Quantum simulation of spin diffusion in a Heisenberg chain

Understanding universal aspects of quantum dynamics is an exciting problem in statistical mechanics that has enjoyed renewed attention with the advent of modern-day quantum simulators. In particular, the spin dynamics of the 1D Heisenberg model have been conjectured to belong to the Kardar-Parisi-Zhang (KPZ) universality class based on the scaling of the infinite-temperature spin-spin correlation function. In a chain of 46 superconducting qubits, we study the probability distribution of the magnetization transferred across the chain’s center. The first two moments thereof show superdiffusive behavior, a hallmark of KPZ universality. However, the third and fourth moments rule out the KPZ conjecture and allow for evaluating other theories. Our results highlight the importance of studying higher moments in determining dynamic universality classes and provide key insights into universal behavior in quantum systems.Furthermore, we present a scalable protocol for measuring full counting statistics in experiments or tensor-network simulations using an ancilla in the middle of the system, which acts as a turnstile with its phase keeping track of the time-integrated particle flux.