and at infinite temperature.

We probe this conjecture experimentally in a quantum gas microscope in chains of up to 50 spins and confirm the expected superdiffusive spin transport predicted by KPZ.

Moreover, we study the microscopic mechanisms underlying KPZ in Heisenberg systems: Superdiffusive transport vanishes when breaking SU(2) symmetry or integrability of our system.

Finally, the single-spin sensitivity of our quantum gas microscope enables us to extract spin-transport statistics, which provides further direct evidence for the conjectured KPZ scaling.

Our results raise several interesting questions for future research, regarding, for example, the impact of different initial states on transport dynamics.