Observing emergent hydrodynamics in a long-range quantum magnet

Identifying universal properties of non-equilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics emerges universally in the evolution of any interacting quantum system. We study the dynamics of a long-range interacting spin system with non-equilibrium quantum field theory, predicting the emergence of a whole family of hydrodynamic universality classes, ranging from normal diffusion to anomalous superdiffusion. We experimentally test these predictions in the quantum dynamics of 51 individually controlled ions. By measuring space-time resolved correlation functions in an infinite temperature state, we observe the emergence of hydrodynamics at late time. We extract the transport coefficients of the hydrodynamic theory, reflecting the microscopic properties of the system. Our observations demonstrate the potential for engineered quantum systems to provide key insights into universal properties of non-equilibrium states of quantum matter and uncover the transport processes governing long-range interacting systems.