Multifractal and Glassy Signatures of Non-Ergodic 2D Quantum Dynamics

The fate of ergodicity and localization in disordered, interacting quantum systems in two spatial dimensions remains an outstanding open problem in non-equilibrium physics. Theoretical and numerical approaches are severely constrained by exponential Hilbert space growth. Here, we leverage the high data-acquisition rates of superconducting quantum processors to extensively sample Hilbert space configurations, effectively imaging the state as a wavefunction network (WFN). Tracking the bitstring return probability across varied disorder strengths, we find heavy-tailed distributions and power-law typical decay characteristic of glassy relaxation. Furthermore, the distribution of bitstring probabilities transitions from a Porter-Thomas form at low disorder to an eight-decade power law at stronger disorder. In the reconstructed configuration space, WFN connectivity is compatible with a random geometric network at low disorder and becomes scale-free at stronger disorder. Finally, a multifractal analysis based on the binary intrinsic dimension (BID) reveals a non-ergodic regime where the wavefunction support saturates to a finite fraction of the total Hilbert space. Together, these results rule out a direct ergodic-to-localized transition, pointing instead to an extended multifractal regime. By visualizing wavefunction dynamics directly in configuration space, this work complements traditional real-space studies, showing the potential of quantum processors to resolve long-standing questions in non-equilibrium physics.