  Characterizing the nature of hydrodynamical transport properties in quantum
dynamics provides valuable insights into the fundamental understanding of
exotic non-equilibrium phases of matter. Simulating infinite-temperature
transport on large-scale complex quantum systems remains an outstanding
challenge. Here, using a controllable and coherent superconducting quantum
simulator, we experimentally realize the analog quantum circuit, which can
efficiently prepare the Haar-random states, and probe spin transport at
infinite temperature. We observe diffusive spin transport during the unitary
evolution of the ladder-type quantum simulator with ergodic dynamics. Moreover,
we explore the transport properties of the systems subjected to strong disorder
or a titled potential, revealing signatures of anomalous subdiffusion in
accompany with the breakdown of thermalization. Our work demonstrates a
scalable method of probing infinite-temperature spin transport on analog
quantum simulators, which paves the way to study other intriguing
out-of-equilibrium phenomena from the perspective of transport.

Quantum Physics