Abstract

The dynamics of interacting quantum particles in disordered landscapes is a central problem in
non-equilibrium physics. Theoretical and numerical approaches are severely limited by ex-
ponential Hilbert space scaling and the absence of translational symmetry. Here, we leverage the
high data rates of a superconducting qubit quantum processor to efficiently sample Hilbert space
configurations. Using a 2D grid of up to 70 qubits, we measure the return probability R(t) across
a broad range of disorder strengths. At long times, R(t) develops a heavy-tailed distribution, while
its typical value follows a power-law scaling—both suggestive of glass-like dynamics. Furthermore,
the probability distribution of z-configurations evolves from a Porter–Thomas form at low disor-
der to a power-law—spanning eight orders of magnitude—at higher disorder strengths. We cluster
the wavefunctions on the basis of Hamming distance in Hilbert space, identifying three distinct
regimes as a function of disorder strength. By directly probing Hilbert space dynamics, we pro-
vide a complementary perspective to the existing real-space picture of two-dimensional quantum
systems, demonstrating the potential of current quantum processors to yield deeper insights into
non-equilibrium physics.